On the Effects of Monetary Policy Shocks on Income and Consumption Heterogeneity

Layer 1: Overview

This paper asks how conventional and informational monetary policy shocks affect the cross-sectional distributions of labor earnings, consumption, and financial income in the United States. The motivation is the growing concern, particularly in the aftermath of the global financial crisis, about distributional consequences of central bank actions. Existing studies either include scalar inequality statistics in standard VARs — losing information about the full distribution — or rely on indirect approaches that hold household portfolio compositions fixed. Chang and Schorfheide instead apply the functional VAR (fVAR) framework developed in Chang, Chen, and Schorfheide (2024, JPE forthcoming) that stacks macroeconomic aggregates alongside the full time-varying cross-sectional density, represented as a log probability density function approximated via a cubic-spline sieve. This allows simultaneous, internally-consistent IRFs for percentiles, Gini coefficients, 90-10 ratios, standard deviations, and other distributional statistics without the risk of quantile crossings.

The earnings analysis uses monthly micro data from the Current Population Survey (CPS), sample period 1990:M2 to 2016:M12. The consumption and financial income analyses use quarterly Consumer Expenditure Survey (CEX) data from 1990:Q2 to 2016:Q4. Monetary policy shocks are identified via the Jarocinski-Karadi (2020) high-frequency instruments — surprises in the three-month fed funds futures and in S&P 500 index — used as internal instruments in the structural VAR. The instruments isolate (a) conventional monetary policy shocks (interest rate surprise, stock price opposite direction) and (b) informational shocks (interest rate and stock price surprise in the same direction). Sign restrictions set-identify the two shocks. Bayesian estimation uses a Chan (2022) Normal-Inverse Gamma prior suitable for high-dimensional VARs; model selection (sieve order K, lag length p, hyperparameters) is done by maximizing the marginal data density (MDD). The shock normalization corresponds to an unanticipated 25-basis-point cut in the three-month federal funds rate.

Main quantitative findings:

Earnings (conventional shock): An expansionary shock reduces earnings inequality, primarily through the employment (extensive) margin. At the posterior median, the 10th earnings percentile rises by up to 5% relative to steady state, the 20th percentile by up to 1%, while the 80th and 90th percentiles are essentially unaffected. The Gini coefficient for labor earnings falls from approximately 0.431 to 0.428 over a 36-month horizon. The 90-10 earnings ratio falls from approximately 12.27 to 11.76 after 36 months. These effects are driven almost entirely by individuals moving from unemployment into employment (the point mass at zero in the earnings distribution falls as the unemployment rate drops by approximately 0.3 percentage points at the posterior median after three years). When the unemployed point mass is excluded from the inequality computation, the inequality effect is small and short-lived, confirming that the employment channel dominates. The estimated Gini drop of 0.001–0.003 is broadly consistent with the HANK model of Ma (2021) with indivisible labor, which predicts a drop of approximately 0.001 for a comparable shock.

Consumption (conventional shock): The expansionary shock generates a weakly positive (inequality-increasing) effect on consumption inequality at the posterior median, but with wide credible bands that span both positive and negative values. The cross-sectional standard deviation of consumption, the 90-10 ratio, and the Gini coefficient all peak upon impact and remain above steady state. The slight increase appears concentrated in durable goods expenditure; nondurable and service consumption inequality shows little response at the posterior median. The contrast with the earnings result reflects: (i) only labor income is captured in the earnings analysis, while wealthy households’ capital income (rising with equity and bond prices) also rises; (ii) potentially higher interest-rate sensitivity of high-consumption households.

Financial income (conventional shock): No statistically significant effect on financial income inequality. The cross-sectional standard deviation and Gini coefficient of financial income do not respond to the shock. An important caveat is that the CEX misses the top-10 percent of households by financial income (visible from CDF comparison with the Survey of Consumer Finances in 2012). The households most likely to benefit from equity and bond price appreciation — captured in other studies — are absent from the sample.

Informational shock: A negative informational shock (unexpected simultaneous drop in interest rates and stock prices, signaling worse-than-expected output) increases earnings inequality, mainly via a rise in unemployment. The 10th earnings percentile drops by about 2% at the posterior median. Consumption inequality, by contrast, shows the opposite pattern: the 90-10 ratio and Gini coefficient for consumption decrease, and the posterior median responses are negative, though uncertainty is substantial.

Policy implication: The authors conclude that earnings inequality effects of conventional monetary policy are well-proxied by the unemployment rate response, so standard macro indicators subsume the distributional information for earnings. The small and highly uncertain responses of consumption and financial income inequality provide, in their view, support for central banks continuing to focus primarily on macroeconomic aggregates.

Layer 2: Deep Dive

What is the identification strategy for monetary policy shocks and what are the main threats to validity?

The paper uses the Jarocinski-Karadi (2020) high-frequency instruments as internal instruments in a structural VAR. The two instruments are surprises in the three-month federal funds futures (ff4_hf) and surprises in the S&P 500 index (sp500_hf), measured in narrow windows around FOMC announcements. Sign restrictions separate two shocks: a conventional shock is identified by an interest rate increase combined with a stock price fall; an informational shock by both increasing. The key assumptions are instrument relevance (the instruments are correlated with the policy shocks) and instrument validity (the instrument innovations are uncorrelated with non-policy structural shocks). As a robustness check the authors also use the Nakamura-Steinsson (2018) instruments and report very similar results. The main threat to validity is the standard one for external-instrument SVARs: the instruments may capture other economic news released simultaneously with FOMC decisions, violating the exclusion restriction. The informational shock identification partially addresses this by explicitly modeling the central bank’s information revelation.

What is the functional VAR approach and why is it preferred over simpler alternatives?

The functional VAR stacks macroeconomic aggregates Yt with the time-varying cross-sectional log-density of micro outcomes. The log-density is approximated by a finite-dimensional linear sieve (cubic spline basis of order K). Sieve coefficients are estimated period-by-period by maximum likelihood from the cross-section, then treated as observations in a standard VAR. The MDD selects K, lag order p, and Minnesota-type hyperparameters jointly. Compared to simply including a few inequality statistics in a VAR, the functional approach (a) derives a single coherent model from which arbitrarily many distributional statistics can be computed without quantile crossings; (b) achieves tighter credible intervals by efficiently compressing cross-sectional information through the sieve; (c) avoids the problem of internally inconsistent forward projections of stacked quantile VARs. Compared to indirect approaches (e.g., McKay-Wolf 2023), it does not require the assumption that household income or portfolio composition is fixed in response to the shock. Compared to panel approaches, it does not require high-frequency panel data, which are unavailable for the US at relevant horizons.

How is the earnings distribution modeled to handle unemployment?

The earnings distribution is treated as a mixture of a point mass at zero (representing unemployed individuals, whose weight equals the CPS-based unemployment rate) and a continuous part (the density of positive earnings of employed individuals, normalized to integrate to one minus the unemployment rate). The sieve density is estimated only from the positive-earnings observations, with a top-coding adjustment for right-censored values. The unemployment rate is included separately as an aggregate variable in the Yt vector. This mixture representation allows the analysis to separately identify the extensive-margin (employment) channel — changes in the probability mass at zero — from the intensive-margin channel (changes within the positive-earnings density). The key finding is that inequality effects are driven almost entirely by the extensive margin.

What heterogeneity in earnings responses is documented?

In percentage terms, the expansionary monetary policy shock has the largest impact at the 10th earnings percentile (posterior median response of 0 to 5%), capturing workers moving out of unemployment. The 20th percentile rises by 0 to 1%. The 80th and 90th percentiles show essentially zero response. Earnings above 2 times GDP per capita (roughly twice the labor share of GDP per capita) are essentially unaffected. When the point mass at zero is excluded and only the continuous part of the earnings distribution is analyzed, the effect on inequality statistics (Gini, 90-10 ratio) is small and short-lived, confirming that the heterogeneous response across the full distribution is driven almost entirely by the employment transition at the bottom.

What heterogeneity in consumption responses is documented, and why might consumption inequality rise while earnings inequality falls?

At the posterior median, both the 10th and 20th consumption percentiles initially rise above steady state (h=1), then fall 0.9% to 1.3% below baseline from h=5 onwards. The 80th and 90th percentile responses are quantitatively similar in shape but slightly larger in magnitude, leading to a weakly positive net inequality effect. The Gini coefficient and 90-10 ratio for consumption peak upon impact and stay above steady state. The authors offer two explanations for the inequality-increasing result despite earnings inequality falling: (i) wealthy households also earn substantial capital income (equities, bonds) that rises with the expansionary shock, boosting their total resources and hence consumption, a channel not captured by earnings alone; (ii) higher-consumption households may have more interest-rate-sensitive consumption decisions (larger direct Euler-equation effect), or may be wealthy hand-to-mouth consumers with high MPCs. The component analysis shows the increase is concentrated in durable goods, while nondurable and services Gini responses are near zero at the posterior median.

What does the financial income analysis find and what data limitation is most important?

The financial income distribution estimated from the CEX shows no statistically significant response to either the level or inequality of financial income following a conventional monetary policy shock. The cross-sectional standard deviation and Gini coefficient of financial income are essentially flat. The most important caveat is that the CEX substantially underrepresents high-financial-income households. A CDF comparison with the Survey of Consumer Finances for 2012 shows that the CEX misses the top-10 percent of households by financial income. These are precisely the households most likely to experience capital gains from equity and bond price appreciation following an interest rate cut. The fraction of households with essentially zero financial income (the point mass κt) fluctuates between 0.65 and 0.82 over the sample, so the analysis is largely capturing the lower 65–82 percent of the financial income distribution.

What is the informational shock and how do its distributional effects differ from the conventional shock?

An informational shock is defined as an unanticipated change in interest rates that conveys private central-bank information about the state of the economy — for example, a rate cut that signals the central bank expects worse output and prices than the public. It is identified by the simultaneous drop in interest rates and stock prices, the opposite pattern from the conventional shock. Aggregate effects: real GDP drops approximately 20 basis points and unemployment rises up to 0.15 percentage points after one year. Earnings distributional effects are roughly the mirror image of the conventional shock: the 10th earnings percentile drops about 2% at the posterior median, while other percentiles change little. The Gini coefficient and 90-10 ratio for earnings rise in the long run, driven by the increase in unemployment. Consumption distributional effects are different: relative consumption at the 10th and 20th percentiles rises, while the 90th percentile falls slightly, so consumption inequality (90-10 ratio, Gini) decreases. However, since aggregate consumption also falls, the rise in relative consumption at the bottom does not imply an absolute gain.

How does this paper relate to and differ from Coibion, Gorodnichenko, Kueng, and Silvia (2017)?

CGKS (2017) include inequality statistics directly in a VAR and use the Romer-Romer shock measure. For earnings, they find the Gini coefficient rises by about 0.0025 per 100bp contractionary shock (i.e., falls by 0.0025 for an expansionary shock); adjusting for shock size this is slightly smaller than the Chang-Schorfheide estimate of a 0.001–0.003 Gini drop per 25bp expansionary shock (which scales to 0.004–0.012 per 100bp). For consumption, CGKS find that inequality decreases in response to an expansionary shock, the opposite sign from Chang-Schorfheide’s posterior-median result (weakly increasing). The discrepancy may reflect: (i) the functional approach’s more flexible modeling of the full distribution versus using a single Gini; (ii) differences in shock identification (Romer-Romer vs. JK instruments); (iii) sample period differences. The wide credible bands in the consumption result mean the two findings are not statistically inconsistent.

What robustness checks are conducted?

The authors run the following robustness exercises: (i) Nakamura-Steinsson (2018) instruments instead of Jarocinski-Karadi (2020) for the earnings VAR — results are very similar. (ii) Model selection across sieve order K ∈ {4,6,8,10} and lag length p ∈ {1,2,3,4} via MDD maximization, confirming that results are robust to the choice of approximation order. (iii) For the earnings inequality analysis, the paper explicitly separates the contribution of the employment margin from the wage distribution within employment, by recomputing inequality statistics excluding the point mass at zero — confirming that the employment channel dominates. (iv) Comparison of aggregate IRFs across all four model specifications (aggregate VAR, earnings fVAR, consumption fVAR, financial income fVAR) showing that inclusion of cross-sectional data does not substantially alter inference about aggregate variables. (v) Comparison with time-aggregated monthly-to-quarterly rescaled IRFs to validate that monthly and quarterly specifications produce consistent results.

What are the scope conditions and limitations of the findings?

Key scope conditions: (a) The sample runs through 2016:Q4/M12, so the post-2016 period and the 2020 pandemic episode are excluded. (b) The paper uses repeated cross-sections rather than a panel, so it directly estimates how the cross-sectional distribution evolves but cannot separately identify cohort effects, individual trajectories, or nonlinearities in unit-level histories. (c) The CEX substantially misses high-financial-income households, making the financial income results inapplicable to the top 10% of the financial income distribution. (d) The functional VAR models the unconditional distribution; it does not identify heterogeneous responses by subgroup in the sense of comparing specific groups (e.g., mortgagors vs. owners) as pseudo-panel approaches do. (e) The approach identifies the average linear response to a 25bp shock; nonlinear or asymmetric effects (large shocks, ZLB periods) are not modeled. (f) The simultaneous drop in earnings inequality and (weakly) rising consumption inequality cannot be fully reconciled without a complete model including capital income; the paper acknowledges this limitation explicitly.

How do the quantitative results compare to the Ma (2021) HANK model benchmark?

Ma (2021) incorporates an indivisible labor supply mechanism into a HANK model and shows that an expansionary monetary policy shock raises wages, inducing low-productivity workers to enter the labor market, raising earnings in the left tail. His calibration produces a Gini coefficient drop of approximately 0.001 for a comparable shock (scaled from his Figure 3: −0.4/(4×100) = −0.001 on a 0-to-1 scale for a 100bp shock). The Chang-Schorfheide empirical estimate is a drop of between 0.001 and 0.003 for a 25bp shock, which is broadly consistent with Ma’s model. The qualitative mechanism — earnings inequality reduction driven by low-productivity workers transitioning out of unemployment — is also consistent with the Chang-Kim (2006) heterogeneous-agent model with indivisible labor, which generates a negative correlation between idiosyncratic productivity and reservation wage.

What are the policy implications for central banks?

The paper provides semi-structural empirical evidence relevant for central banks concerned about distributional effects. The main conclusion is that for labor earnings inequality, the distributional effect of conventional monetary policy is well-summarized by the unemployment rate response: reducing unemployment compresses earnings inequality, and a central bank that targets unemployment de facto targets earnings inequality. The small, uncertain, and sometimes-positive effects on consumption and financial income inequality suggest that tracking these additional distributional statistics adds little actionable information beyond what standard macro aggregates already convey. The authors therefore conclude that there is an empirical case for central banks to continue focusing on macroeconomic aggregates. An important qualifier is that the financial income results are constrained by CEX top-coding, so the analysis cannot speak to very-high-income households’ welfare.

Key Concepts

Functional VAR (fVAR): A vector autoregression in which macroeconomic aggregates are stacked with the full cross-sectional log-probability density function of micro outcomes. The log-density is approximated by a finite-dimensional sieve (cubic spline basis), with sieve coefficients estimated period-by-period from cross-sectional data and then entered as observations in a linear VAR. This yields coherent IRFs for the entire distribution — percentiles, Gini, 90-10 ratio, etc. — from a single model, avoiding the quantile-crossing inconsistency of stacked-quantile approaches.

Employment channel (extensive margin): In this paper, the mechanism by which an expansionary monetary policy shock lowers earnings inequality: it reduces the unemployment rate, moving workers from a point mass of zero earnings into the positive-earnings distribution. The paper distinguishes this from the intensive margin (changes in wage rates conditional on employment), and finds empirically that the extensive margin dominates the inequality response of labor earnings.

Informational shock (central bank information shock): As defined following Jarocinski-Karadi (2020): an unanticipated change in short-term interest rates that conveys the central bank’s private assessment of economic conditions. Identified by the simultaneous movement of interest rates and stock prices in the same direction, opposite to a conventional monetary policy shock. A negative informational shock (rates and equity prices both fall) signals that the central bank expects weaker output and prices than the public, and leads in this paper to rising earnings inequality via higher unemployment.

Point mass at zero (earnings distribution): The concentration of probability mass at zero earnings, corresponding to the fraction of individuals in the labor force who are unemployed (the CPS-based unemployment rate). The total earnings density is modeled as a mixture of this point mass and a continuous density for positive earnings. The IRF for the point mass is the IRF for the unemployment rate; including it in inequality computations is necessary to capture the full distributional effect of employment transitions.

Log probability density function (log-pdf) sieve representation: The modeling device that represents each period’s cross-sectional distribution as the logarithm of a probability density, approximated by a finite linear combination of cubic spline basis functions (order K chosen by MDD). Working in log-pdf space avoids non-negativity and monotonicity constraints, enabling coherent linear propagation through the VAR law of motion; the density is recovered by exponential normalization in each period.

Marginal data density (MDD) model selection: The Bayesian integrated likelihood used in this paper to jointly select the sieve approximation order K, lag length p, and Minnesota-type hyperparameters. The MDD balances in-sample fit (the log-spline likelihood) against a dimensionality penalty, thereby avoiding overfitting. A key result is that the preferred earnings fVAR uses K = 10 with a single lag, while the smoother consumption distribution is adequately captured with K = 6.

κt (financial income point mass): The time-varying fraction of households in the CEX with financial income below a threshold x (set at the 10th percentile of pooled standardized financial income ≈ 0.0014 of the capital share of per-capita GDP). κt fluctuates between 0.65 and 0.82 over 1990–2016, meaning 65–82 percent of households have negligible financial income in a given quarter. The CEX data constraint — missing the top-10 percent of high-financial-income households — is the principal limitation on the financial income analysis.