Ralph Luetticke | Macro Paper Warehouse

A Temporary VAT Cut as Unconventional Fiscal Policy

The paper studies Germany’s temporary 3 percentage-point VAT cut from July 1 to December 31, 2020 (standard rate 19%→16%, reduced rate 7%→5%), combining two causal identification strategies with microdata and a HANK model to establish that intertemporal substitution drove a large spending response concentrated in durable goods.

Ex-ante approach (July 2020 BOP-HH survey, fielded immediately after the cut took effect): The survey distinguishes households informed about the January 2021 reversal (treated) from those who believed the cut was permanent (control). Treated households are approximately 10 percentage points more likely to increase durable purchases on the extensive margin. This is a lower bound on the intertemporal substitution effect because some “control” households likely learned about the reversal before the survey, attenuating the control group’s spending behavior toward that of the treated group.

An endogenous gridpoint method for distributional dynamics

This paper introduces the Distributional Endogenous Gridpoint Method (DEGM), a novel numerical technique for solving the distributional dynamics that arise in heterogeneous agent macroeconomic models. The core problem is how to efficiently update the distribution of agents over the state space as the economy evolves. The dominant existing approach — the “lottery method” of Young (2010) — discretizes the state space and represents policy functions as lotteries over nearby gridpoints, producing a transition matrix that is linear in optimal policies. This linearity renders the lottery method incapable of capturing nonlinear effects in distributional dynamics, a limitation that becomes quantitatively significant for higher-order perturbation solutions.

Financial Frictions: Micro versus Macro Volatility

Research Question. How do consumer credit spreads — the gap between household borrowing rates and deposit rates — affect aggregate business cycle dynamics and the distribution of consumption across the wealth distribution? And what is the welfare trade-off between macroeconomic stabilization and household-level consumption volatility when bank capital requirements are tightened?

Data and Empirical Approach. The empirical analysis draws on Danish administrative register data for 2003–2018, combining approximately 15.5 million household-year observations. Income tax return data, which capture housing wealth, portfolio wealth, bank deposits, and bank and mortgage debt, are merged with bank-level reporting of interest rates submitted to Danmarks Nationalbank (MFI data). Household-specific credit spreads are constructed as the difference between the loan rate at a household’s primary loan bank and the deposit rate at its primary deposit bank in a given year. Consumption is imputed from household balance sheets following the method of Crawley and Kuchler (2023). The empirical specifications include household and time fixed effects, and quantile regressions are run across bins of the net wealth distribution.

Solving discrete time heterogeneous agent models with aggregate risk and many idiosyncratic states by perturbation

This is a solution method for discrete-time heterogeneous-agent models with aggregate risk. It extends the perturbation approach of Reiter (2002, 2009) and complements the continuous-time work of Ahn, Kaplan, Moll, Winberry and Wolf (2017) by placing the dimensionality reduction at a new point in the pipeline: after the stationary equilibrium without aggregate risk has been solved, but before the nonlinear difference equation is linearized. Two reductions do the work. Value (or policy) functions are written as sparse expansions around their stationary-equilibrium counterparts using the discrete cosine transform, with only the largest coefficients allowed to move and the rest held at stationary values — the authors’ analogy is lossy video compression against a lightly compressed reference frame. The joint distribution over idiosyncratic states is factored into its marginal histograms, which vary freely, and a copula, which is held fixed at its stationary value. Because the deviation being zero exactly reproduces the stationary value function, the compression introduces no approximation error in the stationary equilibrium “irrespective of the degree of sparseness that is used in the calculation of the model dynamics.” The problem being solved is concrete: for a household problem with two assets and idiosyncratic income at 50 × 50 × 9 grid points, the distribution and value function are each vectors of 22,500 entries, the Jacobian blocks exceed 45,000 × 45,000, and each would occupy more than 7 GB stored densely. On the Krusell-Smith (1998) benchmark with the JEDC comparison-project calibration, the reduced method’s simulated log capital stock differs from the original Krusell-Smith algorithm’s by 0.0324% on average, exactly as the unreduced Reiter method does, and from the unreduced Reiter solution by 0.0003% on average; its Den Haan error is 0.0100% mean and 0.0191% max, against 0.0051% and 0.0131% for the Krusell-Smith algorithm, which remains the more accurate of the two. Run time is 0.38 seconds versus 91.61 for Krusell-Smith and 1.19 unreduced — “more than 240 times faster,” or 13 times faster once the 7.05 seconds for the stationary equilibrium are included. The scalability claim rests on a two-asset HANK model with 120,000 states and 240,000 controls that “is infeasible to solve for the aggregate dynamics… on the full histogram”: the fixed copula cuts states to 236 and DCT compression at 99.9999% energy cuts controls to 1427, giving a 5-minute solve plus 22 minutes for the stationary equilibrium on a laptop, with Den Haan errors of 0.033% mean and 0.092% max for capital. The costs are stated openly. The selection of retained coefficients is a heuristic, and the coefficients dropped “are only unimportant in the stationary equilibrium,” so robustness must be checked with Den Haan’s test rather than guaranteed. And the fixed copula is not innocuous for every shock: under TFP shocks the Jensen-Shannon distance between the reduced and unreduced joint distributions is a negligible 0.0005, but under idiosyncratic income-uncertainty shocks — which hit the joint distribution directly — the difference “attains a significant order of magnitude,” and recovering accuracy requires perturbing the copula’s own largest DCT coefficients (41 out of a possible 2100 in their example).

Transmission of Monetary Policy with Heterogeneity in Household Portfolios

This paper builds a two-asset Heterogeneous-Agent New Keynesian (HANK) model – households hold a liquid asset (government and household bonds) and an illiquid asset (real capital, traded only with a per-period probability and priced by q-theory) subject to uninsurable idiosyncratic income risk – to ask how heterogeneity in household portfolios shapes monetary transmission. Its central finding is that monetary transmission works predominantly through investment rather than consumption, and that portfolio heterogeneity systematically dampens the investment response: aggregate investment falls by one-third less after a monetary tightening in the model with portfolio heterogeneity than in an otherwise identical model with a representative portfolio, while the direct effect of the policy rate itself explains 86% of the investment response but only one-third of the consumption response, with equilibrium changes in income accounting for the remaining two-thirds of the consumption effect. The dampening of investment operates through two channels tied to redistribution: first, a monetary tightening redistributes income and wealth toward wealthy households who have a low marginal value of liquidity, which lowers the endogenous liquidity premium (the illiquid asset’s return over the liquid asset’s) by 16 basis points and produces incomplete pass-through of the policy rate to the return on capital; second, because wealthy households have high marginal propensities to invest (MPI) but low marginal propensities to consume (MPC) – close to 40% MPC but under 5% MPI near the borrowing constraint, versus roughly twice the MPI above median wealth – redistributing resources toward them stabilizes aggregate investment while amplifying the fall in consumption among wealth-poor, high-MPC households. The paper also shows the Fisher channel of unexpected disinflation, which redistributes from nominal borrowers to savers, quantitatively amplifies the demand-driven output response by about 9% when prices are sticky, but reverses sign under flexible prices, generating an investment boom instead, because only the marginal-propensity-to-invest heterogeneity is then operative. Two empirical exercises corroborate the mechanism: regressing Survey of Consumer Finances household portfolio data on identified monetary shocks, the paper documents that households below median wealth reduce portfolio liquidity after a monetary tightening while households above median wealth increase it – a differential pattern the model can only replicate when capital is imperfectly liquid – and local projections using two measures of the liquidity premium (the Gomme et al. return on capital and the return on housing, both over the risk-free rate, identified via Romer-Romer narrative monetary shocks) show both premia fall after a tightening, consistent with the model’s prediction. The analysis abstracts from financial frictions on the firm side to isolate household-portfolio frictions specifically.

Unconventional but Different After All? A Unified Series of Narrative Monetary Policy Shocks

Asking whether unconventional monetary policy works differently from an interest-rate cut has been hard to answer because the two kinds of policy have been measured with different tools, so any difference in the estimated effects could be a difference in the measuring rather than in the policy. This paper builds one shock series for both, running Romer and Romer’s (2004) narrative regression — policy-rate changes on the Federal Reserve’s own Greenbook/Tealbook forecasts — but substituting Wu and Xia’s (2016) shadow rate for the federal funds rate over the 2009–16 zero-lower-bound period, which yields shocks for 1969–2008 and 2009–16 built the same way. Estimating local projections on the pooled sample with a structural break at the zero lower bound, the authors cannot reject equality of the peak responses of the interest rate, industrial production, unemployment and the consumer price index across regimes (p-values from 0.09 to 0.56), which they read as unconventional policy being about as effective as rate cuts for aggregate activity. Joint Wald tests do reject equality for wealth shares and for the stock-to-house price ratio, and the sign flips: an expansionary conventional shock normalised to 25 basis points lowers the top 10% wealth share by about 0.3% at the trough, while the equivalent unconventional shock raises it by up to about 0.36% and lowers the middle 40% share by about 0.7%. The authors attribute the difference to asset prices — unconventional easing raises the stock-to-house price ratio by over 3% where conventional easing lowers it by about 3.13% — and a mechanical revaluation of Survey of Consumer Finances portfolios reproduces the pattern, with the equity-heavy top 10% capturing most of the gains and households in the bottom groups, who hold little equity and often no housing, receiving comparatively little. The distributional evidence rests on short samples — 1989–2008 for conventional and 2009–15 for unconventional shocks, at quarterly frequency — and the authors do not address the Fed-information-effect and Fed-reaction-to-news concerns directly, assessing them only indirectly by comparison with shock series that are robust to them.