Financial Frictions: Micro versus Macro Volatility

Overview

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.

Model. The authors develop a Heterogeneous Agent New Keynesian (HANK) model with explicit banking intermediation. Banks, subject to an agency friction following Gertler and Karadi (2011) — in which bankers can divert a fraction λ = 0.381 of assets — combine household deposits with net worth to invest in corporate equity and consumer loans. This leverage constraint generates an endogenous, countercyclical spread between borrowing and saving rates. Households face idiosyncratic income risk and a kink in their budget constraint at zero net worth due to the spread. The supply side features New Keynesian sticky prices (Rotemberg quadratic adjustment costs) and a Taylor rule. Aggregate shocks include monetary policy surprises, total factor productivity (TFP), and capital quality shocks (affecting bank net worth). The model is solved by first-order perturbation using the method of Bayer and Luetticke (2020) and calibrated to Danish macro and micro moments for 2003–2018.

Main Empirical Findings.

• The average consumer credit spread in Denmark is strongly countercyclical, with a cross-correlation with HP-filtered output of −0.44 in the data (−0.31 in the model).
• Higher credit spreads increase the transition rate into the zero net wealth state for households with moderately positive wealth at the beginning of the year, and reduce the outflow rate for households already at zero net wealth.
• Pooled OLS (with household and time fixed effects) finds that a higher spread is negatively associated with consumption (coefficient −0.266), and the interaction between spread and log income is positive (coefficient 1.366), indicating that higher spreads raise income sensitivity of consumption. For below-median wealth households, the income–consumption link is stronger and the negative spread effect on consumption is larger.
• The consumption-income elasticity derived from quantile regression estimates has a standard deviation of 2.4 percent and a cross-correlation with output of −0.53 when spread variation is incorporated; holding spreads constant roughly halves the volatility (to 1.3 percent) and reduces the countercyclicality (cross-correlation −0.31).

Model Aggregate Findings.

• Consumer credit is procyclical (cross-correlation with output 0.56 in data, 0.67 in model) and more than twice as volatile as output (standard deviation ratio 2.11 in data, 1.51 in model).
• Capital quality shocks and monetary policy shocks are amplified at the aggregate level through a financial accelerator working through endogenous spread movements. TFP shocks generate little spread amplification because households’ labor supply responses partially insulate banks’ net worth.
• A 1 percentage point contractionary monetary policy shock leads to a sharp, persistent decline in aggregate output and investment, and is amplified relative to a constant-spread HANK benchmark.

Distributional Findings.

• In response to a contractionary monetary policy shock, consumption of households at the 10th percentile of the consumption distribution (who are indebted) falls sharply in the short run, while consumption of the 90th percentile (wealthy households) rises in the short run due to higher returns on savings. The responses converge across the distribution in the medium run as spreads normalize.
• When the consumer credit spread is held constant, consumption paths move in parallel across the wealth distribution, demonstrating that endogenous spread movements are the key driver of distributional effects for monetary policy and capital quality shocks.
• The MPC is countercyclical in the model, with a cross-correlation with output of −0.60 (unconditional), compared with −0.53 for the empirically-estimated consumption-income elasticity. The consumption-income elasticity and MPC are correlated at 90 percent in the model at the annual rate.

Macroprudential Regulation.

• A tightening of bank capital requirements reducing leverage by 10 percent (diversion parameter λ rising from 0.381 to 0.445) reduces output volatility by 5.5 percent and investment volatility by 10.1 percent, and does so at apparently no long-run aggregate cost in the HANK setting (precautionary savings stimulate output and consumption in the stationary equilibrium).
• However, the regulation increases the annual consumer credit spread by 40 basis points, raises household consumption volatility across the wealth distribution (from about 8 percent to 10 percent for the poorest households under idiosyncratic shocks alone), and generates welfare losses across all deciles equivalent to 0.24–4.28 percent of consumption (with aggregate welfare loss of 0.79 percent).
• When aggregate shocks are included, the lower cyclical sensitivity of spreads partially mitigates welfare losses for the poorest 80 percent of the population, but the overall welfare effect remains negative with an aggregate loss equivalent to 0.58 percent of consumption. The paper thus documents a trade-off between macro volatility (stabilized) and micro volatility (increased).
• Results are robust to the extension of the model to three assets (including illiquid assets), which provides a better fit to micro data without materially changing the welfare conclusions.

Q&A

Q1: What is the specific Danish dataset used, and how is consumption constructed? A: The dataset covers 2003–2018 from Statistics Denmark administrative registers, combining income tax return data (which report end-of-year balances on all bank accounts, housing wealth, portfolio wealth, bank deposits, bank loans, and mortgage debt) with bank-level MFI interest rate reporting submitted to Danmarks Nationalbank. The total sample is approximately 15.5 million household-year observations (about 1.76–1.97 million households per year). Consumption is imputed as after-tax labor income plus after-tax financial income minus the change in end-of-year net worth, following Crawley and Kuchler (2023). Households with self-employment, housing transactions in the current or prior year, negative imputed consumption, or in the bottom and top 1 percent of wealth or income distributions are excluded.

Q2: How are household-specific credit spreads constructed from the administrative data? A: Each household’s primary loan bank is defined as the bank where it holds the largest loan balance at end of calendar year, and the primary deposit bank as the one holding the largest deposit balance. The household-specific spread is the difference between the loan rate applied by the primary loan bank and the deposit rate applied by the primary deposit bank, both measured as averages over the calendar year. If a household has no loans, the loan rate of the primary deposit bank is used. This construction yields a household-level interest rate spread that moves countercyclically at the aggregate level (cross-correlation with HP-filtered output of −0.44).

Q3: What do the empirical results say about the relationship between spreads and the probability of a household reaching zero net wealth? A: Equation (2) is estimated as a linear probability model for the transition to zero net wealth (defined as net assets within plus or minus two weeks of 2007 median weekly income). Higher spreads significantly increase the transition rate into zero net wealth for households with moderately positive net wealth at the beginning of the year (those in the third to sixth net wealth bins), and reduce the outflow rate from zero net wealth for households already in that state. Higher spreads also appear to increase debt repayments for indebted households (third to fifth bins), making it more difficult for them to accumulate wealth. Households at the extremes of the wealth distribution (very poor or very wealthy) show essentially no sensitivity of transition rates to spread movements.

Q4: What do the consumption regressions in Table 1 find, and what is the key identification caveat? A: The pooled regression (column 1) finds a positive income–consumption coefficient of 0.372, a negative spread coefficient of −0.266, and a positive income–spread interaction of 1.366, all statistically significant with standard errors clustered at the household level (15,610,327 observations, R² = 0.591). When interacted with below-median wealth (column 2), the income coefficient is larger (0.397 versus 0.335 for above-median), the spread effect is more negative for below-median wealth (−0.362 versus −0.101 for above-median), and the income–spread interaction is stronger for below-median wealth (1.640 versus 0.875). The authors explicitly note that these results should not be given a causal interpretation, as income and consumption are likely jointly determined. Institutional features of the Danish mortgage market (covered bonds, competitive market, rates independent of borrower credit situation) minimize confounding from mortgage rate correlation with consumer credit spreads.

Q5: How do the quantile regression results and the derived consumption-income elasticity demonstrate countercyclical MPC? A: Quantile regressions across five-percent bins of the net wealth distribution show that income coefficients decline with wealth (from nearly 0.5 for the poorest to about 0.35 for the wealthiest households), spread coefficients are negative for households with negative, zero, and moderately positive wealth and positive for significantly wealthy households, and the income–spread interaction term is positive for all but the richest households (largest near zero net wealth). The consumption-income elasticity is computed as β₀,ⱼ + β₂,ⱼ × spread at the household level, then averaged cross-sectionally. When only wealth distribution shifts are allowed, the elasticity’s standard deviation is 1.3 percent and its cross-correlation with HP-filtered output is −0.31. When spread variation is also incorporated, standard deviation rises to 2.4 percent and the cross-correlation becomes −0.53. This measure is highly correlated (90 percent) with the model MPC, supporting the inference that the MPC is countercyclical.

Q6: What is the structure of the banking sector in the HANK model, and how does the agency friction generate a countercyclical spread? A: A continuum of banks combines household deposits with net worth to invest in corporate equity and consumer loans. Bankers can divert a fraction λ = 0.381 of assets, and if they do so, depositors can recover only the remaining fraction (1 − λ). This threat of diversion constrains the supply of deposits, resulting in banks needing to earn excess returns — Et(RK,t+1 − RS,t+1) > 0 — on their assets relative to the deposit rate. The leverage ratio is bounded above by ϱt/λ, where ϱt is a value multiplier that depends on current and expected future excess returns. When an adverse shock (capital quality shock or monetary tightening) reduces banking sector net worth, the leverage constraint tightens, banks reduce asset supply, and the spread between the return on capital (and hence the consumer loan rate, which is proportional to RK at markup ωB = 0.0075) and the deposit rate rises. This generates the observed countercyclical credit spread.

Q7: In the model, how do aggregate shocks affect the distribution of consumption, and why is the monetary policy shock particularly distributional? A: A one-percent capital quality shock reduces both wages and bank net worth, causing spreads to rise. In the baseline economy, rising borrowing rates lead to a large reduction in consumption for indebted households (10th percentile) while the constant spread model shows near-parallel movements across the distribution. A one-percentage-point monetary policy shock reduces equity returns, depressing bank net worth and (with a lag) raising spreads. Indebted households face both lower labor income and higher borrowing costs, producing a sharp consumption decline at the 10th percentile; wealthy households gain from higher returns on savings, so their consumption rises in the short run. Responses converge as spreads return to normal over the medium run. This matches empirical evidence from Holm, Paul, and Tischbirek (2021) for Norway. For TFP shocks, banks’ net worth is less affected because households’ higher labor supply partially offsets the productivity decline, so spreads move little and distributional effects are smaller (driven mainly by wage effects across the distribution).

Q8: How does the financial accelerator in the HANK model compare to the RANK version? A: In response to capital quality shocks and monetary policy shocks, the HANK model with banking frictions generates amplification relative to a constant-spread HANK benchmark, confirming the presence of a financial accelerator. However, relative to the RANK model, the incomplete markets model implies slightly less amplification of aggregate investment and consumption. This is because, in the HANK model, households facing higher credit spreads increase their labor supply (precautionary motive), which partially stabilizes aggregate income and moderates the financial accelerator. The finding that heterogeneous agent aspects are less important at the aggregate level is consistent with Berger, Bocola, and Dovis (2020). For TFP shocks, the financial accelerator through spreads is largely absent in both HANK and RANK, as spread changes are minor.

Q9: What are the long-run aggregate effects of tightening bank capital requirements (reducing leverage by 10 percent) in the HANK versus RANK model? A: In the RANK model, higher capital requirements increase the annual spread between the return on capital and the deposit rate by 25 basis points, reduce the aggregate capital stock by 2.4 percent, output by 0.5 percent, and aggregate consumption by 0.8 percent. In the HANK model, the spread increases by 40 basis points annually, but the mechanism differs: much of the spread change is absorbed by a reduction in the deposit rate (from 3.81 percent to 3.54 percent annually) rather than an increase in the capital return. Households respond to the lower deposit rate and higher credit costs by increasing precautionary savings and labor supply, so aggregate output and consumption actually rise slightly in the HANK stationary equilibrium. The capital requirements thus appear costless at the aggregate level in the HANK model — but this masks welfare costs that operate through the idiosyncratic risk channel.

Q10: What are the quantitative welfare costs of macroprudential regulation, and how do they vary across the wealth distribution and between idiosyncratic and aggregate shocks? A: Welfare is measured as the fraction of lifetime consumption households are willing to give up to stay in the unregulated baseline. In the face of idiosyncratic shocks only, welfare losses range from 0.24 to 0.43 percent of consumption for the first seven wealth deciles, and reach 4.28 percent for the richest decile (primarily because of the reduction in the return on their savings), with an average welfare loss of 0.79 percent. When aggregate shocks are added, the losses are substantially reduced for the poorest 80 percent (due to lower cyclical sensitivity of spreads), but remain large for the wealthiest decile (4.23 percent) and in aggregate (0.58 percent). These results are robust to the three-asset model extension, where the poorest households are approximately welfare-neutral under the regulation when aggregate shocks are included (0.00 percent), but aggregate welfare losses remain at 0.75 percent.

Q11: How does the three-asset model extension (with illiquid assets) affect the key results? A: In the three-asset extension, households can hold illiquid capital (calibrated with an adjustment probability of φk = 0.0025 per quarter, targeting the Danish ratio of bank deposits to output of 34 percent), creating wealthy hand-to-mouth households who have illiquid assets but no liquid assets. The consumption impulse responses across the wealth distribution remain very similar to the two-asset baseline: endogenous spread movements generate heterogeneous consumption dynamics in response to capital quality and monetary shocks, while constant-spread models produce near-parallel responses. The three-asset model provides a better fit to the micro data (consumption-spread-income relationship across the wealth distribution), but the welfare conclusions from macroprudential regulation are essentially unchanged: welfare losses across the distribution in the stationary equilibrium, partially mitigated when aggregate shocks are added, with losses concentrated in the richest decile.

Q12: What robustness checks are reported for the empirical consumption regressions? A: Three robustness exercises are reported. First, capitalizing car purchases using their official tax value (rather than treating car purchases as current expenditure) yields coefficients similar to the baseline (Table 10). Second, excluding households who purchase a car in the current or prior year (reducing the sample to 13.24 million observations) also leaves results unchanged. Third, first-differenced specifications (equation 42, with and without household fixed effects) produce results similar to the levels specification; the main exception is the spread effect for above-median wealth households when household fixed effects are omitted from the differenced specification (Table 11). The income–spread interaction is consistently positive and significant across all robustness checks.

Q13: What evidence does the paper provide that the model’s MPC is countercyclical and that credit spreads are the primary driver? A: Figure 7 shows impulse response functions of the average MPC to each of the three aggregate shocks. In all three cases, the MPC rises in recessions (countercyclical). The key mechanism is that adverse shocks cause spreads to rise, increasing the mass of households at the kink in the budget constraint (zero liquid assets), where MPCs are highest. When the consumer credit spread is held constant, the MPC remains countercyclical but close to constant, indicating that spread movements account for most of the cyclical variation in MPC. Eliminating the spread altogether implies an acyclical MPC (Table 12, Appendix D). The unconditional cross-correlation of the model MPC with output is −0.60, compared with −0.53 for the empirically estimated consumption-income elasticity in the Danish data.

Key Concepts

Consumer credit spread (borrowing-saving spread): In the paper, this is the difference between the gross real interest rate on consumer loans (RL,t) charged by banks and the gross real return on deposits (RS,t) received by savers. It is not an abstract measure of credit conditions but a household-specific, bank-derived rate gap that moves countercyclically due to banking agency frictions and creates a kink in households’ budget constraints at zero net worth. Distinct from mortgage spreads (which in Denmark are market-determined and independent of borrower credit conditions).

Kink in the budget constraint: The household budget constraint has a kink at zero net assets because borrowers face RL,t > RS,t; households at exactly zero liquid assets (type IV in the paper’s taxonomy) face a discrete jump in the cost of additional borrowing. This kink creates a mass point in the wealth distribution at zero net wealth, and households at this kink have higher MPCs than unconstrained savers or borrowers. The size of the mass point increases when the spread rises.

Financial accelerator (in the HANK-with-banking context): The amplification mechanism in which shocks that reduce banking sector net worth tighten banks’ leverage constraints, raise credit spreads, reduce asset supply to both the corporate sector and households, and further depress investment and consumption — which in turn reduces bank net worth further. In this paper, the accelerator operates through the consumer credit spread channel in addition to the standard corporate lending channel, and is present for capital quality and monetary policy shocks but not materially for TFP shocks.

Countercyclical MPC: The MPC — defined as the response of consumption to a small transitory income shock — rises during recessions and falls during expansions in this model. The mechanism is that recessions are associated with higher consumer credit spreads, which expand the mass of households at or near the zero net wealth kink (high MPC), and contract the mass of unconstrained savers (low MPC). This is a distinct source of MPC cyclicality from the wealth distribution channel alone.

Agency friction (diversion problem): Banks can divert a fraction λ of their assets; if they do so, depositors can recover only the fraction (1 − λ) and the bank is liquidated. This threat limits depositors’ willingness to supply funds, resulting in an incentive-compatibility constraint on bank leverage: assets cannot exceed ϱt/λ (where ϱt is the bank’s franchise value multiplier). When ϱt declines (because expected excess returns fall), the constraint binds more tightly and the spread between the return on assets and the deposit rate must be positive to sustain bank participation.

Macro versus micro volatility trade-off: The paper uses this phrase to describe the finding that tighter bank capital requirements (restricting leverage) reduce the cyclical volatility of aggregate output and investment (macro volatility falls) while simultaneously increasing the volatility of individual household consumption streams due to higher credit spreads and lower deposit returns (micro volatility rises). Welfare costs from increased micro volatility outweigh the aggregate stabilization benefits.

Consumption-income elasticity (d log c / d log y): A time-varying cross-sectional average measure derived from quantile regression parameter estimates, equal to β₀,ⱼ + β₂,ⱼ × RSi,t for household i in wealth bin j. It is used in the paper as an empirical proxy for the MPC (not a direct estimate), and is shown to be highly correlated with the model MPC (cross-correlation of 90 percent at the annual rate). Its cyclicality is stronger when spread variation is incorporated (standard deviation 2.4 percent, cross-correlation with output −0.53) than when spreads are held fixed (standard deviation 1.3 percent, cross-correlation −0.31).