Debt Burdens and the Interest Rate Response to Fiscal Stimulus: Theory and Cross-Country Evidence (Preliminary and Incomplete*)

Transcription

1 Debt Burdens and the Interest Rate Response to Fiscal Stimulus: Theory and Cross-Country Evidence (Preliminary and Incomplete*) Jorge Miranda-Pinto 1, Daniel Murphy 2, Kieran James Walsh 3, and Eric R. Young 4 1 University of Queensland 2 University of Virginia Darden School of Business 3 University of Virginia Darden School of Business 4 University of Virginia and Zhejiang University September 5, 2018 Abstract We develop a theory of saving-constrained households to explain the following facts: 1) Consumption is excessively volatile relative to income (established fact), 2) the fraction of households with marginal propensities to consume near zero increases with the level of households debt, 3) lagged high expenditure is associated with low contemporaneous spending propensities. Our proposed interpretation of these facts is that household expenditure depends on time-varying minimum consumption thresholds that, if violated, yield substantial utility costs. Our theory has implications for the propagation of macroeconomic shocks. Evidence from cross-county variation in the effects of fiscal stimulus on credit markets is consistent with the theory s implications. j.mirandapinto@uq.edu.au murphyd@darden.virginia.edu walshk@darden.virginia.edu ey2d@virginia.edu 1

2 1 Introduction A large literature, building on Hall (1978), documents that the dynamics of consumption deviate substantially from the predictions of the Permanent-Income-Hypothesis. Relative to theory, consumption is excessively volatile and insufficiently persistent given the dynamics of income. Theories of consumer behavior featuring credit constraints have some hope of rationalizing this evidence: when consumption is constrained from above by debt limits, consumption moves with income. Yet recent evidence from microdata documents that many high-debt/low-wealth households exhibit behavior that is inconsistent with credit constraints. Rather than exhibiting large marginal propensities to consume (MPCs) out of income shocks, many high-debt/low-wealth households save all additional income (Sahm et al. (2015), Jappelli and Pistaferri (2014), Misra and Surico (2014)). Why do so many households, especially those with low wealth, save rather than spend out of additional income? And how is it possible to reconcile the existence of many low-mpc households with the fact that consumption tends to be excessively volatile? In this paper we propose a model of consumer behavior to rationalize this evidence. We begin by presenting a new fact that will guide and validate our theory. Using data from the Panel Study of Income and Dynamics (PSID), we show that, conditional on wealth, high lagged expenditure is associated with lower current MPCs out of income, especially for lowwealth households. The notion that prior expenditure is inversely related (or related at all) to current MPCs is, at first glance, both counterintuitive and contrary to standard theory. If anything, modifications to standard theory would predict a positive relationship. Theories of habit formation, for example, would predict that high lagged expenditure should be associated with high desired current expenditure and therefore, if income is mean-reverting, a high contemporaneous MPC. Our proposed interpretation of these facts is that household expenditure depends on time-varying minimum consumption thresholds that, if violated, yield substantial utility costs. These minimum consumption thresholds represent unanticipated shocks such as medical emergencies and auto repairs. When an adverse shock hits a household, it chooses to accumulate debt (reduce wealth) rather than let consumption fall below a threshold level. For example, rather than move out of a house or slash food consumption, households simply accumulate debt when faced with a large, unanticipated expenditure. Maintaining a low net asset position is optimal for these households but it is costly in the sense that, in the event of another adverse shock, households may be forced to consume below the threshold level (e.g., move out of a home or forgo medical care), which is associated with a large utility 1

3 cost. Therefore, households for which consumption is against the minimum threshold use additional income to pay off debt (increase net assets) as a precautionary measure. We refer to these households as saving-constrained households to capture the notion that, in the absence of minimum consumption thresholds, households would save rather than reduce their asset position. Minimum consumption thresholds effectively constrain households saving relative to a frictionless benchmark, just as credit constraints constrain consumption relative to a frictionless benchmark. We develop a heterogeneous-agent model featuring minimum consumption thresholds and calibrate it to match within-household dynamics of expenditure and income from the PSID. The model with time-varying minimum consumption thresholds easily fits the data, including the large within-household ratio of consumption volatility to income volatility, while standard one-asset heterogeneous agent models do not. Furthermore, the model generates the pathdependence of spending propensities that we observe in the PSID. High lagged expenditure is associated with lower contemporaneous propensities to spend because high expenditure is a proxy for households being saving-constrained by high minimum consumption thresholds. The model helps to rationalize a number of additional features of the empirical MPC distribution. Households with high (non-mortgage) debt are more prone to being creditconstrained or savings-constrained, and therefore exhibit a higher prevalence of MPCs near unity or near zero. We show that this pattern is consistent with the MPC distribution from Misra and Surico (2014). Our theory is able to rationalize a number of additional features of the MPC distribution, and we expect that future extensions to the theory, such as incorporating additional assets and liquidity-constrained rich households (Kaplan and Violante (2014)), will further improve the match between theory and data. Our theory has important implications for the propagation of macroeconomic shocks. We show that saving constraints are important for understanding the cross-county relationship between fiscal effects on credit markets and inequality. In particular, high inequality is associated with a larger share of saving-constrained households with low MPCs. Fiscal shocks relax credit markets more (increase interest rates less) in countries with high inequality. A tractable extension of our model with minimum consumption constraints shows that the interest rate response to fiscal stimulus depends on income inequality as in the data. 2 New Evidence on the Joint Dynamics of Income and Consumption It is well-documented that, on average, within-household consumption (C) is nearly as volatile as income (I). Table 1 presents the average coefficient of variation of consumption and income and the AR persistent coefficient of consumption and income from the PSID 2

4 and the same statistics implied by a standard Bewley model. One possible explanation for this fact is that many households are credit-constrained and thus have MPCs out of income near unity. However, recent evidence from microdata documents that a large fraction of high-debt households who would be most likely to be credit-constrained have MPCs near zero. These zero-mpc households suggest that alternative explanations are necessary to rationalize the excess volatility of consumption. Table 1 Volatility and persistence of consumption and income: PSID and Bewley model PSID Bewley Model Avg. Coefficient of Variation (I t ) AR coeff. (I t ) Avg. Coefficient of Variation (C t ) AR coeff. (C t ) Note: The coefficient of variation for consumption (income) is defined as the within-household ratio between the mean and standard deviation of consumption (income) ( σ ). The PSID AR coefficients are estimated after removing household and time µ fixed effects. Model statistics are from quarterly simulations aggregated to a 2-year frequency. The model is a standard Bewley model with uninsured idiosyncratic shocks, one asset, and borrowing constraints. Details of the calibration are in section 3. Here we present a new, likewise puzzling, fact about the joint movement of consumption and income: lagged high expenditure is associated with low contemporaneous MPCs. The PSID is a unique biennial panel dataset that contains household-level information on expenditure and income. The expenditure data is available as of Using this data, we identify episodes of high expenditure (income) for each household based on whether expenditure (income) exceeds its within-household average by a standard deviation. Our main specification is logc it = β 0 High_I it + β 1 High_C it 1 + β 2 High_I it High_C it 1 + γx t + ɛ it, (1) where High_I it is a dummy variable that equals one when the income of households i exceeds the within-household average by a standard deviation at period t. High_C it 1 is defined analogously. X t includes household wealth, the interaction of wealth with high income, and time fixed effects. We also control for household fixed effects. Table 2 shows that the dependence of consumption on having a high-income episode is lower when a household had a high-expenditure episode in the previous period. The effect of lagged high expenditure on current spending propensities is especially strong for low-wealth households (Column 1). One possible interpretation of this evidence is that high lagged expenditure is simply a proxy for lagged high income or wealth (which may be associated with lower spending propensities). The regressions in columns (1) and (2) partially account for this possibility by controlling for wealth (and its interaction with high income). further isolate the role of lagged high expenditure, columns (3) and (4) limit the sample to 3 To

5 Table 2 Effect of Lagged Expenditure on Spending Propensities (PSID) Dependent Variable: Log Consumption (t) [only if High_I t 1 = 0] Low Wealth High Wealth Low Wealth High Wealth High_I t High_C t *** *** *** (0.027) (0.021) (0.034) (0.025) Fraction of av. effect of High Income N 26,166 26,159 21,939 22,038 R Note: A household has high income (consumption) in periods in which income (consumption) is over a standard deviation above average income (consumption) for the household. All regressions control for polynomial terms in household wealth and the interaction of wealth terms with high income. Low-wealth households have average wealth (across time) below the sample median. Robust standard errors in parentheses. households that do not experience high income in the previous period. In these specifications, the role of lagged high expenditure is strong for both high-wealth and low-wealth households, and it is especially strong for low-wealth households. Similar results are obtained when using different measures of expenditure, including expenditure on exclusively non-durable goods. We also report the ratio between our interaction coefficient (β 2 ) and the coefficient of high income in the current period (β 0 ). This represents how important is previous consumption in today s consumption relative to the direct effect of just having higher income today. Consistent with our previous results, the effect of past consumption in current consumption is more important for low wealth households and households that did not experience high income in the previous period. 3 A Theory of Saving-Constrained Households Here we present a theory to rationalize the large volatility and persistence of consumption. We first introduce minimum consumption thresholds into a standard Huggett (1993) model and calibrate it to match the consumption and income dynamics from the PSID. We then demonstrate that the model replicates the dependence of spending propensities on lagged high expenditure (Section 2). Finally, we examine the model s predictions relative to recent evidence that many high-debt households have MPCs near zero. The model features households subject to idiosyncratic income risk and random minimum consumption thresholds. We explore partial equilibrium to illustrate the puzzling nature of our PSID findings and to show that saving-constraints offer a potential resolution. In Section ongoing work we demonstrate how to incorporate saving constraints into a calibrated general equilibrium model with multiple assets, including capital. 4

6 3.1 Model There are many households, each of which has exogenous idiosyncratic stochastic income y and minimum consumption level c. The recursive optimization problem is subject to V (a,y,c) = max c 0,a a { c 1 γ 1 γ λmax{c c,0} + βe[v (a,y,c )] c + 1 R a = y + a, where V is the value function, a is savings, R is the gross interest rate, and c is consumption. If a household consumes below the current realization of the minimum consumption level c it suffers a utility penalty λ(c c), where λ > 0. Given a particular realization of c, a wealthy household voluntarily consumes above it, extremely poor borrowers pay the utility penalty, and households with intermediate wealth borrow/dis-save just enough to consume the minimum. In MPC terms, for a given c, the extremely poor are effectively hand to mouth, the rich have normal MPCs, and many intermediate wealth households have MPCs of exactly zero. Indeed, for an intermediate range of wealth, households facing a minimum consumption shock borrow/dis-save simply to avoid paying the utility penalty. In the absence of the shock, they would have saved more and are thus saving constrained: with an unexpected splash of income, all they do is save and pay down debts, that is, their MPCs are zero. } 3.2 Calibration We assume households make decisions at the quarterly frequency and set γ = 2, β =.99, and a = 2. For simplicity, we set the real quarterly interest rate to 0 (R = 1). For income, we employ a very simple three-state Markov chain that matches two key moment of income (after the removal time and household fixed-effects) from the PSID. In particular, if y {.05, 1, 1.95}, the probability of staying the current state is.7, and the probability of switching to any other state is.15, then aggregating quarterly simulations to the two year frequency yields a coefficient of variation 1 of.46 and an autocorrelation of.10, which approximates what we find in the PSID (after removing fixed effects). Lastly, we choose the minimum consumption process and utility penalty to generate reasonable consumption dynamics. With λ = 100, c {0,.85,1.75}, a.85 probability of staying the current state, and a.075 chance of switching to any other state, we get a consumption coefficient of variation of.41 and an autocorrelation of The coefficient of variation is the standard deviation divided by the mean. 5

7 3.3 Results As we see in Table 3, including the minimum consumption shock improves the fit of the simple model to the PSID. Without this new feature, consumption is far too persistent (.77) and has an unreasonably low coefficient of variation (.14). Introducing c, the coefficient of variation rises to.41 and autocorrelation falls to.32, much closer to the PSID numbers of.40 and.20. Table 3 Summary Statistics: Model vs. PSID PSID Model (c = 0) Model (c > 0) Ave. σ µ (inc.) AR coeff. (inc.) Ave. σ µ (cons.) AR coeff. (cons.) Note: PSID AR coefficients estimated after removing household and time fixed effects. Model statistics are from quarterly simulations aggregated to 2 year frequency. Minimum consumption thresholds help rationalize the inverse relationship between MPCs and lagged expenditure. Table 4 shows that, among low-wealth households, spending propensities out of a high-income realization are lower when households experienced high expenditure in the previous period. To make the results comparable with the PSID, we aggregate eight-quarter episodes into a period and define income and consumption over that period as their eight-quarter average. The intuition for the dependence of MPCs on lagged expenditure is that high lagged expenditure is a proxy for a binding minimum consumption threshold and an associated MPC of zero. The zero-mpc households are evident from the consumption functions of households with different realizations of c. Figure 1 shows that households with the median value of c tend to have consumption that is flat with respect to wealth (MPCs of zero) until wealth is sufficiently high that the minimum consumption threshold is no longer binding. These constrained households use all additional wealth/income to save. However, not all low-wealth households with high realizations of c have MPCs of zero. The poorest households are creditconstrained and cannot even achieve the minimum consumption level. They experience severe dis-utility and consume all additional income, up until they are able to consume at the threshold. What does this imply for the MPC distribution across households? Figure 2 shows the average consumption function across realizations of y and c. Comparing this consumption function with the ergodic wealth distribution (Figure 3), we see that in the ergodic distribu- 6

8 Interaction term Table 4 Effect of Lagged Expenditure on Spending Propensities (Model) Dependent Variable: Log Consumption (t) [only if High_I t 1 = 0] Low Wealth High Wealth Low Wealth High Wealth PSID -0.06*** *** -0.08*** Model (standard) Model with Saving Constraints -0.08*** ** -0.01*** Fraction of av. effect of high income PSID Model (standard) Model with Saving Constraints Note: The model-based estimates are derived from simulations with 100 quarters and 10,000 agents. Standard errors omitted due to high precision of tion many agents have an MPC of zero and the highest MPCs come from the very rich and poor. While MPCs are U shaped in wealth, averaged over coarse wealth quantiles there is not much variation in MPCs by wealth. In Figure 4 we explicitly report the fraction of zero MPC households across wealth quintiles, for households with low wealth. We observe that most of saving-constrained households (binding at c) are in the second and third quantile of wealth. The very poor households in quintile one pay the utility cost of consuming below c, while the richer households in quintile 5 are able to move away from the constraint. 4 Evidence of Saving-Constrained Households from the Consumer Expensiture Survey (CEX) Here we examine the theory s predictions of low-wealth, zero-mpc households using recent estimates of MPC heterogeneity from the CEX. The evidence here complements recent work that documents that large shares of high-debt households plan to save rather than spend additional disposable income (e.g., Sahm et al. (2015)). We follow Misra and Surico (2014) and estimate households consumption response to the 2001 tax rebates in the U.S. We augment their analysis by gathering data on households total wealth and non-mortgage debt. With the additional data at hand, we study whether the micro evidence supports the existence of low-wealth and indebted households with MPCs 7

9 Consumption cbar = 0 cbar =.85 cbar = Wealth Figure 1 Note: The figure shows consumption by wealth (a) for different realizations of c. near zero. The advantage of using the quantile regression approach in Misra and Surico (2014) is that we estimate marginal propensities to consume (MPC) that are heterogeneous across households, even for households with similar observed characteristics. Therefore, taking the MPC estimates we are able to relate the MPC heterogeneity to proxies of debt-burdened households implied by our model. 4.1 The 2001 Tax Rebate The mailing of the 2001 tax rebate was randomized based on the penultimate number of the tax filer social security number. Hence, the rebate receipt was exogenous to individual characteristics. Using households level data on consumption from the CEX and individual tax records, Johnson et al. (2006) estimate the consumption responses to the tax rebate receipt. The main specification in Johnson et al. (2006) is C it+1 = s α 0s M s + α 1X it + α 2 R it+1 + u it+1, (2) 8

10 2 Consumption stochastic cbar cbar = Wealth Figure 2 Note: The figure shows consumption by wealth (a), averaged across realizations of y and c, with and without stochastic c. where C it+1 is household i change in nondurable consumption in the three month periods where the tax rebate was received. M s is a set of time controls that capture seasonal effects and aggregate shocks. The matrix X it contains household controls, in particular average age and the change in the number of family members. The main variable R it+1 is the total dollar amount of tax rebate received by households i in the three months period t + 1. The authors find that between 20 to 40 percent of the tax rebate in 2001 was spent on non-durable goods. To capture the heterogeneity in the consumption responses, Johnson et al. (2006) interact the tax rebate variable R it+1 with indicators variables describing households with low (high) income and low (high) level of liquid assets. The results suggest that households with low income and low assets liquidity have larger responses. Misra and Surico (2014) amend the approach in Johnson et al. (2006) to account for the possibility that consumption responses may be heterogeneous, even within subgroups based on income. The authors estimate a version of equation (1) using quantile regression and find that high-income households are likely to have very low and very high consumption 9

11 Frequency Wealth Figure 3 Note: The figure shows the ergodic wealth distribution with stochastic c. responses to the 2001 (and 2008) tax rebate. As we are interested in understanding the determinants low MPCs, we exploit the Misra and Surico (2014) approach. The main specification is a linear quantile model of the form C it+1 = q(r it+1,x it,m s,λ it+1 ) with λ it+1 R it+1,x it,m s U(0,1), (3) where λ it+1 captures the unobserved heterogeneity in households with similar observed characteristics (R it+1,x it,m s ). Let q(r it+1,x it,m s,τ) the conditional τ-th quintile of C it+1, given observables, for each τ (0,1), the linear quantile model is 2 C it+1 = q(r it+1,x it,m s,τ) = s α 0s (τ) M s + α 1 (τ) X it + α 2 (τ)r it+1. (4) As mentioned above, this model does not impose common MPCs among households with similar observable characteristics. The estimated consumption responses are only common within a quantile τ but are heterogeneous across quantiles, representing unobserved hetero- 2 Misra and Surico (2014) extend the set of households controls X by adding squared age and changes in the squared number of family members. 10

12 Figure 4 Note: The figure shows MPC across wealth quintiles households with wealth below median. geneity. 4.2 Extending the Misra and Surico (2014) Analysis We start by replicating the estimation of α 2 in equation (3) in Misra and Surico (2014). We focus on the estimated tax rebate coefficient of non-durable consumption for the 2001 tax rebate. Then, we gather additional from the CEX on households total wealth and nonmortgage debt. We define wealth as the sum of the balance in checking accounts, saving accounts, U.S. bond, value of stocks, and the value of properties, minus the outstanding mortgage debt and outstanding non-mortgage debt. Non-mortgage debt is composed of credit card debt, bank loans, credit union debt, dentist and hospital debt, finance companies debt, and excludes business debt and car loans. Figure 5 shows the distribution of MPC for the group of low-wealth households (below median wealth). Consistent with our theory, there is large fraction of low-wealth households with very low MPCs. 11

13 Figure 5 MPC distribution low-wealth Households We now study who these zero-mpc households are. We define a dummy variable called zero-mpc that equals one when the MPC is below 0.05 and equal to zero otherwise. Figures 6 and 7 show the fraction of zero-mpc households across quantiles of non-mortgage debt and mortgage debt, respectively. We observe that, consistent with our theory in Figure 4, the fraction of zero-mpc households grows with debt. 12

14 Figure 6 Fraction of low-mpc HH by non-mortgage debt quintile Figure 7 Fraction of low-mpc HH by mortgage debt quintile 5 Cross-Country Testable Implications Our theory has implications for the transmission mechanism of fiscal shocks. In this section, we take advantage of cross-country heterogeneity in income inequality to show that in countries with more debt-burdened households (higher inequality) fiscal shocks generate smaller 13

15 increases (larger decreases) in interest rates. 5.1 The interest rate response to fiscal stimulus and Inequality To estimate country-level fiscal shocks and the interest response to fiscal shocks (IRRFs), we collect quarterly data on real government consumption, real GDP, and interest rates across countries. Obtaining reliable country-level estimates of fiscal shocks requires a sufficient time span of data. Therefore we limit our focus to OECD countries, most of which provide quarterly data that spans a period of over twenty years. The primary data source is the OECD. We supplement the OECD numbers with data from Haver when the Haver sample extends the OECD sample. A detailed description of the data used to estimate fiscal shocks is in Table 6 of our Appendix. Our study focuses on government bond yields because they are the interest rate that is the most widely available for our sample. An advantage of examining yields on longerdated bonds is that yields are not directly controlled by central banks but depend on credit conditions more generally. Our sample includes all OECD countries for which we observe government bond yields for at least 10 consecutive years prior to the end of our estimation period, Our baseline estimation period ends in 2007 in order to avoid structural breaks that may have been associated with the global financial crisis. The results presented below are similar when we include the most recent data, however. We also examine data on shorter-term interest rates, which we refer to as policy rates. We use direct measures of central bank policy rates when available. For countries that do not have policy rate data, we use the short-term interest rate series in Ilzetzki et al. (2013). The policy rates for members of the European Monetary Union (EMU) are equal to European Central Bank rates Country-level estimates of fiscal shocks We identify government spending shocks following the approach in Blanchard and Perotti (2002). The key identification assumption is that, within a quarter, government spending is predetermined with respect to other macro variables. Hence government spending responds contemporaneously to its own shock but not to other shocks in the economy. Based on the delay in the political process that typically justifies this restriction, much of the literature has adopted the Blanchard-Perotti approach (e.g., Bachmann and Sims (2012), Auerbach and Gorodnichenko (2012), Rossi and Zubairy (2011), Brinca et al. (2016)). Despite the widespread use of the Blanchard-Perotti approach and the plausibility of its identifying assumptions, there are potential limitations. If changes in government spending are anticipated, the Blanchard-Perotti approach will not capture the exogenous component of government spending (Ramey (2011)). To overcome this challenge, Ramey (2011) uses news 14

16 about future defense spending to identify fiscal shocks. As Ilzetzki et al. (2013) point out, this approach is not viable when estimating fiscal shocks across countries. Data on military buildups on which the estimates are based are not available across countries, and even within the U.S. there is little variation in the military measure in the post-war period. Therefore, we adapt the Blanchard-Perotti approach. We acknowledge the potential limitations of this approach but note that the estimated effects of stimulus on interest rates are relatively consistent across empirical specifications, at least for the U.S. (Murphy and Walsh (2017)). As a robustness check, we also identify shocks using semi-annual data on forecast errors for government spending, as in Auerbach and Gorodnichenko (2013). We identify fiscal shocks independently for each country in our sample. To do so, we estimate 4 A 0 X t = A j X t j + ε t, (5) j=1 where X t = [G t,y t,r t ] consists of log real government spending G t, log real GDP, and government bond yields r t. ε t = [ ν t,ε 2 t,ε 3 t ] is a vector of structural shocks, and vt is the shock to government spending. The identifying assumption amounts to a zero restriction on the (1,2) and (1,3) elements of A 0. Unlike Blanchard and Perotti (2002), we do not have quarterly data on tax revenue for our sample. 3, Inequality and the IRRF Here we demonstrate that higher inequality is associated with a lower IRRF, as predicted by our theory. Our measure of inequality is the ratio of the income of the richest 10 percent of the population to the income of the poorest 10 percent, which is provided by the OECD. For each country, we take the average over (inequality is stable over time within countries). There is substantial cross-sectional dispersion in income inequality in our sample. The U.S. is the most unequal country of the sample with an average ratio of 6.2, while Denmark has a ratio of 2.8. Figure 8 documents the inverse relationship between the IRRF and inequality. Indeed, the U.S., which is among the most unequal countries, also has one of the lowest (most negative) IRRFs. 5 What else could account for this inverse relationship? One possibility is that monetary 3 To explore how important is the omission of the tax revenue data, we check how the interest response to fiscal shocks in the VAR changes when tax revenue is included for the U.S. We find that the cumulative one year interest rate response is practically unchanged when tax revenue is added to the VAR. This is consistent with the findings in Ilzetzki et al. (2013) with respect to the output multiplier. 4 We follow Auerbach and Gorodnichenko (2012) and estimate the VAR with the variables in log levels to preserve the cointegration relations. The fiscal shocks backed out from the VAR are stationary. 5 We provide the variance adjusted IRRFs in Figure 2. In Figure 6 of the appendix, we show that a similar relationship holds when using the IRRFs point estimates. Similarly, we find a similar negative relationship between the IRRF and inequality when identify fiscal shocks based on Blanchard and Perotti (2002). See Figure 10 in our Appendix. 15

17 Figure 8 Inequality and Gov. Bond Yield Response policy may be more accommodative of fiscal shocks in unequal countries. The same relationship does not hold when examining policy rates, suggesting that government spending relaxes credit markets relatively more in unequal countries, beyond any response of monetary policy to government spending shocks. 6 This is consistent with the evidence in Murphy and Walsh (2017) that monetary accommodation cannot fully account for the negative IRRF in the U.S. To further isolate the role of inequality from central bank policy and other determinants, we regress the IRRF on measures of central bank independence and financial openness. We use inflation volatility as a measure of central bank independence. There exists a central bank independence (CBI) index from Dincer and Eichengreen (2014). However, this index is only available for a sub-sample of 14 countries. Thus, motivated by Alesina and Summers (1993), who find that the CBI is negatively correlated with the average inflation rate and the volatility of inflation for 16 developed countries in their sample, we use the volatility of inflation as a proxy for central bank independence. Our inflation measures are from the OECD. There is substantial variation: in Iceland and the Slovak Republic the standard deviation of inflation exceeds 3%, while in Germany and Switzerland it is below 1%. Our measure 6 See Figure 11 in our Appendix. 16

18 of financial openness, from Lane and Milesi-Ferretti (2007), is financial assets plus liabilities, over GDP. Mundell-Fleming predicts that countries that are more open to international financial markets have smaller or zero response of interest rates to fiscal shocks. Table 5 shows that the dependence of the IRRF on inequality, conditional on these other determinants. A one standard deviation increase in inequality is associated with an 15 basis point decline in the IRRF. This relationship remains when adding inflation volatility and financial openness in the regression (columns 2 and 3). It is possible that the relationship between inequality and the IRRF is due to a higher elasticity of output with respect to fiscal stimulus (perhaps due to slack, as in Murphy and Walsh (2017)) in countries with high inequality. In this case, interest rates would increase less in countries with more inequality, resulting in higher fiscal multipliers. One way to control for this channel is to include the fiscal multiplier in the regression. Here we define the fiscal multiplier as the cumulative multiplier over a horizon of one year, consistent with Ilzetzki et al. (2013): 3h=0 y h 3h=0 g h, (6) where y h and g h are the impulse responses of output and government consumption at horizon h. Including the cumulative multiplier has no effect on the estimated dependence of the IRRF on inequality (column 4). These results suggest that the measured relationship is not driven by other mechanisms associated with high fiscal multipliers. 7 6 A Simple Model of Debt-Burdened While the previous cross-country facts are indirectly implied by our theory of saving constrained households, in this section we develop a simple model that analytically relates income inequality (the fraction of debt-burdened households) with the interest rate response to fiscal stimulus. Suppose there are two agent types, rich(r) and non-rich (p). The measure of non-rich agents is π [1/2,1), and the measure of rich agents is 1 π. Each agent elastically supplies up to L units of labor in each period, of which there are two: t {0,1}. In each period, there is a representative private firm that solves Π = max (Al α wl), l where w is the wage, which is stuck, and 0 < α < 1. Given w, firm labor demand is l = (w/(αa)) 1/(α 1). We assume that (1) L > l, (2) the firm randomly hires amongst the agents, 7 A similar relationship between inequality and the IRRF (as in Table 5) holds if we use the GINI coefficient of income instead of the ratio p90p10. 17

19 Table 5 Gov. Bond Yields Response and Country Characteristics (1) (2) (3) (4) VARIABLES Bond IRRF Bond IRRF Bond IRRF Bond IRRF p ** -0.13** -0.12* -0.13* (0.07) (0.06) (0.07) (0.07) St. Dev. Inflation (0.08) (0.09) (0.08) Financial Openness (0.08) (0.08) Fiscal Mult. 4 qtrs (0.08) Constant 0.78* (0.38) (0.37) (0.38) (0.44) Observations R-squared * Note: The standard deviation of inflation is measured using the 4 quarters percent change of the CPI index from the OECD databases. Our measure of financial openness is the ratio financial assets plus liabilities to GDP (Lane and Milesi-Ferretti (2007)). Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 and (3) A = (w/α) α (a simplifying normalization). Therefore, firm and worker optimization imply that Π + wl = Al α = 1, that l = α/w, and that each agent s private sector labor income is wl = α, a fraction π of which goes to non-rich agents. Moreover, since l < L there is slack in the labor market in the sense that each agent is willing to supply more labor that the private sector is unwilling to hire at the stuck wage w. In t = 0, the government also hires the agents (again, randomly across types). Specifically, the government demands G = G/w < L l units of labor, which the agents are willing to supply since G + l < L. The government uses the workers to produce government goods and effectively buys these goods from itself. For the purposes of national accounting, these public purchases are valued at their cost. So, G = Gw = π Gw +(1 π) Gw is both the public wage paid to each agent and the value of government purchases in the national accounts. GDP or national income is, in the two periods, Y 0 = Π + wl + w G = Al α + G = 1 + G Y 1 = Π + wl + w G = Al α = 1 We assume that the rich collectively own half of firm profits. Thus, the total private sector pre-tax income of the rich is Π/2+(1 π)wl, while the income of a rich individual is y r = Π/(2(1 π))+wl. Similarly, the private sector pre-tax income of a non-rich individual 18

20 is y p = Π/(2π) + wl, so (1 π)y r + πy p = 1. A useful feature of this setup is that a single parameter, π, governs inequality. As π varies between 1/2 and 1, total private income is fixed at Π+wl = 1. However, since the poorest 50% of agents are always non-rich, the total private pre-tax income of the richest 50% of agents is Π + wl 1 2 ( ) Π 2π + wl, which is monotonically increasing in π. Also, as π 1, half of firm profits are owned by an increasingly small fraction of agents. In the first period, the agents and the government trade zero net supply bonds at gross interest rate R. The government pays for purchases with a flat proportional tax τ on private income in the second period. Since (1 π)y r +πy p = 1, the government budget constraint is RG = τ. The problem of an arbitrary agent of type i {r,p} is max {log(c c 0,c 0 ) + log(c 1 )} subject to 1 (i) : c R c 1 = y i + 1 R yi (1 τ) + G (ii) : c 0 c, where c is the minimum consumption level. Recall that G = Gw is wage income from government work, and y i includes both private profits and wages. Since taxes are proportional to private income but government wages are uniform across agents, fiscal policy redistributes from rich to non-rich. Under the above assumptions, equilibrium with slack in the labor market consists of an interest rate R, agent consumption, and taxes τ such that goods markets clear (π ( c p 0,cp 1) + (1 π)(c r 0,c r 1) = (1,1)), consumption solves the agents problems given prices and taxes, and the government budget constraint is satisfied (RG = τ). 8 To restrict attention to the case of interest in which c r 0 > c p 0 = c, we impose the following additional parameter restriction: Π 4 ( 2π 1 π ) G + Π 2π + wl c < 1. Since Π/(2π) + wl < 1 for π > 1/2, there exists c (0,1) satisfying this condition provided 8 The government goods market clears for free since, by assumption, the government consumes whatever it produces. The labor market doesn t clear since each agent is willing to supply L, while at stuck wage w private and public firms only demand l + G < L units of labor from each agent. 19

21 π > 1/2 and G is sufficiently small. In this case, optimal rich consumption satisfies c r 0 = 1 2 G yr ( R (1 τ) ), which after plugging in the government budget constraint becomes c r 0 = 1 2 (1 yr )G + 1 ( 2 yr ). R Finally, imposing market clearing (πc p 0 + (1 π)cr 0 = 1) and y r = Π/(2(1 π)) + wl, we get 1 R = It immediately follows that 2(1 πc) Π 2 + wl (1 π) 1 ( 1 2(1 πc) = R (1 π)y r 1 yr y r G 1 2 (1/R) G π > 0 Π 2(1 π) + wl ) Π 2(1 π) + G 1 wl = 2 R G π < 0. In other words, the impact of G on R is declining in inequality. Note, however, that in this stripped-down model increasing government purchases actually unambiguously decreases the interest rate, contrary to standard intuition. This is because here government spending destroys no resources. It is straightforward to extend the model to include private goods in government production, in which case the sign of R/ G is ambiguous, and in that case we still have 2 R/( G π) < 0. 7 Conclusions We have presented a new set of micro facts on the consumption behavior of U.S households. In particular, using PSID data we find that low wealth households with high lagged expenditure present low contemporaneous spending propensities. On the other hand, using CEX data we find that the share of households with near zero marginal propensities to consume out of tax rebates increases with household debt. To explain these facts, we develop a theory of saving-constrained household. Our proposed interpretation of these facts is that household expenditure depends on time-varying minimum consumption thresholds that, if violated, yield substantial utility costs. In our setting, debt burdens do not reflect credit constraints but rather result from households 20

22 minimum consumption needs. Adverse idiosyncratic shocks, such as emergency expenditures or temporary declines in income, cause households to take on debt rather than experience a decline in non-emergency consumption. This additional debt is burdensome in the sense that households pay it off more quickly out of additional income than they would in the absence of a minimum consumption constraint. Quick debt repayment helps households avoid very low future consumption (and associated welfare loss) in the event of future adverse shocks. Our theory has implications for the propagation of macroeconomic shocks. Evidence from cross-county variation in the effects of fiscal stimulus on credit markets is consistent with the theory s implications. In the cross section, fiscal shocks increase interest rates less (decrease interest rate more) in countries with high income inequality. Motivated by our main model and the additional facts, we present a tractable model of debt-burdened households where the interest rate response to fiscal shocks depends on income inequality as in the data. 21

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25 8 Appendix Figure 9 Inequality and Gov. Bond Yield Response (not variance adjusted) Figure 10 Inequality and Gov. Bond Yield Response (Robustness check that controls for anticipated changes in G) 24

26 Figure 11 Inequality and Policy Rates Response 25

27 Table 6 Sample for VAR estimation G GDP Interest Rates Credit Country OECD Haver OECD Haver bond ylds. policy rate BIS Australia 1959-Q Q Q Q Q4 Austria 1988-Q Q Q Q Q4 Belgium 1995-Q Q Q Q4 Canada 1957-Q Q Q Q Q2 Czech Republic 1996-Q Q Q Q Q4 Denmark 1977-Q Q Q Q Q4 Finland 1990-Q Q Q Q Q4 France 1955-Q Q Q Q Q4 Germany 1970-Q Q Q Q Q1 Greece 1970-Q Q Q Q Q1 Hungary 1995-Q Q Q Q Q4 Iceland 1997-Q Q Q Q1 Ireland 1997-Q Q Q Q Q1 Italy 1981-Q Q Q Q Q4 Japan 1957-Q Q Q Q Q4 Korea 1960-Q Q Q Q Q4 Netherlands 1988-Q Q Q Q4 New Zealand 1987-Q Q Q Q Q4 Norway 1961-Q Q Q Q Q1 Poland 1995-Q Q Q Q Q4 Portugal 1995-Q Q Q Q Q4 Slovak Republic 1997-Q Q Q Q2 Slovenia 1995-Q Q Q Q1 Spain 1995-Q Q Q Q Q4 Sweden 1960-Q Q Q Q Q1 Switzerland 1980-Q Q Q Q Q4 United Kingdom 1955-Q Q Q Q Q4 United States 1955-Q Q Q Q Q3 * Supplemented by ECB policy rates since 1999-Q1 ** Supplemented by by short term rates from Ilzetzki et al. (2013) and ECB rates Note: Information in cursive means data were not originally seasonally adjusted 26