Economic Modelling 126 (2023) 106380 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.journals.elsevier.com/economic-modelling Unconventional monetary policy and economic inequality✩ Karen Davtyan Department of Applied Economics, Autonomous University of Barcelona, Spain ARTICLE INFO ABSTRACT JEL classification: This paper evaluates the distributional effects of US unconventional monetary policy (UMP) implemented as C32 an additional measure to confront recessions. In line with the literature, the results show that the UMP reduces D31 the unemployment rate, moderately increases prices, and stabilizes financial conditions. Yet, it also increases E52 income and wealth inequality, with a stronger effect on the latter. Central bank balance sheet policies tend to Keywords: be the key measures that shape its general effects. The UMP raises capital income more than labor earnings, Unconventional monetary policy which leads to the relatively higher increase in income at the upper part of the distribution and as a result to Identification the growth of income inequality. Also, the UMP increases stock prices more than house prices, which results in Inequality the relatively larger growth of wealth at the top end of the distribution, leading to the rise of wealth inequality. These results indicate the need for complementary fiscal policy measures. 1. Introduction about economic inequality (Kuhn et al., 2020), it is also perceived as a concern for the transmission and effectiveness of monetary policy In the period preceding the global financial crisis, a key leading (Voinea et al., 2018). In any case, as with any remedy, it is important practice in the implementation of conventional monetary policy (CMP) to know all its effects. The objective of this paper is to provide evidence was to set the level of the policy interest rate. In response to the on the distributional impact of the UMP. global financial crisis, many central banks substantially lowered their The contribution of this paper is comprehensive and consistent policy rates up to the zero lower bound (Rossi, 2021). To improve evidence on the impact of the UMP on income and wealth inequality deteriorated economic conditions and to ease financial conditions, they in the case of the US. The consistent framework allows comparing the also resorted to unconventional monetary policy (UMP) measures such effects of the UMP on income and wealth inequality. The economic as forward guidance and large scale asset purchases (LSAPs, known also mechanism of these effects is considered examining the distributional as quantitative easing or balance sheet policy). Monetary authorities channels of monetary policy. This paper also uncovers the type of the have used forward guidance to communicate the implementation of UMP that drives the general impact of the UMP. monetary policy, including the likely future path of the policy rate. At The (general) UMP shock is identified with zero and sign restrictions the same time, LSAPs have been implemented with the announcement in line with the identification approach by Arias et al. (2019) for the of the amounts of asset purchases and the time horizon for transactions case of the CMP. An alternative identification of the UMP shock with (Swanson, 2021). Thus, in comparison to the CMP, the UMP is more instrumental variables (Eberly et al., 2020) provides similar results. The multidimensional and it can directly affect asset prices (Eberly et al., LSAP shock is also identified to disentangle it from the general shock of 2020). the UMP. This paper computes proxy inequality measures, which are at Given the broader spectrum of the UMP measures, they have widely the same frequency as other variables. To complement the analysis with been utilized to confront recessions. The records of the implementation standard inequality measures, this paper applies a mixed frequency of the UMP measures have been used to evaluate their macroeco- framework (Foroni and Marcellino, 2016) given that the inequality data nomic and financial effects while their distributional impact has not are available at the lower frequency. systematically been explored yet. The examination of the distributional The results indicate that the UMP fosters real economic activity, impact is especially important given the nature of the UMP that can moderately increases prices, and eases financial conditions. At the same directly affect asset prices. Moreover, in addition to general concerns ✩ This paper was mainly written during my previous work in the Department of Statistics at the University Carlos III of Madrid. I gratefully acknowledge helpful comments and suggestions from Stefania Albanesi, Jonas Arias, Christiane Baumeister, Luca Benati, Florin Bilbiie, Matthias Doepke, Josep Lluís Carrion-i-Silvestre, Enrique López-Bazo, Gernot Müller, Thomas Piketty, Raul Ramos, Barbara Rossi, Moritz Schularick, and the editor Sushanta Mallick and three anonymous referees. I also thank Boris Hofmann and Jonathan Wright for sharing their data. All errors are my own. E-mail address: karen.davtyan@uab.cat. https://doi.org/10.1016/j.econmod.2023.106380 Received 8 December 2022; Received in revised form 21 May 2023; Accepted 22 May 2023 Available online 28 May 2023 0264-9993/© 2023 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). K. Davtyan Economic Modelling 126 (2023) 106380 time, it raises economic inequality. The estimated general effects of the Gertler and Karadi, 2015; Rogers et al., 2018). A recent comprehensive UMP are mainly driven by LSAPs. The UMP leads to the relatively larger review of the identifications methods and the economic effects of the increase in capital income than in labor earnings. This impact of the UMP can be found in the article by Rossi (2021). The current paper UMP results in the growth of income inequality because lower and mid- provides complementary evidence on the economic effects of the UMP dle earners mainly receive labor earnings while higher earners mostly using those two identification approaches, which give similar results. gain capital income. The application of standard inequality measures The rest of the paper is organized as follows. Section 2 discusses the shows that the monetary policy expansion leads to the relatively higher distribution channels of monetary policy. Section 3 presents the empir- increase in income at the upper part of the distribution. Moreover, it ical approach while Section 4 describes the data. Section 5 provides the reduces the income shares of lower and middle earners while it raises results and Section 6 concludes. the income share of higher earners. This paper finds that the UMP increases stock prices more than 2. Distribution channels of monetary policy house prices. This impact leads to the growth of wealth inequality given that the groups in the lower and the middle parts of the wealth The main objective of UMP measures is to lower long term in- distribution mostly own non-financial assets such as houses while the terest rates to support private borrowing of households and busi- portfolio of the group at the top of the wealth distribution is mainly nesses, thereby fostering aggregate demand and real economic activity composed of financial assets such as stocks. Using standard inequality (Baumeister and Benati, 2013). This can be beneficial for households measures, this paper finds that the UMP lowers the bottom and the who mainly rely on labor income, which might be adversely affected middle wealth shares whereas it raises the top wealth share. The during the crisis. Labor earnings are the primary source of income for impact of UMP measures on wealth inequality is generally stronger. In the most of households, and these earnings are mostly exposed to reces- particular, the variance decomposition analysis reveals that the UMP sions (Coibion et al., 2017). Besides, the UMP measures help to recover accounts for the higher variation in wealth inequality than in income prices for houses, which are the main class of assets in the portfolio inequality. of low and middle income households. At the same time, LSAPs tend The topic on the distributional impact of the UMP has lately gained to change the relative supply of bonds and other assets, consequently growing interest but the literature on this topic is still scarce, given that affecting their prices and the flow of funds in the economy. This could these policy measures have relatively recently been implemented. On benefit high income households, who mostly own these bonds and the other hand, there is already some literature on the distributional assets.1 effects of the CMP. Particularly, in this area of research, some of the Thus, the implementation of the UMP could facilitate to overcome first studies are the influential articles by Doepke and Schneider (2006), the financial crisis. At the same time, it might also affect the income Albanesi (2007), and Coibion et al. (2017). and the wealth distribution. On the one hand, it could restore the The evidence on the distributional effects of monetary policy is labor earnings and the wealth of low income households. On the other mixed. Coibion et al. (2017) provide evidence for the US that contrac- hand, the UMP might increase the capital income and the wealth of tionary CMP increases economic inequality. Dolado et al. (2021) show high income households. As a result, monetary policy might affect that expansionary monetary policy raises earnings inequality between income and wealth inequality but its impact is ambiguous because of low and high skilled workers in the US. Based on survey data for the opposite effects. 2010, Adam and Tzamourani (2016) provide evidence that the increase The overall distributional effect of monetary policy depends on in equity prices profits the richest households while the growth of different channels through which monetary policy can have an impact house prices benefits the median household. Guerello (2018) shows on income and wealth inequality. Based on the distribution channels that expansionary CMP reduces income inequality while the UMP specified by Coibion et al. (2017) and Koedijk et al. (2018), this paper raises it in the euro area. For the UK, Mumtaz and Theophilopoulou categorizes the following income and wealth distribution channels of (2020) provide evidence that expansionary monetary policy raises monetary policy: wealth inequality and accounts for its substantial variation. Income distribution channels The most closely related papers are the works by Lenza and Slacalek (2018), Saiki and Frost (2020), and Evgenidis and Fasianos (2021) • Income composition: It is related to the heterogeneity in the pri- who also focus their analyses on the distributional effects of the UMP. mary sources of income (labor earnings and capital income) Lenza and Slacalek (2018) provide evidence for the euro area that across households. Low income households mostly get labor in- quantitative easing decreases income inequality and has a small effect come while high income households tend to receive the higher on wealth inequality. They first estimate the aggregate effects of the proportion of capital income. The income distribution changes UMP and then distribute them on the survey data for 2014. This when monetary policy affects one component of income more paper complements their work by estimating the dynamic responses of than the other. If expansionary monetary policy boosts capital inequality measures to the UMP. returns more than labor earnings, income inequality increases. Saiki and Frost (2020) show that the UMP raises income inequality • Labor income (earnings) heterogeneity: It represents the tendency in the case of Japan. They focus on the features of Japanese economy that the labor income of the poorest population is primarily and the relatively longer history of the implementation of the UMP in exposed to business cycle fluctuations. In Table 1, this paper Japan. The current paper provides additional evidence and estimates provides the data on the composition of income in the US in the impact of the UMP on wealth inequality too. 2007 (just before the global financial crisis). It can be observed In the case of Great Britain, Evgenidis and Fasianos (2021) find that that labor earnings are the primary source of income for the poor the UMP widens wealth inequality. Their main identification approach while capital income is gained mostly by the rich. Low income of the UMP shock is through the recursive scheme. The current paper households usually gain from the increase in labor market activ- presents further evidence by differently identifying the UMP shock. ity, mostly through the reduction in unemployment. Therefore, Besides, this paper evaluates the effects of the UMP on both income and expansionary monetary policy is likely to benefit low income wealth inequality to relate these effects within a consistent framework. households more and reduce income inequality. The current paper is also related to the large literature on the evaluation of the economic effects of the UMP with the identifcation approaches based on sign restrictions (among others, Arias et al., 2019; 1 The ownership of bonds and assets across income quantiles can be inferred Baumeister and Benati, 2013; Boeckx et al., 2017; Gambacorta et al., from Table 1 while the more explicit distribution of household portfolios across 2014) and external instruments (among others, Eberly et al., 2020; wealth groups can be found in the work by Kuhn et al. (2020). 2 K. Davtyan Economic Modelling 126 (2023) 106380 Table 1 of models are commonly used for the evaluation of the effects of Income composition. monetary policy in the literature (among others, Arias et al., 2019; Income Quantiles Top 1% Baumeister and Benati, 2013; Boeckx et al., 2017; Gertler and Karadi, 1st 2nd 3rd 4th 5th 2015). Besides, they have a flexible structure, which allows using a Labor 35.6 60.8 72.6 77.8 60.5 39.0 mixed frequency framework and different identification approaches Capital −1.9 1.8 1.9 2.9 15.5 30.4 of a monetary policy shock. Moreover, the use of a VAR model is Business 0.7 4.6 5.5 7.6 19.0 28.3 particularly suited for the empirical analysis given that the considered Transfers 59.9 30.3 18.4 10.5 4.3 2.1 Other 5.7 2.5 1.6 1.2 0.7 0.2 variables can affect each other and it is important to treat them as endogenous, which a VAR model allows. The current section describes Source: 2007 Survey of Consumer Finances (Díaz-Giménez et al., 2011). the specification and the estimation of the VAR model, including a mixed frequency approach, and the identification of the UMP shock. • Capital income heterogeneity: The returns of various assets are 3.1. Specification differently affected by monetary policy, and the portfolio compo- sition of households differs along the distribution. So, the impact In line with Arias et al. (2019), the structural VAR model of order of expansionary monetary policy on inequality depends on the 𝑝, is formulated as follows: combination of heterogeneous asset returns and portfolios. 𝑌𝑡′ 𝖠 = 𝐴0 + 𝑌𝑡−1 ′ ′ 𝐴1 + ⋯ + 𝑌𝑡−𝑝 𝐴𝑝 + 𝜀′𝑡 (1) Wealth distribution channels where 𝑌𝑡 is a (6 × 1) vector of endogenous variables, 𝐴0 is a (1 × 6) • Portfolio channel: The asset composition of households is differ- vector of intercepts, 𝖠 and 𝐴𝑗𝑠 (for 𝑗 = 1, … , 𝑝) are (6 × 6) matrices of ent across the distribution. The wealth of households generally parameters, and 𝜀𝑡 is a (6 × 1) vector of structural shocks. It is assumed consists of capital assets and housing, and the net wealth are that conditional on 𝑌0 , … , 𝑌1−𝑝 , the vector 𝜀𝑡 ∼ 𝑁(0, 𝐼6 ). The variables determined by deducting debts from that amount. The portfolio are included in levels in the empirical analysis. The implementation of of low income and middle class households mainly consists of the analysis in levels allows for implicit cointegration relations among nonfinancial assets such as houses while wealthy households them2 (Sims et al., 1990). tend to have capital assets such as stocks. So, monetary policy The reduced form representation of the VAR model is the following: affects household wealth through its impact on the prices of these different assets. Given the heterogeneous structure of portfolios, 𝑌𝑡′ = 𝐵0 + 𝑌𝑡−1 ′ ′ 𝐵1 + ⋯ + 𝑌𝑡−𝑝 𝐵𝑝 + 𝑣′𝑡 (2) monetary policy have different effects on household wealth. Thus, where 𝐵𝑗 = 𝐴𝑗 𝖠−1 𝑣′𝑡 (for 𝑗 = 0, … , 𝑝), = 𝜀′𝑡 𝖠−1 and the reduced form the impact of monetary policy on wealth inequality depends on ′ error covariance matrix is E(𝑣𝑡 𝑣′𝑡 ) = 𝛴𝑣 = 𝖠−1 𝖠−1 . its effects on asset prices and the balance sheet structure of The vector of endogenous variables 𝑌𝑡 consists of a measure of households. real economic activity, prices, a financial indicator, an economic in- • Savings redistribution channel: Households keep their savings dif- equality measure,3 and the CMP and the UMP instruments: 𝑌𝑡 = ferently. Low income households tend to hold relatively more (𝑢𝑡 , 𝑝𝑡 , 𝑚𝑡 , 𝑧𝑡 , 𝑖𝑡 , 𝑠𝑡 )′ . In particular, the baseline specification includes currency while high income households mostly have deposits and the unemployment rate, the PCE deflator, the excess bond premium, the given loans. Consequently, both cash holders and lenders are ex- posed to inflation, which reduces the real value of currency, and income inequality ratio, the federal funds rate, and the yield spread that deposits and debt that are fixed in nominal terms. The impact of is defined as a spread between the 10-year and the 3-month treasury expansionary monetary policy on wealth inequality hinges on its constant maturity rates. proportional effects on household savings along the distribution. It is common in the literature (e.g., Eberly et al., 2020; Gertler and That is, it can either increase or reduce inequality depending on Karadi, 2015) to include the variables for a real economic activity, household savings. prices, and financial market frictions in the specification of VAR models to control for economic conditions when the effects of monetary policy Monetary policy could have different distributional effects through are evaluated. The consideration of these variables is also important for the channels. They can operate with different intensity with the CMP explaining inequality dynamics. The effects of real economic activity and the UMP, which include different types of tools. That is, the CMP and prices on inequality are discussed within the description of the and the UMP could have disproportionate effects via the channels. distributional channels of monetary policy in Section 2. The impact of Moreover, the magnitude of their impact through the channels might financial conditions on inequality is documented in the literature (e.g., be different too, and consequently, they can have different overall Agnello et al., 2012; Baiardi and Morana, 2018). distributional effects (Guerello, 2018). Both indicators of the CMP and the UMP are included in the This paper aims to evaluate the distributional effects of the UMP via specification of the model in order to disentangle the UMP shock from the income composition, the earnings heterogeneity, and the portfolio the CMP shock, as discussed in Section 3.3. As a general indicator of the channels. First of all, the current paper controls for real economic UMP, the yield spread is considered because the objective of conducted activity, prices, and financial conditions in the considered model for the UMP was to lower the long term interest rate, that is the spread the analysis. Since the distributional effects of monetary policy through between the long term and the short term interest rates, given that the the channels generally depend on relative components, this paper short term interest rate was mostly at the zero lower bound during the mainly uses relative measures to capture the channels. In particular, implementation of UMP measures. The yield spread is considered as to examine the earnings heterogeneity and the income composition the UMP indicator also in the literature (among others, Baumeister and channels, the current paper includes the unemployment rate and the Benati, 2013; Eberly et al., 2020). ratio of capital income to labor earnings in the model. To explore the The variables of the model specification also capture the dynamics portfolio channel, this paper incorporates the ratio of stock prices to of inequality and the distributional effects of the UMP. The specification house prices in the model. 3. Empirical approach 2 In the case of the CMP, an explicit cointegration analysis of the variables can be found in the paper by Davtyan (2017). This paper considers a structural vector autoregression (VAR) model 3 As an economic inequality measure, either income or wealth inequality for the analysis of the distributional impact of the UMP. These types measure is considered. 3 K. Davtyan Economic Modelling 126 (2023) 106380 includes the key variables discussed in Section 2 on the distributional where channels of monetary policy. For instance, as a measure of real eco- ⎡𝜔(𝐿) 𝐼 0 ⎤ 𝐻(𝐿) = ⎢ (1×1) nomic activity, the unemployment rate is considered because it is (1×5)⎥ closely related to labor income (the earnings heterogeneity channel). (6×6) ⎢ 0 𝐼 ⎥ ⎣ (5×1) (5×5)⎦ The direct measure of labor income is also considered. It is included This model in Eqs. (3) and (4) is cast in a state space form. Given in the specification as a denominator of the income inequality ratio. 𝑝 ≤ 𝑙 + 1, the state space representation is the following: This ratio measures the relation between capital income and labor earnings and serves as a proxy of income inequality as well as it allows 𝖷𝑡 = 𝐶𝖷𝑡−1 + 𝐷𝜉𝑡 (5) examining the income composition channel. Analogously, the wealth 𝖸𝑡 = 𝐸𝖷𝑡 (6) inequality ratio is also considered to measure the relation between stock and house prices (the portfolio channel). That is, the objective where 𝜉𝑡 ∼ 𝑁(0, 𝐼6 ), the state vector is specified as is to capture the relative dynamics between these variables as proxy inequality measures. 𝖷𝑡 = (𝖸∗𝑡 , ⋯ , 𝖸∗𝑡−𝑙 )′ (6(𝑙+1)×1) and the coefficient matrices of the state space form are defined as 3.2. Estimation follows: [ ] The data for the macroeconomic variables are available at the 𝛷1 ⋯ 𝛷𝑝 06×6(𝑙+1−𝑝) 𝐶 = monthly frequency. However, the data for the inequality measure are 6(𝑙+1)×6(𝑙+1) 𝐼6𝑙 06𝑙×6 [ ] mainly available only at the annual frequency. Whereas the inequality 1∕2 𝛴𝜂 measures that are computed in this paper are at the monthly fre- 𝐷 = 6(𝑙+1)×6 06𝑙×6 quency, the standard measures of income and wealth inequality are [ ] 𝐸 = 𝐻0 ⋯ 𝐻𝑙 only at the annual frequency. Therefore, in order not to aggregate the 6×6(𝑙+1) monthly macroeconomic variables or interpolate the annual inequality Since 𝖸𝑡 is observed only every twelfth month, the state space model is measures, this paper adopts a mixed frequency approach. estimated by replacing the missing observations with zeros and using The current paper applies the mixed frequency approach for the the Kalman filter, in line with Foroni and Marcellino (2016), and structural VAR model following Foroni and Marcellino (2016). This Mariano and Murasawa (2010). Therefore, the first stage of this mixed mixed frequency approach can straightforwardly be combined with the frequency approach involves the estimation of monthly inequality se- available methods for the identification of a monetary policy shock. ries with the Kalman filter. In the next stage, the estimated inequality The application of the mixed frequency approach allows incorporating series is included in the monthly VAR model, which is used to iden- annual inequality data with monthly macroeconomic variables within tify a monetary policy shock and assess its effects. The subsequent the same VAR model. This paper treats the lower frequency variable, consideration of the monthly VAR model provides a general basis for an inequality measure, as a high frequency variable with missing comparison with the results obtained using the inequality measures that observations, which are subsequently estimated with the Kalman filter. are observed at the monthly frequency. In line with Foroni and Marcellino (2016), and Mariano and Murasawa The estimation of the monthly VAR model is implemented by (2010), this procedure is implemented by presenting the VAR model the Bayesian approach, following Arias et al. (2019). In particular, in a state space form and estimating it with the maximum likelihood a uniform-normal-inverse-Wishart distribution is considered for the method. priors over the orthogonal reduced-form parametrization. The prior The high frequency variables 𝑢𝑡 , 𝑝𝑡 , 𝑚𝑡 , 𝑖𝑡 , and 𝑠𝑡 are observable density parametrization is also in line with the approach by Arias et al. every period. Since the highest frequency of the variables is monthly, (2019). It leads to the prior densities that are equivalent to the ones the low frequency series 𝑧𝑡 is observable only once in every twelfth considered by Uhlig (2005). period. The unobservable high frequency series is denoted by 𝑧∗𝑡 . It Given that the estimation sample is relatively short, the objective is an underlying series for 𝑧𝑡 so that, for each 𝑡, 𝑧𝑡 = 𝜔(𝐿) 𝑧∗𝑡 where is to have a parsimonious VAR model. Based on information criteria, 𝜔(𝐿) is a lag polynomial of order 𝑙: 𝜔(𝐿) = 𝜔0 + 𝜔1 𝐿 + ⋯ + 𝜔𝑙 𝐿𝑙 . In the lag order of two is selected for the VAR model. At the same time, the current case of the mixed frequency combination of monthly and robustness checks with higher lag orders are also implemented. annual data, 𝑙 is thirteen. Thus, the lag polynomial 𝜔(𝐿), which can be considered as a one-sided filter, provides an aggregation scheme from 3.3. Identification the high frequency to the low frequency. Then, the aggregated series 𝜔(𝐿) 𝑧∗𝑡 is skip-sampled so that the variable is observed only every The identification of the UMP shock is implemented in line with 𝑛 period (twelfth month). Following Foroni and Marcellino (2016), the approach by Arias et al. (2019) for the case of the CMP. This paper for simplicity, the case is considered when the observed value of the combines zero and sign restrictions on the parameters4 of the structural low frequency variable corresponds to the 𝑧∗𝑡 value for every 𝑛 period monetary policy rule (the last column of 𝖠) and on impulse response (twelfth month). functions (the last row of 𝖠−1 ) on impact. Sign restrictions are imposed For further derivations, the following (6 × 1) vectors are specified: on impact because there is no independent identification information 𝖸𝑡 = (𝑧𝑡 , 𝑢𝑡 , 𝑝𝑡 , 𝑚𝑡 , 𝑖𝑡 , 𝑠𝑡 )′ and 𝖸∗𝑡 = (𝑧∗𝑡 , 𝑢𝑡 , 𝑝𝑡 , 𝑚𝑡 , 𝑖𝑡 , 𝑠𝑡 )′ , at longer horizons as shown by Baumeister and Hamilton (2015). where the low frequency variable 𝑧𝑡 and the underlying unobservable Since the UMP is generally regarded as an expansionary policy, this high frequency variable 𝑧∗𝑡 is univariate while the subvector of the paper identifies an expansionary monetary policy shock. Consequently, high frequency variables (𝑢𝑡 , 𝑝𝑡 , 𝑚𝑡 , 𝑖𝑡 , 𝑠𝑡 )′ is five-variate. Given these this paper considers the normalization that the yield spread has a notations, the following VAR model is formulated: negative sign when, as a monetary policy instrument, it is on the left side of the policy equation. Analogously, this paper normalizes the 𝛷(𝐿) 𝖸∗𝑡 = 𝜂𝑡 (3) response of the yield spread to be negative on impact in response to where 𝜂𝑡 ∼ 𝑁(0, 𝛴𝜂 ) while 𝛷(𝐿) is a lag polynomial of order 𝑝, which an expansionary monetary policy shock. Therefore, all sign restrictions is specified to be one. At the same time, the following relation between 𝖸𝑡 and 𝖸∗𝑡 must hold: 4 The parameters are normalized with respect to the monetary policy 𝖸𝑡 = 𝐻(𝐿) 𝖸∗𝑡 (4) indicator. 4 K. Davtyan Economic Modelling 126 (2023) 106380 Table 2 For the slope shock, an external instrument is considered from Zero and sign restrictions for the identification of an expansionary monetary policy Eberly et al. (2020). It is the series of changes in the 10-year Treasury shock. yield measured within two-hour windows following monetary policy Restrictions on the monetary policy rule announcements. The estimation results show that the instrument is 𝑢𝑡 𝑝𝑡 𝑚𝑡 𝑧𝑡 𝑖𝑡 𝑠𝑡 strong6 for the slope shock. In particular, the values obtained for the + – ? ?/0 ? −1 F-statistic are above 22. Restrictions on the IRFs on impact The IRFs are normalized to be the responses of the variables to a 0 0 – 0/? 0 – one unit expansionary monetary policy shock. In the case of the iden- Note: + and − indicate that the parameters are restricted to be positive and negative, tification with zero and sign restrictions, this paper provides posterior respectively, while ? means that the parameter is left unconstrained. ∕ distinguishes median IRFs together with the 68% credible interval of the posterior restrictions on either income or wealth inequality 𝑧𝑡 , respectively. 1 implies the distribution based on 10,000 draws. In the case of the SVAR–IV method, normalization with respect to the monetary policy indicator. this paper reports median IRFs together with 68% confidence intervals using 10,000 bootstrap replications. The IRFs are presented for 20 periods. are imposed in accordance with this normalization to consider an expansionary monetary policy shock. 4. Data On the monetary policy rule, the following contemporaneous re- strictions are imposed. First of all, the current paper takes into account The empirical analysis is implemented in the case of the US. The the dual mandate of maximum employment and price stability of monthly estimation sample is from 2008:M1 to 2019:M12. The sample the Federal Reserve System (Eberly et al., 2020) and imposes sign is chosen to coincide with the period of the implementation of the UMP restrictions on the parameters of the unemployment rate and prices. In measures by the Fed before the Great Lockdown. The focus on this particular, given the normalization of the monetary policy indicator, it period also provides the stability of the parameter estimates. Besides, is considered that the contemporaneous reaction of the monetary policy the end of the estimation period is also related to the availability of indicator to the unemployment rate is positive while it is negative for standard inequality measures, which are released later than typical prices. If a wealth inequality measure is considered as an economic economic data get available for the same period. inequality measure in the specification of the VAR model, a zero Some estimation sub-samples are considered because of data avail- restriction is imposed on the response of the policy indicator to wealth ability related to the identification of the UMP shock. The estimation inequality. The responses of the policy indicator to the other variables sample for the SVAR–IV method is 2008:M1–2019:M3 given that the are left unrestricted. series of the instrument is available until 2019:M3. The series is from Since monthly macroeconomic data are used for estimation, it is Eberly et al. (2020). The estimation period for the identification of plausible to impose common zero restrictions on impact for the im- an LSAP shock is 2008:M1–2015:M12 because LSAPs were generally pulse response functions (IRFs). In particular, this paper imposes zero conducted within this period. As a monetary policy indicator of LSAPs, restrictions on the contemporaneous responses of the unemployment the series of their announcements is considered and it is from Hesse rate, prices, income inequality,5 and the federal funds rate. The zero et al. (2018). restriction on the response of the federal funds rate is a key restriction The data on the economic variables are taken from different sources. to disentangle the UMP shock from a CMP shock (Baumeister and The data source for the unemployment rate is the U.S. Bureau of Labor Benati, 2013; Boeckx et al., 2017). Statistics. As an alternative measure for real economic activity, this Overall, one zero restriction is imposed on economic inequality. If paper uses the monthly estimates of the real gross domestic product income inequality is considered, a zero restriction is imposed on its (GDP) from IHS Markit. The data on personal consumption expendi- response to a monetary policy shock given it should not change within tures (PCE) excluding food and energy chain-type price index (deflator) a month. If wealth inequality is included in the model, a zero restriction are from the U.S. Bureau of Economic Analysis. As an alternative is imposed on the response of monetary policy to wealth inequality indicator for prices, the consumer price index (CPI) is considered from given it might change within a month. In addition to economic reason- the Organization for Economic Co-operation and Development (OECD). ing, this framework of zero restrictions is not too restrictive and allows The variables are seasonally adjusted. The real GDP and the price obtaining admissible set of draws, which satisfies the restrictions. All indices are scaled with respect to the base year of 2009 and used in the restrictions are summarized in Table 2. logs in the empirical analysis. Alternatively, this paper identifies the UMP shock using the struc- This paper considers various financial series, which are from the tural VAR–instrumental variables (SVAR–IV) approach, which does not Board of Governors of the Federal Reserve System. The excess bond use zero and sign restrictions. This paper applies this identification premium (Gilchrist and Zakrajšek, 2012) is used to control for financial following the approach developed by Gertler and Karadi (2015). When conditions. As an alternative indicator of financial conditions, this this identification approach is applied, the VAR model is estimated with paper uses the Chicago Board Options Exchange (CBOE) Volatility the method of ordinary least squares. Index (VIX), which measures expected future volatility (Kumar et al., This paper uses an analogous specification of the VAR model to 2023). The federal funds effective rate is considered as a CMP tool. the one provided in the work by Eberly et al. (2020), who also use As a general indicator of the UMP measures, this paper uses the yield the SVAR–IV methodology to estimate the effects of the CMP and the spread that is specified as a spread between the 10-year and the 3- UMP. In particular, Following Eberly et al. (2020), the general effects month treasury constant maturity rates. Alternatively, this paper also of the UMP are identified through its combined impact on the slope of considers the yield spread that is computed as the difference between the term structure, which, as previously specified, is the yield spread the 10-year government bond rate and the federal funds rate. between the 10-year and the 3-month interest rates. They refer to it as Proxy inequality measures are computed for the empirical analy- a slope shock and this term is also used in the current paper to indicate sis. As an income inequality measure, this paper computes the ratio the general the UMP shock. between the personal income receipts on assets and the compensation 5 6 If wealth inequality is included instead of income inequality, its contem- Following Stock et al. (2002), the instrument is considered strong if the poraneous responses to a monetary policy shock is not restricted given that it F-statistic from the first-stage regression of the reduced form residuals of the can change within a month. policy indicator on the instrument is above the threshold value of 10. 5 K. Davtyan Economic Modelling 126 (2023) 106380 of employees. The data on these variables are from the U.S. Bureau of Economic Analysis. The series are seasonally adjusted. As a wealth inequality measure, this paper computes the ratio between the S&P 500 Index (SP500) and the S&P/Case–Shiller U.S. National Home Price Index (CSUSHPISA). The series are from S&P Dow Jones Indices LLC. The house price index is seasonally adjusted. The indices of the stock and the house prices are scaled with respect to the base year of 2009. The proxy inequality measures are used in logs in the empirical analysis. Standard income inequality measures are considered from the report by Shrider et al. (2021) on the Current Population Survey (CPS) of the U.S. Census Bureau. The inequality measures are based on money income, i.e., the income that is not taxed and does not include govern- ment transfers. As a general inequality measure, this paper considers the Gini index, which is in percent. Based on the percentiles provided in the report by Shrider et al. (2021), the 50-10 and the 90-50 percentile ratios are computed to measure the relation among different parts of Fig. 1. Income inequality ratio. the income distribution. The percentile ratios are in logs. This paper Note: The figure includes the graph of the ratio of the personal income receipts on also uses the income shares of the lowest, the middle, and the highest assets to the compensation of employees (in percent). The data source for the asset quitiles, which are in percent. income and the compensation of employees is the U.S. Bureau of Economic Analysis. Standard wealth inequality measures are also considered though their availability is more limited compared to income inequality mea- sures. This paper uses the bottom 50%, the middle 40%, and the top estimated contains one inequality measure only. This empirical analysis 10% shares of net personal wealth from the World Inequality Database allows the reflection of the distributional impact of the UMP through (WID). Net personal wealth is defined as personal financial and non- the standard inequality measures. Besides, the consideration of inequal- financial assets less personal debt. The middle 40% share is specified as ity measures is useful for the estimation of the impact of the UMP on the share of net personal wealth held by the group between percentiles different parts of the income and the wealth distribution. Within this 50 and 90. The wealth shares are expressed in percent. analysis, the focus is on the responses of inequality measures only to The economic and the financial series as well as the proxy inequality outline their pattern. measures are at the monthly frequency while the standard inequality Finally, to assess the relative importance of the UMP shock, a measures are at the annual frequency. Therefore, when the standard variance decomposition analysis is implemented. It is informative to inequality measures are included in the empirical analysis, this paper observe the contribution of the UMP shock to the variation in the applies the mix frequency approach. The descriptive statistics of the inequality measures. The analysis is implemented in the cases of the inequality measures are provided in Table A.1. income and the wealth inequality ratios, which are computed at the monthly frequency. 5. Empirical analysis 5.1. Ratio between capital and labor income First, the empirical analysis is implemented in the cases when income inequality measures are computed at the monthly frequency. The ratio between capital and labor income is considered as a In particular, this paper considers proxy inequality measures between baseline income inequality measure. This paper uses personal income capital and labor income, and between stock and house prices. This receipts on assets and the compensation of employees, as proxies paper conducts the various robustness checks of the results, including for capital income and earnings, respectively. The dynamics of asset the alternative identification of the UMP shock with the SVAR-IV income and earnings are presented in Fig. A.1. As can be seen, both method. variables generally have similar dynamics. After the decline during To focus on the measures of the UMP, the impact of LSAPs is 2008 and 2009, they had growing trends over the period from 2010 disentangled from the general effect of the UMP given that they were to 2019. key policy measures. The LSAP shock is identified considering that To explore the relation between capital and labor income, this LSAPs were previously announced before their actual implementation. paper computes the ratio of personal income receipts on assets to That is, the announcements came as surprises while actual purchases the compensation of employees. It is assumed that the increase in were already anticipated. Consequently, the series of the announce- asset income mostly benefits high income households while the rise in ments (Hesse et al., 2018) is considered as a monetary policy indicator earnings mainly relates to the income of low income households. Yet, of LSAPs. The LSAP shock is identified using the zero and the sign the ratio is not a standard inequality measure and has a limitation to restrictions described in Section 3.3. In the current case, the IRFs are reflect the whole income distribution. Fig. 1 provides the graph of the just normalized to be the responses to a 0.5 trillion USD LSAP shock. ratio. As can be observed, after the initial decline in 2008 and 2009, the This normalization provides the quantitative responses that align well ratio generally had an increasing trend from 2010 onward, indicating with the magnitudes of the IRFs based on the baseline normalization. that capital income grew at a faster rate than earnings. The spike of the This paper evaluates the impact of the UMP using standard income graph for December of 2012 appears to capture the additional stimulus inequality measures too. Since such measures are generally available within the third round of quantitative easing (QE3), which lasted from at the annual frequency, this paper uses the mixed frequency approach September 2012 to October 2014. It reflects the proportionally higher described in Section 3.2. The approach is helpful to combine monthly increase of capital income in comparison with the rise in labor income economic data and annual inequality measures, and to identify a mon- in December 2012, as can be seen from Fig. A.1. Thus, for the relation etary policy shock within a monthly framework. At the same time, the between capital and labor income, this ratio is considered as an income mixed frequency estimates have higher uncertainty than the results of inequality proxy variable, which is at the monthly frequency as the the empirical analysis with solely monthly data. other macroeconomic variables. As an inequality measure, various standard inequality indicators are The estimation results of the IRFs for the VAR model with the included in the VAR model one by one. That is, each VAR model that is income inequality ratio are provided in Fig. 2. Given the normalization, 6 K. Davtyan Economic Modelling 126 (2023) 106380 Fig. 2. IRFs to a slope monetary policy shock (the model with the income inequality Fig. 3. IRFs to a LSAP shock (the model with the income inequality ratio). ratio). Note: The figure reports posterior median impulse responses to a 0.5 trillion USD LSAP Note: The figure reports posterior median impulse responses to a one percentage point shock and 68% credible intervals of the posterior distribution. slope monetary policy shock and 68% credible intervals of the posterior distribution. instead of the unemployment rate. The PCE deflator is substituted with the UMP shock leads to the decrease of the yield spread by 1 percentage the CPI. Instead of the excess bond premium, VIX is considered. The point. The shock reduces the unemployment rate up to 0.6 percentage yield spread is alternatively specified as the difference between the 10- points. The response is in line with the corresponding result obtained by year government bond rate and the federal funds rate. The baseline Eberly et al. (2020). The shock leads to an increase in the PCE deflator specification of the model is estimated both with the lag orders of by approximately 0.2 percent. The result is similar to the response of three and four instead of the selected lag order of two. In all the cases, prices to a LSAP shock7 provided by Hesse et al. (2018). It reduces the results are generally similar to the IRFs obtained with the baseline the excess bond premium on impact by around 0.9 percentage points. specification of the model. The response is analogous to the respective result found by Gertler and The aforementioned results are obtained for the general effect of the Karadi (2015). Following the expansion, the federal funds rate initially UMP. Yet, they might be related to different elements of UMP measures rises up to 0.2 percentage points and then it decreases, responding to such as forward guidance and LSAPs. Especially, LSAPs were important the decline in the unemployment rate and to the increase in prices. policy measures, which helped to overcome the global financial crisis, Thus, the response of the federal funds rate reflects the interaction and affected the relative supply of financial assets and their prices in between the CMP and the UMP found also in the literature (e.g., Boeckx the economy. Therefore, this paper tries to disentangle the impact of et al., 2017; Burriel and Galesi, 2018). LSAPs (Fig. A.3) to check whether they drive the results obtained for Fig. 2 also shows that the UMP shock significantly increases the the overall effect of the UMP. income inequality ratio by approximately 2 percent. That is, the UMP Fig. 3 contains the IRFs to a LSAP (announcement) shock. Their raises capital income more than labor earnings, leading to the increase dynamics and magnitudes are similar to the initial IRFs provided in in income inequality.8 As Fig. A.4 shows, both capital income and labor Fig. 2. A LSAP shock reduces the unemployment rate by around 0.4 earnings increase following the monetary policy expansion. Thus, the percentage points. It raises prices up to 0.25 percent. Following the UMP raises income inequality via the income composition channel and expansion, the excess bond premium decreases on impact by approxi- this impact outweighs its alleviating effect on inequality through the mately 0.8 percentage points and the federal funds rate rises by about earnings heterogeneity channel. 0.2 percentage points. The shock increases the income inequality ratio Various robustness checks of the results are implemented. First, the up to 1.2 percent. Thus, all these results are analogous to the IRFs alternative identification of the UMP shock (SVAR–IV) is implemented. obtained initially. Fig. A.5 contains the resulting IRFs. Although quantitative responses It can be claimed that the overall impact of the UMP is mainly of the variables are a bit smaller, their dynamics are analogous to the driven by LSAPs although there are some caveats to this inference. results obtained with the baseline identification. In particular, the UMP LSAPs were generally implemented until 2015 and consequently the fosters real economic activity, moderately increases prices, and loosens sample is shorter for the estimation of their effects. Nevertheless, financial conditions. In response to this expansion, the federal funds principal payments and maturing securities were reinvested, and the rate increases. Besides, the UMP leads to the relatively larger growth balance sheet of the Fed remained largely expanded until the final point in capital income than in earnings, resulting in the increase in income of the baseline estimation period 2019:M12 (Swanson, 2021). So, the inequality. At the same time, the contemporaneous response of the overall effect of the UMP that this paper evaluates can capture these income inequality rate is not significant in line with the corresponding effects in addition to accounting for the impact of LSAPs implemented zero restriction imposed in the case of the baseline identification. Other until 2015. Thus, balance sheet policies appear to be the key measures robustness checks are provided in Online Appendix A. The variables of that shape the overall impact of the UMP. the model are replaced with their corresponding alternative measures one by one. As an alternative measure for real economic activity, 5.2. Standard income inequality measures this paper uses the real GDP (monthly estimates from IHS Markit) This paper uses standard income inequality measures for the further analysis of the distributional effects of the UMP. This analysis allows to 7 Hesse et al. (2018) identify the LSAP shock through zero and sign uncover the heterogeneous effects of UMP measures. Fig. 4 displays the restrictions on IRFs. IRFs of income inequality measures to a slope monetary policy shock. In 8 Standard inequality measures are considered later in the text. particular, the figure includes the response of the Gini index, which is a 7 K. Davtyan Economic Modelling 126 (2023) 106380 and 0.17 percentage points, respectively. At the same time, the shock raises the income share of the highest quintile up to 0.5 percentage points. The dynamics of the responses of the lowest and the middle quintiles are analogous but the response of the lowest quintile is more pronounced. Moreover, their responses are actually asymmetric to the response of the highest quintile. The effects of the UMP on the income shares are in line with the results of the theoretical model by Kakar and Daniels Jr. (2019). Analo- geousely, El Herradia and Leroy (2021) find that expancionary CMP Fig. 4. IRFs of income inequality measures to a slope monetary policy shock. increases top income shares. The current results are also in line with the Note: The figure reports posterior median impulse responses to a one percentage point empirical results of Ballabriga and Davtyan (2022) in case of the UK. slope monetary policy shock and 68% credible intervals of the posterior distribution. The income inequality measures are included in the VAR model one by one. In particular, using a consistent empirical framework, Ballabriga and Davtyan (2022) show that the impact of the UMP on income inequality is stronger than those of the CMP and that the UMP raises the top income share while it decreases the low and the mid income shares. At the same time, the current paper provide complimentary evidence on the impact of the UMP on various income inequality measures and also on wealth inequality, tracing out the impact through the distributional channels. Consistently with the analysis of the percentile ratios, the UMP re- duces the income shares of lower and middle earners while it raises the income share of higher earners. Moreover, the income share of lower Fig. 5. IRFs of income shares to a slope monetary policy shock. earners decreases more than that of middle earners because, the latter Note: The figure reports posterior median impulse responses to a one percentage point generally has higher skills, which are more complementary to capital slope monetary policy shock and 68% credible intervals of the posterior distribution. (Dolado et al., 2021). Thus, all these results corroborate the finding that The income shares are included in the VAR model one by one. the UMP increases capital income more than labor income given that lower and middle earners mainly receive labor income whereas higher earners mostly gain capital income. That is, the impact of the UMP on general measure of inequality. The UMP shock raises the Gini index up income inequality through the income composition channel outweighs to 0.7 percentage points. The response is equivalent to the increase of its impact on inequality through the earnings heterogeneity channel. the Gini index by around of 1.4 percent, which is in line with the result obtained in the case of the income inequality ratio. The magnitude of 5.3. Ratio between stock and house prices the response of the Gini index is economically significant given that the Gini index increased by 1.8 percentage points from 2008 (the value of UMP measures, especially LSAPs, tend to change the relative supply 46.60) to 2019 (the value of 48.40). of assets and consequently to affect their prices. For instance, as can The response of the Gini index is of opposite sign from the respective be observed from Fig. A.2, stock prices initially dropped and they result found by Coibion et al. (2017) in the case of the CMP. Some of generally rose after 2009 throughout the rest of the considered period the reasons for the opposite results might be related to the differences from 2008 to 2019. On the other hand, house prices decreased from in methodologies and estimation samples. Yet, the main reason for 2008 to 2012 and grew up afterwards for the rest of the period. All the opposite results is probably related to the UMP measures. As the these changes in the asset prices should be reflected in the dynamics results show, UMP measures are effective in fostering real economic of wealth inequality. Therefore, this paper estimates the impact of the activity and easing financial conditions but they tend to increase capital UMP on wealth inequality over the study period. income more than earnings. That is, the impact of the UMP via the The dynamics of wealth inequality depend on the changes in the income composition channel prevails over its effect through the earn- portfolio composition and the savings flows of households. In par- ings heterogeneity channel. Analogeousely, Guerello (2018) finds that ticular, if portfolios differ along the distribution, asset prices lead to expansionary CMP lowers income inequality while the UMP increases different capital gains and so to the changes in wealth inequality. Kuhn it. Thus, the CMP and the UMP can have different distributional effects et al. (2020) show that the effect of asset prices on wealth inequality is given their different instruments, as discussed in Section 2. more prominent than savings flows when aggregate wealth to income This paper evaluates the impact of the UMP on the different parts of ratio is high. Piketty and Zucman (2014) provide evidence of the the income distribution. The lower and the upper parts of the income considerable rise of this ratio in the US over recent decades. That is, distribution are proxied by the 50-10 and the 90-50 percentile ratios, the dynamics of asset prices have been a decisive factor for the recent respectively. The VAR model is modified by incorporating each of the dynamics of US wealth inequality. percentile ratios as an inequality measure one at a time. As can be The portfolio of low income and middle class households mainly observed from Fig. 4, the UMP shock increases the 50-10 and the 90-50 consists of nonfinancial assets such as houses while wealthy households ratios by approximately 1 and 4 percent, respectively. That is, following mostly tend to have capital assets such as stocks. Because of these dif- the monetary policy expansion, the income of middle earners grows up ferences in the portfolio composition of households, the changes in the with respect to the income of lower earners. Nevertheless, the monetary stock and the housing prices shape the dynamics of wealth inequality. policy expansion leads to the much larger increase in the income of For instance, Adam and Tzamourani (2016) provide evidence in the higher earners relative to the income of middle earners. Furthermore, case of the Euro Area that the increase in equity prices benefits wealthy the responses of 90-50 ratio and the Gini index are analogous. That is, households while the rise in house prices is beneficial for middle class the response of the Gini index is mainly driven by the response in the households. upper part of the income distribution. Since the dynamics of wealth inequality are primarily affected by The consideration of income shares complements the analysis on the the changes in the stock and the house prices, their relative dynamics impact of the UMP on the different parts of the income distribution. The are examined for the study period. The ratio of stock prices to house results are presented in Fig. 5. A slope monetary policy shock reduces prices is computed as a proxy indicator of wealth inequality. Fig. 6 the income shares of the lowest and the middle quintiles by around 0.2 show that stock prices mostly grew at faster rate than house prices after 8 K. Davtyan Economic Modelling 126 (2023) 106380 Fig. 6. Wealth inequality ratio. Note: The figure includes the graph of the ratio of the S&P 500 Index to the S&P/Case– Fig. 8. IRFs to a LSAP shock (the model with the wealth inequality ratio). Shiller U.S. National Home Price Index (in percent). The data source for the stock and Note: The figure reports posterior median impulse responses to a 0.5 trillion USD LSAP the house indices is S&P Dow Jones Indices LLC. The indices are scaled to 2009=100 shock and 68% credible intervals of the posterior distribution. before computing the ratio. alternatively identified with the SVAR-IV method. The results presented in Fig. A.6. As in the case of the previous results, the UMP spurs real economic activity, raises prices, and eases financial conditions. Following the expansion, the federal funds rate rises. The UMP raises stock prices relatively more than house prices, leading to the increase in wealth inequality. In particular, the strongest response of the wealth inequality ratio is on impact to the monetary policy expansion. This contemporaneous response of the wealth inequality ratio might be ex- plained by the fact that the stock and the house prices can immediately react to a monetary policy shock. It is also in line with the respective result in case of the baseline identification. The set of other robustness checks is analogous to the case when the income inequality ratio is considered. The variables of the model are substituted by their respective alternative measures one by one. Instead of the selected lag order of two, the baseline specification of the model is estimated both with the lag orders of three and four. These robustness checks are reported in Online Appendix. In general, the results are Fig. 7. IRFs to a slope monetary policy shock (the model with the wealth inequality robust to these different modifications. ratio). As previously, this paper studies the impact of LSAPs disentangling Note: The figure reports posterior median impulse responses to a one percentage point slope monetary policy shock and 68% credible intervals of the posterior distribution. it from the combined effect of the UMP. The impact of LSAPs is evaluated as in the case of the consideration of the income inequality ratio. Fig. 8 displays the resulting IRFs, which are analogous to the results presented in Fig. 7. A LSAP shock reduces the unemployment 2009. That is, the wealth inequality ratio generally had an increasing rate and the excess bond premium, and increases prices. Following the trend during the considered period. Yet, wealth inequality is an impor- expansion, the federal funds rate rises. At the same time, LSAPs increase tant factor for an economic system (Grigoryan, 2013; Shao and Silos, the wealth inequality ratio up to 12 percent. This response of the wealth 2017). inequality ratio is just slightly lower than its response of around 18 Fig. 7 provides the IRFs of the VAR model that includes the wealth percent in the baseline case. As in the cases of the responses of the inequality ratio as an inequality measure. As previously, the UMP shock other variables, the dynamics of the responses of the wealth inequality leads to the reduction in the unemployment rate and the excess bond ratio are similar in both case. Thus, the combined impact of the UMP premium, and to the increase in prices. The federal funds rate increases is mainly driven by the balance sheet policies. in response to this expansion, reflecting the interplay between the CMP and the UMP (Boeckx et al., 2017; Burriel and Galesi, 2018). 5.4. Standard wealth inequality measures As Fig. 7 also show, the shock significantly raises the wealth in- equality ratio up to 18 percent, which is the largest response among This paper evaluates the effect of the UMP on wealth inequality the considered inequality indicators. That is, this response indicates using standard inequality measures too. In particular, the bottom 50%, that the UMP increases wealth inequality by raising stock prices more the middle 40%, and the top 10% shares of net personal wealth are than house prices through the portfolio channel. Following the UMP considered. Yet, these measures are not the most common standard shock, the positive responses of the stock and the house prices are inequality indicators and they are considered because the availability of presented in Fig. A.4. Yet, the response of house prices is not significant. wealth inequality measures is much more limited than the availability As Feroli et al. (2012) show, housing market problems weakened the of income inequality measures. So, the results should be interpreted transmission mechanism of monetary policy after the financial crisis. with some caution. In any case, the consideration of available standard As in the case of the income inequality ratio, this paper curries wealth inequality measures is useful for complementing the empirical out different robustness checks of the results. First, the UMP shock is analysis. 9 K. Davtyan Economic Modelling 126 (2023) 106380 Table 3 Variation in inequality measures due to a slope monetary policy shock. Periods Income Wealth (in Months) inequality ratio inequality ratio 4 2.16 25.03 8 6.70 37.73 12 10.97 39.28 16 14.49 39.02 20 16.15 37.45 Note: The table reports the posterior median variation in inequality measures due to a Fig. 9. IRFs of wealth shares to a slope monetary policy shock. slope monetary policy shock. The variation is expressed in percent. Note: The figure reports posterior median impulse responses to a one percentage point slope monetary policy shock and 68% credible intervals of the posterior distribution. The wealth shares are included in the VAR model one by one. The middle 40% is the share between percentiles 50 and 90. 6. Conclusion This paper evaluates the distributional impact of US the UMP con- Fig. 9 displays the estimation results of the impact of the UMP on the ducted in response to the global financial crisis. The results indicate different parts of the wealth distribution. A slope monetary policy shock that the monetary policy expansion fosters real economic activity and reduces the bottom 50% and the middle 40% wealth shares on impact moderately increases prices as well as eases financial conditions. At the by around 0.17 and 1.5 percentage points, respectively. Following the same time, the UMP measures increase income and wealth inequality, shock, the top 10% wealth share increases on impact by approximately having a stronger effect on the latter. The estimated overall effects of 1.6 percentage points. The dynamics of the responses of the bottom the UMP are mainly driven by LSAPs. The UMP shock is identified both 50% and the middle 40% wealth shares are similar but the response of with zero and sign restrictions, and with the SVAR-IV method. The the middle 40% wealth share is stronger. Besides, the response of the results are also robust to the application of the standard and the mixed middle 40% wealth share is almost fully asymmetric to the response frequency approaches, and the different modifications of the model of the top 10% wealth share. The results are similar to the evidence specification. provided for wealth shares by Evgenidis and Fasianos (2021). The results show that the UMP increases capital income more than The responses of different parts of the wealth distribution are in line labor earnings. This impact of the UMP results in the growth of income with the response of the wealth inequality ratio. The group at the bot- inequality measured with standard indicators. In particular, the UMP tom of the wealth distribution generally posses less non-financial assets raises the 50-10 and the 90-50 percentile ratios, and the Gini index. The than the group in the middle of the wealth distribution. Consequently, results are mostly driven by the relatively higher increase in income the response of the wealth share of the former group is weaker, in line at the upper part of the distribution. Besides, UMP measures reduce with the results by Adam and Tzamourani (2016). At the same time, the the income shares of the lowest and the middle quintiles while they group in the middle of wealth distribution mainly owns non-financial increase the income share of the highest quintile. Given that lower and assets such as houses while the group at the upper part of the wealth middle earners mostly receive labor income whereas higher earners distribution mostly possesses financial assets such as stocks. Therefore, mainly gain capital income, the relatively higher increase of capital the relatively larger increase of stock prices with respect to house prices income compared to labor earnings leads to the growth of income generally leads to the redistribution of wealth to the top through the inequality following the monetary policy expansion. portfolio channel. The results indicate that the UMP raises stock prices more than house prices. This effect of UMP measures leads to the increase in 5.5. Variance decomposition wealth inequality measured with the shares of the wealth distribution. This paper implements a variance decomposition analysis to evalu- Particularly, the UMP reduces the bottom 50% and the middle 40% ate the contribution of the UMP shock to the variation in the income wealth shares while it increases the top 10% wealth share. The results and the wealth inequality ratios. Table 3 provides the results of the are related to the fact that the groups in the lower and the middle variation in the inequality measures due to a slope monetary policy parts of the wealth distribution mainly own non-financial assets such as shock over the initial 20 months. The results indicate that the shock houses while the portfolio of the group at the top of the wealth distri- accounts for the higher variation in the wealth inequality ratio than bution mostly consists of financial assets such as stocks. Consequently, in the income inequality measure over all considered periods. For following the monetary policy expansion, the relatively larger growth instance, in the fourth period, the shock explains 25.03 percent of the of stock prices with respect to house prices results in the increase variation in the wealth inequality ratio while the shock accounts for of wealth inequality. Moreover, the variance decomposition analysis only 2.16 percent of the variation in the income inequality indicator. shows that the UMP explains the higher variation in wealth inequality Similarly, in the twentieth period, the contribution of the shock to the than in income inequality. variation in the wealth inequality ratio is 37.45 percent whereas the Thus, the UMP was helpful in recovering from the global financial shock explains 16.15 percent of the variation in the income inequality crisis. Yet, it came at the cost of increased income and especially measure. wealth inequality. This distributional impact of the UMP points out Thus, analogous to the results of Mumtaz and Theophilopoulou the need for complementary fiscal policy measures. Especially, given (2020) for the UK, this paper finds that the UMP substantially affects the complementary effects of the UMP, they will probably be used the variation in wealth inequality. This impact is stronger than in permanently along with the CMP in the future. the case of income inequality. In the fourth period, the considerable difference in the results might be related to the fact that the income Declaration of competing interest inequality ratio does not contemporaneously react to the monetary policy shock in contrast to the contemporaneous response of the wealth The author declares that he has no known competing financial in- inequality indicator. In any case, over all the considered periods, the terests or personal relationships that could have appeared to influence monetary policy shock accounts for the substantially higher variation the work reported in this paper. in the wealth inequality ratio than in the income inequality measure. At the same time, the distributional impact depends on the proportional Data availability effects of the UMP on the capital and the labor income, and the stock and the house prices, as discussed in Sections 5.1 and 5.3. Data will be made available on request. 10 K. Davtyan Economic Modelling 126 (2023) 106380 Appendix A A.1. Inequality measures See Table A.1. A.2. Income and wealth indicators See Figs. A.1 and A.2. A.3. LSAPs See Fig. A.3. A.4. Responses of income and wealth indicators Fig. A.2. Stock and house prices. See Fig. A.4. Note: The figure includes the graphs of the S&P 500 Index and the S&P/Case–Shiller U.S. National Home Price Index. The data source is S&P Dow Jones Indices LLC. The indices are scaled to the base year of 2009=100. A.5. SVAR-IV identification See Figs. A.5 and A.6. Appendix B. Supplementary data Supplementary material related to this article can be found online at https://doi.org/10.1016/j.econmod.2023.106380. Fig. A.3. LSAP announcements. Source: Hesse et al. (2018). Fig. A.1. Asset income and compensation of employees. Note: The figure includes the graphs of the personal income receipts on assets and the compensation of employees. The data source is the U.S. Bureau of Economic Analysis. Table A.1 Statistical information on inequality measures. Inequality Frequency Mean Max Min SD RSD measures Income Monthly 24.97 28.21 22.26 1.47 0.06 inequality ratio 50-10 ratio Annual 4.25 4.39 4.11 0.10 0.02 90-50 ratio Annual 2.87 2.93 2.75 0.06 0.02 Gini index Annual 47.77 48.60 46.60 0.64 0.01 Lowest quintile Annual 3.18 3.40 3.10 0.12 0.04 Middle quintile Annual 14.35 14.70 14.10 0.19 0.01 Highest quintile Annual 51.11 52.00 50.00 0.63 0.01 Wealth Monthly 165.84 237.18 76.74 38.33 0.23 inequality ratio Bottom 50% Annual 1.11 1.51 0.87 0.24 0.22 Middle 40 % Annual 27.47 29.44 26.12 1.16 0.04 Top 10% Annual 71.43 72.88 69.44 1.22 0.02 Note: The table reports the statistical measures for the inequality indicators. The Fig. A.4. IRFs of income and wealth indicators to a slope monetary policy shock. CPS and the WID are the data sources for annual income and wealth inequality Note: The figure reports posterior median impulse responses to a one percentage point measures, respectively. 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