Computational evidence on the distributive properties of monetary policy

Chen, Siyan; Desiderio, Saul Working Paper Computational evidence on the distributive properties of monetary policy Economics Discussion Papers, No. 2018-38 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Chen, Siyan; Desiderio, Saul (2018) : Computational evidence on the distributive properties of monetary policy, Economics Discussion Papers, No. 2018-38, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/178670 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. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. 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. http://creativecommons.org/licenses/by/4.0/ Discussion Paper No. 2018-38 | May 11, 2018 | http://www.economics-ejournal.org/economics/discussionpapers/2018-38 Computational evidence on the distributive properties of monetary policy Siyan Chen and Saul Desiderio Abstract Empirical studies have pointed out that monetary policy may significantly affect income and wealth inequality. To investigate the distributive properties of monetary policy the authors resort to an agent-based macroeconomic model where firms, households and one bank interact on the basis of limited information and adaptive rules-of-thumb. Simulations show that the model can replicate fairly well a number of stylized facts, specially those relative to the business cycle. The authors address the issue using three types of computational experiments, including a global sensitivity analysis carried out through a novel methodology which greatly reduces the computational burden of simulations. The result emerges that a more restrictive monetary policy increases inequality, even though this effect may differ across groups of households. This may put into question the principle of the independence of central banks. In addition, this effect appears to be attenuated if the bank’s willingness to lend is lower. JEL C63 D31 D50 E52 Keywords Economic inequality; monetary policy; agent-based models; NK-DSGE models; stock-flow consistency; global sensitivity analysis Authors Siyan Chen, Business School, Shantou University, Daxue Road 243, Shantou, Guangdong, P. R. China Saul Desiderio, Business School, Shantou University, Daxue Road 243, Shantou, Guangdong, P. R. China, [email protected], , saul1[email protected] Citation Siyan Chen and Saul Desiderio (2018). Computational evidence on the distributive properties of monetary policy. Economics Discussion Papers, No 2018-38, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2018-38 Received May 2, 2018 Accepted as Economics Discussion Paper May 4, 2018 Published May 11, 2018 © Author(s) 2018. Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0) Economics Discussion Paper 1 Introduction Common wisdom about monetary policy holds that its real effects are only temporary and that, consequently, its role be to keep the macroeconomy ‘in order’ by providing a non-inflationary environment. One logical consequence of this view is that central banks should be as independent as possible from political influence because independence has been shown to promote price stability (e.g. Alesina and Summers, 1993). Although arguments in favor of independence are convincing, in the long run monetary policy could have deeper implications for the economy than just affecting prices. Among other things, in fact, its potential ability to influence income, wealth and consumption inequality has been argued. This prompts that central banks may possess more social responsibility than usually deemed, and could make the case for a more democratic control of monetary policy actions. Monetary policy can affect inequality through different channels. For example, an expansionary monetary policy that reduces unemployment can also reduce income inequality. In addition, low interest rates decrease capital income, which is relatively more important for richer individuals. As a consequence, income inequality may decline. But at the same time low interest rates boost financial assets prices and therefore increase wealth inequality. On the other hand, a contractionary monetary policy aimed at reducing inflation may well have the opposite effects1. Clearly, the overall effect of monetary policy on economic inequality can hardly be predicted in advance because of the many channels through which it operates. The relatively few empirical studies which have investigated the redistributive effects of monetary policy provide contrasting evidence. Among these, Coibion et al. (2017) find that expansionary monetary policy has decreased both income and consumption inequality in the US, whereas Mumtaz and Theophilopoulou (2017) find the same evidence for the UK. Conversely, Davtyan (2017) finds the opposite result for the US if the top 1% of the population is included in the analysis. Along the same line is a study of the Bank of England (2012), which also suggests that expansionary unconventional (asset-buying) monetary policies might have increased inequality in the UK. Romer and Romer (1999) found a decrease of inequality and poverty due to expansionary monetary policies in the short run, but their result is quite the opposite in the long run, where it is prudent (non-inflationary) monetary policy that appears to have reduced inequality through price stability. The effect of monetary policy through inflation is considered also by Erosa and Ventura (2002), who find that generally lower-income households are less protected against inflation than higher-income 1A detailed taxonomy of the different channels can be found in Nakajima (2015). www.economics-ejournal.org 2 Economics Discussion Paper classes; by Doepke and Schneider (2006), who find that rising inflation can redistribute wealth in favor of middle-class households; and by Albanesi (2007), who finds a positive correlation between inflation and income inequality. Because of the different data-sets, methodologies and time spans considered, and because of the very nature of observational data, the answer provided by empirical works is far from unanimous. Thus, resorting to economic models could contribute to make greater clarity. Indeed, from the theoretical point of view the subject has attracted very little attention, mainly because the assumption of representative agents in mainstream methodology is obviously inadequate to address distributional issues. Recent exceptions are NK-DSGE models that introduce some kind of household heterogeneity (‘HANK’ models) such as Gornemann et al. (2012), Areosa and Areosa (2016), Gornemann et al. (2016), Kaplan et al. (2016) and Sterk and Ravn (2017), which in general find that rising interest rates increase inequality. However, these models can be questioned under different angles. Besides being subject to usual criticisms that apply to mainstream macro models, such as the use of representative agents, perfect rationality and excessive centrality of equilibrium solutions (for a thorough discussion see e.g. Delli Gatti et al., 2011), HANK models also lose some of the appeal which generally characterizes NK-DSGE models as they “typically require heavy computational methods which may obscure intuition and overlook equilibria” (Sterk and Ravn, 2017). But we want to point out that another and more subtle issue has gone unnoticed thus far - namely that NK-DSGE models are inadequate to assess monetary policy. Monetary policy in fact produces real effects on the economy mainly as long as it influences nominal variables, for instance through the ‘balance sheet’ channel (Bernanke and Gertler, 1995). On the contrary, as NK-DSGE models embody the classical dichotomy through rational expectations, the transmission of monetary policy to the real economy can be attained in this class of models only by introducing nominal stickiness. In other words, in NK-DSGE models monetary policy generates real effects as long as it does not influence nominal variables. We therefore believe that something deeply flawed lies in mainstream macro models. If inequality and monetary policy are the objects of interest, a valid (if not ideal) alternative to HANK models are agent-based models, as individual heterogeneity is one of their constitutive features. Moreover, this modeling approach can easily accommodate for all the complex relationships that characterize real economies. The principal goal of this paper is therefore to shed some light on the distributive properties of monetary policy through the analysis of artificial data produced by computational experiments in a multi-agent environment. Moreover, the usefulness and advantage of computer simulations is that, unlike empirical studies, they allow to study a given subject in a true ceteris paribus fashion. The second goal of the paper is therefore to assess whether the distributive effects of monetary policy are affected by other variables. In particular, we will consider the www.economics-ejournal.org 3 Economics Discussion Paper role of banks’ lending attitude, which is an important channel for the transmission of monetary policy. This is another advantage of our approach over NK-DSGE models, which in general do not include a banking sector. Finally, the third goal of the paper is to provide a methodological contribution, as we will propose a computationally-light approach to global sensitivity analysis. Our experiments will be conducted in the virtual economic environment generated by a novel agent-based model which builds upon previous works like Delli Gatti et al. (2011), Delli Gatti and Desiderio (2015) and Chen and Desiderio (2018). An important characteristic of our model is stock-flow consistency (SFC), which has witnessed increasing application in agent-based literature in recent years (e.g. Delli Gatti and Desiderio, 2015; Riccetti et al., 2015; Caiani et al., 2016). SFC, basically consisting in the implementation of precise accounting rules, is of particular importance when money and credit are explicitly introduced into the model and monetary policy is considered. Besides, SFC provides a correct link between income and wealth, whose evolution constitutes the main focus of the paper. SFC is therefore introduced to increase the degree of realism of the model as well as its ability to simulate monetary policy interventions. In the model we are going to present, households have two different income sources: wages and capital income (the latter being generated by the return on bank deposits). Monetary policy affects income and wealth inequality through the so-called ‘income channel’, as it influences both wages (along with unemployment) and the return on financial assets. However, as the relative weight of the two income sources is generally different for different households, the impact of monetary policy will vary from household to household. Thus, the overall effect can hardly be determined in advance, also because it is the result of the interaction between monetary policy and other mechanisms like the availability of credit. We point out that one important limitation of our model is that the effect of monetary policy on asset values is not considered. Hence, changes in wealth inequality are mainlyaconsequenceofchangesin income inequality. Another limitation is given by the absence of households’ debts, which have probably played a non-secondary role in the increase of inequality witnessed in the last decades. Basically, in the model we will not consider the so-called ‘portfolio channel’. In recent years the analysis of inequality has been a hot topic in the context of agent-based macroeconomics. For instance, Desiderio and Chen (2016), Riccetti et al. (2016) and Russo et al. (2016) study how functional and personal income distributions are affected by financial factors. The role of monetary policy is considered by Dosi et al. (2013) and Dosi et al. (2015). These two works, however, differ substantially from ours as they study the impact of inequality on monetary policy, whereas we will focus on the opposite direction of causality, i.e. the effect of monetary policy on inequality. www.economics-ejournal.org 4 Economics Discussion Paper The paper continues as follows. In section 2 we describe the model and in section 3 we simulate it. In spite of its relative simplicity, we will show that our model is able to match a good deal of empirical evidence, performing particularly well in replicating business cycle stylized facts. In section 4 we will study the distributive properties of monetary policy. To this scope we will use three different techniques: a policy experiment, a local sensitivity analysis and a global sensitivity analysis. The latter will be carried out employing an original approach aimed at economizing on the computational effort necessary to perform this kind of analysis. All the techniques employed suggest that a more restrictive monetary policy increases economic inequality, in line with findings obtained in HANK literature. But our inequality analysis is conducted at a finer level of detail than mainstream models: we will in fact consider different classes of households and the role of the banking sector. Finally, section 5 concludes. 2 The model We consider a dynamic economy populated by Ffirms, Hinfinitely lived households (workers-consumers) and one commercial bank, while we leave both the Government and the central bank unmodeled. All agents take decisions on the basis of limited private information. The households supply labor, buy consumption goods and hold deposits at the bank. The firms demand labor, produce and sell consumption goods, demand bank loans and hold deposits. The bank receives deposits and extend loans to firms. There are therefore four markets: for labor, consumption goods, bank loans, and deposits. Agents enter their relevant markets and interact with a number of partners according to a decentralized search and matching process. All transactions are therefore characterized by persistent uncertainty. The economy evolves over time for a number of periodst=1...T. Each period the same sequence of events takes place: 1. Firms decide the amount of output to be produced, the level of desired workforce and the price to be charged. 2. Firms post their vacancies along with wage offers. 3. Unemployed workers randomly contact a given number of firms to get a job. 4. Newly employed workers sign a job contract lasting Dperiods. 5. Firms pay the wage bill. If internal financial resources are insufficient, firms may borrow from the bank. www.economics-ejournal.org 5 Economics Discussion Paper 6. The bank extends loans to credit-worthy firms and pays interests on households’ deposits. 7. Households decide their consumption budget and enter the goods market. Each consumer randomly chooses a fixed number of firms. 8. Firms collect revenues and validate debt commitments to the bank. 9. Firms not able to validate debt commitments go bankrupt and are replaced by an equal number of new firms. The initial capital of new firms is financed by taxes levied on households’ deposits. 10. As a consequence of firms’ bankruptcies, the bank registers a bad debt (nonperforming loan). 11. Households update their wealth according to their income and consumption expenditure. 2.1 The balance sheets Agents are characterized by state variables summarized by their balance sheets. The evolution of these variables satisfies the rules of a complete accounting system, which ensures consistency between flows and stocks (assets and liabilities). This consistency implies model closure, in the sense that no external resource is incorrectly added to the system and no internal resource is lost. This property is clearly important in itself, but it is even more so to our analysis because it assures that income and wealth inequality do not undergo undue alterations. In addition, changes in the balance sheets play a relevant role in the transmission of monetary policy (Bernanke and Gertler, 1995). Table 1 shows the aggregate balance sheets for each group of agents. Households Firms Bank Total Deposits DhDf−(Dh+Df)0 Reserves H H Loans −L L 0 Total EhEfEbH Table 1: Balance sheets Dhand Dfare households and firms’ deposits (liquid assets), Lrepresents bank loans, Eh,Efand Ebare households, firms and the bank’s equity (net worth) respectively; His high powered money (HPM). There is no currency in circulation www.economics-ejournal.org 6 Economics Discussion Paper so that the only use of HPM is as a liquidity buffer for the bank (reserves). Hence, for simplicity we set H=0. In the aggregate assets and liabilities must sum to zero, thus the following accounting identity holds: Eh+Ef+Eb=H=0 (1) Agents’ behavior determines the dynamics of stocks. Market transactions producing flows of funds are illustrated by Table 22.Cis consumption, wN is the Households Firms Bank Total Goods −C Y =C+I I Wages wN −wN 0 New loans ∆L−∆L0 Loan interests −iL iL 0 Deposit interests rDh−rDh0 New deposits −∆Dh−∆Df∆D0 Savings ShSfSbI Table 2: Flow of funds wage bill (wis the wage rate and Nis employment), Yis total production, Iis the change in inventories, iis the loan interest rate and ris the return on bank deposits. As firms invest only in inventories, the flow of current savings must be equal to the change in inventories: Sh+Sf+Sb=I,(2) where Sh=∆Eh=∆Dh;Sf=∆Ef=∆Df;Sb=∆Eb. As we will explain later, we assume that firms do not retain unsold goods (I=0). Hence, total savings are always equal to zero. As already stated, we assume that there is no currency in circulation as firms and households keep always all their liquid assets in form of bank deposits. This implies a causal relation going from loans to deposits. In fact, every transaction between firms and households is implemented through bank accounts without any actual exchange of currency outside the bank. Hence, the level of deposits changes only when a new loan is granted, an outstanding loan is repaid and interests are paid to, or paid by, the bank. 2Items representing outflows are identified by the minus sign. www.economics-ejournal.org 7 Economics Discussion Paper 2.2 Firms Due to uncertainty, firms have only an imperfect knowledge of market conditions and, consequently, they have to form expectations De it on demand. Because firms do not accumulate inventories (see below), the desired quantity of goods to supply Y∗ it is set at the level of expected demand. However, actual production Yit may differ from the desired level Y∗ it if firms are constrained on the credit market or on the labor market. Though firms produce the same homogeneous consumption good, imperfect competition caused by uncertainty and consumer search costs entails that they have some degree of market power. The firm’s strategy is therefore the couple (Pit,Yit), where Pit is the firm’s price level at time t. At price Pit, and given the competitors’ prices, the actual demand for firm iis Dit, which may differ from productionYit. The difference between production and demand shows up in inventories Iit =Yit −Dit. We assume the goods to be perishable and non-storable. This means that firms cannot take inventories to the next period to satisfy future demand. Ignoring the inventory cycle is clearly a limitation of the model, but it can be considered as quite a realistic approximation of modern economies, whose GDP is mainly composed of non-storable services. Although goods cannot be stored, inventories are used by firms as market signals: positive inventories, in fact, signal that demand has been overestimated (excess supply), whereas no inventory accumulation (Iit =0) indicates that demand has been underestimated (excess demand) or exactly estimated (equilibrium). Price and quantity decisions At the beginning of each period, the generic firm iadjusts the price Pit or the desired quantity to supply Y∗ it to adapt to changing market conditions. We assume that the firm cannot simultaneously change price and quantity. This is of course a simplifying assumption, but at the same time it is consistent with the empirical evidence on price and quantity adjustment of firms over the business cycle (Kawasaki et al., 1982; Bhaskar et al., 1993). The firm’s strategies depend both on its internal conditions and on market signals. The relevant information at timetfor firm iconsists of the average market price Pt−1(which is a proxy for the prices of firm i’s competitors) and of the individual excess demand/supply recorded in the previous period and captured by unsold inventories Iit−1. The firm adjusts the price according to the following adaptive rule-of-thumb: Pit =Pit−1(1+ η it)if Iit−1=0 and Pit−1<Pt−1 Pit−1(1− η it)if Iit−1>0 and Pit−1≥Pt−1(3) www.economics-ejournal.org 8 Economics Discussion Paper Table 3, and then we present some robustness checks. The aim of this section, therefore, is to validate our model by confronting its properties with comparable empirical evidence. In spite of its simplicity, the model is able to replicate several stylized facts both at macro and micro level. Parameter Description Value TNumber of periods 500 FNumber of firms 100 HNumber of workers 600 ZNumber of firms visited by a consumer 2 MNumber of labor applications 4 DJob contract length 8 h η Maximum growth rate of prices 0.1 h ρ Maximum growth rate of quantities 0.1 h ξ Maximum growth rate of wages 0.05 h χ Maximum % decrease of reservation wages 0.05 ψ Recapitalization coefficient 0.01 itPolicy rate 0.01 θ Credit rating threshold 0.2 τ Debt repayment rate 0.05 ΦDefaulting window 10 1− κ Share of bad debt 0.05 Table 3: Parameters. Fig. 1 shows six time series relative to a representative simulation. In our model business cycles are not the consequence of exogenous aggregate shocks but are caused by a combination of idiosyncratic random shocks and non-linearities. Bounded-rational individual decisions and decentralized interactions produce an alternation of periods of economic expansions and recessions with no tendency to settle down to some long-run equilibrium (Panel 1(a)). The unemployment rate (Panel 1(b)), although not very realistic in absolute value, closely follows the business cycle. This cyclical behavior cannot be explained in terms of microeconomic frictions such as downward nominal wage rigidity and search costs (which are fixed), but is the product of coordination failures within and between markets. In fact, the close similarity between the evolution of unemployment and unsold production (that we do not report) signals the contemporaneous occurrence during recessions of excess supply for both labor and goods and, therefore, points in the direction of a Keynesian (demand-driven) interpretation of unemployment. A key variable in shaping fluctuations is firms’ cash flow. During expansions, in fact, unemployment drops, wages rise and firms build up debts to finance inwww.economics-ejournal.org 15 Economics Discussion Paper creasing production. As long as revenues allow firms to validate their financial commitments with the bank, production continues to expand. However, rising costs and accumulation of debts reduce firms’ cash flow, eventually increasing the rate of default. If the number of bankrupted firms is large enough, or if big firms are among them, aggregate production starts shrinking and unemployment increases. Then, the subsequent loss of employment causes a reduction in households’ spending that negatively reverberates on other firms’ sales and profits. Furthermore, this vicious cycle is exacerbated by a financial accelerator mechanism: bankruptcies, in fact, lower firms’ credit worthiness and leads to credit rationing by the bank (Eq. 19). However, recessions have also an important function: they wipe less efficient and more indebted firms out. This natural selection mechanism makes the economy financially sounder and, eventually, leads to a new expansion phase. We now show the model properties at business-cycle frequencies. We compare artificial and empirical cyclical components of four variables: real GDP, real consumption, unemployment rate and CPI. Cyclical components are extracted by applying the Hodrick-Prescott filter with smoothing parameter set at 1600. Empirical data are post-war U.S. seasonally-adjusted quarterly time series, retrieved from FRED database4. Fig. 2 shows the results of a co-movement analysis exercise: against each value of lag on the x-axis we plot the correlation between the cyclical component of GDP at time twith the cyclical component of the other variables at time t+lag (with a negative lag corresponding to a lead). We can see that artificial cross-correlations are more pronounced than the observed ones, but their patterns are very similar. Less satisfactory is the result for labor productivity (computed as the ratio between total production and total employment) and real wage (which we omit to report). The former in fact, although able to reproduce the pattern of real data, shows cross-correlations substantially smaller than the empirical counterparts. On the contrary, the latter features a strong (and leading) pro-cyclicality which we can barely find in real time series. To assess the robustness of above results, we also calculate the average crosscorrelations for the same set of variables over 100 independent simulations. Table 4 shows that the averages are quite close to the cross-correlations of the representative simulation. Moreover, the Monte Carlo standard errors shown in parentheses are small, proving that our results are robust. Finally, we end our business cycles analysis by reporting in Table 5 the Monte Carlo averages of the first-order autocorrelations of the cyclical components of the four variables, showing that the agreement between simulated and real data is 4We used the files GDPC1, PCECC96, UNRATE and PCECTPI, U.S. Bureau of Economic Analysis, retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/GDPC1, March 13, 2018. www.economics-ejournal.org 16 Economics Discussion Paper 0 50 100 150 200 250 300 350 400 Time 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 (a) 0 50 100 150 200 250 300 350 400 Time 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 (b) 0 50 100 150 200 250 300 350 400 Time 4.8 5 5.2 5.4 5.6 5.8 6 (c) 0 50 100 150 200 250 300 350 400 Time 0.5 0.55 0.6 0.65 0.7 0.75 0.8 (d) 0 50 100 150 200 250 300 350 400 Time -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 (e) 0 50 100 150 200 250 300 350 400 Time 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (f) Figure 1: (a): Real output (on logarithmic scale); (b): Unemployment rate; (c): Consumption; (d): Real wage; (e): inflation rate; (f): Gini coefficients for wealth (blue line) and income (red line). www.economics-ejournal.org 17 Economics Discussion Paper -4 -3 -2 -1 0 1 2 3 4 Lag 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (a) -4 -3 -2 -1 0 1 2 3 4 Lag 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (b) -4 -3 -2 -1 0 1 2 3 4 Lag -1 -0.8 -0.6 -0.4 -0.2 0 0.2 (c) -4 -3 -2 -1 0 1 2 3 4 Lag -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 (d) Figure 2: Cross-correlations for simulated (continuous line) and observed U.S. time series (dashed line). The pictures show the correlation between the cyclical component of GDP at time twith those at time t+lag of (a): Real GDP; (b): Consumption; (c): Unemployment rate; (d): CPI. www.economics-ejournal.org 18 Economics Discussion Paper Lag -4 -3 -2 -1 0 +1 +2 +3 +4 GDP .4248 (.0455).5560 (.0392).6955 (.0312).8496 (.01833)1 (0).8496 (.01833).6955 (.0312).5560 (.0392).4248 (.0455) Cons .5336 (.0468).6173 (.0431).6993 (.0380).7669 (.0304).8362 (.0212).7088 (.0297).5574 (.0385).4090 (.0425).2644 (.0469) Unem −.3514 (.0495) −.4750 (.0441) −.6093 (.0364) −.7627 (.0257) −.9283 (.0132) −.8263 (.0242) −.7148 (.0353) −.5963 (.0406) −.4731 (.0455) CPI −.5365 (.0749) −.5198 (.0791) −.4757 (.0801) −.3915 (.0805) −.2547 (.0817) −.1089 (.0812).0233 (.0787).1307 (.0742).2119 (.0689) Table 4: Cross-correlations between the cyclical component of GDP at time twith those at time t+lag of (a): Real GDP; (b): Consumption; (c): Unemployment rate; (d): CPI. Averages over 100 simulations (standard errors in parentheses). www.economics-ejournal.org 19 Economics Discussion Paper rather satisfactory. In this case, the agreement is good also for labor productivity and real wage (which we do not report). GDP Consumption Unemployment CPI Observed 0.8773 0.8977 0.8992 0.8675 Simulated 0.8496 0.7238 0.8374 0.9489 Table 5: First-lag autocorrelation of cyclical components. Averages over 100 simulations. In terms of replication of stylized facts our model works quite well also at lower aggregation levels. Fig. 3 reports three well-known statistical regularities describing the relationship between business cycles and labor market dynamics, which we calculate for the representative simulation after discarding the first 100 transient periods. Panel (a) shows the Phillips Curve, featuring a strong and statistically significant negative correlation (-0.6128) between inflation rate and unemployment rate. Panel (b) shows a negative relationship between the output growth rate and the unemployment growth rate - i.e. an Okun curve (correlation of -0.8607). The third emerging regularity is the Beveridge curve (Panel (c)), i.e. a negative relationship between the rate of vacancies (the ratio between the number of job openings and the total number of workers) and the unemployment rate. Also in this case the correlation between the two variables, although not very strong (-0.3936), shows the correct sign and is once again statistically significant. In addition, Panel (d) shows the households’ wealth distribution, which coherently with empirical observations exhibits positive skewness and a fat right tail. At a lower level of aggregation the model replicates, at least qualitatively, also some empirical regularities concerning job flows. We find in fact that unemployment is positively correlated to long-term unemployment (defined as the workforce that has been unemployed for more than three periods); layoffs and hirings, i.e. job destruction and job creation, have strong positive correlation both in levels and in differences; layoffs show higher volatility and are more correlated to unemployment than hiring (Blanchard and Diamond, 1990; Davis et al., 1996). In conclusion, although relatively simple, the model is able to reproduce a good deal of stylized facts at different levels of aggregation. Hence, in the next section we are going to employ it as a computational laboratory to study the distributional effects of monetary policy. 4 Monetary Policy and inequality In this section we are going to assess the effect of monetary policy on personal income and wealth inequality. Changes in monetary policy will be captured by www.economics-ejournal.org 20 Economics Discussion Paper -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 Unemployment rate 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Inflation rate data1 linear (a) -0.1 -0.05 0 0.05 0.1 0.15 0.2 Unemployment growth rate -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 Output growth rate data1 linear (b) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 Unemployment rate 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Vacancy rate data1 linear (c) (d) Figure 3: (a): Phillips curve, (b): Okun curve, (c): Beveridge curve, (d): Wealth distribution at t=500. www.economics-ejournal.org 21 Economics Discussion Paper changes in the policy rate it. Inequality will be measured through two indexes. One is the Gini coefficient, which will also be computed for three different groups of households: the bottom 50%, the middle 40% and the top 10% of the distribution. The other index is the ratio SS of the cumulative income (or wealth) belonging to the top 20% households to the cumulative income (or wealth) belonging to the bottom 20%. In both cases, the higher the indexes, the higher the inequality. In thefollowing wewill makeuse ofthree kinds ofanalysis: first, in section4.1 we will perform a policy experiment simulating a more restrictive monetary policy intervention; second, in section 4.2 we will perform a local sensitivity analysis exercise involving only the policy rate and, finally, in section 4.3 we will conduct a global sensitivity analysis aimed at assessing how monetary policy distributive properties are influenced by the bank’s lending attitude. Before turning to the results, we want to remark how inferring causality in agent-based models may be a delicate issue. Unlike mainstream micro-founded models, in fact, in multi-agent frameworks there is in general no one-to-one relationship between micro and macro variables. Consequently, the lack of clear causal links between emergent macro-phenomena and individual behavioral equations makes the interpretation of the results quite an arduous, if not totally futile, task. Nonetheless, looking at the data we can identify three main macro effects produced by the policy shock: unemployment increases, both average wage and wage dispersion fall (as in general firms paying higher wages are more likely to fail) and capital income increases. We therefore believe that the impact of monetary policy on inequality passes through the composition of these three effects, which in addition seem to have different weight according to the group considered. 4.1 A Policy experiment In this section we show the consequences of a restrictive monetary policy. We will consider two scenarios: in the first one the policy interest rate is fixed and equal to 1% (it=0.01∀t), whereas in the second scenario a policy shock occurs at time 301, when the rate is increased to 2%. For both scenarios we will run 100 independent Monte Carlo simulations, and then we will consider the average across simulations. Figs. 4 and 5 show the evolution of Gini coefficient relative to income and wealth respectively, whereas Fig. 6 shows the SS ratio. Qualitatively, the results are the same. In Panel (a) of Fig. 4 we can see that the Gini index for the overall income distribution decreases after the interest rate is raised to 2% (red line). Hence, the restrictive policy intervention reduces income inequality. This overall effect can be broken down into the partial effects on the three subgroups of households, which show heterogeneous responses to the policy shock. Panel (b) shows in fact that inequality increases for the bottom 50%. This group is made up of unwww.economics-ejournal.org 22 Economics Discussion Paper employed (mostly) and employed workers with little or no capital income. Hence, inequality increases because unemployment increases (so labor income becomes zero for many of the households belonging to this class). Panel (c) reports the Gini for the middle 40%. This group is mainly made up of employed workers with some capital income who are not hit by increasing unemployment. At the same time, the decrease of wages lower the differences in labor income, whereas capital income remains grossly the same. It is no surprise therefore that inequality decreases for this group. The same is true for the top 10% group, constituted by employed workers with large capital incomes. Also in this case, increasing inequality due to increasing capital income is totally offset by falling wages. Similar patterns are displayed by wealth, with inequality increasing for the bottom 50% and decreasing for the wealthier groups. 0 50 100 150 200 250 300 350 400 450 500 Time 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 (a) 0 50 100 150 200 250 300 350 400 450 500 Time 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (b) 0 50 100 150 200 250 300 350 400 450 500 Time 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (c) 0 50 100 150 200 250 300 350 400 450 500 Time 0 0.05 0.1 0.15 0.2 0.25 0.3 (d) Figure 4: Shock 2%, Gini coefficient for income. Panel (a): total; (b): bottom 50%; (c): middle 40%; (d): top 10%. Blue line: no shock; red line: shock at t=301. Averages over 100 simulations. We now repeat the same experiment, with the difference that at time 301 the policy rate is increased to 4%. Again, for both scenarios we will consider the avwww.economics-ejournal.org 23 Economics Discussion Paper 0 50 100 150 200 250 300 350 400 450 500 Time 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 (a) 0 50 100 150 200 250 300 350 400 450 500 Time 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (b) 0 50 100 150 200 250 300 350 400 450 500 Time 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (c) 0 50 100 150 200 250 300 350 400 450 500 Time 0.35 0.4 0.45 0.5 0.55 0.6 0.65 (d) Figure 5: Shock 2%, Gini coefficient for wealth. Panel (a): total; (b): bottom 50%; (c): middle 40%; (d): top 10%. Blue line: no shock; red line: shock at t=301. Averages over 100 simulations. 0 50 100 150 200 250 300 350 400 450 500 Time 0 50 100 150 200 250 300 350 (a) 0 50 100 150 200 250 300 350 400 450 500 Time 0 500 1000 1500 2000 2500 3000 3500 (b) Figure 6: Shock 2%, Ratio SS. Panel (a): wealth; (b): income. Blue line: no shock; red line: shock at t=301. Averages over 100 simulations. www.economics-ejournal.org 24 Economics Discussion Paper Parameter N. of values Range it100 [0.001-0.05] θ 100 [0.2-0.9] τ 100 [0.01-0.2] D14 [1-14] ψ 100 [0.005-0.2] c100 [0.1-0.99] Table 6: Parameter space. Now, in order to discover how the distributive properties of monetary policy are affected by the bank’s behavior, we augment the basic model by adding the interaction terms of the policy rate with θ and τ . Column (2) of Table 7 reports the results, which confirm our previous findings. In addition, we can see that the effect of iton the Gini index is attenuated by a more restrictive bank’s lending attitude (the estimated coefficient on it· θ is negative). This means that changes in monetary policy may have a stronger impact on inequality during normal times than during recessions, when commercial banks are more reluctant to make loans. Notice that, although the two interaction terms are not individually significant (probably because their introduction generates multicollinearity), they turn out to be jointly significant when performing Ftests with the other parameters. Regressors (1) (2) it5.11185 (.4196)6.85907 (1.40744) θ .38738 (.02888).44829 (.061083) τ −.36972 (.10946) −.23129 (.22761) D−.00756 (.00149) −.00749 (.0015) ψ .09282 (.10572).09511 (.1058) c.17731 (.02359).1784 (.02361) it· θ -−2.29057 (2.0702) it· τ -−5.04173 (7.73829) constant .2953 (.02945).24743 (.04714) R20.4898 0.4915 Table 7: Dependent variable: income Gini index. Observations =500. www.economics-ejournal.org 31 Economics Discussion Paper Our analysis can be refined by estimating the complete model with the interaction terms also for the usual three sub-groups of households: bottom 50%, middle 40% and top 10%. Table 8 shows that rising interest rates increase income inequality for the bottom class and, in particular, for the middle class, whereas the effect is null or even negative for the top class. These results are again consistent with our previous findings. Moreover, we can notice the asymmetric effect of the bank’s lending attitude: a more restrictive monetary policy increases the top class income inequality more when the bank’s willingness to lend is lower (the estimated coefficient on it· θ is positive), while the opposite is true for the other two classes. In conclusion, a more restrictive monetary policy appears to increase overall income inequality, but this effect is different according to the sub-group considered. Moreover, the distributional properties of monetary policy seem to be affected by the bank’s lending attitude. Regressors (1) (2) (3) it3.06367 (1.08758)11.7852 (2.2985)−.94368 (.88026) θ .22586 (.0472).75475 (.09975).13804 (.0382) τ −.2310 (.17588).02182 (.37172).08023 (.14236) D.0025 (.00116)−.0087 (.00245).00336 (.00094) ψ .27582 (.08175).08684 (.17278)−.29696 (.06617) c.26373 (.01825).32139 (.03856).18745 (.01477) it· θ −1.25337 (1.59972) −1.93154 (3.38087)6.25041 (1.29478) it· τ .020356 (5.97967)−16.52367 (12.63749) −7.55663 (4.8398) constant .4472 (.03643)−.35583 (.07699) −.08137 (.02948) R20.4494 0.5259 0.5480 Table 8: Dependent variable: income Gini index. Column (1): bottom 50%; column (2): middle 40%; column (3): top 10%. Observations =500. 5 Conclusive remarks Recent empirical studies have pointed out that monetary policy may significantly affect income and wealth inequality through several channels. This influence is www.economics-ejournal.org 32 Economics Discussion Paper exerted not only because monetary policy can affect different income sources in different ways, but also because households are heterogeneous with regards to the relative size of their income sources. Despite its relevance, this subject has gone relatively ignored by economic theory, mainly because the use of representative agents makes mainstream models inadequate to assess distributions and inequality (with the recent exception of the HANK models). To properly investigate the distributive properties of monetary policy, therefore, in thispaper we resortto agent-basedtechniques inwhich agents’ heterogeneity plays a fundamental role. The theoretical framework we set up is an agent-based macroeconomic model where firms, households and one bank interact on the basis of limited information and adaptive rules-of-thumb. Simulations show that the model is able to replicate fairly well a number of stylized facts, specially those relative to the business cycle. Subsequently, we employ the model as a computational laboratory through which we can simulate changes in monetary policy and assess their influence on income and wealth inequality. Our analysis is three-fold. As a preliminary step we simulate a monetary policy shock that consists in a rise of the policy interest rate occurring in the course of a single simulation. The second step is to perform Monte Carlo experiments involving the policy rate only. Finally, we carry out a global sensitivity analysis exercise in order to control for other parameters, in particular to evaluate possible interactions between the monetary policy and the credit policy adopted by the banking system. We point out that the last kind of analysis is implemented through a novel methodology which greatly reduces the computational burden of simulations. Consistently with part of the empirical literature, from all the three experiments the robust result emerges that a more restrictive monetary policy increases economic inequality. This is an interesting result in itself, but also because puts into question one of the central tenets of contemporaneous monetary economics, i.e. the necessity for central banks to be independent from political influences. Conversely, our finding suggests that the social responsibility of central banks may go beyond their role of keeping price stability, and could constitute an argument in favor of a more democratic control of monetary policy actions. Moreover, we find that the effect of monetary policy on inequality seems to be smaller when the bank’s willingness to lend is lower. This entails that the ability of monetary policy to affect inequality may be reduced during recessions, when “credit crunches” are more likely to occur. As a consequence, fears of possible distortionary effects caused by expansionary monetary policy interventions may be unmotivated if the economy is in recession. Finally, our analysis highlights that the influence of monetary policy on inequality is asymmetric, as different groups of households are hit by policy shocks in different ways. In particular, a restrictive monetary policy appears to increase www.economics-ejournal.org 33 Economics Discussion Paper inequality for the lower and middle-income classes, but not for the top class. This additional insight hints that it could be useful for empirical studies to focus not only on the whole population of households but also on sub-groups. Although rich enough to provide non-trivial insights, we concede that our model suffers from some important limitations such as the absence of households’ debts and more diversified portfolio investment opportunities. However, the introduction of these features is left for future works. References [1] Albanesi, S., (2007). Inflation and inequality. Journal of Monetary Economics, 54(4), 1088-1114. http://www.sciencedirect.com/science/article/pii/S0304-3932(06)00212-1 [2] Alesina, A., Summers, L. H., (1993). Central Bank Independence and Macroeconomic Performance: Some Comparative Evidence. Journal of Money, Credit and Banking, 25, 151-162. http://www.jstor.org/stable/2077833 [3] Areosa, W. D., Areosa, M. B. M., (2016). The inequality channel of monetary transmission. Journal of Macroeconomics, 48, 214-230. http://dx.doi.org/10.1016/j.jmacro.2016.03.004 [4] Assenza, T., Delli Gatti, D., Grazzini, J., (2015). Emergent dynamics of a macroeconomic agent based model with capital and credit. Journal of Economic Dynamics and Control, 50, 5-28. https://doi.org/10.1016/j.jedc.2014.07.001 [5] Bank of England, (2012). The Distributional Effects of Asset Purchases. Quarterly Bulletin, 3, 254-266. [6] Bargigli, L., Riccetti, L., Russo, A., Gallegati, M., (2018). Network calibration and metamodeling of a financial accelerator agent based model. Journal of Economic Interaction and Coordination. https://doi.org/10.1007/s11403-018-0217-8 [7] Bernanke, B., Gertler, M., (1989). Financial fragility and economic performance. Quarterly Journal of Economics, 105, 87-114. http://www.jstor.org/stable/2937820 [8] Bernanke, B., Gertler, M., (1990). Agency costs, net worth, and business fluctuations. American Economic Review, 79, 14-31. http://www.jstor.org/stable/1804770 www.economics-ejournal.org 34 Economics Discussion Paper [9] Bernanke, B., Gertler, M., (1995). Inside the black box: the credit channel of monetary policy transmission. Journal of Economic Perspectives, 9(4), 27-48. https://www.aeaweb.org/articles?id=10.1257/jep.9.4.27 [10] Bewely, T., (1999). Why wages donât fall during recessions. Cambridge, Harvard University Press. [11] Bhaskar, V., Machin, S., Reid, G., (1993). Price and quantity adjustment over the business cycle: evidence from survey data. Oxford Economic Paper 45, 257-268. http://www.jstor.org/stable/2663638 [12] Blanchard, O. and Diamond, P., (1990). The cyclical behavior of the gross flows of U.S. workers. Brookings Papers on Economic Activity, 2, 85-143. http://www.jstor.org/stable/2534505 [13] Caiani, A., Godin, A., Caversazi, E., Gallegati, M., Kinsella, S., Stiglitz, J. E., (2016). Agent based-stock flow consistent macroeconomics: towards a benchmark model. Journal of Economic Dynamics and Control, 69, 375-408. https://www.sciencedirect.com/science/article/pii/S0165188915301020 [14] Campbell, C., Kamlani, K., (1997). The reasons for wage rigidity: evidence from a survey of firms. Quarterly Journal of Economics, 112, 759â789. http://www.jstor.org/stable/2951255 [15] Chen, S., Desiderio, S., (2018). What moves the Beveridge curve and the Phillips curve: an agent-based analysis. Economics: The Open-Access, OpenAssessment E-Journal, 12 (2018-2), 1-30. http://www.economics-ejournal.org/economics/journalarticles/2018-2 [16] Coibion, O., Gorodnichenko, Y., Kueng, L., Silvia, J., (2017). Innocent Bystanders? Monetary policy and inequality. Journal of Monetary Economics, 88, 70-89. http://dx.doi.org/10.1016/j.jmoneco.2017.05.005 [17] Daly, M. C., Hobijn, B., Ni, T., (2013). The path of wage growth and unemployment. Federal Reserve Bank of San Francisco Economic Letter, July 15. https://www.frbsf.org/economic-research/publications/economicletter/2013/july/wages-unemployment-rate/ [18] Davis, S., Haltiwanger, J., Schuh, S., (1996). Job creation and destruction. MIT Press, Cambridge, MA. www.economics-ejournal.org 35 Economics Discussion Paper [19] Davtyan, K., (2017). The distributive effect of monetary policy: The top one percent makes the difference. Economic Modelling, 65, 106-118. http://dx.doi.org/10.1016/j.econmod.2017.05.011 [20] Delli Gatti, D., Desiderio, S., (2015). Monetary policy experiments in an agent-based model with financial frictions. Journal of Economic Interaction and Coordination, 10(2), 265-286. https://link.springer.com/article/10.1007/s11403-014-0123-7 [21] Delli Gatti, D., Desiderio, S., Gaffeo, E., Gallegati, M., Cirillo, P., (2011). Macroeconomics from the bottom-up. Springer, Milan. [22] Desiderio, S., Chen, S., (2016). Why the rich become richer: insights from an agent-based model. International Journal of Computational Economics and Econometrics, 6, 258-275. http://www.inderscience.com/link.php?id=77249 [23] Doepke, M., Schneider, M., (2006). Inflation and the Redistribution of Nominal Wealth. Journal of Political Economy, 114(6), 1,069-1,097. http://dx.doi.org/10.1086/508379 [24] Dosi, G., Fagiolo, G., Napoletano, M., Roventini, A., (2013). Income distribution, credit and fiscal policies in an agent-based Keynesian model. Journal of Economic Dynamics and Control, 37, 1598â1625. https://doi.org/10.1016/j.jedc.2012.11.008 [25] Dosi, G., Fagiolo, G., Napoletano, M., Roventini, A., Treibich, T., (2015). Fiscal and monetary policies in complex evolving economies. Journal of Economic Dynamics and Control, 52, 166-189. http://dx.doi.org/10.1016/j.jedc.2014.11.014 [26] Dosi, G., Pereira, M. C., Virgillito, M. E., (2018). On the robustness of the fat-tailed distribution of firm growth rates: a global sensitivity analysis. Journal of Economic Interaction and Coordination, 13, 173-193. https://doi.org/10.1007/s11403-017-0193-4 [27] Erosa, A., Ventura, G., (2002). On Inflation as a Regressive Consumption Tax. Journal of Monetary Economics, 49(4), 761-795. http://www.sciencedirect.com/science/article/pii/S0304-3932(02)00115-0 [28] Gornemann, N., Kuester, K., Nakajima, M., (2012). Monetary Policy with Heterogeneous Agents. Federal Reserve Bank of Philadelphia Working Papers, 12(21), 1-48. www.economics-ejournal.org 36 Economics Discussion Paper http://www.philadelphiafed.org/research-and-data/publications/workingpapers/2012/wp12-21.pdf [29] Gornemann, N., Kuester, K., Nakajima, M., (2016). Doves for the Rich, Hawks for the Poor? Distributional Consequences of Monetary Policy. International Finance Discussion Papers 1167, Board of Governors of the Federal Reserve System (U.S.). http://www.federalreserve.gov/econresdata/ifdp/2016/files/ifdp1167.pdf [30] Kaplan, G., Moll, B., Violante, G. L., (2016). Monetary Policy According to HANK. Working Paper 1602, Council on Economic Policies. https://www.cepweb.org/wp-content/uploads/CEP-WP-2016-2-MonetaryPolicy-According-to-HANK.pdf [31] Kawasaki, S., McMillan, J., Zimmerman, K., (1982). Disequilibrium dynamics: an empirical study. American Economic Review, 72, 992-1004. http://www.jstor.org/stable/1812018 [32] Myers, S.C., Majluf, N.S., (1984). Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics, 13, 87-224. https://doi.org/10.1016/0304-405X(84)90023-0 [33] Mumtaz, H., Theophilopoulou, A., (2017). The impact of monetary policy on inequality in the UK. An empirical analysis. European Economic Review, 98, 410-423. http://dx.doi.org/10.1016/j.euroecorev.2017.07.008 [34] Nakajima, M., (2015). The Redistributive Consequences of Monetary Policy. Federal Reserve Bank of Philadelphia Business Review (Second Quarter 2015). https://www.philadelphiafed.org/-/media/research-anddata/publications/business-review/2015/q2/brQ215_the_redistributive _consequences_of_monetary_policy.pdf [35] Riccetti, L., Russo, A., Gallegati, M., (2015). An agent-based decentralized matching macroeconomic model. Journal of Economic Interaction and Coordination, 10(2), 305-332. https://link.springer.com/article/10.1007/s11403-014-0130-8 [36] Riccetti, L., Russo, A., Gallegati, M., (2016). Financialisation and crisis in an agent based macroeconomic model. Economic Modelling, 52, 162â172. https://doi.org/10.1016/j.econmod.2014.11.028 www.economics-ejournal.org 37 Economics Discussion Paper [37] Romer, C. D., Romer, D., (1999). Monetary policy and the well-being of the poor. Economic Review, Federal Reserve Bank of Kansas City, issue QI, 21-49. http://www.kansascityfed.org/publicat/econrev/PDF/1q99romr.pdf [38] Russo, A., Riccetti, L., Gallegati, M., (2016). Increasing inequality, consumer credit and financial fragility in an agent based macroeconomic model. Journal of Evolutionary Economics, 26(1), 25-47. http://link.springer.com/10.1007/s00191-015-0410-z [39] Sterk, V., Ravn, M., (2017). Macroeconomic Fluctuations with HANK & SAM: an Analytical Approach. 2017 Meeting Papers 1067, Society for Economic Dynamics. https://economicdynamics.org/meetpapers/2017/paper_1067.pdf www.economics-ejournal.org 38 Please note: You are most sincerely encouraged to participate in the open assessment of this discussion paper. You can do so by either recommending the paper or by posting your comments. Please go to: http://www.economics-ejournal.org/economics/discussionpapers/2018-38 The Editor © Author(s) 2018. Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0).