Policy and business cycle shocks: A structural factor model representation of the US economy

Forni, Mario; Gambetti, Luca Article Policy and business cycle shocks: A structural factor model representation of the US economy Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Forni, Mario; Gambetti, Luca (2021) : Policy and business cycle shocks: A structural factor model representation of the US economy, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 14, Iss. 8, pp. 1-21, https://doi.org/10.3390/jrfm14080371 This Version is available at: https://hdl.handle.net/10419/258475 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Risk and Financial Management Article Policy and Business Cycle Shocks: A Structural Factor Model Representation of the US Economy † Mario Forni 1,2 and Luca Gambetti 3,4,5,6,*,‡   Citation: Forni, Mario, and Luca Gambetti. 2021. Policy and Business Cycle Shocks: A Structural Factor Model Representation of the US Economy. Journal of Risk and Financial Management 14: 371. https:// doi.org/10.3390/jrfm14080371 Academic Editor: Donald Lien Received: 2 July 2021 Accepted: 30 July 2021 Published: 13 August 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Dipartimento di Economia Marco Biagi and ReCent, Università di Modena e Reggio Emilia, 41100 Modena, Italy; [email protected] 2Center for Economic Policy Research, London EC1V 0DX, UK 3Departament d’Economia i d’Historia Economica, Universitat Autònoma de Barcelona, 08290 Cerdanyola del Vallès, Spain 4Barcelona GSE, 08005 Barcelona, Spain 5 Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche, Università di Torino, 10124 Torino, Italy 6Collegio Carlo Alberto, 10122 Torino, Italy *Correspondence: [email protected] † This is a new and revised version of an old paper titled “Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model”. ‡ The authors acknowledge the financial support of the Italian Ministry of Research and University, PRIN 2017, grant J44I20000180001. Luca Gambetti acknowledges the financial support from the Spanish Ministry of Science and Innovation, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S), the financial support of the Spanish Ministry of Science, Innovation and Universities through grant PGC2018-094364-B-I00, and the Barcelona Graduate School Research Network. Abstract: We use a dynamic factor model to provide a semi-structural representation for 101 quarterly US macroeconomic series. We find that (i) the US economy is well described by a number of structural shocks between two and five. Focusing on the four-shock specification, we identify, using sign restrictions, two policy shocks, monetary and fiscal, and two non-policy shocks, demand and supply. We obtain the following results. (ii) Both supply and demand shocks are important sources of fluctuations; supply prevails for GDP, while demand prevails for employment and inflation. (ii) Monetary and fiscal policy shocks have sizable effects on output and prices, with no evidence of crowding-out of private aggregate demand components; both monetary and fiscal authorities implement important systematic countercyclical policies reacting to demand shocks. (iii) Negative demand shocks have a large long-run positive effect on productivity, consistently with the Schumpeterian “cleansing” view of recessions. Keywords: demand; supply; fiscal policy; monetary policy; sign restrictions; structural factor model JEL Classification: C32; E32; E52; F31 1. Introduction How many shocks drive the business cycle? What is the relative importance of supply and demand disturbances? What are the effects of macroeconomic policies? These questions have been and still are at the core of the research in macroeconomic since the answer is key to assessing competing theories of the business cycle and the implied policy recommendations. Since Sims (1980) seminal paper, structural Vector Autoregressive models (SVAR) have been a major tool to address the questions above. Such models replaced large scale econometric models, their main advantage being that they do not require the imposition of “incredible” identifying restrictions. Over the last three decades, the SVAR literature has substantially contributed to improve our knowledge of macroeconomic dynamics, providing evidence often used as a guideline by both policymakers and theorists. Nonetheless, J. Risk Financial Manag. 2021,14, 371. https://doi.org/10.3390/jrfm14080371 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2021,14, 371 2 of 21 we believe that SVAR models have an important limitation: the amount of information that they can handle is perforce small, owing to the so-called “curse of dimensionality”. The relevance of this information issue is stressed in several papers, including Quah (1990), Sims (1992) ,Lippi and Reichlin (1994), Bernanke and Boivin (2003), and Bernanke et al. (2005) . If, as plausible, both policy makers and private economic agents base their decisions on all of the available macroeconomic information, structural shocks should be innovations with respect to a large information set, perhaps larger than the one that can be included in a standard VAR. An alternative to SVAR models is represented by a new generation of large dimensional structural models: the “generalized” or “approximate” dynamic factor models introduced by Forni et al. (2000), Forni and Lippi (2001), Stock and Watson (2002a), (2002b) , and recently proposed for structural economic analysis (Stock and Watson 2005; Forni et al. 2009 ). Such models have been successful in solving well known VAR puzzles ( Bernanke et al. 2005 ;Forni and Gambetti 2010;Alessi and Kerssenfischer 2019). Their key advantage is that they combine a large number of macroeconomic variables with a reduced number of macroeconomic shocks. Two basic features distinguish large factor models from old-fashioned large scale models. First, identification can be reached in just the same way as in VAR models, without relying on “incredible” restrictions. Second, the forecasting performance is good (Stock and Watson 2002a,2002b;Altissimo et al. 2010).1 In this paper, we use a large structural factor model to address the questions raised at the beginning of this introduction. Specifically, we apply the model and the estimation method of Forni et al. (2009) to 101 US quarterly series, covering the pre-zero lower bound sample period 1959-I to 2007-IV. Following Uhlig (2005), we adopt an identification scheme based on inequality constraints. Such constraints are milder than the traditional zero restrictions commonly used in the VAR literature, in that only the sign of the impulse response functions at a few specific lags are imposed. Sign restrictions are particularly appropriate in our data-rich framework, since they can be imposed on a broad set of variables and this, in turn, is likely to deliver a better characterization of the shocks. The main difference with the existing literature, which has been focusing on the identification of a single shock, see for instance Forni and Gambetti (2010) and Alessi and Kerssenfischer (2019), and the main novelty is that we provide a global identification of the model and this allows us to provide a semi-structural representation of the US economy. In this way we can assess the relative importance for economic fluctuations of various types of economic disturbances. As a first step in our analysis we address the fundamental question: how many shocks drive macroeconomic fluctuations? This question has largely been ignored in the empirical literature, probably because it is not meaningful within a VAR framework, where the number of economic shocks is determined by the number of variables included in the model. Using some popular information criteria, we find that the US economy can be well described by a number of shocks between 2 and 5. The finding is at odds with theories relying on a single source of fluctuations, like early RBC models. Furthermore, the numbers are slightly smaller than the number of shocks typically included in modern DSGE models, like for instance Smets and Wouters (2007) which considers seven structural shocks. We then focus on a four-shock specification and identify two non-policy shocks, demand and supply, and two policy shocks, monetary and fiscal. All shocks are normalized as expansionary by imposing positive effects on output (GDP and industrial production). We further impose that supply reduce prices, whereas the other three shocks raise prices (CPI and GDP deflator). Moreover, we impose that expansionary monetary policy reduces the federal funds rate and expansionary fiscal policy raises federal deficit. Our main findings are the following: (i) Both supply and demand shocks explain a considerable fraction of the fluctuations in real variables. However, their relative importance depends on the specific variable considered. Supply shocks explain most of GDP volatility, while demand shocks prevail for employment and other labor market variables. Demand shocks are less persistent than supply shocks and their long-run effect on GDP J. Risk Financial Manag. 2021,14, 371 3 of 21 is not significant. Concerning inflation, both supply and demand have relevant effects; however, demand shocks prevail, particularly in the long-run. (ii) Policy is important. Discretionary monetary policy shocks have sizable effects on output and prices and are responsible for the early 1980s recession and disinflation. Discretionary fiscal policy shocks have sizable effects on GDP and do not have important crowding-out effects on private consumption and investment, with the sole exception of residential investment. As for systematic policy, there is evidence of a strong countercyclical response of both monetary and fiscal authorities to demand and, to a lesser extent, supply shocks. (iii) Positive demand shocks have a persistent negative effect on labor productivity. This finding, while being at odds with most of the business cycle literature, is consistent with a stream of empirical and theoretical work concerning the interactions between growth and cycle and the Schumpeterian view of recessions as providing a cleansing mechanism for reducing organizational inefficiencies and resource misallocations. The remainder of the paper is organized as follows. Section 2presents the model. Section 3 shows results concerning the number of shocks and presents in detail the definition of the shocks and the identification scheme. Section 4presents the main results. Section 5concludes. 2. Theory In the present section we provide a presentation of our model and estimation procedure. For additional details see Forni et al. (2009), FGLR from now on. 2.1. The Factor Model We assume that each variable xit of our macroeconomic data set is the sum of two mutually orthogonal unobservable components, the common component χit and the idiosyncratic component ξit: xit =χit +ξit. (1) The idiosyncratic components are poorly correlated in the cross-sectional dimension (see FGLR, Assumption 5 for a precise statement). They arise from shocks or sources of variation which considerably affect only a single variable or a small group of variables; in this sense, we could say that they are not “macroeconomic” shocks. For variables related to particular sectors, like industrial production indexes or production prices, the idiosyncratic component may reflect sector specific variations (with a slight abuse of language we could say “microeconomic” fluctuations); for strictly macroeconomic variables, like GDP, investment or consumption, the idiosyncratic component must be interpreted essentially as a measurement error. The common components are responsible for the main bulk of the co-movements between macroeconomic variables, being linear combinations of a relatively small number rof factors f1t,f2t,· · · ,frt, not depending on i: χit =a1if1t+a2if2t+· · · +ari frt =aif f ft. (2) The dynamic relations between the macroeconomic variables arise from the fact that the vector f f ftof the common factors follows the VAR relation f f ft=D1f f ft−1+· · · +Dpf f ft−p+e e et e e et=Ru u ut,(3) where R is a r×q matrix and u u ut= (u1tu2t· · · uqt)0 is a q -dimensional vector of orthonormal white noises, with q≤r . Such white noises are the “common” or “primitive” shocks or “dynamic factors” (whereas the entries of f f ftare the “static factors”).2 From Equations (1)–(3) it is seen that the model can be written in the dynamic form xit =bi(L)u u ut+ξit, (4) J. Risk Financial Manag. 2021,14, 371 4 of 21 where bi(L) = ai(I−D1L− · · · − DpLp)−1R. (5) The dynamic factors u u ut and bi(L) are “structural” macroeconomic shocks and impulse– response functions respectively.3 2.2. Identification Representation (4) is not unique, since the impulse-response functions and the related primitive shocks are not identified. In particular, if H is any orthogonal q×q matrix, then Ru u ut in (3) is equal to Sv v vt , where S=RH0 and v v vt=Hu u ut , so that χ χ χit =ci(L)v v vt , with ci(L) = bi(L)H0=ai(I−D1L− · · · − DpLp)−1S . However, assuming mutually orthogonal structural shocks, post-multiplication by H0 is the only admissible transformation, i.e., the impulse–response functions are unique up to orthogonal transformations, just like in structural VAR models (FGLR, Proposition 2). As a consequence, structural analysis in factor models can be carried on along lines very similar to those of standard SVAR analysis. To be precise, let us assume that economic theory implies a set of restrictions on the impulse–response functions of some variables, the first m≤n with no loss of generality. Let us write such functions in matrix notation as Bm(L) = (b1(L)0b2(L)0· · · bm(L)0)0 . Given any non-structural representation χ χ χmt =Cm(L)v v vt, (6) along with the relation Bm(L) = Cm(L)H, (7) if theory-based restrictions on Bm(L) are sufficient to obtain H , then bi(L) is uniquely determined for any i(just identification). In the present paper, however, we do not identify uniquely the shocks and the impulse– response functions; rather, following Uhlig (2005), we identify a distribution of shocks and related impulse–response functions by imposing a set of sign restrictions on the impulseresponse functions themselves. Formally, let bik be the coefficient of the term of degree k of bi(L) . We impose bik > 0 for i∈ I , k∈ K and bjh < 0 for j∈ J , h∈ H , where I , K , J and H are sets of integers. The precise set of restrictions that we impose in the present paper is discussed below. A quite natural parameterization of the orthogonal matrices H is given by the hyperspherical coordinates of the unit sphere Sw of dimension w= (q2−q)/ 2, i.e., H=H(θ) , θ being a w -dimensional vector of angles such that 0 ≤θj<π , j= 1, . . . , w− 1, 0 ≤θw< 2 π . Given the non-structural representation Cn(L)v v vt , the sign restrictions above define an admissible region Θ on the unit sphere, such that for θ∈ΘBn(L) = Cn(L)H(θ) satisfies such inequalities. Following Uhlig (2005) we assume that the true shocks and impulse–response functions are associated with a point θ with uniform probability density in the region Θ . This in turn implies upper and lower bounds and a probability density for each coefficient of the impulse–response functions Bn(L). 2.3. Estimation As for estimation, we proceed as follows. First, starting with an estimate ˆ r of the number of static factors, we estimate the static factors themselves by means of the first ˆ r ordinary principal components of the variables in the data set, and the factor loadings by means of the associated eigenvectors. Precisely, let ˆ Γx be the sample variance-covariance matrix of the data: our estimated loading matrix ˆ An= (ˆ a0 1ˆ a0 2· · · ˆ a0 n)0 is the n×r matrix having on the columns the normalized eigenvectors corresponding to the first largest ˆ r eigenvalues of ˆ Γx, and our estimated factors are f f ft=ˆ A0 n(x1tx2t· · · xnt)0. Second, we set a number of lags ˆ p and run a VAR( ˆ p ) with f f ft to get estimates of D(L) and the residuals e e et, say ˆ D(L)and ˆ e e et. Now, let ˆ Γe be the sample variance–covariance matrix of ˆ e e et . As the third step, having an estimate ˆ q of the number of dynamic factors, we obtain an estimate of a non-structural J. Risk Financial Manag. 2021,14, 371 5 of 21 representation of the common components by using the spectral decomposition of ˆ Γe . Precisely, let ˆ µe j,j=1, . . . , ˆ q, be the j-th eigenvalue of ˆ Γe, in decreasing order, ˆ Mthe q×q diagonal matrix with qˆ µe j as its (j , j) entry, ˆ K the r×q matrix with the corresponding normalized eigenvectors on the columns. Setting ˆ S=ˆ Kˆ M , our estimated matrix of non-structural impulse–response functions is ˆ Cn(L) = ˆ Anˆ D(L)−1ˆ S. (8) To account for estimation uncertainty, we adopt the following standard non-overlapping block bootstrap technique. Let X= [xit] be the T×n matrix of data. Such matrix is partitioned into S sub-matrices Xs (blocks), s= 1, . . . , S , of dimension τ×n , τ being the integer part of T/S . 4 An integer hs between 1 and S is drawn randomly with reintroduction S times to obtain the sequence h1 , . . . , hS . A new artificial sample of dimension τS×n is then generated as X∗=hX0 h1X0 h2· · · X0 hSi0 and the corresponding impulse–response functions are estimated. A set of non-structural impulse–response functions is obtained by repeating drawing and estimation. Finally, we obtain a distribution of impulse–response functions by imposing our sign identification restrictions. Precisely, we proceed as follows. For each artificial sample X∗ we compute the corresponding non-structural impulse–response functions ˆ Cn(L) . Then we draw N times a vector of angles θ with dimension w= (q2−q)/ 2 from a uniform distribution in the range 0 ≤θj<π , j= 1, . . . , w− 1, 0 ≤θw< 2 π and retain the related ˆ Bn(L) = Cn(L)H(θ) as long as they satisfy the sign restrictions. This gives a distribution of estimated ˆ Bn(L) ’s. We get a point estimate and the related confidence bands by retaining the median along with the relevant percentiles of such a distribution.5 2.4. Discussion FGLR is a special case of the generalized dynamic factor model proposed by (Forni et al. 2000,2005) and Forni and Lippi (2001). Such model differ from the traditional dynamic factor model of Sargent and Sims (1977) and Geweke (1977) in that the number of cross-sectional variables is infinite and the idiosyncratic components are allowed to be mutually correlated to some extent, along the lines of Chamberlain (1983), Chamberlain and Rothschild (1983), and Connor and Korajczyk (1988). Closely related models have been studied by (Stock and Watson 2002a,2002b,2005), (Bai and Ng 2002,2007), Bai (2003), and Bernanke et al. (2005). Large statistical factor models are compatible with a variety of economic models, including both neo-classical and Neo-Keynesian DSGE models, augmented with measurement errors (see Sargent and Sims 1977;Sargent 1989;Altug 1989;Ireland 2004 and the literature mentioned therein). However, in the present work we do not propose a fully developed economic model characterized by “deep” parameters. Rather, our approach is very much in the spirit of Sims (1980) and the “structural” VAR literature. Our impulse response functions can indeed be labeled as “semi-structural”, rather than “structural”: while not being reduced form coefficients, they are still a mixture of behavioral and policy parameters, so that we cannot tell, say, what would happen in absence of systematic fiscal or monetary policy. The results of the present paper should then be interpreted essentially as stylized facts, conditional on the identified shocks. Why using a structural factor model rather then a structural VAR? Factor models impose a considerable amount of structure on the data, implying restricted VAR relations among variables (see Stock and Watson (2005) for a comprehensive analysis). In this sense, they are less general than VAR models. On the other hand, factor models have a few advantages that can be important in the present context. First, within a factor model we can study how many shocks are there in the macro economy, an economic question which has been largely ignored in the literature simply because it does not even make sense within the statistical VAR framework, where the J. Risk Financial Manag. 2021,14, 371 6 of 21 number of shocks is necessarily equal to the number of variables that the econometrician chooses to include in the data set. However we believe that investigating the number of shocks driving the economy is of crucial importance since it can provide evidence that can be used as guidance for building macroeconomic models. Second, being much more parsimonious in terms of parameters, factor models can handle a much larger amount of information. The data set used in this paper, for instance, is made up of 101 variables. A VAR model with the same number of series would have too many parameters to estimate, given the number of observations available in the time dimension. Having a large data set is important for three reasons. First, we can study the impulse response functions of virtually all relevant macro variables within a unified framework. We exploit this opportunity here by showing results for key macro variables. Second, it enables us to impose identifying restrictions on several variables, reducing the region of admissible impulse response functions and causing the confidence bands to shrink. For instance, we identify an expansive demand shock by imposing positive effects on output and prices; as output series we use both GDP and the industrial production index, while prices are measured by both the GDP deflator and the CPI. Last, but not least, large information is likely to produce better results. The relevance of the information issue is stressed in several influential papers, including Quah (1990) and Sims (1992). If, as is reasonable, central banks and private economic agents base their decisions on all of the available macroeconomic information, structural shocks should be innovations with respect to a large information set, perhaps larger than the one that can be included in a standard VAR model. In fact, large dimensional factor models have proven useful in solving well known VAR puzzles (Bernanke et al. 2005;Forni and Gambetti 2010). The discussion above could call to mind the old controversy concerning the properties of large and small econometric models. In this respect, it should be observed that a major difference between the large econometric models prevailing fifty years ago and the large factor models proposed in the modern literature is that the former had bad forecasting performances, whereas the latter have been proven successful in forecasting (Stock and Watson 2002a,2002b). 3. Identifying the Structural Shocks In this section, we describe the data, identify the number of structural shocks and describe the set of inequality restrictions used to estimate the impulse response functions. 3.1. Data, Data Treatment and Specification of the Number of Factors The data set used in this paper is made up of 101 US quarterly series, covering the period 1959-I to 2007-IV. Most series are taken from the FRED data base. A few stock market and leading indicators are taken from Data Stream. Some series have been constructed by ourselves as transformations of the original FRED series. The series include both national accounting data like GDP, investment, consumption and the GDP deflator, which are available only at quarterly frequency, and series like industrial production indices, CPI, PPI, and employment, which are produced monthly. Monthly data have been temporally aggregated to get quarterly figures. As required by the model, the data were transformed to obtain stationarity. Stationarity tests were taken seriously, so that prices and nominal variables were taken in second differences of logs, rather than first differences of logs, and interest rates in first differences, rather than in levels. With these transformations all variables are stationary according to both the ADF and the KPSS tests.6 The full list of variables along with the corresponding transformations is reported in the Appendix A. The number of static factors r was set to 15 as suggested by the popular criterion IC2 (r=10), proposed by Bai and Ng (2002). J. Risk Financial Manag. 2021,14, 371 7 of 21 Finally, the number of lags p to include in the VAR which is part of our estimation procedure was set to 2, the average of AIC (3 lags) and BIC (1 lag). 3.2. How Many Macroeconomic Shocks? Determining the number of shocks, besides being an important step for the specification of our model, has intrinsic economic interest. For instance, early real business cycle models assume the existence of just one supply shock driving economic fluctuations, whereas, on the other extreme, Smets and Wouters (2007) propose a new Keynesian DSGE seven structural shocks. In the present factor model framework we have both tests and consistent information criteria which can provide useful indications for economic modeling. 7 The number of shocks can be determined by a few consistent information criteria. Here we use three groups of criteria, proposed by Amengual and Watson (2007), Bai and Ng (2007) and Hallin and Liska (2007). The criterion ˆ BNICP(ˆ yA) by Amengual and Watson in the ICp2 version (with ˆ r= 15 and p= 2) gives 4 primitive factors. The four criteria of Bai and Ng (2007), namely q1 , q2 , q3 and q4 , give 5, 4, 4, and 3 shocks, respectively (with ˆ r= 15 and p= 2). 8 Finally, the log criterion proposed by Hallin and Liska (2007) gives 2 and 4 shocks. In summary, information criteria do not provide a unique result, the number of shocks being between 2 and 5. We conclude in favor of a four-shock specification which is the specification suggested by all of the criteria. 3.3. Identifying Restrictions We identify three demand shocks and one supply shock. We think particularly appealing a characterization of the demand shocks as “discretionary fiscal policy”, “discretionary monetary policy”, and “private demand” (independent of discretionary monetary policy). To characterize such shocks we adopt the following definitions. The expansionary monetary policy shock is defined as a shock having a positive effect on both output and prices, but a negative effect on the federal funds rate. We expect that expansionary monetary policy enlarges money aggregates, but prefer not to impose such a restriction as part of the definition of the shock, in order to keep the definition itself as simple as possible. An obvious logical implication of the above characterization is that positive private demand and fiscal policy shock do not have a negative effect on the federal funds rate. Despite this, we do not impose such constraint, since in the present framework imposing a non-negative effect is equivalent to imposing a significant positive effect, which would be unnecessarily restrictive. Interestingly, it turns out that the restriction is satisfied confirming the non-monetary nature of the two shocks. The expansionary fiscal policy shock is defined as a shock having a positive effect on output, prices and the real federal deficit. 9 Again, a logical implication is that the expansionary private demand shock does not have a positive effect on the federal deficit. Indeed, we expect a significant negative effect, but do not impose such constraint. Most of the restrictions above are imposed on the first three coefficients of the impulse response functions, i.e., on the impact effect as well as the effects delayed by one and two quarters. However, there are two exceptions. First, we do not impose any restriction on the impact effects of monetary policy on output and prices. This is because both output and prices might react to monetary policy with some delay. In the structural VAR literature such a delayed reaction is commonly assumed to identify monetary policy (see Christiano et al. 1999 for a review). Here it is not assumed, the impact response can be zero or different from zero, the data will speak. Second, the positive effect of expansionary fiscal policy on the federal deficit, output and prices are imposed only on lag 1 and 2. The reason is the following. On one hand, the effects of fiscal policy decisions on public expenditures or receipts are often delayed by several months as discussed in the fiscal foresight literature, see Leeper et al. (2013). On the other hand, the sign and the size of the impact effects of such decisions on output and prices are not obvious. For instance, consumers might anticipate a larger income in the near future, but also a reduced public expenditure or higher taxes in J. Risk Financial Manag. 2021,14, 371 8 of 21 the medium run. If public expenditure is delayed and consumption does not increase on impact, output and prices do not necessarily increase contemporaneously. Summing up, the supply shock increases GDP and industrial production and reduces the GDP deflator and the CPI at lags 0, 1, and 2; the private demand shock increases GDP, industrial production, the GDP deflator and the CPI at lags 0, 1, and 2; the monetary policy shock reduces the federal funds rate at lags 0, 1, and 2 and increases GDP, industrial production, the GDP deflator and the CPI at lags 1 and 2; the fiscal policy shock increases GDP, industrial production, the GDP deflator, the CPI and the real federal deficit at lag 2. Such constraints are not sufficient per se to guarantee that all shocks are well defined. In addition we need that (i) the private demand shock does not reduce the federal fund rate for at least one of the lags 0, 1, or 2; (ii) the private demand shock does not increase the real federal deficit at lag 2; (iii) at least one of the following conditions holds: (iii.1) the monetary policy shock does not increase the federal deficit at lag 2, (iii.2) the fiscal policy shock does not reduce the federal funds rate for at least one of the lags 0, 1, or 2. Conditions (i) and (ii) are needed to characterize the private demand shock, whereas condition (iii) is needed to distinguish monetary from fiscal policy. 4. Results In this section, we present our main findings. We begin by showing a few results validating our identification scheme. Then we show results concerning the size and the timing of the effects of supply and demand shocks. Finally, we address policy issues and discuss the effects of demand on productivity. 4.1. Validating the Identification of Structural Shocks The purpose of this subsection is to validate our identification procedure along two dimensions. First, we check whether the inequality restrictions are sufficient to get a full characterization of the three demand shocks, i.e., conditions (i)–(iii) above are satisfied. Second, we show that the response of some relevant variables conform to the consensus view. The first column of Figure 1shows the mean impulse response functions (solid lines) of the federal funds rate to the four shocks, along with the 68% confidence bands (gray areas). First, both a positive demand shock and an expansionary fiscal policy shock generate an immediate positive effect on the federal funds rate. Hence conditions (i) and (iii.2) are satisfied. Second, deficit significantly reduces at all horizons after a demand shock, thus ensuring condition (ii), whereas it is essentially unaffected by the monetary policy shock, the effects being remarkably small and not significant at all horizons, consistently with condition (iii.1). The results suggest that the identifying restrictions are sufficient for a proper characterization of the three demand shocks. Next we show the effect of our identified shocks on a few selected variables, in order to verify whether they conform to some basic features emerging from previous literature and to gain additional insights about their sources and their nature. The non-policy demand shock is the only one that affects significantly, on impact, both new orders and real exports, see Figure 2. Furthermore, the demand shock is the primary source of unexpected change in investment on impact, explaining almost one half of the forecast error variance at lag 0 (as against 20% of consumption, see Table 2 below). While new orders and investment mainly capture factors that increase domestic demand, real exports indicates that the shock is also related to external factors. As far as the supply shock is concerned, Figure 2shows that both the producer price index of crude materials and the unit labor cost immediately and significantly fall, indicating that the supply shocks are partly made up of unexpected changes in some key production costs. Moreover, the shock has a large and significant positive impact on labor productivity (Figure 6), in line with the consensus view that supply shocks include an important technological component. J. Risk Financial Manag. 2021,14, 371 15 of 21 There is little evidence, however, of an active behavior of fiscal authorities on the receipt side, since current receipts essentially follow fluctuations in GDP. Both supply and demand bring about a significant positive and permanent increase in current receipts, which reduces government deficit. 4.4. Demand Shocks, Employment and Labor Productivity As discussed above, while non-policy demand shocks have temporary effects on GDP, they generate permanent effects on employment. This implies that labor productivity significantly and permanently decreases after a positive demand shock (Figure 6). 10 Such an effect is also quantitatively important. A unit variance shock, increasing GDP by 0.2 per cent on impact, reduces labor productivity by almost 0.4% in a couple of years: a change which, in absolute value, is even larger than that of the supply shock. Figure 6. Impulse-response functions. Solid line point estimate, gray areas 68% confidence bands. The finding above is consistent with a stream of empirical and theoretical work concerning the interactions between growth and cycle. Empirical evidence of a long-run negative effect of a positive demand shock on productivity is reported in Bean (1990), Saint-Paul (1993), and Galí and Hammour (1992), where an impulse response function almost identical to the one obtained here is found by using a structural VAR approach. Possible explanations are provided by theoretical works which, in various ways, revive the Schumpeterian view of recessions as providing a cleansing mechanism for reducing organizational inefficiencies and resource misallocations. During recessions, less efficient firms become unprofitable and shut down, thus improving average productivity (Caballero and Hammour 1994). Moreover, the opportunity cost of undertaking productivity-enhancing activities are lower, so that recessions are the right time to reorganize production, and/or improve the matching between workers and firms, implement new technologies, invest in J. Risk Financial Manag. 2021,14, 371 16 of 21 human capital (Davis and Haltiwanger 1992;Hall 1991;Aghion and Saint-Paul 1998). Such efficiency effects are long-lasting.11 The above finding has a relevant implication for the empirical research. A widespread practice in structural VAR literature is to identify technology shocks as the only ones having long-run effects on productivity (Galí 1999;Christiano et al. 2004). However, if demand also affects productivity, this identification assumption may produce a mixture of true positive technology shocks and negative demand shocks, leading to incorrect conclusions. For instance, the finding that technology reduces hours worked (Galí 1999) could be due to the negative demand component. Indeed, our supply shock have a significant positive impact on hours worked (not shown). Moreover, the puzzling finding that technology has little effect on investment (Christiano et al. 2004) may result from positive technology effects canceling out with negative demand effects. Actually with our identification procedure supply shocks account for about 45% of fluctuations in investment at the 6-year horizon (see Table 2). 4.5. Policy Implications From the previous results we draw a few policy implications. First, policy matter. Indeed both fiscal and monetary policy have sizable effects on output, employment and other real economic activity variables. Monetary policy appear to be very important for price fluctuations explaining around one third of the variance of GDP deflator inflation. On the contrary, fiscal policy seems to play a more limited role for prices. Second, the evidence suggests a strong countercyclical systematic response of both monetary and fiscal authorities to non-policy demand shocks. Given that discretionary policy has sizable effects on both output and prices, systematic policy could be effective in controlling inflation and reducing output fluctuations arising from non-policy demand. As a consequence, output fluctuations originated by non-policy demand, which, as documented above, are fairly small in comparison with supply-driven variations, could be much larger if systematic policy where not in place. Unfortunately, with the present model we cannot proceed to evaluate the quantitative importance of stabilization policies, nor we can say whether the corresponding variance reduction over-compensates for discretionary policies, which, as we have seen, are non-negligible sources of additional fluctuations. Third, systematic counter-cyclical policies, if successful in reducing fluctuation, may have long-run ’side effects’. Specifically, expansive measures following negative demand shocks, while not hurting GDP growth, may permanently support employment on one hand, and reduce per capita GDP and real wages, on the other hand. On balance, such effects are not necessarily undesirable. However, policy makers should be fully aware of the efficiency issues related to public support for employment and shaky companies, in order to design intervention properly. 5. Conclusions This paper studies the sources of business cycle fluctuations and the role of macroeconomic policies using a structural factor model. Our main results are the following. First, theories based on the existence of a single source of fluctuations as well as theories relying on a large number of shocks are inconsistent with our evidence. The US economy can be well described by a number of shocks between 2 and 5. Second, by specifying a four-shock model we find that both demand and supply components are important to explain fluctuations in real macroeconomic variables, although the relative importance varies, depending on the specific variable considered. Supply explains most of GDP volatility while demand prevails for employment and other labor market variables. Fluctuations in prices are mostly explained by demand shocks. Third, policy is important. Discretionary policies produce sizable effects on output and prices, with little evidence of crowding out effects of public expenditure. Both fiscal and monetary authorities follow systematic policy rules reacting mainly to private demand J. Risk Financial Manag. 2021,14, 371 17 of 21 shocks. Such stabilization policies could in principle be very effective in reducing demand driven fluctuations. Finally, non-policy demand shocks, while being long run neutral on GDP, have a large and permanent negative effect on productivity. Such a result is consistent with the Schumpeterian view of crises as providing a “cleansing” device for reducing inefficiencies and resource misallocations. Author Contributions: Conceptualization: L.G. and M.F.; methodology: M.F.; software: L.G.; formal analysis: M.F.; data curation: L.G.; writing—original draft: L.G. and M.F.; writing—review and editing: L.G.; visualization: L.G.; supervision: M.F and L.G.; funding acquisition: L.G. and M.F. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Italian Ministry of Research and University, PRIN 2017, grant J44I20000180001, the Spanish Ministry of Science and Innovation, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S), the Spanish Ministry of Science, Innovation and Universities through grant PGC2018-094364-B-I00. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available since some series was taken from Data Stream and several publicly available series were transformed by the authors (see Section 3.1 and Appendix Afor details). Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Appendix A. Data Transformations: 1 = levels, 2 = first differences of the original series, 5 = first differences of logs of the original series. No. Series Transf. Mnemonic Long Label 1 5 GDPC1 Real Gross Domestic Product, 1 Decimal 2 5 GNPC96 Real Gross National Product 3 5 NICUR/GDPDEF National Income/GDPDEF 4 5 DPIC96 Real Disposable Personal Income 5 5 OUTNFB Nonfarm Business Sector: Output 6 5 FINSLC1 Real Final Sales of Domestic Product, 1 Decimal 7 5 FPIC1 Real Private Fixed Investment, 1 Decimal 8 5 PRFIC1 Real Private Residential Fixed Investment, 1 Decimal 9 5 PNFIC1 Real Private Nonresidential Fixed Investment, 1 Decimal 10 5 GPDIC1 Real Gross Private Domestic Investment, 1 Decimal 11 5 PCECC96 Real Personal Consumption Expenditures 12 5 PCNDGC96 Real Personal Consumption Expenditures: Nondurable Goods 13 5 PCDGCC96 Real Personal Consumption Expenditures: Durable Goods 14 5 PCESVC96 Real Personal Consumption Expenditures: Services 15 5 GPSAVE/GDPDEF Gross Private Saving/GDP Deflator 16 5 FGCEC1 Real Federal Consumption Expenditures & Gross Investment, 1 Decimal 17 5 FGEXPND/GDPDEF Federal Government: Current Expenditures/GDP deflator 18 5 FGRECPT/GDPDEF Federal Government Current Receipts/GDP deflator 19 2 FGDEF Federal Real Expend-Real Receipts 20 1 CBIC1 Real Change in Private Inventories, 1 Decimal 21 5 EXPGSC1 Real Exports of Goods & Services, 1 Decimal 22 5 IMPGSC1 Real Imports of Goods & Services, 1 Decimal 23 5 CP/GDPDEF Corporate Profits After Tax/GDP deflator 24 5 NFCPATAX/GDPDEF Nonfinancial Corporate Business: Profits After Tax/GDP deflator 25 5 CNCF/GDPDEF Corporate Net Cash Flow/GDP deflator J. Risk Financial Manag. 2021,14, 371 18 of 21 No. Series Transf. Mnemonic Long Label 26 5 DIVIDEND/GDPDEF Net Corporate Dividends/GDP deflator 27 5 HOANBS Nonfarm Business Sector: Hours of All Persons 28 5 OPHNFB Nonfarm Business Sector: Output Per Hour of All Persons 29 5 UNLPNBS Nonfarm Business Sector: Unit Nonlabor Payments 30 5 ULCNFB Nonfarm Business Sector: Unit Labor Cost 31 5 WASCUR/CPI Compensation of Employees: Wages & Salary Accruals/CPI 32 5 COMPNFB Nonfarm Business Sector: Compensation Per Hour 33 5 COMPRNFB Nonfarm Business Sector: Real Compensation Per Hour 34 5 GDPCTPI Gross Domestic Product: Chain-type Price Index 35 5 GNPCTPI Gross National Product: Chain-type Price Index 36 5 GDPDEF Gross Domestic Product: Implicit Price Deflator 37 5 GNPDEF Gross National Product: Implicit Price Deflator 38 5 INDPRO Industrial Production Index 39 5 IPBUSEQ Industrial Production: Business Equipment 40 5 IPCONGD Industrial Production: Consumer Goods 41 5 IPDCONGD Industrial Production: Durable Consumer Goods 42 5 IPFINAL Industrial Production: Final Products (Market Group) 43 5 IPMAT Industrial Production: Materials 44 5 IPNCONGD Industrial Production: Nondurable Consumer Goods 45 1 AWHMAN Average Weekly Hours: Manufacturing 46 2 AWOTMAN Average Weekly Hours: Overtime: Manufacturing 47 2 CIVPART Civilian Participation Rate 48 5 CLF16OV Civilian Labor Force 49 5 CE16OV Civilian Employment 50 5 USPRIV All Employees: Total Private Industries 51 5 USGOOD All Employees: Goods-Producing Industries 52 5 SRVPRD All Employees: Service-Providing Industries 53 5 UNEMPLOY Unemployed 54 5 UEMPMEAN Average (Mean) Duration of Unemployment 55 1 UNRATE Civilian Unemployment Rate 56 5 HOUST Housing Starts: Total: New Privately Owned Housing Units Started 57 1 FEDFUNDS Effective Federal Funds Rate 58 1 TB3MS 3-Month Treasury Bill: Secondary Market Rate 59 1 GS1 1-Year Treasury Constant Maturity Rate 60 1 GS10 10-Year Treasury Constant Maturity Rate 61 1 AAA Moody’s Seasoned Aaa Corporate Bond Yield 62 1 BAA Moody’s Seasoned Baa Corporate Bond Yield 63 1 MPRIME Bank Prime Loan Rate 64 5 BOGNONBR Non-Borrowed Reserves of Depository Institutions 65 5 TRARR Board of Governors Total Reserves, Adjusted for Changes in Reserve 66 5 BOGAMBSL Board of Governors Monetary Base, Adjusted for Changes in Reserve 67 5 M1SL M1 Money Stock 68 5 M2MSL M2 Minus 69 5 M2SL M2 Money Stock 70 5 BUSLOANS Commercial and Industrial Loans at All Commercial Banks 71 5 CONSUMER Consumer (Individual) Loans at All Commercial Banks 72 5 LOANINV Total Loans and Investments at All Commercial Banks 73 5 REALLN Real Estate Loans at All Commercial Banks 74 5 TOTALSL Total Consumer Credit Outstanding 75 5 CPIAUCSL Consumer Price Index For All Urban Consumers: All Items 76 5 CPIULFSL Consumer Price Index for All Urban Consumers: All Items Less Food 77 5 CPILEGSL Consumer Price Index for All Urban Consumers: All Items Less Energy 78 5 CPILFESL Consumer Price Index for All Urban Consumers: All Items Less Food & Energy 79 5 CPIENGSL Consumer Price Index for All Urban Consumers: Energy 80 5 CPIUFDSL Consumer Price Index for All Urban Consumers: Food J. Risk Financial Manag. 2021,14, 371 19 of 21 No. Series Transf. Mnemonic Long Label 81 5 PPICPE Producer Price Index Finished Goods: Capital Equipment 82 5 PPICRM Producer Price Index: Crude Materials for Further Processing 83 5 PPIFCG Producer Price Index: Finished Consumer Goods 84 5 PPIFGS Producer Price Index: Finished Goods 85 5 OILPRICE Spot Oil Price: West Texas Intermediate 86 5 USSHRPRCF US Dow Jones Industrials Share Price Index (EP) NADJ 87 5 US500STK US Standard & Poor’s Index if 500 Common Stocks 88 5 USI62...F US Share Price Index NADJ 89 5 USNOIDN.D US Manufacturers New Orders for Non Defense Capital Goods (BCI 27) 90 5 USCNORCGD US New Orders of Consumer Goods & Materials (BCI 8) CONA 91 1 USNAPMNO US ISM Manufacturers Survey: New Orders Index SADJ 92 5 USVACTOTO US Index of Help Wanted Advertising VOLA 93 5 USCYLEAD US The Conference Board Leading Economic Indicators Index SADJ 94 5 USECRIWLH US Economic Cycle Research Institute Weekly Leading Index 95 5 GS10-FEDFUNDS 96 5 GS1-FEDFUNDS 97 5 BAA-FEDFUNDS 98 5 GEXPND/GDPDEF Government Current Expenditures/GDP deflator 99 5 GRECPT/GDPDEF Government Current Receipts/GDP deflator 100 1 GDEF Governnent Real Expend-Real Receipts 101 5 GCEC1 Real Government Consumption Expenditures & Gross Investment, 1 Decimal 102 1 GS5 5-Year Treasury Constant Maturity Rate Notes 1 An alternative approach is represented by Banbura et al. (2010), which develops a Bayesian VAR model that can handle many economic time series. 2 Observe that, if q<r , the residuals of the above VAR relation have a singular variance covariance matrix.Equations (1) to (3) need further qualification to ensure that all of the factors are loaded, so to speak, by enough variables with large enough loadings (see FGLR, Assumption 4); this “pervasiveness” condition is necessary to have uniqueness of the common and the idiosyncratic components, as well as the number of static factors rand dynamic factors q. 3 Unlike the dynamic factors, the static factors do not have a structural economic interpretation; rather, they are a statistical tool which is useful to model the dynamics of the system. Loosely speaking, given the number of primitive shocks q , the number of “static factors” r governs the “degree of heterogeneity” of the impulse–response functions. For instance, in the simple case q= 1, if r= 1 all the impulse–response functions are proportional. On the other hand, if r is larger, different variables can load the shock with different delays, so that we may have leading, coincident and lagging variables. If ris large enough, any (finite order) MA dynamics can be written in the form (1)–(3) (FGLR, Section 2). 4Note that τhas to be large enough to retain relevant lagged auto- and cross-covariances. 5 We impose an upper bound to the number of impulse–response functions to retain for each step of the bootstrap procedure in order to avoid that a single bootstrap provide a disproportionately large number of functions. 6 Outliers were detected as values differing from the median more than 6 times the interquartile difference and replaced with the median of the five previous observations. 7 The test has two parameters identifying the lower and the upper bound of the frequencies of interest. Since we are mainly interested in business cycle fluctuations, we set such parameters in such a way to include waves of periodicity between 2 and 12 years. 8 The Bai and Ng criteria have two parameters. We set δ= 0.1 for all criteria and m(q1) = 1.25, m(q2) = 2.5, m(q3) = 2, m(q4) = 4.5. Such values produced good results in our simulations (not shown here). 9 The real federal deficit is constructed as the difference between current federal expenditures and current federal receipts, divided by the GDP deflator. 10 For the monetary policy shock a similar picture emerges but the effect on labor productivity is not significant. 11 According to the above explanations, productivity is related to the business cycle, rather than demand per se). This is consistent with our estimated response of productivity to supply shocks, which reaches its maximum after about one year and then declines sharply, dissipating about one half of the impact effect in the following six quarters (see Figure 6). J. 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