Information frictions and policy in DSGE models
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Facultad de Economía y Empresa Departamento del Análisis Económico Information frictions and policy in DSGE models Pablo Aguilara Ph.D Thesis Advisor: Jesús Vázquez Bilbao, April 2021 aDepartamento del Análisis Económico, Facultad de Economía y Empresa, Universidad del País Vasco (UPV/EHU), Av. Lehendakari Aguirre 83, 48015 Bilbao (Spain) ∗This research was partially supported by the pre-doctoral scholarship from the University of the Basque Country (UPV/EHU), the Spanish Ministry of Economy and Competition under grants numbers ECO2013-43773P and ECO2016-78749-P, and the Basque Government (Spain) under grants numbers IT-793-13 and IT-1336-19. Additional support funding was provided by the Bank of Spain. 1 (cc)2021 PABLO ALBERTO AGUILAR GARCIA (cc by-nc-nd 4.0)
Acknowledgments I would like to take this opportunity to sincerely thank thesis advisor, Professor Jesús Vázquez, who has made this thesis posible, from you I had always a close guidance, encouragement, care for the details and great advise -not only in the matter of this thesis. I also want to thank Professor Luca Pensieroso, for hosting me during my period in Louvain and following this thesis all these years and to the members of the jury. This has been a long journy and I would like to share my gratitude to all of you that have helped along, especially to Raf Wouters, Stephan Farh, Samuel Hurtado, Alberto Urtasun, and to the rest of colleagues from the differents places where I have been, Málaga, Bilbao, Louvain, Frankfurt and Madrid. Finally I want to express my gratitude to Mercedes, my wife, for accompying me all these years and to my family, that has always encourage me pursue my career. 2
Contents I Adaptive learning with term structure information 9 1 Introduction 9 2 An AL model with term structure 12 2.1 TheDSGEmodel........................................... 12 2.2 Thetermstructureextension .................................... 13 2.3 Adaptive learning with term structure information . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Estimation results 19 3.1 Dataandestimationapproach.................................... 19 3.2 Posteriorestimates.......................................... 22 3.3 Modelfit ............................................... 27 3.4 Variancedecomposition ....................................... 29 3.5 Termpremiumestimates....................................... 30 4 The empirical validity of the PLM 35 5 Conclusions 41 II Learning with ELMo: inflation expectations and monetary policy rules 47 1 Introduction 47 2 A DSGE model with multi-period expectations for the Euro Area 52 2.1 Estimation .............................................. 53 2.2 The evolution of expectations: cycle and trend . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.3 Internationalcomparison....................................... 56 3 Monetary policy under learning: Transitional effects 58 3.1 Transitionalexcercise......................................... 58 3.2 Results................................................. 59 4 Conclusions 63 3
III The importance of data revisions 66 1 Introduction 66 2 Data revisions 69 2.1 Theconceptofdatarevisions.................................... 69 2.2 Regression analysis of data revisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3 Real-time data within a DSGE model 76 3.1 An explicit specification of the revisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.2 Thenewsetofequations....................................... 79 3.2.1 TheEulerequation...................................... 79 3.2.2 Monetarypolicyrule..................................... 81 4 Data and estimation procedure 83 5 Estimation results 84 5.1 Parameterestimates ......................................... 84 5.2 Second-momentstatistics ...................................... 86 5.3 Variancedecomposition ....................................... 87 6 Conclusions 87 IV Borrower-based measures in a DSGE model 105 1 Introduction 105 2 Macroprudential policies in the 3D model 108 2.1 Borrower-based measures: Modelling strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.2 Calibrationinsteadystate...................................... 111 2.3 Effects of varying household leverage in the 3D model . . . . . . . . . . . . . . . . . . . . . . 114 3 Relating LTV and LTI policies at loan origination to the dynamic model 119 3.1 LTV (LTI) limits and its effects on average credit standards at loan origination . . . . . . . . 120 3.2 Linking credit standards at loan origination to outstanding loans . . . . . . . . . . . . . . . . 124 3.3 Policysimulation........................................... 126 4 Conclusions 132 4
General introduction In this thesis I explore key aspects of general equilibrium models widely used in Central Banks, both in terms of theoretical assumptions and practical implications for policy makers. This document is divided in four chapters. In the first two chapters I study an alternative to the rational expectation assumption and its implications in the understanding of the business cycle, while in the last two chapters I explore policy questions related to the use of these models in policy. General equilibrium models traditionally used in the design of monetary policy start from the premise that agents form their expectations about the economy in a rational manner. Under rational expectations, agents have full information about the true economic model, and use it accordingly to form their predictions. In particular, agents are capable of understanding the nature of macroeconomic shocks and their duration, and have the ability to consistently incorporate news about the expected evolution of the economy or changes in monetary policy into their expectations. The theory of rational expectations has been embedded not only into real business cycle models, but also into more realistic New Keynesian models, including many of the DSGE models that are used for policy purposes in central banks. However, in reality, agents are unlikely to have perfect ability to observe and process in an efficient manner all available information. Thus, on many occasions, the nature of the disturbances, or their transmission channels, are only imperfectly known by the agents or partially ignored. Alternatives to this hypothesis have been largely debated in the literature, the first two chapters explore different aspects of the adaptive learning approach as an alternative to rational expectations hypothesis, while the last two chapter explore modelling implications in the policy use of DSGE models. More precisely, the first chapter assesses the importance of term structure and survey data information to the adaptive learning literature and the capability of macro-financial DSGE models with learning expectations to estimate a measure of the term premium associated 5
with the 10-year US Treasury bond yield. The introduction of survey data adds a source of discipline in expectations under adaptive learning, which otherwise, are often criticized of arbitrary. In this context, this chapter finds that adding term structure information in agent’s forecasting models improves the overall fit and does a great job in matching the expectations reported in the SPF across all forward-looking variables of the DSGE model. The rationale for this finding is that the SPF forecasts are based on real-time data and the term spread information included in our small forecasting models is also available in real time. These two pieces of real-time data—SPF and the yield curve— may therefore share important information in forecasting the economic outlook. This is consistent with the previous finding that the term structure contains useful information for forecasting real-time macroeconomic data. The second part of the chapter extends this model up to 10-years to estimate a measure of the term premium associated with the 10-year US Treasury bond yield from the medium-scale DSGE model under AL, showing that the inclusion of both term structure and survey data improves the estimation of the bond term premium, in line with the from no-arbitrage affine term structure models. The second chapter looks at the anchoring of inflation expectations in the Euro Area and the performance of alternative monetary policy rules using a DSGE model with adaptive learning. The approach used allows a distinction to be drawn between which portion of the low inflation phenomenon might be due to temporary factors and which might be considered permanent. The results of the analysis for the euro area suggest that agents perceive the inflation rate’s recent departure from the monetary policy objective to be predominantly temporary, although the deviations from target are marked by a considerable degree of persistence. Another relevant aspect is the impact of a prolonged period of low inflation in the effectiveness of monetary policy, and more importantly, under the presence of the effective lower bound. The second part of the chapter studies the properties of the monetary policy regime under the current expectations and studies the transitional effects caused by the change in inflation expectations of alternative regimes such as asymmetric inflation targeting 6
and price-level targeting, now popular in the academic debate. The results show that while current expectations are curbing the effectiveness of monetary policy under the presence of the zero lower bound, alternative rules such asymmetric inflation targeting rules (that respond stronger when inflation is below trend) are beneficial to the economy. In addition, this chapter states the implications in the transition from one monetary policy rule to another, showing that changing the rule is not very effective until agents have had time to learn about it. The the announcement of the new rule has the maximum effect agents observe their implementation and learn about it, which requires time, which is very different from what the standard rational expectations models, where the announcement perfectly anchors agents’ expectations and has immediate effects in the economy. The third chapter devotes to the importance of real-time data and data revisions in the business cycle analysis. The main macroeconomic series are regularly revised relative to their real-time release to incorporate new information, which often, are significant and, if ignored, may lead to a bias in the study of the business cycle. This chapter provides a detailed analysis of the statistical properties of data revisions for the euro area and studies the appropriate modeling of real-time data and its revision in DSGE models for business cycle analysis. The first part of the chapter provides studies the statistical properties of data revisions in the euro area, showing that the series of GDP, consumption and inflation are predictable (they are correlated with the initial announcement) and have high volatility, suggesting that they are not well-behaved and studies the appropriate characterization of the data revision processes for its later inclusion in DSGE models. The second part of the paper details how to include real-time data and its revision in a DSGE model, by assuming that decisions related to GDP, Consumption and inflation are based on the initial announcement, and acknowledging that they are subject to revisions. This approach delivers two important results: first, it confirms the empirical findings from the reduced-form analysis and second, data revisions become an important source in the business cycle decomposition analysis. In the case of the Euro Area, they account for one third of the output variability, leading to the conclusion that DSGE 7
models omitting real-time data and data revisions might be ignoring important sources of aggregate fluctuations. Finally the fourth chapter has an important policy viewpoint, by assessing quantitatively the transmissions of macroprudential policies in the economy. Macroprudential policies are an important toolkit of central banks nowadays, this includes borrower-based macroprudential measures such as limits on loan-to-value and loan-to-income which their assessment has been traditionally in partial equilibrium models. By combining the model with information on the distribution of loan-to-value and loan-to-income ratios contained in the loan data, this paper tracks the impact of borrower-based measures from their impact on credit conditions at loan origination to the long-term macroeconomic effects on GDP, credit, real estate investment as well as mortgage defaults and mortgage spreads. The assessment reveals that borrowerbased measures have sizable effects on credit amounts and can reduce long-run defaults. Its assessment is nevertheless limited to long-term effects, given limitation in the relatively simple way the real estate market is modeled. It opens up extension possibilities to develop additional models to shed light on the detailed working of the real estate market by focusing on additional sources of shocks and the role played by expectations for real estate prices. 8
Part I Adaptive learning with term structure information 1 Introduction Since the pioneering publications by Marcet and Sargent (1989) and Evans and Honkapohja (2001) a growing body of literature (including Preston, 2005; Milani, 2007, 2008, 2011; Eusepi and Preston, 2011; Slobodyan and Wouters, 2012a,b) has considered adaptive learning (AL) as an alternative to the rational expectations (RE) assumption in characterizing highly persistent macroeconomic dynamics. Recent papers (Sinha 2015, 2016) focus on some implications of AL in the yield curve, but there are still a few papers (e.g. Aguilar and Vázquez, 2019) that analyze how term structure information may interact with both learning and macroeconomic dynamics. This paper considers the Euler-equation approach to AL suggested in Slobodyan and Wouters (2012a) to understand the contribution of term structure information in dealing with the incomplete knowledge issue addressed in the related AL literature.1,2Term structure With Jesús Vázquez (UPV/EHU) 1There are two main approaches to AL in the recent literature. The Euler-equation approach focuses on short-sighted agents, for whom optimal current decisions are based on just one-period-ahead expectations that show up in the standard Euler equations (e.g. Milani, 2007; Slobodyan and Wouters, 2012a,b), while the other approach focuses on long-sighted agents (e.g. Preston, 2005; Eusepi and Preston, 2011; Sinha, 2015; and Sinha; 2016), taking into account infinite-horizon forecasts driven by their intertemporal decision problem. This distinction can be crucial because the second approach results in a much stronger source of persistent dynamics (see Eusepi and Preston, 2011). By including the term structure of interest rates, our approach certainly goes beyond the one-period-ahead expectations, but still follows the Euler-equation approach. 2More generally, the Euler-equation approach falls under the broad class of a restricted perceptions equilibrium, where agents use a small misspecified model but form their beliefs optimally given the misspecification (Sargent, 1991; Hommes and Sorger, 1998; Milani, 2007; Honkapohja, Mitra, and Evans, 2013). Other papers (Adam, 2005; Orphanides and Williams, 2005; Branch and Evans, 2006; Hommes and Zhu, 2014, Ormeño and Molnár, 2015) also provide support for the use of small forecasting models on several grounds, including their forecast performance, their usefulness for facilitating coordination, and their ability to approximate the Survey of Professional Forecasters well. 9
deviation of output from its underlying neutral productivity process), and sp{4} t=r{4} t−rt denotes the term spread associated with the 1-year maturity yield.11 2.3 Adaptive learning with term structure information This section provides a brief explanation of how AL expectation formation works.12 A DSGE model can be represented in matrix form as follows: A0 yt−1 wt−1 +A1 yt wt +A2Etyt+j+B0t= 0, where ytis the vector of endogenous variables at time t, Etyt+jcontains multi-period-ahead expectations, and wtis a vector including eight exogenous shocks and the lagged innovations, t−1, of the priceand wage-markup shocks since they are modeled as ARMA(1, 1) processes. Agents are assumed to have a limited view of the economy under AL. Their so-called “perceived law of motion” (PLM) processes—i.e. their small forecasting models— are generally defined as follows: yt+j=Xtβ{j} t−1+ut+j, for j = 1,2, ..., n, where yis the vector containing the forward-looking variables of the model, Xis the matrix of regressors, β{j}is the vector of updating parameters, which includes an intercept, and uis a vector of errors. These errors are linear combinations of the true model innovations. The variance-covariance matrices, Σ=E[ut+juT t+j], are therefore non-diagonal. Agents are further assumed to use simple econometric tools under AL. In particular, they use a linear least squares projection scheme in which the parameters are updated to form their expectations for each forward-looking variable: Etyt+j=Xtβ{j} t−1. The updating parameter vector, β, which results from stacking all the vectors β{j}, is further assumed to follow an autoregressive 11As in SlW, all but a few of the structural shocks follow AR(1) processes. The priceand wage-markup shocks follow ARMA(1,1) processes, and the AR(1) productivity shock allows for an interaction with the government spending shock. 12For a detailed explanation see Slobodyan and Wouters (2012a,b). 16
process where agents’ beliefs are updated through a Kalman filter as described below. This updating expectation process can be represented as in SlW by the equation: βt−¯ β= F(βt−1−¯ β) + vt, where Fis a diagonal matrix with the learning parameter |ρ|≤ 1on the main diagonal and vtare i.i.d. errors with variance-covariance matrix V. This standard AL approach assumes that agents do not take into account the fact that their belief coefficients will be revised in the future (e.g. Sinha (2016) and Eusepi and Preston (2011, 2018)). This assumption can be rationalized by using an anticipated utility approach put forward in Kreps (1998) and Sargent (1999).13 Notice that each expectational horizon is estimated separately in our AL approach. This is in clear contrast to the maintained beliefs hypothesis suggested in Preston (2005)—an approach also followed in Eusepi and Preston (2011) and Sinha (2015, 2016)— which not only imposes an infinite forecast horizon, but also considers iterated forecasts used under the MSV approach. Nevertheless, our approach shares with other AL approaches the use of forecasting models based on linear least squares projections, which implies that the law of iterated expectations holds: Et(Et+hyt+j) = Etyt+j, for any j > h > 0(see Sargent (1987, chapter X, pp. 223-229) for a formal discussion), and this is consistent with the law of iterated expectations assumed in the derivation of the log pure version of the EH, equation (2), above. Once the expectations of the forward-looking variables,Etyt+j, are computed they are plugged into the matrix representation of the DSGE model to obtain a backward-looking representation of the model as follows yt wt =µt+Tt yt−1 wt−1 +Rtt, where the time-varying matrices µt,Ttand Rtare nonlinear functions of structural parameters 13The anticipated utility approach assumes that agents do not take into account future updates of beliefs when making current decisions but are otherwise fully optimal. This is in contrast to the Bayesian belief approach, which takes belief updates into account. 17
(entering into matrices A0,A1,A2and B0) together with the learning coefficients, β. This representation of the model is called the actual law of motion (ALM). The standard Kalman-filter updating and transition equations for the belief coefficients and their corresponding covariance matrix are given by βt|t=βt|t−1+Rt|t−1Xt−1Σ+XT t−1R−1 t|t−1Xt−1−1yt−Xt−1βt|t−1, where (βt+1|t−¯ β) = F(βt|t−¯ β).βt|t−1is the estimate of βusing the information up to time t−1(but further considering the autoregressive process followed by β), Rt|t−1is the mean squared error associated with βt|t−1. Therefore, the updated learning vector βt|tis equal to the previous one, βt|t−1, plus a correction term that depends on the previous forecast error, yt−Xt−1βt|t−1. The mean squared error, Rt|t, associated with this updated estimate is given by Rt|t=Rt|t−1−Rt|t−1Xt−1Σ+XT t−1R−1 t|t−1Xt−1−1XT t−1R−1 t|t−1, with Rt+1|t=FRt|tFT+V. The initialization of this Kalman filter for the belief coefficients requires the specification of β1|0=β,R1|0,Σ, and V. We follow Slobodyan and Wouters (2012a), where all these expressions are derived from the correlations between the model variables implied by the RE equilibrium evaluated at the corresponding structural parameter vector. A PLM with term structure information The baseline small forecasting models assumed in SlW are simple AR(2) processes. That is, the PLM of each forward-looking variable of the DSGE model is described by Etyt+j=θ{j} y,t−1+β{j} y,1,t−1yt+β{j} y,2,t−1yt−1,(5) where the intercept of the PLM, θ{j} y,t−1, captures the low frequency movements of the corresponding forward-looking variable, Etyt+j, and the coefficients β{j} y,1,t−1and β{j} y,2,t−1together 18
measure the persistence of beliefs. We analyze the importance of introducing TS information by simply augmenting these PLM with the term spread sp{4} t: Etyt+j=θ{j} y,t−1+β{j} y,1,t−1yt+β{j} y,2,t−1yt−1+β{j} y,3,t−1sp{4} t,(6) where the coefficient β{j} y,3,t−1captures agents’ reaction to the term spread information while forecasting Etyt+j. This small modification in the PLM enables us to clearly identify the contribution of TS information beyond that provided by current and lagged values of the forward-looking variables considered in SlW.14 3 Estimation results We begin this section by describing the data and the estimation approach, then proceed to discuss the model fit, estimation results, a comparison of actual and simulated moments, the variance decomposition of shocks, and the estimate of the smoothed AL term premium. 3.1 Data and estimation approach We estimate the AL model extended with TS for the alternative specifications of the PLM using US data for two sample periods: The whole sample period running from 1965:4 until 2009:1 and a subsample from 1981:4 until 2009:1. The set of observable variables used for the whole sample period estimation is the same one used by Slobodyan and Wouters (2012a) (i.e. the quarterly series of the inflation rate, the Fed funds rate, the log of hours worked, the quarterly log differences in real consumption, real investment, real wages, and real GDP) 14Aguilar and Vázquez (2019) also consider TS information but they deviate much further from the PLM assumed in SlW by considering only the term spread in the PLM. The approach followed here makes it easier to identify the contribution made by adding TS information over and above the information provided by AR processes. 19
plus the 1-year zero-coupon Treasury yield (i.e. a set of eight observable variables).15 The estimation of the shorter sample period extends the set of observables considered in the whole sample period to include six observable forecasts reported in the SPF. More precisely, we consider the SPF forecasts available, which have counterparts in forward-looking variables in the DSGE model: 1-quarter-ahead forecasts of inflation, 1-quarter-ahead forecasts of the consumption and investment growth rates, and 1-, 2and 3-quarter-ahead forecasts of the short-term nominal interest rate16,17 Analyzing this shorter sample period, but with a larger number of observables, enables us to assess the importance of TS information in disciplining model expectations by fitting SPF forecasts as well as assessing the robustness of results by studying a sample period featuring both milder aggregate fluctuations (the Great Moderation) and an inflation downtrend, which is in sharp contrast with the stagflation in the 1970s and early 1980s present in the first-half of the whole sample period. 15The zero-coupon Treasury bond yields come from the Gürkaynak, Sack and Wright (2007) data set available on the research data website of the Board of Governors of the Federal Reserve. 16Del Negro and Eusepi (2011) pioneer the use of SPF expectation data to discipline RE in DSGE models. A few more recent papers (Ormeño and Molnar, 2015; Aguilar and Vázquez, 2018) also use SPF data to discipline AL expectations in DSGE models. 17SPF forecasts were downloaded from the website of the Federal Reserve Bank of Philadelphia. Inflation forecasts are reported back to the late 1960’s, but the rest of the forecast time series starts at 1981:3. Thus, data availability partially determines the choice of the first period in the short sample. Moreover, the initial quarter of the short sample roughly coincides with the start of a successful disinflation period. 20
The measurement equation is Xt= dlGDPt dlCONSt dlINVt dlWAGt dlPt lHourst FEDFUNDSt 1−year TB yieldt dlCONSSPF t+1 dlINV SP F t+1 dlPSPF t rSPF{1} t rSPF {2} t rSPF {3} t = γ γ γ γ π l r r{4} γSPF c γSPF i πSPF rSPF rSPF rSPF + yt−yt−1 ct−ct−1 it−it−1 wt−wt−1 πt lt rt r{4} t Et(ct+1 −ct−1) + c,t Et(it+1 −it−1) + i,t Etπt+j+π,t Et(rt+1) + {1} r,t Et(rt+2) + {2} r,t Et(rt+2) + {3} r,t ,(7) where land dl represent the log and the log difference, respectively. γ= 100(γ−1) is the common quarterly trend growth rate for real GDP, real consumption, real investment, and real wages. ¯ l,π,rand r{4}are the steady-state levels of hours worked, inflation, the federal funds rate, and the 1-year (4-quarter) bond yield, respectively. The superscripts SPF and {j}in the last six rows of the measurement equation denote actual forecasts from the SPF and the corresponding forecast horizon for j= 1,2,3; respectively. As in Ormeño and Molnár (2015), the measurement errors, , showing the deviations of model expectations from the actual forecasts reported in the SPF, are assumed to be i.i.d. processes. We also allow for differences in trend growth rates across SPF (consumption and investment) forecasts as well as differences between the steady-state levels of actual and SPF forecast data. The measurement equation (7) reduces to the first eight equations when the alternative 21
versions of the AL model are estimated for the whole sample period, whereas the complete system (7) is used for the short sample period when SPF data is considered in the estimation procedure. We follow a Bayesian estimation procedure. First, the log posterior function is maximized by combining prior information on the parameters with the likelihood of the data. The prior assumptions are exactly the same as in Slobodyan and Wouters (2012a). In addition, we consider loose priors for the parameters characterizing both the 1-year yield dynamics and the measurement error processes. The Metropolis-Hastings algorithm is used to generate the posterior distribution and to compute the log density of the model.18 3.2 Posterior estimates Our estimated AL model with TS (henceforth called the SlW-TS model) only differs from that of Slobodyan and Wouters (2012a) (henceforth called the SlW model) in the specification of the small forecasting models. Table 1 shows the estimation results for the various PLM specifications and the various samples considered. Our sample period is almost identical to the one considered in SlW. Thus, the first column of Table 1 shows the estimation results of the SlW model for the whole sample period 1966:1-2009:1 using their original set of seven observable variables, whereas the second and third columns report the estimation results using the PLM of SlW and the PLM augmented with TS information (SlW-TS) as described by equations (5) and (6), respectively. The remaining two columns show the estimation results for the two PLM specifications for the short sample period running from 1981:4 until 2009:1, where the SPF time series are also included in the set of observables as described in the measurement equation (7).19 For each model estimated, Table 1 firstly reports the number of observable time series, 18The DSGE models are estimated using Dynare codes kindly provided by Sergey Slobodyan and Raf Wouters with a few modifications to accommodate the presence of TS information in both the structural model and the small forecasting models, as described above. 19For the short sample period, we find that simpler specifications of the two PLM built on AR(1) processes— i.e. imposing β{j} y,2,t−1= 0 in equations (5) and (6)— improve the model fit. The estimation results reported for the short sample period are based on these simpler specifications. 22
and the model fit based on the log data density. The remaining rows show the posterior mean and the corresponding 90 percent interval of the posterior distribution—in parentheses—for four groups of selected parameters. The first and second groups contain the parameters for real and nominal rigidities, respectively. The third group contains the parameters which describe the ARMA coefficients characterizing price and wage markup shocks. Finally, the fourth group contains the policy rule parameters.20 A comparison of column 1 in Table 1 with the figures reported in Slobodyan and Wouters (2012a, Table 1, p. 74) shows a similar fit and almost identical parameter estimates. This suggests that including or ignoring a few quarterly observations and assuming a logarithmic utility function has no impact on the estimation results. The consequences of considering the 1-year Treasury bill A comparison of columns 1 and 2 shows that including the 1-year Treasury bill as an observable in the SlW model decreases the importance of a few sources of endogenous rigidity, such as Calvo price and wage parameters, price and wage indexation parameters, and the parameter featuring the capital utilization adjusting cost, ψ. The rationale for this decrease in a few sources of endogenous persistence is that considering the EH of the term structure (equation (3)) brings with it additional persistence in (the expected path of) the short-term rate that is transmitted to other aggregate variables. Moreover, there is a large increase in persistence driven by the increase in the AR coefficients that describe the processes of price and wage markup shocks. 20All parameter estimates are reported in a supplementary appendix available from the authors upon request. 23
Table 1. Selected parameter estimates Without SPF data (1965:4-2009:1) With SPF data (1981:4-2009:1) SlW SlW SlW-TS SlW SlW-TS Number of observables 7 8 8 14 14 log data density -984.930 -1092.600 -1057.596 -1070.311 -853.960 Parameters associated with real rigidities habit formation 0.787 0.851 0.759 0.631 0.630 (h)(0.742,0.833) (0.842,0.878) (0.745,0.788) (0.607,0.643) (0.611,0.643) cost of adjusting capital 4.846 7.975 4.616 4.219 5.294 (ϕ)(3.257,6.491) (7.946,8.014) (4.579,4.646) (4.192,4.258) (5.168,5.323) capital utilization adjusting cost 0.611 0.151 0.092 0.163 0.050 (ψ)(0.424,0.819) (0.149,0.180) (0.085,0.100) (0.153,0.171) (0.046,0.053) Parameters associated with nominal rigidities price Calvo probability 0.612 0.472 0.545 0.617 0.715 (ξp)(0.544,0.684) (0.459,0.487) (0.524,0.554) (0.598,0.630) (0.702,0.730) wage Calvo probability 0.774 0.565 0.464 0.495 0.259 (ξw)(0.721,0.831) (0.549,0.589) (0.456,0.482) (0.485,0.511) (0.245,0.268) price indexation 0.372 0.178 0.377 0.896 0.820 (ιp)(0.169,0.566) (0.151,0.192) (0.325,0.401) (0.884,0.928) (0.796,0.863) wage indexation 0.386 0.185 0.470 0.218 0.400 (ιw)(0.203,0.582) (0.107,0.229) (0.410,0.486) (0.195,0.237) (0.337,0.437) 24
Table 1. (Continued) Without SPF data (1965:4-2009:1) With SPF data (1981:4-2009:1) SlW SlW SlW-TS SlW SlW-TS Parameters associated with price and wage markups markup price AR coef. 0.457 0.880 0.875 0.609 0.575 (ρp)(0.130,0.786) (0.860,0.904) (0.875,0.911) (0.584,0.690) (0.558,0.602) markup wage AR coef. 0.554 0.838 0.918 0.843 0.938 (ρw)(0.287,0.827) (0.827,0.853) (0.909,0.928) (0.833,0.858) (0.929,0.950) markup price MA coef. 0.476 0.608 0.693 0.590 0.747 (µp)(0.224,0.742) (0.591,0.635) (0.676,0.711) (0.547,0.638) (0.741,0.769) markup wage MA coef. 0.494 0.325 0.477 0.556 0.450 (µw)(0.209,0.793) (0.309,0.368) (0.454,0.517) (0.543,0.569) (0.422,0.487) Policy rule parameters inertia 0.880 0.884 0.886 0.834 0.835 (ρr)(0.85,0.92) (0.881,0.907) (0.878,0.896) (0.808,0.845) (0.819,0.849) inflation 1.692 1.662 1.617 2.373 1.854 (rπ)(1.384,2.01) (1.659,1.683) (1.570,1.643) (2.291,2.394) (1.762,1.888) output 0.101 0.075 0.038 0.080 0.082 (ry)(0.043,0.159) (0.065,0.095) (0.033,0.047) (0.068,0.089) (0.075,0.092) output growth 0.118 0.122 0.144 0.075 0.040 (r∆y)(0.087,0.150) (0.104,0.131) (0.132,0.154) (0.068,0.090) (0.036,0.053) term spread - 0.255 0.140 0.112 0.155 (rsp )- (0.218,0.284) (0.118,0.159) (0.086,0.145) (0.129,0.174) Notes: Parameter notation and 90% intervals of the posterior distribution in parentheses. 25
200 basis points around 1984 for one of the AL measures, but the discrepancy between the ACM and DB term premia is much larger for the same period (roughly 450 basis points!). Another substantial discrepancy appears around the 2001-2002 recession, when the differences between the DB term premium and any other term premium take values close to 5%, whereas the differences between any pair of the rest of the term premium measures are around 1% in all cases. These discrepancies across models are not, however, explained by fitting errors implied by the alternative models, as all models tend to fit the yield data very well (as indeed our AL-DSGE model does (see Figure 2 below)). In spite of large discrepancies for a few periods, the differences between alternative term premia are in general less than 100 basis points. Focusing on the comparison between the AL and ACM term premia, it can be observed that the fluctuations in the ACM term premium are slightly milder than those in the AL term premium: The standard deviations of these two term premium measures are 1.13 and 1.38, respectively (1.28 when the ACM term premium is not included in the set of observables). Moreover, both AL and ACM measures exhibit an upward trend during the Stagflation period and a downward trend during the disinflation period, which implies that the two measures are contemporaneously correlated (0.86 with the ACM measure in the set of observables and 0.65 without it). They also exhibit a high degree of persistence (the first-order autocorrelation coefficient is 0.96 for the ACM term premium and roughly 0.93 for the two AL term premia). Furthermore, the correlations between the ACM and AL and the cyclical measure of GDP obtained from the Hodrick and Prescott filter (Hodrick and Prescott, 1997) show a weak countercyclicality (-0.30, and -0.26, respectively) somewhat in line with the findings in the related literature (e.g. in Campbell and Cochrane, 1999; Cochrane and Piazzesi, 2005; Bauer, Rudebusch and Wu, 2014). This correlation is a little lower at -0.17 when the ACM term premium is removed from the set of observables. 32
Figure 1. 10-year term premia Note: The annualized AL term premia shown in this figure are computed as hr{40}−r+ξ{40} ti×4. Figure 2 shows the actual figure and the forecast for the 10-year yield based on the ALDSGE model together with the estimated average of the expected path of the short-term rate over 10 years (i.e. the estimated 10-year yield implied by the EH of the term structure). It is clear that the estimated 10-year yield implied by the EH under AL shows great variability over the sample period, but it also shows a relatively small variability in the early 1980s when the 10-year yield shows the twin-peak fluctuations, which results in the large fluctuations of the estimated AL term premium shown in Figure 1. Figure 2. Actual and forecast 10-year yields, and the estimated average of the expected path of the short-term rate over 10 years The relatively small variability of the expectations of the short-term rate in the early 1980’s is confirmed in Figure 3, where the belief coefficients associated with a few forward33
looking variables are shown. Thus, the bottom left graph in Figure 3 shows that the average of the short-term belief coefficients for the 12and 3-quarter ahead AL expectations does not capture the high variability of the federal funds rate in the early 1980s. Figure 3 also shows that the term spread coefficients associated with the PLM of the alternative forward-looking variables exhibit great variability in general, capturing a strong reaction by agents to the spread while forecasting key macroeconomic variables. This is true in particular for investment beliefs, for which the term spread coefficient increases around recessions (in the mid and late 1970s, early 1980s, the 2001-2002 period, and before the Great Recession). Figure 3. Time variation of belief coefficients Note: The coefficients shown for the short-term interest rate are the averages of the corresponding belief coefficients for the 12and 3-quarter ahead AL expectations. An analysis of the contemporaneous cross-correlations between the three types of belief coefficient (i.e. the intercept, the sum of the AR coefficients, and the term spread coefficient) 34
also shows an interesting finding: There is a strong correlation between the term spread belief coefficient and the corresponding PLM’s intercept of real variables (consumption and investment), indicating that the variability in the agent’s reaction to the term spread is somewhat linked to the perception on the low-frequency movements of consumption and investment. Thus, the estimated correlation between the intercept and the term spread coefficient is negative at -0.73 for consumption beliefs, and positive at 0.79 for investment beliefs. Similarly, we also find a strong negative correlation between the intercept and the sum of the AR coefficients for consumption (-0.71), inflation (-0.85), and short-term rate (-0.77) beliefs indicating that both types of belief coefficient also compete to capture expectations about the low-frequency movements of these variables. 4 The empirical validity of the PLM This section analyzes the empirical validity of the PLM implied by the two specification options in order to assess the contribution of TS information to both improve model fit and match SPF forecasts. Table 4 shows the RMSE statistics from the PLM forecasts for the forward-looking variables that have observable counterparts. We also include the 1-year yield implied by the pure EH (i.e. the one-year yield implied by (2) where the term premium is restricted to zero). To assess the PLM (i.e. perceived law of motion) performance further, we also report the RMSE for the ALM (i.e. actual law of motion) for the observable variables. Notice that these statistics are all based on in-sample forecasts. ALM forecast errors are also minimized in the estimation procedure, so they provide a minimum bound against which the PLM performance can be assessed. Furthermore, since the log marginal density is a function of the ALM forecast errors, the RMSE statistics computed for alternative variables provide valuable information about the sources of the improvement in the model fit based on the log marginal density implied by introducing TS information into the PLM. Table 4 has three panels. The first two show the RMSE statistics associated with the 35
ALM and the PLM for the whole sample—together with the PLM statistics associated with specific periods such as the Stagflation period (1966:1-1981:4), the disinflation period (1982:12009:1), and the contraction periods as dated by the NBER business cycle committee— for the DSGE model estimated under the two specifications of the PLM (equations (5) and (6)). The first two panels also show the RMSE statistics for the two PLM specifications using the first announcements (real-time data) instead of the actual (revised) data used in the estimation procedure. To facilitate discussion, we also report the RMSE statistics obtained from the estimation in the Slobodyan and Wouters (2012a) model (i.e. muting the TS part of the model and removing the 1-year yield from the set of observables) in the third panel. Several important conclusions emerge from Table 4. First, the RMSE statistics associated with the ALM are lower for the learning specification that includes TS information across all three real variables (i.e. the growth rates of consumption, investment and the real wage), whereas the fit of the nominal variables is similar for the two AL specifications. A comparison of these statistics with those reported in the third panel suggests that including the 1-year yield as an observable variable and characterizing the 1-year yield in the model have only a slight effect on the model fit across variables, with a small improvement in the fit of consumption, investment, and inflation. Second, the RMSE statistics associated with the PLM are also lower for the learning specification with TS information across all variables but the 1-year yield. This outperformance by the PLM with TS is fairly robust across alternative subsample periods: The accelerating inflation period (1966:1-1981:4), the downtrend inflation period (1982:1-2009:1), and the periods of economic contraction. Interestingly, the PLM associated with the SlW specification does a much better job in forecasting the 1-year yield in the disinflation period than in the Stagflation period, but the opposite is true for the PLM with TS information. Finally, the outperformance by the PLM with TS extends to the case where the RMSE statistics are computed with real-time data as a reference instead of the actual revised data used in the rest of the table. This suggests that by helping to improve the forecasts of the first announcements of macroeconomic data, the yield curve (which is 36
observed in real time) provides useful information for characterizing agents’ expectations above and beyond that included in revised macroeconomic data.22 Table 4. RMSE comparison of PLM forecasts (1966:1-2009:1) SlW-TS ∆c∆inv ∆w π r r{4} ALM 0.686 1.757 0.669 0.257 0.234 0.208 PLM 0.779 1.819 2.450 0.282 0.266 1.024 PLM (period 66:1-81:4) 0.823 2.145 2.682 0.379 0.365 0.484 PLM (period 82:1-09:1) 0.753 1.601 2.306 0.206 0.186 1.232 PLM (contraction periods) 1.353 2.889 2.181 0.305 0.391 0.411 PLM (real-time data) 0.775 4.320 – 0.325 – – SlW ALM 0.726 1.792 0.763 0.256 0.232 0.209 PLM 1.335 2.001 2.650 0.300 0.268 0.930 PLM (period 66:1-81:4) 1.227 2.201 2.601 0.369 0.354 1.439 PLM (period 82:1-09:1) 1.394 1.876 2.679 0.252 0.202 0.409 PLM (contraction periods) 1.827 3.121 2.099 0.297 0.358 0.439 PLM (real-time data) 1.335 4.478 – 0.348 – – SlW with 7 observables ALM 0.700 1.784 0.657 0.260 – – PLM 0.705 1.812 0.673 0.281 – – As pointed out by Slobodyan and Wouters (2012a), a sound performance by the expectation models in terms of RMSE may help obtain a good overall fit of the model, but it provides only indirect evidence on the empirical validity of those expectations. Next, we assess the forecasting performance of the two PLM specifications studied in this paper against 22See Croushore (2011) for an outstanding review of the literature on real-time macroeconomic data and the analysis of data revisions. 37
the forecasts reported in the SPF. Specifically, the SPF reports private sector quarterly expectations on consumption, investment, GDP deflator inflation, and the short-term interest rate (3-month TB yield) from late 1981 onward.23 Table 5 shows the RMSE comparison of PLM forecasts with SPF data rather than the actual data used in the estimation procedure. Clearly, the PLM forecasts including TS information do a much better job in matching the expectations reported in the SPF across all forward variables than the PLM forecasts without TS information. The rationale for this finding is that the SPF forecasts are based on real-time data and the term spread information included in our PLM specification is also available in real time, whereas the PLM forecasts under the SlW specification are based only on ex-post revised data. The two pieces of real-time data (SPF and the yield curve) may thus share important information available in real time. This finding is consistent with our previous finding that TS information provides useful information for matching forecasts on real-time macroeconomic data. These findings suggest that the use of SPF data may help to discipline model expectations and improve the empirical fit of model expectations. Table 5. RMSE comparison of PLM forecasts w.r.t. SPF data Estimation period: 1966:1-2009:1 Comparison period : 1982:1-2009:1 ∆c∆inv π r SlW-TS 0.363 1.240 0.442 1.007 SlW 1.358 2.106 1.206 1.580 The previous section looks at the implications for the parameters estimated of considering SPF data in the estimation procedure, as described in the measurement equation (7), for the 23Although SPF expectations on inflation are available for 1968 onward, we decided to focus on the period starting in the first quarter of 1982, when SPF expectations became available for all forward-looking variables considered in this analysis. 1982:1 also roughly coincides with the time when the rate of inflation started to go down. Furthermore, note that we consider the SPF forecasts of the 3-month TB rate as a good proxy of the expectations of the federal funds rate because the actual time series of these two short-term rates are almost perfectly correlated. 38
short sample period characterized by the Great Moderation. Table 6 shows the corresponding RMSE statistics of PLM forecasts obtained from the model estimated for the short sample period. As a reference, the first panel in this table shows the RMSE statistics for the SPF forecasts. The remaining two panels show the RMSE statistics for the two specifications of the small forecasting models associated with the ALM and the PLM. The numbers in parentheses below the RMSE statistics associated with the PLM forecasts indicate the percentage changes in the corresponding RMSE-statistics when model expectations are disciplined with SPF data (i.e. the percentage changes between the figures reported in the row labeled as “PLM (period 82:1-09:1)” in Table 4 and the corresponding figures in Table 6). Table 6. RMSE comparison of PLM forecasts (1982:1-2009:1) ∆c∆inv ∆w π r r{4} SPF 0.589 1.699 – 0.229 0.161 – SlW-TS ALM 0.754 1.636 0.854 0.213 0.166 0.176 PLM 0.667 2.222 5.246 0.215 0.201 0.493 (-11%) (39%) (127%) (4%) (8%) (-60%) SlW ALM 0.667 1.517 1.017 0.246 0.155 0.154 PLM 0.660 2.044 3.628 0.217 0.263 0.455 (-53%) (9%) (35%) (-14%) (30%) (11%) Interestingly, the forecasts based on the ALM from the two AL specifications are as good as those reported in the SPF when SPF is considered in the set of observables. It is also important to highlight that the AL specification with TS results in similar RMSE statistics even when SPF is not used in the set of observables, as shown in Table 4. Interestingly, including SPF in the estimation procedure results in a greater improvement in the forecasts 39
for those variables that perform worst when SPF data is not used. Thus, the improvement in the consumption growth forecast is greater for the SlW specification (a reduction in the RMSE of 53%) than for the specification that includes TS information (a reduction of 11%). Moreover, the performance of the PLM with TS information is lower for the rest of the variables, except for the 1-year yield, when SPF is included in the set of observables.24 Thus, including SPF data improves the PLM forecasts of the 1-year yield when the PLM considers TS information (there is a 60% reduction in the RMSE). However, the opposite occurs (there is an increase of 11%) for the forecasting models based on the SlW formulation. In line with the results shown in Table 5 for the DSGE models estimated using the whole sample period, Table 7 clearly shows that the PLM forecasts that include TS information (SlW-TS) do a better job than the SlW specification in matching the expectations reported in the SPF across most forward variables when the two AL specifications are estimated using the shorter sample (1982:1-2009:1) and SPF data is included in the estimation procedure. The figures in parentheses show the percentage changes in the RMSE-statistics when SPF data are considered in the set of observables (i.e. the percentage changes between the figures reported in Table 5 and the corresponding figures in Table 7). As expected, the forecasts from the two PLM specifications become closer to the SPF forecasts when those forecasts are used in the estimation procedure to discipline model expectations. Moreover, the improvement in the two PLM specifications is inversely related to their relative ability to match SPF forecasts when these forecasts are not used as observables in the estimation procedure (shown in Table 5). Put differently, the need to discipline expectations is greatly reduced for the real forward-looking variables (and to a lesser extent for the nominal variables) by including TS information in the small forecasting models. 24This deterioration observed for some variables may be due to the fact that learning requires time and information. That is, the RMSE-statistics computed for the period 1982:1-2009:1 using the whole sample period in the estimation procedure (those reported in Table 4) may be somewhat superior to those RMSEstatistics computed for the period 1982:1-2009:1 using the estimates for this shorter period (reported in Table 6) because the AL processes associated with the former take into account information predating 1982. 40
Table 7. RMSE comparison of PLM forecasts w.r.t. SPF data Comparison period : 1982:1-2009:1 ∆c∆inv π r SlW-TS 0.301 1.024 0.179 0.293 (-17%) (-17%) (-60%) (-71%) SlW 0.374 1.180 0.175 0.338 (-72%) (-44%) (-85%) (-79%) 5 Conclusions This paper considers an estimated DSGE model with adaptive learning (AL) in which the forecasting models of agents include term structure information. More precisely, we extend the AL model of Slobodyan and Wouters (2012a) by introducing the term structure of interest rates and then including term structure information observed in addition to the current and lagged values of the forward-looking variables. The estimation results show that including term structure information in the agents’ forecasting models results in an improvement in model fit. Moreover, the learning specification augmented with term structure information improves the performance of AL in forecasting actual revised macroeconomic data used in the estimation procedure as well as real-time (i.e. the first announcements of) macroeconomic data. The latter finding suggests that the yield curve contains important information available in real time, which is very useful in forecasting aggregate variables above and beyond that provided by revised macroeconomic data. In line with these findings, our estimation results also show that term structure information helps AL expectations to match the forecasts of aggregate variables reported in the Survey of Professional Forecasters, which are formed using information available in real time. Therefore, term structure information further contributes to the empirical validity of AL. 41
below its previous figures. For the 2009-2019 period, the rate of change of core inflation was 1.1%, 0.6 pp down on the phase prior to the global financial crisis. And further to the outbreak of COVID-19, this disinflationary process has tended to become more acute. Such a prolonged period of moderate inflation might be due either to temporary causes, albeit with high persistence, or, alternatively, to more structural reasons. The first group of explanatory factors, namely the temporary ones, would include elements such as the decline in energy prices or the durable presence over this period of a high degree of slack both in the Euro Area and global economies. The structural causes influencing long-term inflation movements relate to changes in certain fundamentals of the economy. These include most notably sectoral composition (with an increase in the weight of the services sector1), globalization (which would give rise to a greater interconnectedness of inflation rates across different economies, against the backdrop of the progressive incorporation into global trade of countries with lower production costs) and changes in consumption patterns linked to population aging. A stable path of inflation expectations consistent with the price stability objective smooths monetary policy implementation, leading generally to a reduction in the volatility of the economic cycle. However, the prolongation over time of the current low-inflation phase has given rise to a debate on some deanchoring of inflation expectations in relation to the central bank’s medium-term objective, and potential feedback between actual inflation and expectations. As a result, the diminished pace of price changes would be exerting a downward impact on economic agents’ inflation expectations, which would in turn affect actual inflation in the same direction. Most models traditionally used in monetary policy design start from the premise that agents form expectations about the economy rationally.2This hypothesis implies that, in the shaping of their expectations, agents observe and process efficiently all available information. 1In particular, there is a growing body of evidence indicating that services prices are adjusting with less frequency than in other sectors of the economy. See, for example, Bouakez, H., Cardia, E. and Ruge-Murcia, F. (2014), and Álvarez et al. (2006). 2For example, some of the general equilibrium models that are commonly used by the New York Federal Reserve (FRBNY DSGE) or the European Central Bank (EAGLE), mainly for conducting simulation exercises, are based on rational expectations. 48
In particular, agents are able to understand the nature of macroeconomic shocks and their duration, and have the capacity to consistently incorporate news on monetary policy changes or on expected developments in the economy into their expectations. However, in reality, it is unlikely that agents are able to observe and process all available information.3On numerous occasions, the nature of shocks and their transmission channels are only imperfectly known by agents and are difficult to identify. Alternatives to this hypothesis have been largely debated in the literature.4In this paper we explore the alternative of adaptive learning expectations. This alternative assumes that agents’ expectations about future events are partly and progressively updated with the information they receive about developments in the main macroeconomic aggregates. It is further assumed that, when shaping their expectations, agents use a limited amount of information, which they incorporate every period upon the arrival of new information. The model used in the paper is an Extended Learning Model (ELMo) version of Smets and Wouters (SW, 2007) as in Aguilar and Vazquez (2019) estimated for the EA. The model builds on the DSGE of Smets and Wouters (2007) under the assumption of adaptive learning expectations and the incorporation of the term structure of interest rates through multiple Euler equations associated with the different bond maturities. The extended model results in multi-period-ahead expectations appearing in the different Euler equations. More precisely, in this version of the model, agents form expectations on inflation (and consumption) from one quarter up to five years. The model, estimated for the Euro Area as a whole for the period from 1999 Q1 to 2019 Q4, combines macroeconomic information, (consumption and inflation, among others) with financial information relating to the yield curve. The inclusion of the yield curve enables financial-market information on the future course of the economy 3The empirical literature generally finds deviations in survey-based data from rational expectations. As it is explained in Coibion et al. (2018), surveys of expectations reveal that there are biases across different demographic groups, and that, for example, perceived inflation is affected by each agent’s consumption basket, even if there is a commitment from a central bank. 4Since the pioneering publications by Marcet and Sargent (1989) and Evans and Honkapohja (2001) a growing literature (including Preston, 2005; Milani, 2007, 2008, 2011; Eusepi and Preston, 2011; Slobodyan and Wouters, 2012) , see the discussion in this regard in Aguilar and Vazquez (2019) and Vazquez and Aguilar (2021). 49
to be incorporated.5Accordingly, this specification allows a more complete characterization of expectations, by combining macroeconomic and financial information. This paper focuses on the nature of the deviations from the inflation objective through a learning scheme, this allows us to understand to what extent agents perceive current deviations in the inflation rate as temporary or permanent and shed some light on the (de)anchoring of inflation expectations in the EA. The recent conclusions in the literature related to the EA point in two directions. On the one hand, Natoli and Sigalotti (2018) look at co-movements between shortand long-term inflation expectations and find higher correlation and negative shocks affecting short-run beliefs that impact long-run expectations, suggesting a risk of de-anchoring in the long-run. On the other hand, Grishchenko et al (2019) study the behavior of survey data for the US and EA in a dynamic factor model, finding that the expectations remain anchored in both economies. Another aspect relevant is the presence of the Effective Lower Bound (ELB) during a prolonged period of low inflation and poor economic activity. The presence of the ELB curves the ability of the central bank to implement its monetary policy and has the risk of making low inflation episodes longer than in its absence. Alternatives to reduce the frequency and duration of ELB episodes with respect to the current framework are now in the debate in Bernanke (2017), and Mertens and Williams (2019) among others. These papers show that alternatives to the current framework such as, Inflation Targeting (IT) and Price-level Targeting (PLT), with the addition of an asymmetric version of each: Asymmetric Inflation Targeting (AsIT) and Temporary Price-level Targeting (TPLT), reduce the presence of ELB episodes, however, these results hinge on the assumption that the new rule is credible. There is a bunch of papers studying the interaction between monetary policy and expectations under adaptive learning. Evans et al. (2008) argue that aggressive fiscal policy measures may reduce the severity of liquidity traps. Evans and Honkapohja (2005) study 5In particular, the breakdown of nominal interest rates into the real, risk-free interest rate, inflation expectations and a risk component enables the relationship between the implied yield on a bond and the inflation rate to be exploited 50
the ability of aggressive money supply rules to overcome ELB episodes. In Honkapohja and Mitra (2020), price-level targeting is a potent tool by means of escaping liquidity traps, even if the price-level targeting policy is imperfectly credible. Findings in Eusepi and Preston (2011, 2018) suggest that active fiscal theory may help stabilize inflation in economies with interest rate pegs and learning agents. Mertens and Ravn (2014) simulate an economy with learning agents and a one-time ELB episode and show that the learning economy can escape the ELB when expectations are not too pessimistic. In this matter this paper goes further and studies the transitional effects of new policy rules to inflation expectations. The results show that current expectations are shaping the effects of monetary policy. An asymmetric inflation targeting rule, with a stronger response to inflation when it is below its trend, seems to be a robust alternative that provides improvements over standard inflation targeting, in terms of reducing the presence of ELB episodes, however there is one important consideration: changing the rule is not very effective until agents have had time to learn about it: in this model, the announcement of the new rule has no effect on agents’ expectations; instead, they only update them as they see the central bank behaving in a different way and learn about it, which requires time. This is very different from what we observe in models with rational expectations, where the announcement perfectly anchors agents’ expectations and has immediate effects in the economy. The paper is structured as follows. Section 2 introduces the DSGE model with multiperiod expectations estimated for the EA. Section 3 studies the determinants of inflation expectations in the EA since its creation. Section 4 analyses the transitional effects of alternatives to the current monetary policy framework, and section 5 concludes. 51
2 A DSGE model with multi-period expectations for the Euro Area The model builds on the SW model and its AL extensions studied by Slobodyan and Wouters (2012) and Aguilar and Vázquez (2019). This standard medium-scale estimated DSGE model contains both nominal and real frictions affecting the choices of households and firms. The assumption of adaptive learning implies that expectations are based on a limited information set, meaning that agents use small forecasting models in forming their beliefs about future realizations of forward-looking variables, in this case by using simple autoregressive models, and that they adapt the coefficients of these forecasting models by a simple Kalman filter updating procedure. In addition, the extension of the model to account for the term structure of interest rates through the Euler equation results into a multi-period forecasting model, with expectations about the key macroeconomic variables ranging from one quarter to five years ahead. More specifically, the expectations-formation mechanism of consumption, investment and inflation in the model rests, in each period, on simple learning rules that take into consideration the latest observed value and the size of the previous error forecasts to update the learning coefficients. In the concrete case of inflation, the rule for updating expectations is as follows: Etπt+i=αi,t−1+βπi,t−1πt−1, where πt−1is the deviation from target observed in the last quarter and βπi,t−1measures the degree of transmission of the observed deviation to expectations i(denoting a number) quarters ahead. That is to say, under this rule agents incorporate the latest available information on the deviation by inflation from target into their inflation expectations at different horizons (up to 5 years) target. Moreover, this learning rule captures through αi,t−1the possibility that deviations from the inflation objective may have long-lasting effects on inflation 52
expectations over a forecast horizon of i quarters. Three possible values are considered in the analysis for i: one, four and 20 quarters. The greater the persistence of the deviations perceived by agents (πt−1) is, for a given horizon i, the greaterβπi,t−1will be and, therefore, the higher the pass-through of these deviations to expectations. By way of illustration, a perceived value of βπi,t−1equals to 0.5 means that agents expect the latest observed deviation from target to halve in i quarter. Alternatively, a unit value for this coefficient would mean that agents expect the deviation to hold in full over the next i quarters. Moreover, if agents were to believe that deviations from target are permanent, which would be tantamount to a change in the inflation target, then the coefficient αi,t−1would be observed to be other than zero. Testing the anchoring of expectations Under this simple expectations-formation framework, it is possible to estimate both learning coefficients and, on the basis thereof, to analyze the degree of temporariness associated with the deviations from inflation assigned by agents in constructing their expectations. Under a scenario of fully credible monetary policy, agents would not perceive permanent deviations from target αi,t−1= 0 and temporary deviations would diminish over the course of the forecast horizon (βπ1> βπ4> βπ20 ). 2.1 Estimation The DSGE model is estimated for the sample period from 1999Q1:2019Q4, using the quarterly series of the inflation rate, the short term interest rate, the log of hours worked, and the quarterly log differences of real consumption, real investment, real wages, and real GDP with the addition of the 1, 3 and 5-year government benchmark bond yields. The measurement equation is 53
Xt= dlGDPt dlCONSt dlINVt dlWAGt dlPt lHourst ECBratet 1−year TB yieldt 1−3year TB yieldt 1−5year TB yieldt = γ γ γ γ π l r r{4} r{12} r{20} + yt−yt−1 ct−ct−1 it−it−1 wt−wt−1 πt lt rt r{4} t r{12} t r{20} t ,(9) where land dl represent the log and the log difference, respectively. γ= 100(γ−1) is the common quarterly trend growth rate for real GDP, real consumption, real investment, and real wages. ¯ l,π,rand r{j}are the steady-state levels of hours worked, inflation, the ECB interest rate, and the 1,3,5-year (ie. for j equal to 4,12,20 quarters) bond yields, respectively. We follow a Bayesian estimation procedure. First, the log posterior function is maximized by combining prior information on the parameters with the likelihood of the data. The prior assumptions are exactly the same as in Slobodyan and Wouters (2012). In addition, we consider loose priors for the parameters characterizing both the 1,3,5-year yield dynamics and the measurement error processes. The Metropolis-Hastings algorithm is used to generate the posterior distribution and to compute the log density of the model. We report the key parameter estimates in the model in Appendix A.1. 2.2 The evolution of expectations: cycle and trend Figure 1 shows, for the different horizons analyzed, the estimated coefficients for the Euro Area for the period 1999-2019. As might be expected, the value of the coefficients indicates 54
that, except for some isolated period, the weight assigned by agents to past inflation in their formation of expectations about price growth diminishes as the time horizon increases (βπ1> βπ4> βπ20 ). The value of the coefficient at one quarter (βπ1) is close to unity, suggesting that agents expect, at three months, that the deviations of inflation from target will hold unchanged. Moreover, this coefficient has been highly stable since the start of Economic and Monetary Union. In the case of medium-term expectations, i.e. four and 20 quarters ahead (βπ4and βπ20 ), the estimates suggest that agents reduce, as the time horizon increases, the weight they assign in their learning rule to the latest observed figure. The course of both coefficients shows a positive correlation with the behavior of actual inflation, indicating that, in periods with higher inflation rates (2001-2002 and 2007-2008), agents estimate that deviations have a higher persistence. This finding suggests that prices show a different degree of adjustment according to the level of the inflation rate through the cycle.6 In any event, according to the model, in the longer run inflation would return, in the absence of fresh shocks, to the medium-term monetary policy objective, since the value estimated for (αi,t−1) is very close to zero at any forecast horizon.7 6One possible explanation is the greater ease with which firms can, in periods of excess demand, raise prices instead of increasing productive capacity. Conversely, in periods of low demand, they can opt to reduce their capacity temporarily. See Bobeica and Sokol (2019). 7The chart depicts the coefficient estimated when i= 20 quarters. In practice, the estimated value when i is equal to 1 or 4 is very similar, which can be explained by the fact that agents have the same information to estimate the long-term deviation by inflation from target irrespective of the horizon i at which they formulate their short or medium-term expectations. 55
Figure 1. Inflation expectations coefficient’s evolution 2.3 International comparison When comparing with the estimates from Aguilar and Vazquez (2019) for the United States (US), see figure 2 below, the degree of persistence of inflation over the past 20 years on average can be seen to be less in the US than in the Euro Area. That might be indicative of less nominal rigidities in the US economy. A shock to inflation will be more or less persistent depending on a series of factors which include, among others, the degree of wage inertia (depending on the degree to which wages are linked to the overall price index), price-setting rigidities and supply-side rigidities (which, in the model, are manifested via a limited capacity to adjust the use of productive factors). In the case of the model estimated for the US, the degree of wage indexation is comparatively lower, while the flexibility of prices is greater. Consequently, inflation expectations in the US economy are less sensitive to past inflation, mainly in the medium and long term. Specifically, the coefficients estimated for βπ4and βπ20 (i.e. 1 and 5 years ahead) are approximately half those obtained for the Euro Area, meaning that the deviation by expectations in the face of a shock is less both in terms of level and duration. 56
Figure 2. Sensitivity of inflation expectation to last value observed: EA vs US The estimation results can be somewhat sensitive to the model used. One way of assessing the estimates offered with is to compare the inflation expectations at the one-year forecast horizon obtained from the model and those drawn from the ECB’s Survey of Professional Forecasters (SPF). This quarterly survey reflects the expectations of participant respondents – who are experts from financial and non-financial institutions alike in the Euro Area – about inflation rates, GDP growth and Euro Area unemployment at different horizons. The comparison between both sources of expectations shows that the dynamics captured in the model are consistent with the SPF series (see Chart 3), which supports the empirical validity of the estimates associated with the adaptive learning expectation formation. Figure 3. ELMo vs SPF one-year-ahead inflation expectations in the EA 57
References •Aguilar, P., and J. Vázquez. 2019. “An estimated DSGE model with learning based on term structure information.” Macroeconomic Dynamics, 1-31. •Álvarez et al. 2006. “Sticky prices in the Euro Area: A summary of new micro evidence.” Journal of the European Economic Association, Vol. 4, No 2/3, pp. 575-584. •Bernanke, B. S. 2017. “Monetary Policy in a New Era.” Peterson Institute for International Economics, October 12–13. •Bobeica, E. A. Sokol. 2019. “Drivers of underlying inflation in the Euro Area over time: a Phillips curve perspective.” ECB Economic Bulletin, Issue 4/2019. •Bouakez, H., Cardia, E. and Ruge-Murcia, F. 2014. “Sectoral Price Rigidity and Aggregate Dynamics.” European Economic Review, Vol. 65(C), pp. 1-22. •Coibion, O., Gorodnichenko, Y. and Kamdar, R. 2018. “The Formation of Expectations, Inflation, and the Phillips Curve” Journal of Economic Literature 56, pp. 1447-91. •Eusepi, S., and B. Preston. 2011. “Expectations, learning, and business cycle fluctuations.” American Economic Review 101, pp. 2844-2872. •Eusepi, S., and B. Preston. 2018. “The Science of Monetary Policy: An Imperfect Knowledge Perspective.” Journal of Economic Literature 56, pp. 3-59. •Evans, G. and S. Honkapohja. 2001. “Learning and Expectations in Economics.” Princeton University Press 376. •Evans, G. and S. Honkapohja. 2005. “Policy interaction, expectations and the liquidity trap.” Review of Economics Dynamics 8, pp. 303-323. 64
•Grishchenko, O. S. Mouabbi, and J.P. Renne. 2019. “Measuring Inflation Anchoring and Uncertainty: A U.S. and Euro Area Comparison.” Journal of Money, Credit, and Banking, Blackwell Publishing 51, pp. 1053-1096. •Honkapohja, S., and Mitra, K. 2020. “Price level targeting with evolving credibility.” Journal of Monetary Economics 116, pp. 88-103. •Marcet, A., and T.J. Sargent. 1989. “Convergence of least-squares learning in environments with hidden states variables and private information.” Journal of Political Economy 97, pp. 1306-1322. •Mertens, T., M and Ravn, M. 2014. “Fiscal Policy in an Expectations-Driven Liquidity Trap.” The Review of Economic Studies 81, pp. 1637–1667. •Mertens, T., M and J., C. Williams. 2019. “Monetary policy frameworks and the effective lower bound on interest rate.” American Economic Association papers and proceedings, pp. 109: 427-32. •Natoli F. and L. Sigalotti. 2018. “Tail Co-movement in Inflation Expectations as an Indicator of Anchoring.” International Journal of Central Banking 14, pp. 35-71. •Slobodyan, Sergey, and R. Wouters. 2012. “Learning in a medium-scale DSGE model with expectations based on small forecasting models.” American Economic Journal: Macroeconomics 4, 65-101. •Smets, F., and R. Wouters. 2007. “Shocks and frictions in US business cycles: A Bayesian DSGE approach.” American Economic Review 97, pp. 586-606. •Vázquez J., and Aguilar P. 2021. “Adaptive learning with term structure information.” European Economic Review 134 65
Part III The importance of data revisions 1 Introduction The existence of data revision must be acknowledged when macroeconomic series are used for business analysis. This chapter provides a detailed analysis of the statistical properties of data revisions for the euro area and studies the appropriate modeling of real-time data and its revision in DSGE models for business cycle analysis. The main macroeconomic series are regularly revised relative to their real-time release to incorporate new information that was not available at the time of the initial announcement or to incorporate changes, such as in the definition of the indicator or the measurement of the variable. A distinction between whether the data comprises initial releases and/or final revised data must be taken into account by researchers when constructing datasets. If data revisions are not well-behaved, meaning that they can be forecasted, researchers who ignore this fact may suffer from a bias in their analysis. This chapter studies the properties of real-time data and their revisions for the euro area and proposes a modeling framework to incorporate this phenomenon into a DSGE model. In one of the earliest studies of data revision properties, Mankiw, Runkle and Shapiro (1984) focus on the predictability of data revisions. They analyze whether the preliminary announcements of money stock are rational forecasts of the final announcements or observations containing a measurement error of the revised series. Mankiw and Shapiro (1986) extend this study to the series of GNP.1These two papers conclude that money stock revisions are predictable but GNP revisions are not. This led to a primary classification of revisions as adding news or reducing noise. Revisions add news when the initial announcement is an optimal forecast of the final data, in which case they are orthogonal to initial data and there1Other relevant papers of the matter during that periods are Mork (1987, 1990) 66
fore unpredictable. Revisions reduce noise when the initial announcement is an estimate of the final data with a measurement error. In that case the initial announcement is correlated with the revision, thus, becoming predictable. Diebold and Rudebusch (1991) subsequently highlight the importance of data revisions in macroeconomics. They show that the US index of leading economic indicators does a fine job at predicting recessions ex-post but fails in predicting future recessions. This is because the indicator is constructed to explain revised past data, and thus ignores the fact that initial data releases may look very different once they are revised. The paper by Croushore and Stark (2001) increased the popularity of real-time data and their revisions by providing a regularly updated real-time dataset of the main macroeconomic variables. In particular, Croushore (2011) extensively reviews the literature and discusses the data implications of real-time data for data revisions, forecasts, monetary policy analysis, macroeconomic research, and current analysis of financial and business conditions. The use of real-time macroeconomic datasets appears to become more important for policy institutions with the development of new datasets by statistical agencies, such as the Federal Reserve Bank of Philadelphia, the European Central Bank, and the OECD. More recently, Aruoba (2008) defines the desirable statistical properties of data revisions, namely i) the mean is expected to be zero; ii) small variance compared to that of the revised variable; and iii) unpredictability. He finds that these properties are not satisfied in the revisions of major macroeconomic variables in the United States, as they have a non zero mean, their volatility is large compared to the final data, and they can be predicted using the information set at the time of the initial announcement.2 Another relevant aspect is the impact of data revisions on the estimation of DSGE models, which are now popular for macroeconomic analysis at central banks. Casares and Vázquez (2016) introduce an extension of the Smets and Wouters DSGE model (2007) that includes both real-time and revised data from the U.S. economy. Their estimates show a level of both 2A similar study is present in Faust et al (2005) for the G7 countries 67
habit formation and price indexation which is lower than the standard model. They also find that shocks in data revisions explain roughly 10% of output variability. This means that omitting revisions may cause two problems: First, a bias in the parameter estimation; and second, overestimation in the sources of business cycle variability. This chapter contributes to the literature on data revisions by providing a detailed analysis of the statistical properties of data revisions for the euro area and studying the appropriate modeling of real-time data and its revision in DSGE modeling. More precisely, following Casares and Vazquez (2016), the Smets and Wouters (2007) DSGE model is augmented to include real-time data (by assuming that indexation rules and the monetary policy rule are based on real-time data) and to incorporate data revisions. The aim is to pinpoint the source of data revisions (whether they reduce noise or add news) and to assess their macroeconomic implications. One of the main findings is that data revisions are not wellbehaved, i.e. they are correlated with initial announcements and show high volatility. These empirical findings are confirmed in reduced-form regression analysis and in an estimated DSGE model augmented with data revisions. These findings are in line with those of Casares and Vázquez (2016) for the US. As a consequence, revisions become a major source in the business cycle decomposition. In the case of the Euro Area they account for one-third of the output variability, which is roughly three times the figure estimated for the US in Casares and Vázquez (2016). This finding leads to the conclusion that DSGE models for business cycle analysis which omit real-time data and data revisions may introduce a major source of bias into the estimated variance decomposition and encourages further improvements in the estimation of real-time data from the statistical agencies. The rest of this chapter is structured as follows: Section Two introduces the concept of revisions, describes their main properties, and proposes a specific framework for the inclusion of data revisions in DSGE models. Section Three derives the real-time equations that enter into the extended DSGE model. Section Four presents the data and estimation procedure and Section Five discusses the main findings of the estimated DSGE-extended model. Section 68
Six concludes. 2 Data revisions This section is divided into two parts and provides a rationale for the inclusion of data revisions in macro models. The first part defines the concept of data revisions and the main points to be considered when taking them into account, some of them often ignored in the literature. The second part studies the statistical properties of data revisions in the euro area and provides an empirical justification for their inclusion in DSGE models. 2.1 The concept of data revisions Data revisions can be defined as the difference between the data initially announced and the final revised data . In the case of the euro area, the first announcements of quarterly real GDP, GPD deflator, and real consumption are generally released with a lag of one quarter, while the final revised data are published between four and twelve quarters later.3This definition can be expressed formally as follows: yt=yr t,t+1 +revy t,t+S,(10) where ytrefers to the final revised observation of GDP, yr t,t+1 represents the initial announcement with one quarter delay, and revy t,t+Scaptures the total value of revision after t+Speriods. A similar formula can be applied to the consumption and inflation revision processes. The vintage matters The literature abstracts from the importance of the vintage in defining data revisions.4 3 Benchmark revisions may also occur during the revision process. They involve methodological changes, such as the concepts included in the definition of the variable or the reference year in the series. 4The paper by Croushore and Stark (2001) is an exception. They discuss the election of data vintages, but in the context of economic forecasting. 69
However, authors such as Croushore and Stark (2001) are an exception in that they focus their research on the choice of data vintages in the context of economic forecasting. The choice of the vintage, however, becomes highly important when it comes to variables expressed in growth rates, as revisions between vintages are a potential source of “noisy” revisions. Table 2.A shows the different vintage publications of US GDP, which help to illustrate the importance of the choice of vintage in computing output growth rates. Table 2.A: GDP US Period\Vintage 1990:Q2 1990:Q3 1990:Q4 1991:Q1 1990:Q1 4195.8 4150.6 4150.6 4150.6 1990:Q2 4163.2 4155.1 4155.1 1990:Q3 4173.6 4170 1990:Q4 4147.6 GDP: Billions of real Dollars Depending on the choice of the vintage, output growth rates can be calculated in two ways: Across different vintages or within the same vintage. In the first case, the growth rate is obtained using the first quarterly data announcements from two consecutive vintages, while in the second growth rates are computed using the first vintage in which both quarterly variables are available. Formally, they can be expressed as follows: g1= (yr t+1,t+2/yr t,t+1 −1) ×100, g2= (yr t+1,t+2/yr t,t+2 −1) ×100. Under the first option, g1, the growth rates are always computed using the first release, while the second method, g2, may already incorporate a revision in the first observation. However, using the same vintage avoids the impact of benchmark revisions between vintages.5 5For our US sample data, 1983Q1:2008Q1, there are in all five benchmark revisions (1985:Q3, 1991:Q3, 1995:Q4, 1999:Q3 and 2003:Q4), while for the euro area there was one main benchmark revision in 2005. Vázquez, María-Dolores, and Londoño (2012) adjust benchmark revisions by replacing them with the average 70
The quarterly growth rate of output in 1990Q2, depending on the method, would be either: ∆y1990Q2,g1= (yr 1990Q2,1990Q3/yr 1990Q1,1990Q2−1)x100 = (4163.2/4195.8−1) ×100 = −0.776%. ∆y1990Q2,g2= (yr 1990Q2,1990Q3/yr 1990Q1,1990Q3−1)x100 = (4150.6/4163.2−1) ×100 = 0.303%. As illustrated in the example, different choices of vintage provide opposite-sign growth rates. The size of the revisions are therefore directly affected by this choice, so this research acknowledges the properties of data revisions under both alternatives. 2.2 Regression analysis of data revisions This subsection studies the main statistical properties of data revisions in the euro area to explain why they are relevant and should be included in macro models. The analysis is divided into two parts: The first sets out the main descriptive statistics of data revisions under both approaches (g1and g2) of the quarterly growth rates of real GDP, consumption, and inflation. The second part estimates the relationship between initial announcements and data revisions to determine whether revisions add news to the initial announcement or reduce errors, and provides an estimation of the process of data revisions. Main descriptive statistics According to Aruoba (2008), if data revisions are well-behaved they should have the following properties: First, the mean is expected to be zero. This would imply that the initial announcement is an unbiased estimate of the final revised value. Second, the variance should be small when compared to that of the revised value. This is measured by the noise to value of the two observations before and after. In this paper, benchmark revisions are managed by replacing them with the value obtained from g2, which greatly simplifies the procedure. 71
signal ratio, which is the ratio between the standard deviation of the final revisions and the final data. Finally, the revision should be uncorrelated with the initial announcement, i.e. it should be unpredictable. Table 2.B shows the main descriptive statistics for data revisions according to the list of interest for the quarterly growth rates (g1and g2) of quarterly real GDP, consumption and inflation. Table 2.B Euro Area descriptive statistics of data revisions Revision in g1Revision in g2 GDP Consumption Inflation GDP Consumption Inflation Mean 0.110 -0.111 -0.126 0.276 0.357 0.079 Absolute Mean 1.645 1.708 0.716 0.940 0.845 0.531 Median 0.172 -0.088 -0.088 0.478 0.413 0.095 Min -4.640 -7.440 -3.003 -2.978 -2.204 -1.637 Max 4.827 4.830 2.055 2.479 3.131 2.202 Std. D. Revision 2.126 2.273 0.957 1.153 1.032 0.686 Noise/Signal 1.602 1.658 0.761 0.720 0.622 0.901 Correlation with Initial -0.708 -0.712 -0.683 -0.376 -0.215 -0.414 Correlation with final 0.415 0.481 0.400 0.337 0.422 0.509 Correlation Initial-Final 0.348 0.272 0.395 0.744 0.793 0.571 The overall results suggest that revisions are not well-behaved. Data revisions of output, consumption, and inflation have statistically non-zero means. The output and consumption revisions also have a noise to signal ratio greater than one under both methods of computation. Finally, all variables show a relatively high level of (negative) correlation between revisions and the initial release.6 Regarding the choice of vintage in terms of the statistical properties of the revisions, it can be seen that when the second method of computing growth rates (i.e. using the same vintage) 6In the case of the US (see Appendix 1.C.2), the results are somewhat similar and the properties listed by Aruoba (2008) are not satisfied either. 72
is used in the case of the US (see Appendix 1.C.2) the results are somewhat similar; nor do they satisfy the properties listed by Aruoba (2008). g2reduces the variability of the revisions (and thus, the noise to signal ratio) and reduces correlation with the initial announcement, but the correlation with the final data remains low. In addition, the correlation between the initial announcement and the final data is closer when growth rates are computed for the same vintage. The fact that the mean is lower when g1is used than when g2is used is a consequence of large error offsetting signs, so the absolute mean is smaller when g2is used. These results may prompt the reader to use growth rates computed for the same vintage, but it must be realized that one revision may already be included in one of the observations used to compute the growth rate. Concerning the use of either method in the literature, Croushore and Stark (2001) rely on growth rates under the same vintage (although they mention the possibility of using g1too), Casares and Vázquez (2016) and Vázquez, Maria-Dolores and Londoño (2012) use the g1approach and make no specific mention of the method used in Aruoba (2008). Noise or news? We formally test the hypothesis of whether revisions reduce noise or add news. They reduce noise when the initial announcement is an early estimate of the revised variable with a measurement error. This implies that the revision is uncorrelated with the final value but correlated with the initial data release. By contrast, revisions add news when the initial announcement is an efficient estimate of the revised variable and the revision is correlated with the final data but uncorrelated with the initial announcement (as the revision is unpredictable). Following Aruoba (2008), we test both hypotheses under the two methods proposed for computing growth rates with real-time data: -Noise: yr t,t+1 =α1+β1yt+u1 t -News: yt=α2+β2yr t,t+1 +u2 t where the first joint hypothesis α1= 0, β1= 1 tests the noise hypothesis and the second 73
across agents, the expression below is achieved ct= (h/γ)cr t−1,t −(h/γ)Etcr t,t+1 +Etct+1 +(1−h/γ)(σc−1)L1+σl σc(lt−Etlt+1)− 1−h/γ σc(Rt−Etπt+1 +εb t).(25) The Etcr t,t+1 refers to the real-time announcement of aggregate consumption in t+ 1 which affects the external habit in t. The definition of this expression can be obtained using ct=Etcr t,t+1+revc t,t+S(as shown in equation 1, but for consumption) and substituting revc t,t+S by revc t,t+S=bc(cr t,t+1 +δccr t−1,t) + ρS chεc t−1,t+S−1+ (δc/ρc)εc t−2,t+S−2i.Consequently we get ct= (1 + bc)cr t,t+1 +bcδccr t−1,t +ρS chεc t−1,t+S−1+ (δc/ρc)εc t−2,t+S−2i, and isolating cr t,t+1, an explicit term is obtained cr t,t+1 = ct−bcδccr t−1,t −ρS chεc t−1,t+S−1+ (δc/ρc)εc t−2,t+S−2i 1 + bc .(26) By substituting the latter equation into (16) ct+(h/γ) 1 + bc ct= (h/γ)cr t−1,t +(h/γ) 1 + bcbcδccr t−1,t −ρS chεc t−1,t+S−1+ (δc/ρc)εc t−2,t+S−2i+ Etct+1 +(1−h/γ)(σc−1)L1+σl σc(lt−Etlt+1)−1−h/γ σc(Rt−Etπt+1 +εb t), and grouping cr t−1,tand isolating ctwe get to final expression for this new Euler equation: ct=c11 + δc(1 + bc)−1cr t−1,t + (1 −c1)Etct+1 +c2(lt−Etlt+1)−c3(Rt−Etπt+1 +εb t)+ c4εc t−1,t+S−1+ (δc/ρc)εc t−2,t+S−2,(27) where: c1=h/γ 1+(h/γ)(1+bcc)−1, c2=(σc−1)wL/(φwC) σc(1+(h/γ)(1+bcc)−1), c3=1−h/γ σc(1+(h/γ)(1+bcc)−1), and c4=(h/γ)ρS cr (1+bcc)(1+(h/γ)(1+bcc)−1). 80
As a result, real-time data enters in the equation in the form of lagged values of external consumption. Moreover, shocks in the revision process of consumption do play a role. Later on, a specific structure will be provided to the shocks and its impact in the estimation discussed. 3.2.2 Monetary policy rule We use equation (1) to rewrite output in the monetary policy rule as we assume that the monetary authority takes decisions based on the information available on output and inflation. This implies that for lagged values of output, the observation that the authority uses corresponds to the first announcement of aggregate output, which is published with a one-quarter delay. Similar reasoning is used in Casares and Vázquez (2016); however, the presence of lagged revisions affects the definition of revisions in output, and requires the derivation of a new monetary policy rule. Starting from the Smets and Wouters (2007) model, we have the following policy rule:11 Rt=ρRt−1+(1−ρ)[rππt−1+ryyt−1−yp t−1]+r∆yyt−1−yp t−1−yt−2−yp t−2+εR t.(28) Including the equations for data revisions on output (7) and inflation (9) into the definition of real-time data (1), we can express define ytand πtas follows: yt= (1 + by)yr t,t+1 +byδyyr t−1,t +ρS yhεy t−1,t+S−1+ (δy/ρy)εy t−2,t+S−2i, πt= (1 + bπ)πr t,t+1 +ρS πεπ t−1,t+S−1. Placing the last two expressions for yt−1,yt−2,πt−1into (19) we have the following expression Rt=ρRt−1+ (1 −ρ)(rπh(1 + bπ)πr t−1,t +ρS−1 πεπ t−2,t+S−2i+ 11Note that in this expression inflation and the output gap are lagged by one more period than in the original version. This makes it easier to introduce inflation in real-time. 81
ryh(1 + by)yr t−1,t +byδyyr t−2,t−1+ρS−1 yεy t−2,t+S−2+ (δy/ρy)εy t−3,t+S−3i−yp t−1)+ r4y(h(1 + by)yr t−1,t +byδyyr t−2,t−1+ρS−1 yεy t−2,t+S−2+ (δy/ρy)εy t−3,t+S−3−yp t−1i− h(1 + by)yr t−2,t−1+byδyyr t−3,t−2+ρS−2 yεy t−3,t+S−3+ (δy/ρy)εy t−4,t+S−4−yp t−2i)+εR t. Finally, operating with the terms measuring the change in the real-time output gap, a new monetary policy rule in real-time is obtained Rt=ρRt−1+ (1 −ρ)(rπh(1 + bπ)πr t−1,t +ρS−1 πεπ t−2,t+S−2i+ ryh(1 + by)yr t−1,t +byδyyr t−2,t−1+ρS−1 yεy t−2,t+S−2+ (δy/ρy)εy t−3,t+S−3i−yp t−1)+ r4y((1 + by)hyr t−1,t −yr t−2,t−1i+byδyhyr t−2,t−1−yr t−3,t−2i+ ρS−1 yhεy t−2,t+S−2−(1/ρy)εy t−3,t+S−3i+ρS−2 yδyhεy t−3,t+S−3−(1/ρy)εy t−4,t+S−4i+ (yp t−1−yp t−2))+εR t.(29) 82
4 Data and estimation procedure This section seeks to study the impact of real-time data and data revisions on DSGE models through the three channels mentioned above. The sample period used for the euro area is 1995Q1-2008Q1. The set of observable variables comprises quarterly series of the inflation rate (expressed as the first difference in logs of the implicit GDP deflator), the ECB interest rate, the log of employment, and the quarterly log differences of real consumption, real investment, real wages, and GDP. In addition, for the extended model we incorporate real-time series of quarterly inflation (expressed as the first difference in logs of the real-time GDP deflator), and quarterly log differences of GDP and real consumption from the ECB Real-Time Database.12 Variables displaying a long-run trend are expressed in log differences to remove the non-stationary component. The list of observable variables is measured as follows: Xt= dlGDPt dlCONSt dlINV dlWAGT dlEMPLt dlPt lECB&lFEDFUNDSt dlGDPrt dlCONSt dlPrt = γ γ γ γ ¯ l π r γ γ π + yt−yt−1 ct−ct−1 it−it−1 wt−wt−1 lt πt rt yr t−yr t−1 cr t−cr t−1 πr t where land dl respectively denote the log and the log difference. γ= 100(γ−1) , is the common quarterly trend growth rate for real GDP, consumption (also for real-time variables) 12Real time growth rates are computed using the g1approach. The extended model is also estimated using g2but is not shown here due to space constraints. The overall result using the latter approach is similar, but the identification of the revision processes becomes more sensitive. 83
investment and wages, which are the variables presenting a long run trend. ¯ l,π,rare the steady state the level of employment per capita, and the steady state values of inflation and the short-term interest rate. The approach used is a two-step Bayesian estimation procedure in Dynare. First, the log posterior function is maximized by combining prior information on the parameters and the likelihood of the data. Then the Metropolis-Hastings algorithm is implemented, which runs a massive sequence of draws for all the possible realizations for each parameter to get a picture of the subsequent distribution. For the SW model this algorithm is executed using 3 blocks of 200,000 realizations each. The same is done for the extended model. The acceptance rates for both models for the US and euro area are between 20-30%. 5 Estimation results This section discusses the main results of the DSGE estimation. The first part argues the main results in terms of parameter estimation for the euro area. The second provides the main findings in terms of second moments and variance decomposition. 5.1 Parameter estimates The baseline SW for the EA vs the US Table 3.A reports the mean and the 5th and 95th percentiles obtained from the MetropolisHastings estimation of both the extended and baseline model (without real-time data) parameters for the euro area. This subsection compares the baseline estimates (right-hand side of the table) with those estimated for the US, as reported in Table 3.B. 3.B.13 The confidence intervals of the main group of parameters overlap to a great extent with those for the US. However, there are some noteworthy discrepancies. The degree of price and wage stickiness (ξp,ξw) is slightly smaller (0.45 and 0.63 for the euro area against 0.66 and 0.70 for the US). Regarding the indexation parameters (iwand ip), the price indexation is roughly the same 13We compare our results with those of Smets and Wouters (2007) since they are the main reference. Nonetheless these comments apply to a large extent to the estimates reported in Casares and Vázquez (2016) 84
(ip= 0.24), while the wage indexation coefficient is less than one-half of the US estimate (0.21 versus 0.58). This makes the wage equation more forward-looking in the case of the euro area. Another important difference lies in investment decisions, namely the elasticity of capital utilization and the level of fixed costs (ψand φ). The former, ψ, is significantly lower (0.19 versus 0.54), while the latter is estimated to be higher (1.90 versus 1.60). With respect to the parameter estimates in the policy rule, the smoothing parameter (ρ) and the coefficient measuring the change in output gap (r4y) are both rather similar to the US. However, the reaction to the inflation gap is smaller (1.72 versus 2.01) and the output gap is nearly zero. Finally, in terms of structural shocks, the results suggest a greater persistence of spending and risk premium shocks (ρb,ρR, 0.77 and 0.48 versus 0.22 and 0.15), while investment adjustment and price and wage mark-up shocks (ρi,µpand µw) are less persistent. The SW model with EA real-time data The assumption that agent’s economic decisions are based on real-time data has two important effects in the Euler equation. It reduces the importance of the habit in consumption parameter (hdrops from 0.68 to 0.4) and reduces the Frisch elasticity (σlincreases from 1.09 to 3.07). In terms of nominal rigidities, it reduces the Calvo probability in wages (ξwdrops from 0.65 to 0.44) but increases wage indexation (iwincreases from 0.21 to 0.45). Thus, wages are updated more frequently but are more backward-looking. Concerning the new monetary policy rule, the estimates show a similar reaction to real-time data as to the model with final data. Regarding the estimates of the structural shocks, the model with real-time data shows a smaller autocorrelation coefficient in the spending and risk premium shocks (ρg,ρR), and a lower estimate in the moving-average component of both prices and wage mark-up shocks (µp,µw). The estimation of the data revision process supports the idea that data revisions are not well-behaved. In the case of output and consumption the initial announcement anticipates a future negative revision (by,bcbeing -0.15 and -0.13 respectively) and they are correlated with past revisions. In the case of inflation the estimates show that the initial release antic85
ipates an upward revision (bπ=2.2). The error component shows a high level of persistence for all the variables (ρyr = 0.66,ρcr = 0.72, and ρπr = 0.94 ) and the estimated volatility of the innovations (σyr,σcr and σπr) is on average twice as high as the rest of the shocks in the model. These results are in line with the regression analysis for the revisions of output and consumption. Both (reduced-form and structural) methodologies capture a negative correlation with the initial release, the persistence in the error term, and the negative coefficient associated with past revision. Concerning the inflation revision process, the estimations of the DSGE and the regression model show opposite signs in the coefficient relating revisions to the initial announcement, which might be due to the aforementioned differences between the Bayesian structural econometric approach and the reduced-form OLS approach. In any case, the overall conclusion (especially for output and consumption) remains robust, data revisions are correlated with their initial announcement, and their errors show high variance and persistence. 5.2 Second-moment statistics Table 4 reports the main second-moment statistics: Standard deviation, contemporaneous correlation with output growth, and first-order autocorrelation. These statistics relate to actual and synthetic data from both the original and the extended SW models. In particular, Panel A of Table 4 reproduces the second-moment statistics for real-time variables (yr,cr, and πr) as well as their revisions (revry,revrc, and revrπ). The extended model fulfills a moderate task when replicating them . First, serial autocorrelation is well approximated for all variables. Second, the estimated volatility of revisions in output and inflation is practically the same as in the actual data. However, the estimated variance of output and consumption growth is three times higher than in the actual data. This higher volatility is due in principle to the inclusion of new shocks (the specific impact is seen in subsections 5.3 and 5.4). Finally, with respect to the correlation with final output growth, the real-time estimates of yr,cr, and πrare very close to the true values, while their revisions are less closely correlated (about half of the actual values). 86
Table 4, Panel B shows the same statistics for the remaining endogenous variables (y, c,i, w,l,Rand π). The first conclusion that can be drawn is that the original model does a better job in terms of volatility. This reinforces the idea that the extended model with real-time data amplifies volatility. Concerning correlation with output, both models fit the data reasonably well. Finally, the model performs moderately well in regard to serial autocorrelation. 5.3 Variance decomposition Table 5 shows the variance decomposition analysis for the EA baseline model and the model with real-time. The variability of output growth is driven by demand-side shocks in both models: the risk-premium shock (ηb), exogenous spending shock (ηg), investment adjustment cost shock (ηi) and interest rate shock (ηR) account for more than half of the total variability (61% in the original model and 57.2% in the extended model), with the risk premium shock as the main source (between 30-40% for both). With respect to supply shocks, the price mark-up shocks (ηp) are the main source of variation for wages, employment, interest rate and inflation. The introduction of data revision shocks in the extended model (ηry,ηrc and ηrπ) accounts for roughly 30% of the variation in inflation and in consumption and output growth. In particular, shocks in the inflation revision process become the major source of business volatility in the model. This result highlights the importance of acknowledging the significance of data revisions. 6 Conclusions This chapter provides a detailed analysis of the statistical properties of data revisions for the EA. It also studies what type of modeling is appropriate for real-time data and its revision in DSGE models. From a practical standpoint, the statistical properties of data revisions are studied under different approaches, leading to this first conclusion: Revisions depend on initial announce87
ments and show high volatility, which suggests that they are not well-behaved. In addition, a reduced-form regression analysis is carried out to propose an empirically based structure of the data revision processes. This characterization of data revisions is introduced into the Smets and Wouters (2007) DSGE model by assuming that the economic decisions of households, firms, and monetary authorities depend on real-time data. As a result, an extended version of the model is derived, enabling us to estimate the implications of real-time data and their revisions in the context of a DSGE model. The estimates of the DSGE model corroborate that data revisions are correlated with their first release, highly volatile, and highly autocorrelated. In the euro area, for instance, a positive announcement of output and consumption is likely to lead to a negative future revision. In the case of inflation, the correlation between the initial release and the first revision is relatively close and positive. Furthermore, in terms of modeling, the incorporation of real-time data and data revisions affects the DSGE model in three relevant aspects. First, the estimated values of some of the main parameters vary, e.g. lower habit formation values are found. Second, revision shocks become a significant source in the business cycle decomposition. For instance, in the case of the euro area they account for up to one-third of output variability. Finally, the introduction of new shocks increases the volatility of the variables observed. In sum, these findings suggest that data revisions are not well-behaved, so DSGE models omitting real-time data and data revisions might be ignoring important sources of aggregate fluctuations. This work presents a way to accommodate this facts in business cycle analysis while it encourages further improvements in the estimation of real-time data from the statistical agencies. 88
References Aruoba, B. S. 2008. “Data Revisions Are Not Well-Behaved”, Journal of Money, Credit and Banking 40, 319-340. Casares, M., and Jesús Vázquez. 2016. "Data revisions in estimated DSGE models." Macroeconomics Dynamics 20, 1683-1716. Christiano, L. J., Martin Eichenbaum, and Charles L. Evans. 2005. “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy”, Journal of Political Economy 113, 1-45. Croushore, D., and Tom Stark. 2001. “A Real-Time Data Set for Macroeconomists”, Journal of Econometrics 105,111-130. Croushore, D., and Charles L. Evans. 2006. “Data Revisions and the Identification of Monetary Policy Shocks”, Journal of Monetary Economics 53, 1135-1160. Croushore, D.. 2011. “Frontiers of Real-Time Data Analysis”, Journal of Economic Literature 49, 72-100. Diebold, F. X., and Glenn D. Rudebusch. 1991. “Forecasting Output With the Composite Leading Index: A Real-Time Analysis,” Journal of the American Statistical Association 86, 603-610. Fagan,G., Henry Jêrome, and Ricardo Mestre. 2005. “An Area-Wide Model for the Euro Area”, European Central Bank, Research Department, Kaiserstrasse 29, D-60311 5, 40. Faust, J., R., John H. and Wright, Jonathan H. 2005. "News and Noise in G-7 GDP Announcements.." Journal of Money, Credit, and Banking 37: 403–419. Mankiw, N. G., David E. Runkle, and Matthew D. Shapiro. 1984. “Are Preliminary Announcements of the Money Stock Rational Forecasts?”, Journal of Monetary Economics 14, 15-27. Mankiw, N. G. and Shapiro, Matthew D. 1986. "News or Noise: An Analysis of GNP Revisions." Survey of Current Business: 20-5. Mork, K. A. 1990. "Forecastable Money-Growth Revisions: A Closer Look at the Data." 89
Table 3.A.1 Priors and estimated posteriors of the structural parameters: Euro Area Priors Posteriors Extended model SW model Distr Mean Std D. Mean 5% 95% Mean 5% 95% ϕNormal 4.00 1.50 7.22 5.24 9.11 6.00 4.22 7.80 hBeta 0.70 0.10 0.40 0.28 0.53 0.68 0.60 0.77 σcNormal 1.50 0.37 1.40 - - 1.40 - - σlNormal 2.00 0.75 3.07 1.95 4.20 1.09 -0.01 2.2 ξpBeta 0.50 0.10 0.42 0.33 0.52 0.45 0.34 0.55 ξwBeta 0.50 0.10 0.44 0.32 0.56 0.63 0.53 0.75 ιwBeta 0.50 0.15 0.45 0.21 0.65 0.21 0.06 0.36 ιpBeta 0.50 0.15 0.17 0.04 0.29 0.24 0.17 0.43 ψBeta 0.50 0.15 0.40 0.22 0.59 0.19 0.07 0.30 ΦNormal 1.25 0.12 1.84 1.69 2.01 1.90 1.79 2.01 rπNormal 1.50 0.25 1.72 1.56 1.89 1.72 1.55 1.89 ρBeta 0.75 0.10 0.81 0.75 0.87 0.79 0.74 0.85 ryNormal 0.12 0.05 0.06 -0.01 0.12 -0.01 -0.05 0.05 r∆yNormal 0.12 0.05 0.07 0.01 0.12 0.20 0.12 0.27 πGamma 0.62 0.10 0.41 0.27 0.54 0.57 0.42 0.72 100(β−1−1) Gamma 0.25 0.10 0.33 0.16 0.50 0.30 0.17 0.43 lNormal 0.00 2.00 -1.60 -3.28 0.81 0.86 -2.15 3.20 100(γ−1) Normal 0.40 0.10 0.4 - - 0.4 - - αNormal 0.30 0.05 0.25 0.18 0.32 0.23 0.16 0.29 96
Table 3.A.2 Priors and estimated posteriors of the shock processes: Euro Area Priors Posteriors Extended model SW model Distr Mean Std D. Mean 5% 95% Mean 5% 95% σaInvgamma 0.10 2.00 0.08 0.064 0.11 0.07 0.05 0.08 σbInvgamma 0.10 2.00 0.07 0.04 0.10 0.03 0.02 0.04 σgInvgamma 0.10 2.00 0.10 0.08 0.13 0.10 0.08 0.12 σiInvgamma 0.10 2.00 0.22 0.15 0.29 0.21 0.15 0.27 σRInvgamma 0.10 2.00 0.07 0.05 0.08 0.09 0.07 0.11 σpInvgamma 0.10 2.00 0.05 0.03 0.07 0.06 0.04 0.08 σwInvgamma 0.10 2.00 0.06 0.04 0.08 0.05 0.03 0.06 ρaBeta 0.50 0.20 0.97 0.94 0.99 0.96 088 0.99 ρbBeta 0.50 0.20 0.92 0.81 0.99 0.77 0.66 0.89 ρgBeta 0.50 0.20 0.82 0.74 0.90 0.92 0.86 0.98 ρiBeta 0.50 0.20 0.43 0.17 0.67 0.32 0.08 0.55 ρRBeta 0.50 0.20 0.39 0.23 0.54 0.48 0.33 0.62 ρpBeta 0.50 0.20 0.99 0.98 0.99 0.99 0.98 0.99 ρwBeta 0.50 0.20 0.96 0.93 0.99 0.91 0.86 0.96 µpBeta 0.50 0.20 0.30 0.07 0.51 0.54 0.24 0.73 µwBeta 0.50 0.20 0.39 0.16 0.61 0.51 0.25 0.76 ρga Beta 0.50 0.20 0.37 0.12 0.61 0.46 0.18 0.73 97
Table 3.A.3 Priors and estimated posteriors of revision processes parameters: Euro Area Priors Posteriors Extended model SW model Distr Mean Std D. Mean 5% 95% Mean 5% 95% δyNormal 0.00 2.00 0.24 -0.14 0.67 - - - δcNormal 0.00 2.00 -0.10 -0.36 0.14 - - - byNormal 0.00 2.00 -0.15 -0.22 0.11 - - - bπNormal 0.00 2.00 2.20 1.35 3.02 - - - bcNormal 0.00 2.00 -0.13 -0.14 -0.11 - - - σyr Invgamma 0.10 2.00 0.21 0.17 0.25 - - - σπr Invgamma 0.10 2.00 0.20 0.16 0.23 - - - σcr Invgamma 0.10 2.00 0.25 0.20 0.30 - - - ρyr Beta 0.50 0.20 0.66 0.33 0.95 - - - ρπr Beta 0.50 0.20 0.94 0.89 0.98 - - - ρcr Beta 0.50 0.20 0.72 0.56 0.89 - - - 98
Table 3.B.1 Priors and estimated posteriors of the structural parameters: US Priors Posteriors Extended model SW model Distr Mean Std D. Mean 5% 95% Mean 5% 95% ϕNormal 4.00 1.50 5.30 3.43 7.13 5.93 4.06 7.85 hBeta 0.70 0.10 0.13 0.10 0.16 0.57 0.45 0.67 σcNormal 1.50 0.37 1.33 1.05 1.59 1.07 0.76 1.35 σlNormal 2.00 0.75 1.79 0.79 2.75 1.95 0.99 2.85 ξpBeta 0.50 0.10 0.66 0.57 0.75 0.72 0.63 0.81 ξwBeta 0.50 0.10 0.51 0.37 0.65 0.59 0.45 0.72 ιwBeta 0.50 0.15 0.34 0.14 0.53 0.48 0.24 0.72 ιpBeta 0.50 0.15 0.09 0.03 0.15 0.33 0.14 0.51 ψBeta 0.50 0.15 0.76 0.57 0.75 0.72 0.57 0.88 ΦNormal 1.25 0.12 1.43 1.30 1.57 1.48 1.34 1.61 rπNormal 1.50 0.25 1.86 1.58 2.15 2.09 1.78 2.42 ρBeta 0.75 0.10 0.84 0.81 0.87 0.83 0.80 0.87 ryNormal 0.12 0.05 -0.01 -0.03 0.01 0.04 0.01 0.08 r∆yNormal 0.12 0.05 0.09 0.07 0.11 0.18 0.13 0.22 πGamma 0.62 0.10 0.67 0.53 0.80 0.70 0.57 0.85 100(β−1−1) Gamma 0.25 0.10 0.17 0.07 0.27 0.20 0.10 0.31 lNormal 0.00 2.00 -1.44 -3.75 0.86 0.18 −1.77 2.30 100(γ−1) Normal 0.40 0.10 0.4 - - 0.39 0.35 0.43 αNormal 0.30 0.05 0.16 0.13 0.20 0.17 0.14 0.21 99
Table 3.B.2 Priors and estimated posteriors of the shock processes: US Priors Posteriors Extended model SW model Distr Mean Std D. Mean 5% 95% Mean 5% 95% σaInvgamma 0.10 2.00 0.39 0.34 0.44 0.38 0.34 0.43 σbInvgamma 0.10 2.00 0.12 0.08 0.16 0.09 0.05 0.13 σgInvgamma 0.10 2.00 0.39 0.35 0.44 0.40 0.35 0.45 σiInvgamma 0.10 2.00 0.29 0.21 0.36 0.35 0.25 0.43 σRInvgamma 0.10 2.00 0.12 0.11 0.14 0.13 0.11 0.14 σpInvgamma 0.10 2.00 0.12 0.09 0.15 0.11 0.09 0.14 σwInvgamma 0.10 2.00 0.33 0.25 0.40 0.30 0.23 0.36 ρaBeta 0.50 0.20 0.91 0.87 0.95 0.92 0.87 0.97 ρbBeta 0.50 0.20 0.84 0.77 0.90 0.74 0.55 0.93 ρgBeta 0.50 0.20 0.98 0.96 0.99 0.97 0.96 0.99 ρiBeta 0.50 0.20 0.82 0.70 0.94 0.70 0.57 0.84 ρRBeta 0.50 0.20 0.09 0.01 0.16 0.27 0.13 0.40 ρpBeta 0.50 0.20 0.87 0.78 0.97 0.81 0.68 0.95 ρwBeta 0.50 0.20 0.97 0.94 0.99 0.96 0.93 0.99 µpBeta 0.50 0.20 0.56 0.35 0.78 0.60 0.38 0.82 µwBeta 0.50 0.20 0.64 0.44 0.87 0.66 0.46 0.86 ρga Beta 0.50 0.20 0.40 0.25 0.56 0.40 0.24 0.56 100
Table 3.B.3 Priors and estimated posteriors of revision processes parameters: US Priors Posteriors Extended model SW model Distr Mean Std D. Mean 5% 95% Mean 5% 95% δyNormal 0.00 2.00 -0.10 -0.32 0.09 - - - δcNormal 0.00 2.00 0 - - - - - byy Normal 0.00 2.00 0.25 0.06 0.43 - - - bππ Normal 0.00 2.00 -0.13 -0.25 -0.1 - - - bcc Normal 0.00 2.00 0.19 0.10 0.28 - - - σyr Invgamma 0.10 2.00 0.65 0.54 0.77 - - - σπr Invgamma 0.10 2.00 0.23 0.19 0.26 - - - σcr Invgamma 0.10 2.00 0.71 0.61 0.81 - - - ρyr Beta 0.50 0.20 0.91 0.85 0.97 - - - ρπr Beta 0.50 0.20 0.09 0.01 0.16 - - - ρcr Beta 0.50 0.20 0.80 0.73 0.87 - - - 101
Table 4. Second-moment statistics: Euro Area Panel A ∆yrπr∆crrev∆yrevπrev∆c Euro Area data: Stand. deviation (%) 0.22 0.02 0.22 0.23 0.13 0.23 Correlation with ∆y0.26 -0.056 0.19 0.63 -0.35 0.47 Autocorrelation 0.11 0.02 0.04 -0.05 0.25 -0.25 Extended model: Stand. deviation (%) 0.64 0.04 0.86 0.24 0.37 0.28 (0.33,0.92) (0.01,0.07) (0.56,1.17) (0.20,0.28) (0.19,0.45) (0.23,0.32) Correlation with ∆y0.22 -0.03 0.24 0.31 -0.13 0.28 (0,0.37) (-0.10,0.01) (0,0.39) (0.05,0.55) (-0.21,-0.06) (0.14,0.4) Autocorrelation 0.22 0.17 0.59 0.00 0.55 -0.13 (0,0.38) (0,0.32) (0.43,0.90) (-0.07,0.07) (0.23,0.83) (-0.19,-0.07) 102
Table 4. (Continued) Panel B ∆y∆c∆i∆w l R π Euro Area data: Stand. deviation (%) 0.14 0.14 0.45 0.13 0.03 0.31 0.13 Correlation with ∆y1 0.47 0.65 0.25 -0.02 -0.06 -0.32 Autocorrelation 0.50 0.01 -0.04 0.34 0.94 0.88 0.27 Extended: Stand. deviation (%) 0.53 0.64 1.05 0.27 2.11 0.19 0.23 (0.28,0.75) (0.36,0.92) (0.47,1.62) (0.08,0.44) (0.47,3.70) (0.04,0.35) (0.10,0.37) Correlation with ∆y1 0.24 0.10 0.19 -0.07 -0.12 -0.11 (0,0.39) (0,0.22) (0,0.33) (-0.12,0) (-0.23,0) (-0.19,0) Autocorrelation 0.23 0.18 0.30 0.41 0.71 0.69 0.64 (0,0.39) (0,0.34) (0,0.49) (0,0.60) (0,0.97) (0,0.95) (0,0.90) SW model: ∆y∆c∆i∆w l R π Stand. deviation (%) 0.24 0.16 0.82 0.12 10.6 0.55 0.56 (0.14,0.34) (0.09,0.24) (0.43,1.23) (0.05,0.18) (1.21,20.3) (0.07,1.17 (0.08,1.16) Correlation with ∆y1 0.30 0.22 0.18 0 -0.08 -0.11 (0,0.66) (0,0.52) (0,0.45) (-0.02,0) (-0.23,0) (-0.32,0) Autocorrelation 0.28 0.31 0.26 0.30 0.48 0.47 0.40 (0,0.63) (0,0.69) (0,0.61) (0,0.66) (0,0.99) (0,0.99) (0,0.99) The parenthesis refer to 95% posterior confidence intervals for second-moment statistics 103
Table 5. Variance decomposition (percent) Extended model Innovations ∆y∆yr∆c∆cr∆i∆w l R π πr Technology, ηa1.3 1.2 1.2 0.9 0.2 0.5 0.7 1.5 0.6 0.4 Risk premium, ηb32.8 30.5 37.3 29.5 7.8 22.4 8.3 53.5 25.2 17.2 Fiscal/Net exports, ηg2.9 2.6 0.0 0.1 0.1 0.2 0.6 0.2 0.1 0.1 Investment adj. costs, ηi11.9 11.0 0.0 0.5 75.6 3.3 4.8 7.4 3.2 2.1 Interest-rate, ηR9.6 8.9 10.7 8.4 2.3 7.1 2.7 10.5 7.7 5.2 Wage-push, ηw1.3 1.2 2.8 2.2 0.1 2.5 16.7 1.5 2.2 1.3 Price-push, ηp8.7 8.1 9.7 7.7 0.1 37.5 53.8 19.0 30.9 21.2 Output revision, ηry 0.1 7.0 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.1 Inflation revision, ηrπ 23.2 21.6 22.4 17.4 9.8 20.7 11.1 2.6 28.3 51.2 Consumption revision, ηrc 7.9 7.4 14.5 32.8 1.4 5.4 1.5 3.4 1.5 1.0 SW model Innovations ∆y∆yr∆c∆cr∆i∆w l R π πr Technology, ηa18.5 - 11.0 - 0.9 0.8 1.4 0.4 0.2 - Risk premium, ηb29.8 - 39.3 - 18.0 4.5 3.4 27.5 11.2 - Fiscal/Net exports, ηg7.1 - 0.5 - 0.3 0.3 0.4 0.2 0.7 - Investment adj. costs, ηi8.4 - 2.5 - 43.1 0.2 0.6 1.0 0.4 - Interest-rate, ηR16.1 - 18.9 - 11.9 2.8 2.4 2.8 8.2 - Wage-push, ηw10.9 - 11.5 - 16.0 18.4 11.6 3.4 8.5 - Price-push, ηp25.5 - 28.7 - 9.5 73.0 80.0 64.0 71.2 - 104
Part IV Borrower-based measures in a DSGE model 1 Introduction Macroprudential policies are an important toolkit of central banks nowadays to ensure financial stability. Borrower-based macroprudential measures such as limits on loan-to-value and loan-to-income have been found to be effective to influence credit standards and flows through quantitative restrictions (see Claessens, Ghosh and Mihet (2014); BCBS (2010); JMCB special issue (2015)). Not only do they affect the credit flow for house purchases, but they are particularly important for financial stability by limiting risk-taking of borrowers and lenders. Given their transmission through quantities and directly affecting borrowers, these instruments are important to complement capital-based ones to counter the build-up systemic risks. While cross-country studies indicate that loan-to-value, loan-to-income or debt-servicing-to-income limits are effective to restrict credit, the individual measures differ in their transmission to counter risks and the way they influence financial stability, to this extent, this chapter uses a macro-financial DSGE model to address the feedback effects of macroprudential policies in ensuring financial stability. Limits on LTV ratios limit leverage relative to the value of the collateral and primarily limit losses for the lender in the event of a borrower default. They thereby strengthen the resilience of lenders, mostly banks. In countries where mortgage debt is non-recourse debt, a tighter LTV ratio also reduces the incentives for strategic defaults and thereby reduces probability of defaults, which is especially relevant when house price volatility is structurally high and amortization rates are low. Strategic defaults have played an important role in the With Stephan Fahr (ECB) and Francesco Sanna (ECB) 105
the LTV ratios. The original calibration of the model focused on macroeconomic and banking variables such as total capital, the default rate of banks and the returns on their equity. In order to account for household leverage in form of LTV ratios, the extended calibration strategy incorporates loan-to-value ratios of outstanding loans as a moment to match in addition to the variables in the original calibration. An alternative would be to use the LTI ratio as explicit target. We instead use the LTI ratios as variables to validate the model and compare the LTI ratio in the data to those obtained from the calibrated model. The HFCS provides data on the financial situation of households in European countries. It provides the loan and house value at origination and at the time of the survey, as well as income at time of the interview. The data is used to construct the LTV ratio at the moment of survey for the calibration of LTV ratios of outstanding loans. Using the HFCS as main source for the LTV ratio is consistent with the data source of other two calibrated variables in the model, namely the fraction of borrowers and housing wealth held by borrowers. The LTV ratio for outstanding loans of borrowers is computed by dividing mortgage loans for the household’s main residence (HMR ,HB170x) by the current housing value (HB0900) multiplied by the share of home ownership (HB0500). The average across all borrowers is computed by weighting by mortgage size (HB170x)3. In order to limit the influence of outliers in the HFCS database, LTV ratios for individual borrowers are censored at 200% LTV. We proceed similarly for LTV ratios of at origination. We use loans for the household’s main residence HMR at origination (HB140x) and divide it by the respondent’s reply of the house value at origination (HB0800) and the weighted country mean is obtained by using the loan amount at origination. The LTV ratios for the 1st and 2nd wave are presented in Table 1, whereby wave 1 of the HFCS dataset, conducted in 2010, exhibits a smaller country coverage and wave 2 conducted in 2013 and 2014 provides a larger country coverage and allows assessing evolution over time. 3An additional weighting by survey weights has also been considered, but has not been applied because, first, it does not significantly alter the average value and, second, it is unclear to what degree the social weights help in raising representativity of the borrower’s sample. 112
The values used in the original model calibration slightly differ as the original calibration was done based on a censoring of 150% instead of the 200% used in subsequent assessments. In addition to the LTV ratios, Table 1 also documents loan-to-income (LTI) ratios at origination and for outstanding mortgage loans. While the LTI ratio can be directly computed based on the current outstanding loan for the household’s main residence HMR (HB170x) and the current income (DI2000). For the LTI ratio at origination we use the loan amounts at origination (HB140x) and deflate the current income using the aggregate consumption deflator4. The LTI ratios are censored at 20 times annual incomes (additional series are presented in the appendix). As indicated, the model matches the LTV ratios relatively well and the model-implied LTI ratios are in the range of those in the data, indicating the broad fit of the model to the HFCS data. We do not expect that LTI ratios from the model and in data would fit perfectly given that the model does not account for taxation nor for capital incomes by households. Table 1: LTV and LTI ratios at origination and for outstanding mortgage loans AT BE CY DE ES GR IT LU MT NL PT SI SK LTV ratio at origination of mortgage loans (in %) 200% WM 80.7 93 86.2 83.3 87.2 87.4 83.4 - 90.8 103.8 93.7 71.9 84.8 LTV ratio of outstanding mortgage loans (in %) 200% WM 62.2 52.6 50.5 57.3 49.5 57.2 48.6 56.6 37.1 68.9 60.6 48.2 51.2 150% Model 61.7 52.4 49.5 56.9 58.4 56.7 48.4 55.3 35.1 68.2 59.8 59.5 49.5 LTI ratio of loans at origination of mortgage loans (in years of income) 20 WM 4.0 3.3 4.9 3.0 4.1 3.9 3.8 3.6 3.2 4.0 4.5 2.8 4.0 LTI ratio of outstanding loans (in years of income) 20 WM 3.5 3.1 4.5 2.5 3.7 3.3 3.0 3.2 2.7 3.9 4.0 1.9 3.5 As indicated, the model matches the LTV ratios relatively well and the model-implied 4This approach does not account for the income changes of each individual borrower between the origination of the loan and the current income. Still, an assessment by mean loans using national data for Portugal delivered comparable amounts for mean incomes using income at origination and using deflated income. 113
LTI ratios are in the range of those in the data, indicating the broad fit of the model to the HFCS data. We do not expect that LTI ratios from the model and in data would fit perfectly given that the model does not account for taxation nor for capital incomes by households. 2.3 Effects of varying household leverage in the 3D model A 1 percentage point reduction in LTV ratios of outstanding loans The credit standards in the 3D model are applied to the outstanding loans of the representative household. This section assesses the long-term (steady state) effects of changes to LTV and LTI ratios for outstanding loans. The next section sheds light on the implications for changes in the LTV and LTI ratios on the tail of the distribution of originating loans instruments. The quantification considered focuses on the implications when reducing LTV ratios by 1 p.p. and LTI ratios by one tenth of annual income, i.e. by 10 p.p.. The regulatory constraints are implied by substituting the endogenous loan contract between households and banks through an exogenous credit amount that is lowered from the calibrated value up to the point where it reaches the targeted LTV or LTI restriction 114
Figure 1. Steady state impact of a reduction of LTV ratios of outstanding loans by 1 percentage point Table 1. Steady state impact of a reduction of LTV ratios of outstanding loans by 1 percentage point. Max and min effects LTV LTI GDP Consumption Mortgage Total Housing NFC Inv. Mortgage Mortgage debt debt Inv. Inv. spreads defaults (Outs.) (Outs.) level level level level level level bps % p.p. p.p. % % % % % % bps p.p. Min -1.00 -23.29 -0.29 0.06 -11.95 -6.50 -7.49 -0.34 -12.70 -0.37 Max -1.00 4.12 -0.05 0.23 -5.70 -2.27 -1.86 -0.09 -4.31 -0.13 The effects of a 1 percentage point reduction in LTV ratios of outstanding loans on eight key model variables is depicted in Figure 1. The reduction in LTV ratios has overall a limited effect on aggregate long-term GDP, ranging from 0.02 to 0.30% of national GDP levels. The 115
size of the effects depends on the share of borrowers in the economy and the relative size of the real estate construction sector as well as the initial LTV level. Indeed, an important element explaining the muted response in GDP is the shift in aggregate expenditure away from housing investment towards consumption. In addition, savers increase their expenditure of housing as housing appears relatively cheaper. An economy with sizable housing investment sees a relatively stronger fall in GDP, but also a stronger shift increase in consumption. The LTV restrictions imply a reduction in aggregate debt levels by between 6 and 12% across countries, whereas the effects on aggregate credit are between 2.5 and 7%. The reduced leverage in the household sector implies also a reduction in the mortgage defaults because lower LTV ratios imply that future variations in housing value trigger less of defaults. Default rates decrease by between 0.03 up to 0.15 percentage points. Overall, banks face a reduction in losses from defaults which allow banks to reduce spreads on mortgage loans. These reductions amount to between 1 and 8 bps points. A 10 percentage point reduction in LTI ratios of outstanding loans An alternative to a reduction in LTV ratios consists in a decline in LTI limits. The decline in LTI ratios is implemented by reducing credit amounts by as much is necessary to reduce the imputed LTI ratios by the desired amounts, in line with the methodology for LTV ratios. The effects of a 10 percentage point reduction in the LTI ratio is depicted in Figure 2 and summarized in Table 2. A 10 percentage point reduction consists of a decline from e.g. 3.2 to 3.1 times the annual income. The reduction in LTI ratio by the chosen value has, on average, a slightly larger effect compared to the considered 1 p.p. reduction in the LTV ratio. Nevertheless, the relative effects across countries depend on the relative initial indebtedness. The reduction in LTI ratios implies limited effects on GDP, accompanied by a shift towards consumption and a sizable fall in housing investment. Mortgage debt reduces by between 4 to 11% (17% for one country) reduces mortgage default rates by between 0.1 to 0.8 percentage points and 2.6 p.p. 116
to 26.9 p.p. for spreads. Nevertheless, for some countries major quantitative differences exist. The reason for the differences resides especially in the lower level of mortgage loans and lower housing investment relative to GDP in these countries. This results in a higher percentage variation when reducing LTI ratios in percentage points. Figure 2. Steady state impact of a reduction of loan-to-income ratios of outstanding loans 117
Table 2. Steady state impact of a reduction of LTI ratios of outstanding loans by 10 percentage points. Max and Min effects LTV LTI GDP Consumption Mortgage Total Housing NFC Inv. Mortgage Mortgage debt debt Inv. Inv. spreads defaults (Outs.) (Outs.) level level level level level level bps % p.p. p.p. % % % % % % bps p.p. Min -3.0 -10.0 -0.2 0.1 -17.2 -5.5 -6.2 -0.2 -26.9 -0.8 Max -0.4 -10.0 -0.1 0.1 -4.3 -2.5 -1.5 -0.1 -2.7 -0.1 Caveats of the methodology The simulations provided above are computations for steady state changes in LTV and LTI limits. The choice to focus on steady state impacts is due to the fact that loans in the 3D model are modeled as one-period loans with a roll-over of the entire loan mass every period. As a result, a reduction in LTV or LTI ratios would affect the entire stock of loans, whereas in reality, the policy instruments only affect the flow of loans. Furthermore, the model is set up in real terms. It hence neglects the possibility that inflation could make nominal more sustainable in times of high inflation. Likewise, it neglects the Fisherian debt deflation in consumer goods, while it does account for the effects of declining housing value. An additional limitation is the fact that LTV or LTI ratios are modeled as permanently binding for the representative borrower. This does not allow relaxing credit conditions beyond those prevailing in the market. It is likely that this is a condition for any macroprudential policies. The default of mortgage loans in the 3D model occurs when loan size is larger than the housing value of the borrower (house values are subject to i.i.d shocks). In a situation in which house value shocks are the predominant source of defaults, such modelling is adequate. Instead, when income shocks are the main source of uncertainty and defaults, the 3D model only imperfectly captures the transmission of shocks. The shortcoming is conceptually more relevant when considering limits of LTI ratios instead of LTV ratios. Finally, as mentioned, the LTV and LTI limits are applied to the representative borrower 118
on outstanding loans. In reality, the available policy instruments act only on parts of the cross-sectional distribution of borrowers and only on the flow of lending. By acting on the cross-sectional distribution, the policy instruments curtail loans from the most risky ones. Instead, the model – by acting on the representative borrower – cannot overweight the riskier loans. As a result, the declines in defaults are likely to be an underestimation of what is achievable when reducing the high risk parts of the distribution. In order to address the shortcoming, the next section provides the necessary steps to relate the policy instruments to the model values. 3 Relating LTV and LTI policies at loan origination to the dynamic model The leverage considered in the 3D model relates to that of outstanding loans. Instead, policymakers use instruments that limit credit standards in the flow of loans. This section provides the information to relate credit standards at origination to those for outstanding loans. In order to relate the policy instrument to the model-relevant credit standard requires two steps: 1. Assessing the impact of the LTV or LTI policy limits at loan origination on the mean of the LTV(LTI) distributions at origination. The policy instrument limits the right-hand segment of the distribution and thereby reduces the mean LTV(LTI) ratio at origination. 2. Computing the effect on LTV (LTI) ratios of outstanding loans based on the mean LTV(LTI) ratio at origination. The quantitative effect is obtained by using a long-run relationship between credit conditions at origination and those for outstanding loans, assuming fixed-rate annuity mortgage contract. 119
3.1 LTV (LTI) limits and its effects on average credit standards at loan origination The first step in computing the effects of the policy instrument to the model requires assessing the impact on the average credit condition at origination. The truncation/censoring of the right-hand tail of the LTV or LTI distribution reduces the mean of the distribution. The following assessment relies on two assumptions, discussed in more detail below. First, constrained borrowers are assumed to continue borrowing, but at a lower loan amount. Second, in line with implemented policies, we assume that the LTV limits can be applied only to a proportion of loans while a share of loans is exempted from the credit standard limit. In this case the loans exceeding the credit limit are uniformly reduced in order for their share to equate the imposed exemption share. The upper hand panel of Figure 3 presents a stylized LTV distribution at loan origination. By imposing an LTV limit at a threshold of e.g. 90% implies that all loans above that threshold are curtailed. It is assumed that constrained borrowers continue borrowing, but the amount they borrow is limited to the regulatory LTV limit, resulting in an increase in loan amounts with an LTV ratio of 90%. This increase is identical to the originally affected mass to the right of the limit (blue area). As a result of the restriction, borrowers are now concentrated at the limited LTV ratio which is lower than their originally intended ratio and the average LTV ratio at origination declines (from 62% to 61% in the diagram). The lower panel of Figure 3 illustrates the effects on the distributional mean (vertical axis) of imposing an LTV limit (horizontal axis)5. When reducing the LTV limit to e.g. 110% or 100%, the average mean LTV remains virtually unaffected (62%). This is because the market-based distribution features only very few borrowers at LTV ratios above 100%, given that the mass of the distribution is concentrated at LTV ratios around 75%. Reducing the limit further to 80% results in an average of about 60% and an LTV limit of 70% would imply an average LTV ratio of about 67%. The lower (tighter) the LTV limit, the more 5The example is based on a log-normal distribution. 120
borrowers are affected and the effects would eventually become proportional (a reduction of the LTV limit by 1 p.p. would reduce the mean by 1 p.p.). Figure 3. Stylized distribution of LTV ratios at origination and implication of LTV limits on mean LTV at origination Source: OMR Task Force calculation. Note: The stylized distribution is based on a log-normal distribution. Constrained borrowers are assumed to continue borrowing at the imposed regulatory LTV limit. When setting limits on credit standard, policymakers have in practice also specified a proportion to which the limit applies, indicating that only a share of mortgage loans are required to comply with the limit whereas the remaining share of loans can exceed the limit. For example, the 2016 review of the LTV limits in Ireland imposes a 90% LTV limit from which 5% of loans to first time buyers and 20% to subsequent buyers are exempted. This provides the policymakers two margins of adjustment: the limit on the credit standard and the proportion to which the limit applies. It also implicitly offers a trade-off when adjusting the macroprudential between the limit of the credit standards and the exemption share. In order to assess the implication of the exemption shares requires assuming how credit conditions behave for loans exceeding the limit. For modelling purposes, we assume that 121
cases a reduction in the LTV limits implicitly targets the riskiest borrowers and would make them more resilient. In countries where default rates are strongly correlated with LTV ratios a smaller adjustment in the LTV limits would suffice to reduce aggregate defaults and bolster financial stability. Especially as regards the substitution of housing expenditure with NFC investment and consumption, the macroeconomic effects may be overstated. The model assumes a reallocation between sectors which is only affected in the short-run by capital adjustment costs, but is not affected by skill mismatch of workers. Table 4a. Impact of a 5 p.p. reduction in LTV ratios (from 95 to 90%) at loan origination LTV Policy Min Max LTV limit p.p. -5 -5 Average LTVO p.p. -3.2 -1.2 Average LTV ratio (outstanding) p.p. -1.9 -0.7 Average LTI (outstanding) p.p. -39.9 -2.9 GDP level % -0.55 -0.04 Consumption level % 0.05 0.42 Mortgage debt level % -19.5 -5.1 Total debt level % -12.2 -1.6 Housing inv. level % -14.1 -1.9 NFC inv. level % -0.6 -0.1 Mortgage spread bps -15.1 -7.6 Mortgage default rate p.p. -0.4 -0.2 Source: OMR Task Force calculations based on HFCS data (1st wave) and on 3D model. Note: The reported changes are in percent of the long-term steady state value of the variable. Euro area countries not participating in the first wave of the HFCS are not considered. For some few small and open euro area countries, the model is assessed not to perform adequately and results are therefore excluded from this range. 128
Table 4b Impact of a 5 p.p. reduction in LTV at origination on macro-financial variables AT BE CY DE ES GR IT NL PT SI 4mean LTV at origin p.p. -1.8 -2.5 -1.8 -1.7 -2.3 -2.4 -2.1 -3.2 -2.9 -1.2 4mean ILTV outst. p.p. -1.0 -1.5 -1.1 -1.0 -1.3 -1.4 -1.2 -1.9 -1.7 -0.7 GDP level % -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.1 -0.5 -0.2 0.0 Housing invest. % -4.9 -2.9 -4.5 -5.1 -3.5 -4.2 -2.2 -14.1 -7.0 -1.9 Mortgage debt % -12.3 -8.5 -8.0 -9.9 -8.8 -11.4 -9.5 -19.5 -17.1 -5.1 Mortgage spreads bps -10.7 -7.6 -9.6 -12.5 -10.9 -15.1 -14.2 -8.1 -10.9 -7.9 Mortgage default rate p.p. -0.3 -0.2 -0.3 -0.4 -0.3 -0.4 -0.4 -0.2 -0.3 -0.2 Source: OMR Task Force calculations based on HFCS data (1st wave) and on 3D model. Figure 4. Impact of a 5 p.p. reduction in LTV at origination on macro-financial variables 129
3.3.2 Reductions of LTI limits at origination Similarly to the policy simulations on LTV limits, we consider tighter limits on LTI ratios at loan origination to increase household resilience. The main policy exercise is a decline in LTI limits at loan origination by 50 p.p. from 5 to 4.5 times annual income, while exempting 10% of loans from this limit. The methodology first assesses the impact of the LTI constraint on the mean LTI conditions at loan origination. In a second step it converts the LTI ratio at loan origination into a ratio for outstanding loans. The results for such policy are presented in Table 5a and 5b and Figure 5. Table 5a. Impact on macro-financial variables of a 50 p.p. reduction in LTI at origination from 5 to 4.5 times annual income LTI Policy Min Max LTV limit p.p. -0.5 -0.5 Average LTIO p.p. 23.8 -4.39 Average LTV ratio (outstanding) p.p. -0.9 -0.4 Average LTI (outstanding) p.p. -13.9 -2.6 GDP level % -0.26 -0.03 Consumption level % 0.04 0.2 Mortgage debt level % -9.1 -2.3 Total debt level % -5.7 -1.4 Housing inv. level % -6.6 -0.8 NFC inv. level % -0.3 -0.1 Mortgage spread bps -10.4 -2.1 Mortgage default rate p.p. -0.3 -0.1 Source: OMR Task Force calculations based on HFCS data (1st wave) and on 3D model. Note: The reported changes are in percent of the calibrated steady state value of the variable. The value reported for mortgage default ratios and mortgage spreads are the calibrated value and the value after implementation, for ease of interpretation. A reduction in the LTI ratio from 5 to 4.5 has no impact in Germany and Slovenia, because the mass of the distribution is concentrated at lower LTI ratios. 130
Table 5b. Impact of a 50 p.p. reduction in LTI at origination on macro-financial variables AT BE CY DE ES GR IT NL PT SI 4mean LTV at origin p.p. -12.9 -4.4 -20.9 - -18.4 -15.8 -18.5 -23.9 -20.9 - 4mean ILTV outst. p.p. -7.5 -2.6 -12.2 - -10.7 -9.3 -10.8 -14.0 -12.2 - GDP level % -0.1 0.0 -0.2 - -0.2 -0.1 -0.1 -0.3 -0.1 - Housing invest. % -2.1 -0.8 -3.5 - -2.5 -2.5 -1.7 -6.6 -2.2 - Mortgage debt % -5.3 -2.3 -6.2 - -6.4 -6.9 -7.0 -9.1 -5.3 - Mortgage spreads bps -4.4 -2.1 -7.3 - -8.0 -9.1 -10.4 -3.7 -3.2 - Mortgage default rate p.p. -0.1 -0.1 -0.2 - -0.2 -0.3 -0.3 -0.1 -0.1 - Note: The reported changes are in percent of the calibrated steady state value of the variable. The value reported for mortgage default ratios and mortgage spreads are the calibrated value and the value after implementation, for ease of interpretation. A reduction in the LTI ratio from 5 to 4.5 has no impact in Germany and Slovenia, because the mass of the distribution is concentrated at lower LTI ratios. Figure 5. Impact of a 50 p.p. reduction in LTI at origination on macro-financial variables 131
4 Conclusions This chapter uses a macro-financial DSGE model where excessive risk behavior harms the economy introducing an incentive for macroprudential regulation, in which the benefit of tightening policies in terms of reducing risks may be offset by a reduction in bank activity and leading to a depression in the economy, providing a good set-up for analyzing the macroeconomic benefits of macroprudential regulation. By combining the model with information on the distribution of loans in data, this paper tracks the impact of borrower-based measures from their impact on credit conditions at loan origination, the policy variable, to the variable affecting the economy, outstanding loans, as well as to the long-term macroeconomic effects on GDP, credit, real estate investment as well as mortgage defaults and mortgage spreads. The assessment reveals that borrower-based measures have sizable effects on credit amounts and can reduce long-run defaults. For instance, a reduction of the loan to value limit from 90 to 85% leads to reductions of aggregate credit are between 2.5 and 7%, the resulting lower leverage in the household sector reduces mortgage defaults by between 0.2 and 0.4 p.p. compared with the historical averages used in the calibration. The lower default rates, in turn, allow banks to reduce spreads on mortgage loans by between 7.6 to 15.1 bps. Overall, the macroprudential instrument is effective in reducing credit flows and promoting household resilience through less mortgage defaults. The tighter loan to value limit induces a shift in household expenditure away from housing expenditure, resulting in a strong fall in housing investment, towards consumption, with an overall limit effect on GDP. The assessment reveals that borrower-based measures have sizeable effects on credit amounts and can reduce long-run defaults. Its assessment is nevertheless limited to longterm effects, given limitation in the relatively simple way the real estate market is modeled. It opens up extension possibilities to develop additional models to shed light on the detailed working of the real estate market by focusing on additional sources of shocks and the role played by expectations of house prices. 132
References •Arezki R., Beck T., Deyoung R., V. Duca J.V, Loungani P., and Murphy, A. 2015. "Conference on Housing, Stability, and the Macroeconomy: International Perspectives," Journal of Money, Credit and Banking, special issue 47. •Basel Committee on Banking Supervision. 2010. “An assessment of the long-term economic impact of stronger capital and liquidity requirements”, August. •Bernanke, B. S., M. Gertler and S. Gilchrist. 1999. “The financial accelerator in a quantitative business cycle framework”, Handbook of Macroeconomics 1, p.p. 1341-1393. •Bianchi, J., and Mendoza, E. G. 2018. “Optimal time-consistent macroprudential policy" Journal of Political Economy 126, pp. 588-634. •Bruneau, G., Christensen, I., and Meh C., 2016. "Housing Market Dynamics and Macroprudential Policy," Bank of Canada. Working Papers 16-31, •Chen, J. and F. Columba. 2016. “Macroprudential and Monetary Policy Interactions in a DSGE Model for Sweden”, IMF Working Paper WP/16/74. •Claessens, S., S. R. Ghosh and R. Mihet. 2014. “Macro-Prudential Policies to Mitigate Financial System Vulnerabilities”, IMF Working Paper 14/155. •Clerc, L., A. Derviz, C. Mendicino, S. Moyen, K. Nikolov, L. Stracca, J. Suarez and A. P. Vardoulakis. 2015. "Capital Regulation in a Macroeconomic Model with Three Layers of Default", International Journal of Central Banking , June. •De Nicol, M. G., Favara, G., and Ratnovski, L. 2012. “Macroprudential policy" International Monetary Fund •Farhi, E., and Werning, I. 2016. “A theory of macroprudential policies in the presence of nominal rigidities" Econometrica 84, pp. 1645-1704. 133
•Ferrero, A., R., Harrison, R. and B. Nelson. 2017. "Concerted efforts? Monetary and macro-prudential policies", Mimeo, May. •Mendicino, C., Nikolov, K., Suarez, J., and Supera, D. 2018. “Optimal dynamic capital requirements". Journal of Money, Credit and Banking, 50(6), 1271-1297. •Walentin, K. 2014. “Housing collateral and the monetary transmission mechanism”, The Scandinavian Journal of Economics 116, p.p. 635-668. 134
Figures 135
Appendix Chapter 1 Supplementary appendix (Not intended for publication) Log-linearized dynamic equations In addition to equation (3) with n= 4 characterizing the 1-year bond yield, respectively, the set of the remaining log-linearized dynamic equations characterizing the estimated DSGE model are the following: •Aggregate resource constraint: yt=cyct+iyit+zyzt+εg t,(30) where cy=C Y= 1−gy−iy,iy=I Y= (γ−1 + δ)K Y, and zy=rkK Yare steady-state ratios. As in Smets and Wouters (2007), the depreciation rate and the exogenous spending-GDP ratio are fixed in the estimation procedure at δ= 0.025 and gy= 0.18. •Consumption equation: xt=Etxt+1 −1−x1 σchrt−Etπt+1 +εb ti,(31) where : xt=ct−x1ct−1,x1=h γ,hdenotes the habit formation parameter and γdenotes the balanced-growth rate. •Investment equation: it=i1it−1+ (1 −i1)Etit+1 +i2qt+εi t,(32) where i1=1 1+β, and i2=1 (1+β)γ2ϕwith β=βγ(1−σc). •Arbitrage condition (value of capital, qt): qt=q1Etqt+1 + (1 −q1)Etrk t+1 −(Rt−Etπt+1) + c−1 3εb t,(33) where q1=βγ−1(1 −δ) = (1−δ) (rk+1−δ). 136
•Log-linearized aggregate production function: yt= Φ (αks t+ (1 −α)lt+εa t),(34) where Φ = 1 + φ Y= 1 + Steady-state fixed cost Yand αis the capital-share in the production function.7 •Effective capital (with one period time-to-build): ks t=kt−1+zt.(35) •Capital utilization: zt=z1rk t,(36) where z1=1−ψ ψ. •Capital accumulation equation: kt=k1kt−1+ (1 −k1)it+k2εi t,(37) where k1=1−δ γand k2=1−1−δ γ1 + βγ2ϕ. •Marginal cost: mct= (1 −α)wt+αrk t−εa t.(38) •New-Keynesian Phillips curve (price inflation dynamics): πt=π1πt−1+π2Etπt+1 −π3mct+π4εp t,(39) where π1=ιp 1+βιp,π2=β 1+βιp,π3=A 1+βιp(1−βξp)(1−ξp) ξp, and π4=1+βιp 1+βιp. The coefficient of the curvature of the Kimball goods market aggregator, included in the definition of A, is fixed in the estimation procedure at εp= 10 as in Smets and Wouters (2007). 7From the zero profit condition in steady-state, it should be noticed that φpalso represents the value of the steady-state price mark-up. 137
Appendix Chapter 3 Supplementary appendix (Not intended for publication) List of new equations in the extended model: 1) Equations derived with a new structure in the error term -Euler equation ct=c11 + δc(1 + bc)−1cr t−1,t + (1 −c1)Etct+1 +c2(lt−Etlt+1)−c3(Rt−Etπt+1 +εb t)+ c4εc t−1,t+S−1+ (δc/ρc)εc t−2,t+S−2, where: c1=h/γ 1+(h/γ)(1+bcc)−1, c2=(σc−1)wL/(φwC) σc(1+(h/γ)(1+bcc)−1), c3=1−h/γ σc(1+(h/γ)(1+bcc)−1), and c4=(h/γ)ρS cr (1+bcc)(1+(h/γ)(1+bcc)−1). -Monetary policy rule Rt=ρRt−1+ (1 −ρ)(rπh(1 + bπ)πr t−1,t +ρS−1 πεπ t−2,t+S−2i+ ryh(1 + by)yr t−1,t +byδyyr t−2,t−1+ρS−1 yεy t−2,t+S−2+ (δy/ρy)εy t−3,t+S−3i−yp t−1)+ r4y((1 + by)hyr t−1,t −yr t−2,t−1i+byδyhyr t−2,t−1−yr t−3,t−2i+ ρS−1 yhεy t−2,t+S−2−(1/ρy)εy t−3,t+S−3i+ρS−2 yδyhεy t−3,t+S−3−(1/ρy)εy t−4,t+S−4i+ (yp t−1−yp t−2) + εR t). 144
2) Remaining equations, as in Casares and Vazquez (2012) -NKPC πt=ιp 1+βιpBπr t−1,t +β 1+βιpBEtπt+1 −A(1−βξp)(1−ξp) (1+βιpB)ξpµp t+1+βιp 1+βιpBεp t+βιpB 1+βιpBρS πεπ t−S,t. with β =βγ(1−σc) -Wage dynamics wt=w1wt−1+ (1 −w1) (Etwt+1 +Etπt+1)−w11 + βιwBπt+w2πr t−1,t −w3µw t +w1βιwBρS πεπ t−S,t +εw t. where: w1=1 1 + β, w2=ιw 1 + β, and w3=1 1 + β"1−βξw(1 −ξw) ξw((φw−1) εw+ 1)#. -Wage mark-up equation µw t=wt−mrst=wt−σllt+1 1−h/γ ct−(h/γ)cr t−1,t. . 145
List of parameters A.1. Model parameter description γgamma1 Steady-State growth rate δdelta Capital depreciation rate gygy Steady-state exogenous spending-output ratio σwphiw Steady-state labor mark-up pepsilonp Curvature of the Kimball labor good aggregator wepsilonw Curvature of the Kimball labor market aggregater ϕvarphi Steady-state elasticity of the capital adjusment function hlambda1 Habit formation paramater σcsigmac Inv. Elasticity of the intertemporal substitution between leisure and work σlsigmal Inv. Elasticity of labor supply with respect to real wages ξpxip Calvo probability in prices ξwxiw Calvo probability in wages ιwiotaw wage indexation coefficient ιpiotap price indexation coefficient ψpsi Elasticity of capital utilization Φphip Level of fixed cost (1+level) rπrhopi Inflation coefficient in the MPR ρrho Smoothing paramater in the MPR rYrhoy Output gap coefficient in the MPR πconstpi Constant inflation coefficient 100(β−1−1) beta1 Personal discount factor lconstl Constant labor coefficient 100(γ−1) gamma Steady-state growth rate αalpha Capital share 146
List of parameters A.2 Shock parameters εa tepsa Technology shock εb tepsb Risk premium shock εg tepsg Expenditure shock εi tepsi Investment adjustment shock εR tepsr Monetary policy shock εw tepsw Wage mark-up shock εp tepsp Price mark-up shock εy t,t+Seyr Output revision shock επ t,t+Sepir Inflation revision shock εc t,t+Secr Consumption revision shock σastderr e_a Standard deviation of productivity innovation σbstderr e_b Standard deviation of risk premium innovation σgstderr e_g Standard deviation of exogenous spending innovation σistderr e_i Standard deviation of investment-specific innovation σRstderr e_r Standard deviation of monetary policy rule innovation σpstderr e_p Standard deviation of price mark-up innovation σwstderr e_w Standard deviation of wage mark-up innovation σr ystderr e_yr Standard deviation of output revision innovation σr πstderr e_pir Standard deviation of inflation revision innovation σr cstderr e_cr Standard deviation of consumption revision innovation ρarhoa AR coefficient of productivity shock ρbrhob AR coefficient of risk premium shock ρgrhog AR coefficient of exogenous spending shock ρirhoi AR coefficient of investment-specific shock ρRrhor AR coefficient of policy rule shock ρprhop AR coefficient of price mark-up shock ρwrhow AR coefficient of wage mark-up shock µpcmap MA coefficient of price mark-up shock µwcmaw MA coefficient of wage mark-up shock ρga rhoga Correlation coefficient between productivity and exogenous spending shocks ρyr rhoyr AR coefficient of output revision shock ρπr rhopir AR coefficient of inflation revision shock ρcr rhocr AR coefficient of consumption revision shock bybyy Coefficient measuring the correlation between the initial announcement and revision bπbpipi Coefficient measuring the correlation between the initial announcement and revision bcbcc Coefficient measuring the correlation between the initial announcement and revision δydeltay Coefficient of the lagged revision in the output revision δcdeltac Coefficient of the lagged revision in the consumption revision 147
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List of variables B.1. Endogenous variables yty Output ctc Consumption iti Investment ztz Capital utilization rate ltl Employment level Rtr Interest rate πtpi Inflation qtq Capital value rk trk Rental rate of capital ks tks Capital supply ktk Capital µw tmuw Wage mark-up µp tmup Prices mark-up wtw Wages yr tyr Real-time output πr tpir Real-time inflation cr tcr Real-time consumption ry try Output revision rc trc Consumption revision rπ trpi Inflation revision yp typ Potential Output ip tip Potential interest rate zp tzp Potential capital utilization rate lp tlp Potential employment Rp trp Potential interest rate πp tpip Potential inflation qp tqp Potential capital value rk,p trkp Potential capital interest rate ks,p tksp Potential capital supply kp tkp Potential capital wp twp Potential wages List of variables B.2 Exogenous variables: Shocks εa tepsa Tecnhology shock εb tepsb Risk premium shock εg tepsg Expenditure shock εi tepsi Investment adjustment shock εR tepsr Monetary policy shock εw tepsw Wage mark-up shock εp tepsp Price mark-up shock εy t,t+Seyr Output revision shock επ t,t+Sepir Inflation revision shock εc t,t+Secr Consumption revision shock 149
List of variables B.3 Predeterminated variables ct−1,it−1,kt−1,πt−1,wt−1,Rt−1,yt−1,yr t−1,πr t−1, cr t−1,ry t−1,rπ t−1,rc t−1,cp t−1,ip t−1,kp t−1,rp t−1 150