E60 | Macro Paper Warehouse

Bridging micro and macro production functions: The fiscal multiplier of infrastructure investment

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates the fiscal multiplier of infrastructure investment, specifically by incorporating firm-level investment decisions — a dimension absent from prior literature. The central analytical challenge is bridging the micro (firm-level) and macro (state-level) production functions for infrastructure, given that public capital is non-rivalrous: it can be used simultaneously by all firms without being depleted. The paper demonstrates that this non-rivalry generates a systematic discrepancy between firm-level and aggregate-level estimates of the elasticity of substitution between private and public capital, and it shows how this discrepancy shapes the magnitude of the fiscal multiplier.

Data and Methodology

The authors build and estimate a heterogeneous-firm general equilibrium model. Firms operate a constant-elasticity-of-substitution (CES) production function using private capital, non-rivalrous public capital (infrastructure), and labor. Firms are subject to idiosyncratic productivity shocks and make lumpy investment decisions subject to both fixed and convex capital adjustment costs, following Cooper and Haltiwanger (2006) and Winberry (2021). The economy has two regions — one with poor infrastructure and one with good infrastructure — motivated by the near-invariant cross-state distribution of infrastructure spending observed in U.S. data.

The model is estimated via an extended Simulated Method of Moments (SMM) that treats market clearing prices as additional parameters estimated simultaneously with structural parameters, reducing computational cost relative to standard GE estimation. Estimation uses a multi-block Metropolis-Hastings algorithm. Target moments include lumpy investment fraction (0.14, from Zwick and Mahon 2017), average investment-to-capital ratio (0.10), standard deviation of i/k (0.16), private-to-infrastructure capital ratio (0.75, from BEA), high-infrastructure region’s private capital share (0.83, from Census BDS), and total working hours (0.33).

The identification of the key parameter — the firm-level elasticity of substitution between private and public capital (λ) — comes from the relative size of private capital stocks across the two infrastructure groups: under greater complementarity, regions with more infrastructure should hold relatively more private capital.

External validation is provided by estimating the state-level elasticity from the model’s simulated data using a nonlinear least squares method following An et al. (2019), and comparing it to empirical state-level estimates from actual U.S. state data.

Main Findings with Quantitative Magnitudes

Firm-level vs. aggregate-level elasticity gap. The estimated firm-level elasticity of substitution is λ = 1.185, implying gross substitutability between private and public capital at the firm level. The state-level elasticity implied by the same model is 0.48 (or 0.35 in a decreasing-returns-to-scale specification), implying gross complementarity. The empirical state-level counterpart estimated from actual U.S. data is 0.445. The paper proves theoretically (Proposition 1) that, given non-rivalry and under mild conditions, firm-level gross substitutability implies aggregate-level gross complementarity. Proposition 2 further shows that this same mechanism micro-founds the increasing-returns-to-scale assumption in Baxter and King’s (1993) Cobb-Douglas aggregate production function.
Fiscal multiplier (baseline, 2-year horizon). The aggregate output multiplier over a 2-year horizon in the heterogeneous-firm general equilibrium model is 1.088 in response to a one-time unexpected infrastructure spending shock equal to 1% of steady-state GDP, financed by a lump-sum tax. The corresponding partial-equilibrium output multiplier (holding prices fixed at steady state) is 1.858; the gap reflects crowding out of private investment induced by the general equilibrium interest rate response. In the baseline, the interest rate rises by 0.39% after the shock; the investment multiplier is -0.043.
Comparison with representative-agent model. When the same implied returns-to-scale parameters are used in a representative-agent model (following Baxter and King 1993), the output multiplier is 0.991 and the investment multiplier is -0.157, both substantially lower than the heterogeneous-firm baseline. The key mechanism: under convex adjustment costs, the Jensen’s inequality effect implies that heterogeneous firms face a greater average adjustment burden than the representative firm, making their investment less responsive to the general equilibrium crowding-out pressure.
Sensitivity to elasticity of substitution. Across the heterogeneous-firm model: at λ = 3 (high substitutability), the output multiplier falls to 0.672; at λ = 0.5 (complementarity), it rises to 1.364. The multiplier is significantly more sensitive to λ in the heterogeneous-firm model than in the representative-agent model, because non-rivalry amplifies the effect of any given elasticity value through each firm’s production function.
Cross-state distribution of gains. Under the baseline spending allocation (81% to Good states, 19% to Poor states), per $1 of infrastructure spending, Good states receive $1.072 of the $1.088 total output gain, while Poor states receive only $0.016. In a counterfactual with equal spending across states, the total output multiplier falls to 0.873, Good states’ output multiplier falls to 0.810, and Poor states’ output multiplier rises to approximately 0.062 (about four times the baseline level of 0.016). This quantifies a sharp efficiency-equality trade-off in the allocation of infrastructure investment.
Employment and earnings effects. Compared to steady state, the baseline fiscal shock produces an average annual increase of 0.304% in employment and 0.389% in wages, yielding a $0.713 increase in earnings and a $0.148 increase in consumption per $1 of fiscal spending in general equilibrium. In partial equilibrium (no price changes), earnings increase by $1.294 and consumption by $0.605 per $1 spent.

Scope Conditions

Results are conditional on: (i) lump-sum tax financing of the fiscal shock; (ii) a one-time unexpected (MIT) shock with no persistence; (iii) a closed-economy framework with endogenous real interest rate; (iv) the estimated two-region structure calibrated to U.S. state-level infrastructure data; (v) firm-level investment dynamics calibrated to Compustat and BDS moments. The authors note that incorporating time-to-build assumptions (tested in an appendix) reduces the aggregate fiscal multiplier, consistent with Ramey (2020).

Layer 2 — Q&A

Q1: What is the core theoretical result connecting firm-level and aggregate-level elasticities, and what is the intuition?

A: Proposition 1 proves that, given non-rivalrous public capital and mild data conditions (at least one firm has private capital below total infrastructure, and aggregate private capital exceeds total infrastructure), if the firm-level elasticity of substitution λ ≥ 1 (gross substitutes), then the aggregate-level elasticity ξ < 1 (gross complements). The intuition is that a marginal increase in public capital raises the marginal product of private capital for every firm simultaneously due to non-rivalry; the sum of these MPK gains across all firms exceeds any single firm’s gain. To represent this amplified benefit within an aggregate production function, a stronger complementarity is required than what any single firm faces. Put differently, non-rivalry means aggregate private and public capital “look” more complementary than they truly are at the firm level.

Q2: How does non-rivalry micro-found the Baxter-King aggregate production function?

A: Proposition 2 shows that if firms use a CES production function with gross substitutability (λ ≥ 1) and non-rivalrous public capital, then fitting aggregate output with a Cobb-Douglas production function (as in Baxter and King 1993, H(K,N,L) = zK^α L^{1-α} N^ζ) yields ζ > 0, implying increasing returns to scale (IRS). This is the paper’s micro-foundation for a widely-used but previously ad hoc assumption in the macro-fiscal literature. The corollary states that both gross complementarity in the aggregate CES function and IRS in the aggregate Cobb-Douglas follow from the same non-rivalry mechanism at the firm level.

Q3: Why does the heterogeneous-firm model produce a higher output multiplier than the representative-agent model?

A: Two mechanisms drive the difference. First, due to Jensen’s inequality and the convexity of adjustment costs, heterogeneous firms face a higher average adjustment burden than the representative (average) firm; this means heterogeneous firms are less responsive to interest rate changes that crowd out investment. The investment multiplier is -0.043 in the heterogeneous-agent baseline versus -0.157 in the representative-agent model. Second, the fixed adjustment cost (present in the baseline but absent from the representative-agent model) further dampens investment sensitivity via the extensive margin. Because less private investment is crowded out, more of the direct output boost from infrastructure spending survives into the aggregate multiplier, yielding 1.088 versus 0.991.

Q4: What is the novel estimation procedure and why is it necessary?

A: Standard SMM applied to GE models requires solving for market-clearing prices for every candidate parameter vector, creating a nested optimization loop that is computationally prohibitive. The authors extend SMM by treating market-clearing prices (wage w and marginal utility of consumption p) as additional parameters and appending market-clearing conditions as additional target moments — effectively requiring those moments to equal zero. A multi-block Metropolis-Hastings algorithm jointly draws from the price block and the parameter block. This approach generates posterior draws that simultaneously satisfy market clearing and fit empirical moments, without the inner loop. The resulting market-clearing accuracy is e^{-4} at the posterior mean.

Q5: How is the firm-level elasticity of substitution (λ) identified from the data?

A: λ is identified from the cross-state difference in private capital stocks between high- and low-infrastructure regions. Under the model, if private and public capital are more complementary (lower λ), high-infrastructure regions should attract relatively more private capital. The data moment used is the Good region’s share of aggregate private capital (0.83 from Census BDS data). This identification strategy is analogous to Bartik-instrument approaches in the empirical literature, where a parameter governing cross-state sensitivity to aggregate shocks is identified from cross-sectional variation.

Q6: How is the model validated externally?

A: The authors compute the state-level elasticity from the estimated model by fixing firm-level parameters and re-estimating only the elasticity and regional productivity from the model’s simulated state-level data, using the same NLLS estimator as An et al. (2019). The model-implied state-level elasticity is 0.349 (DRS specification) or 0.482 (CRS specification). The empirical estimate from actual U.S. state-level data following the same estimator is 0.445. Both indicate gross complementarity at the state level, consistent with the theoretical prediction. This external validation is not used in the estimation itself, providing an independent check.

Q7: What are the roles of extensive vs. intensive investment margins in the crowding-out effect?

A: Table 9 decomposes the investment multiplier of -0.043 by investment margin. When only the extensive margin (the discrete decision of whether to invest) is allowed to respond, the investment multiplier is -0.032 — approximately 74% of the baseline crowding-out effect. When only the intensive margin (investment size conditional on adjusting) responds, the multiplier is -0.011 — about 25% of the total. Thus the extensive margin is the dominant channel through which higher interest rates crowd out private investment. When both margins are held fixed, the output multiplier rises to 1.139, confirming that investment crowding-out reduces the output multiplier by about 0.05.

Q8: How does the elasticity of substitution affect the fiscal multiplier quantitatively, and why does this matter more in the heterogeneous-firm model?

A: In the heterogeneous-firm GE model: λ = 3 gives an output multiplier of 0.672, λ = 1.185 (baseline) gives 1.088, and λ = 0.5 gives 1.364 — a range of 0.692. In the representative-agent model, the comparable range across the implied ζ values is much narrower (0.970 to 0.998). The amplification in the heterogeneous-firm model occurs because non-rivalry means each firm’s production function directly incorporates the public capital stock, so the elasticity parameter has first-order consequences for every firm’s investment incentive response to a fiscal shock. This heightened sensitivity underscores why accurately estimating λ at the firm level — rather than importing a state-level estimate — is critical for quantifying infrastructure multipliers.

Q9: What is the efficiency-equality trade-off in cross-state infrastructure allocation?

A: Under the baseline allocation (81% of infrastructure spending to Good states, 19% to Poor states), per $1 of infrastructure spending, the Good states receive $1.072 of output gains and Poor states receive only $0.016. In the equal-spending counterfactual, the total output multiplier falls from 1.088 to 0.873. The Poor states’ output multiplier rises from $0.016 to $0.062 (approximately fourfold), while the Good states’ falls from $1.072 to $0.810. The Poor states also see earnings multipliers more than double (from $0.017 to $0.042). This trade-off arises because Good states have both more private capital (benefiting from non-rivalry) and higher estimated TFP — so each dollar of infrastructure is more productive there. Equal allocation reduces aggregate efficiency while partially mitigating regional inequality.

Q10: How do the paper’s multiplier estimates compare to the existing literature?

A: In partial equilibrium (no GE adjustment), the authors find an output multiplier of 1.858, consistent with Chodorow-Reich’s (2019) cross-sectional multiplier of approximately 1.8. Once the general equilibrium interest rate effect is included, the multiplier falls to 1.09, which falls within the 0.6-1.2 range from Ramey (2011). Literature using representative-agent models without non-rivalry (e.g., Ramey 2020) typically reports multipliers of 0.3 to 0.8 using returns-to-scale parameters of 0.07-0.12; the paper shows these correspond to fiscal multipliers of 0.847-0.882 in the representative-agent framework. The heterogeneous-firm model, once it incorporates the non-rivalry-corrected elasticities, yields a meaningfully higher multiplier of 1.088.

Q11: What role does time-to-build play, and how does the paper handle it?

A: The baseline model assumes a time-to-build period s = 1 year (one-year lag before new infrastructure is productive). The paper notes in Appendix H that incorporating extended time-to-build reduces the aggregate fiscal multiplier, operating through two channels: a news effect (agents adjust behavior upon anticipating future infrastructure) and a general equilibrium effect endogenous to the news effect. This finding is consistent with Ramey (2020). The baseline results are therefore reported under the minimal one-year time-to-build assumption, with longer lags serving as a robustness check.

Q12: What is the role of region-specific TFP heterogeneity in the model?

A: The model includes two regions that differ both in infrastructure levels and in region-specific productivity (TFP) levels. The TFP of the Good region is estimated to be approximately double that of the Poor region (x = 2.064 for Good vs. 1 for Poor). This productivity difference is estimated to partially capture heterogeneous congestion effects (which are not separately modeled) and is estimated jointly with the infrastructure elasticity. The productivity differential is identified from the Good region’s share of aggregate output (0.849 in the data). The large TFP gap is also the reason why equal spending on Poor states generates a much smaller output gain than spending on Good states: not only is infrastructure utilization lower (fewer firms), but underlying productivity is also lower.

Key Concepts

Non-rivalry of public capital: The property by which infrastructure stock (Nj,t) enters each firm’s production function at the full regional level, not divided among firms. Formally, a single marginal unit of public capital raises every firm’s marginal product of private capital simultaneously, so the aggregate marginal product gain summed across firms exceeds any single firm’s gain. This is the central mechanism driving the micro-macro elasticity discrepancy in the paper.

Firm-level elasticity of substitution (λ): The elasticity governing the degree of substitutability between private capital (k) and public infrastructure (N) in the firm’s CES production function. At λ = 1 the production function is Cobb-Douglas; λ > 1 is gross substitutability; λ < 1 is gross complementarity. In the paper’s estimation, λ = 1.185, meaning private and public capital are gross substitutes at the firm level.

Gross substitutability vs. gross complementarity: Two inputs are gross substitutes (complements) if an increase in the quantity of one raises (lowers) the demand for the other, holding output price fixed. In the paper’s framework, private and public capital are gross substitutes at the firm level (λ = 1.185 > 1) but gross complements at the state level (ξ ≈ 0.48 < 1), with non-rivalry explaining the inversion upon aggregation.

Convex adjustment cost: A cost C(I,k) = (µ/2)(I/k)² · k that scales quadratically with the investment rate. In the heterogeneous-firm model, this cost plays a critical role: by Jensen’s inequality, heterogeneous firms’ average adjustment burden under a convex cost exceeds that of the representative (average) firm, making aggregate investment less sensitive to interest rate changes and thereby dampening crowding out.

Fixed adjustment cost (ξ): A one-time overhead cost drawn from a uniform distribution [0, ξ̄], paid only when a firm makes a large-scale investment outside the “inaction band” [−νk, νk]. This cost generates lumpy investment at the firm level, with about 14% of firms making lumpy investments in any given year. It also creates an extensive margin of investment adjustment that accounts for approximately 74% of the baseline crowding-out effect.

Fiscal multiplier (as defined in this paper): The ratio of the present value of aggregate output deviations from steady state to the present value of the fiscal spending shock, both summed over a T-year horizon. For the short run, T = 2 years; for the long run, T = 5 years. This is computed as a perfect-foresight transition path response to a one-time MIT shock equal to 1% of steady-state GDP.

MIT shock (one-time unexpected shock): An unanticipated, non-persistent one-period deviation in infrastructure spending. The term “MIT shock” refers to a deterministic transition experiment where agents have perfect foresight about all future values after the initial shock occurs. This contrasts with persistent policy rules and allows isolating the dynamic effects of a one-time fiscal impulse.

Extended SMM with market-clearing moments: The paper’s estimation innovation. Rather than solving for market-clearing prices at each parameter candidate (the standard costly inner loop), wages (w) and marginal utility of consumption (p) are treated as parameters with associated moments being the market-clearing conditions set to zero. A multi-block Metropolis-Hastings algorithm draws from the price block and the parameter block separately, generating posterior draws that jointly satisfy market clearing and empirical moment conditions.

Income Inequality and Job Creation

Mon, 01 Jan 0001 00:00:00 +0000

The paper establishes a causal link from rising top income shares to reduced net job creation at small firms, working through a bank funding channel rooted in non-homothetic household portfolio allocation: because high-income households hold a smaller fraction of financial wealth in bank deposits (less than one-fifth for the top decile versus two-thirds for the bottom quintile, per the Survey of Consumer Finance), a redistribution of income toward top earners shifts aggregate saving away from deposits toward stocks and bonds. Banks must raise deposit rates to retain funding, which passes through to loan rates; since small, informationally-opaque firms depend disproportionately on bank credit while large firms have direct capital-market access, higher loan rates compress small firms’ net job creation relative to large firms. Using U.S. state-level panel data from 1981 to 2015, a shift-share instrumental variable, and a quantitative general equilibrium model, the paper documents this channel and finds it accounts for 13% of the 4.97 percentage-point rise in large-firm employment share and between 7.5% and 15% of the decline in the labor share since 1980.

Motivating facts (Section 2):

The U.S. net job creation rate of small firms (1–499 employees) declined from roughly +4% in 1980 to near 0% by 2015 and co-moves strongly with the top 10% income share (Figure 1a), suggesting a systematic relationship
SCF data show that the deposit share of financial wealth falls monotonically with income: bottom quintile (Q1) ≈ 65–70%; middle quintile ≈ 45%; top decile < 20% (Figure 2a). Non-financial wealth and stocks/bonds rise sharply with income
FDIC data show deposits account for 93% of total liabilities for the average bank and 75% of total liabilities on aggregate (Figure 2b); average bank raises 98% of deposits in its headquarters state (capital-weighted: 89%), so local deposit supply directly constrains local bank credit

Empirical specification (Section 3): Panel regression at the state–firm-size–year level, 47 states, 1981–2015, 16,435 observations. Dependent variable: net job creation rate (JCR − JDR). Key regressor: interaction of the top 10% income share with a “small firm” dummy (firms 1–499 vs. 500+). Regression includes state–firm-size fixed effects and state–time fixed effects, the latter absorbing all time-varying unobservable state-level factors common to firms of different sizes (e.g., globalization, technology). Identification via a pre-determined share IV: each state’s top 10% income share in 1970 (ten years before the sample) interacted with the leave-one-out national trend in top income shares — exploiting cross-state variation in sensitivity to the aggregate national trend while isolating it from local cyclical conditions.

Empirical results (Table 1, Table 2):

IV estimate: a 10 percentage-point rise in the top 10% income share reduces the relative net job creation rate of small firms by 1.2 percentage points (Table 1, col. 3)
Extensive margin (entry, exit, private-to-public transitions): accounts for approximately 20% of the 1.2pp effect (Table 1, col. 4)
One standard deviation higher top income share (5.4pp) → 0.7pp lower small-firm net JCR (Figure 1b, binned scatter OLS preview)
Counterfactual: had the U.S. top 10% income share remained at its 1980 level (instead of rising ~16pp from 34.5% to 50.5%), small firms’ net job creation rate would be 1.9 percentage points higher — more than 50% above its 2015 level
Bank-level regressions (Table 2): rising top income shares in a bank’s headquarters state lead to higher deposit rates and lower total deposit volumes — consistent with banks raising rates to retain a declining deposit supply

Model (Section 4): General equilibrium model with two types of households and two types of firms. Households differ by income group (high, H, and low, L), each endowed with heterogeneous productivities {si,χ}; households choose consumption, labor supply, and portfolio allocation between bank deposits (providing liquidity services captured by a CES deposit utility term ψd·η) and direct capital investment in public firms. Non-homotheticity: the deposit utility weight is calibrated so high-income households hold fewer deposits per unit of wealth. Firms are either public (large, direct capital-market access, production function with capital share θ and returns to scale γ) or private (small, bank-dependent; labor-only production with bank working capital constraint ϕ̃ governing the loan demand; entry/exit governed by stochastic fixed cost f̃ ~ U[0,f̃max] and a cost of going public κ ~ U[0,κ̃max]). Banks intermediate deposits into loans at a fixed cost, implying a zero-profit loan rate above the deposit rate.

Calibration (Table 3): Two panels:

Panel (a) externally fixed: capital depreciation rate (NIPA), mean US stock market return = 1.08, top 10% income share target = 34.6% (initial, Frank 2009 data), deposit rate = 4% (national average)
Panel (b) internally calibrated to BDS and SCF (early 1980s):
- Labor supply to public firms = 46.9%; private firms = 53.1% (BDS baseline)
- Labor demand to public firms = 46.9%; private firms = 53.1% (matched exactly)
- Deposit share of Q3 household = 0.45; top 10% deposit share = 0.22 (SCF)
- Household discount factor β = 0.9182; deposit utility scale ψd = 0.0632; deposit utility elasticity η = 2.6096
- Capital share in public firms θ; returns to scale γ set to match labor demand targets
- Firm productivity SD σz = 0.0315; bank dependence ϕ̃ and fixed cost bound f̃max matched to Table 1 empirical estimates (intensive and extensive margin); public-share cost bound κ̃max matched to share of firms >500 employees (BDS)

GE experiment (Section 6): Top 10% income share raised permanently from 34.5% to 50.5%, matching Frank (2009) data evolution, via lump-sum transfers from low- to high-income households (holding average income constant to isolate the portfolio reallocation channel). Key aggregate outcomes (Figure 3):

Aggregate deposits fall by more than 2%; savings flow into public firm capital, which rises 2% — the portfolio reallocation effect in levels
Deposit rate rises 0.4pp; loan rate rises 0.7pp; public firm capital return falls 0.14pp — consistent with bank-level empirical estimates
Private firm employment falls ~2%; public firm employment rises ~1%; aggregate employment falls modestly
Private firm employment share falls 0.64 percentage points — the channel explains 13% of the actual 4.97pp BDS decline in employment at firms below 500 employees (1980–2015)
Around one-fifth of the employment share decline comes from the extensive margin (private firm exit and transitions to public status), matching the empirical ratio
Labor share falls 0.3pp, explained by public firms growing relatively larger and being more capital-intensive; this accounts for 7.5% to 15% of the observed 2–4pp decline in the US labor share
Aggregate output falls 0.3%, driven by resource reallocation: private firms have marginal product of labor roughly one-sixth higher than public firms (consistent with the higher small-firm net JCR coefficient), so shifting employment to public firms suppresses aggregate productivity

Welfare effects (Section 6.2, Figure 4): The top 10% experience an increase in consumption-equivalent welfare; bottom 90% experience a decrease. The full model amplifies both effects relative to a counterfactual model with fixed portfolio shares: portfolio reallocation raises top-earner welfare by an additional ~1% (consumption equivalent) relative to the fixed-share benchmark and lowers bottom-earner welfare by ~1% — because in the full model, private firm wages fall (loan rate rise reduces labor demand) while in the fixed-share benchmark private firm wages rise (tops save more deposits, lowering loan rates). Ignoring portfolio heterogeneity thus significantly understates the welfare consequences of income redistribution.

Scope conditions: The mechanism operates through portfolio reallocation only; the paper holds average income constant (lump-sum redistribution) to isolate the channel, abstracting from any direct effects of rising incomes on aggregate savings rates. The IV exploits state-level variation in top income shares; cross-state spillovers in bank credit markets would attenuate estimated coefficients. The model assumes banks cannot replace lost deposits one-for-one with non-deposit liabilities, consistent with institutional frictions documented in the banking literature (Stein, 1998; Hanson et al., 2015). The analysis covers pre-tax income shares; post-tax redistribution through the tax code would dampen the mechanism.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. Why does the portfolio composition of saving matter more than the aggregate savings rate?

The key non-homotheticity is in the composition of saving, not the level: high-income households allocate less than one-fifth of financial wealth to bank deposits while low-income households allocate two-thirds; as income shifts to the top, total deposits decline even if aggregate saving rises modestly. Banks cannot substitute deposit funding with non-deposit liabilities without cost — deposits provide cheap, stable funding because of their unique liquidity and monitoring properties (Stein, 1998; Hanson et al., 2015). An increase in the deposit rate is thus the equilibrating mechanism: banks must bid deposits back from higher-return assets, and the higher funding cost passes through to loan rates.

Q2. Why are small firms disproportionately harmed by higher loan rates?

Small, informationally-opaque firms rely on bank credit for external finance — 92% of small firms in the 1993 National Survey of Small Business Finances use bank loans — while large public firms can raise equity and bonds directly, bypassing banks entirely. When loan rates rise, small firms face a tighter credit constraint on their working capital and fixed costs of operation; the higher loan rate simultaneously reduces their demand for bank credit and raises the value of exiting or transitioning to public status (reducing the private-firm fixed cost burden). Large firms, by contrast, experience lower financing costs as the capital return falls and equity markets absorb more saving — amplifying the relative job creation gap.

The IV uses each state’s top 10% income share in 1970 — ten years before the sample begins, when income shares were flat nationally — interacted with the leave-one-out national trend; any factor driving both job creation outcomes and income inequality in a state would need to have affected firms of different sizes within that state in the same direction as the national trend, while also having had no such effect in all other states. The instrument’s validity rests on: (i) national income share trends after 1980 being driven by aggregate forces (technology, globalization) exogenous to any single state’s labor market; (ii) the pre-1980 period showing no systematic co-movement between state income shares and subsequent employment trends; and (iii) robustness to excluding industries that account for a large share of a state’s employment (Table OA4).

Q4. What explains the aggregate output decline when private firms have higher marginal products?

The output decline of 0.3% arises because the reallocation from private (higher marginal product) to public (lower marginal product) firms outweighs the positive capital accumulation effect: as more saving flows into public firm equity/capital, output would rise, all else equal — but the capital stock increase is modest and aggregate savings rise only slightly, so the dominant effect is misallocation. The marginal product gap between private and public firms is not an assumption of the model but a calibration consequence: matching the empirical estimate that small firms’ net JCR responds more to loan rate changes (Table 1) requires their marginal product to be higher, generating the misallocation loss when resources shift toward large firms.

Q5. How does rising inequality amplify its own effect through welfare and further portfolio reallocation?

In the full model with heterogeneous portfolios, the redistribution from low- to high-income households directly reduces aggregate deposits (because the recipients hold fewer deposits per dollar), which raises deposit and loan rates, which lowers wages at private firms, which further reduces low-income households’ labor income. This GE feedback loop — portfolio composition → bank rates → wages → income distribution → portfolio composition — amplifies the initial redistribution effect by approximately 1 percentage point of consumption-equivalent welfare compared to a model in which households are forced to hold fixed portfolio shares. In the fixed-portfolio model, tops invest more in deposits when they receive transfers, partially offsetting the deposit supply decline, and private firm wages rise — the opposite of the full model.

Q6. What fraction of US macroeconomic trends since 1980 can the channel explain?

The channel accounts for 13% of the 4.97pp rise in large-firm employment share, 7.5–15% of the 2–4pp fall in the aggregate labor share, and a 0.3% output loss from resource misallocation — meaningful but partial contributions to trends that are multi-causal. The partial contributions reflect that rising income inequality is one of several forces driving these trends (technology adoption, trade, market concentration, capital-skill complementarity); the paper explicitly abstracts from these other forces by using lump-sum transfers that hold average income constant, isolating the portfolio reallocation channel alone.

Q7. What happens to firm entry and exit under rising inequality?

A higher loan rate raises the effective cost of operating as a private firm (working capital is more expensive), reducing the threshold productivity level below which private firms exit and raising the threshold above which private firms find it worthwhile to incur the IPO-type cost of going public; both margins reduce the number of private firms in equilibrium, consistent with declining business dynamism. The model implies approximately one-fifth of the employment share decline at small firms comes from this extensive margin — closely matching the data decomposition from the BDS — and the public firm share rises by 0.003pp, consistent with the small but positive trend in the share of large-firm establishments observed in the data.

FDIC data show deposits represent 93% of average bank liabilities and 75% of aggregate bank liabilities; banks rely on their headquarters-state deposit base for the vast majority of funding because regulatory and institutional frictions constrain inter-state deposit gathering — even the four largest US banks (JP Morgan, Citi, Wells Fargo, Bank of America) raise over 70% of deposits in their headquarters state. The literature (Stein, 1998; Jakab and Kumhof, 2015) establishes that deposits provide uniquely stable, cheap funding that cannot be replaced at equivalent cost by wholesale liabilities or interbank borrowing; any substitution requires costly premium over the deposit rate, implying the attenuation bias if anything understates the true causal effect on loan rates.

Key concepts

non-homothetic deposit preference : the empirical regularity that the share of financial wealth allocated to bank deposits declines with income — two-thirds for the bottom quintile, under one-fifth for the top decile; this non-homotheticity means that a mean-preserving income redistribution toward top earners reduces the aggregate deposit supply relative to total saving, the paper’s foundational portfolio channel.

pre-determined share IV : the paper’s instrumental variable for state-level top income shares: each state’s 1970 top 10% income share interacted with the leave-one-out national trend in top 10% shares; identifies causal effects by exploiting differential state sensitivity to national inequality trends, purged of local cyclical factors and large-firm wage premia.

private versus public firm : the model’s key firm heterogeneity; private firms are small, bank-dependent (working capital constrained), and pay fixed operating costs; public firms are large, equity-financed, and face no bank credit constraint. The intensive-margin effect of higher inequality (rising loan rates) and extensive-margin effect (higher exit rates, more IPO transitions) both compress the private firm employment share.

deposit rate pass-through : the mechanism by which a decline in aggregate deposit supply forces banks to raise deposit rates to retain funds; the higher deposit rate is passed through to loan rates via the bank’s zero-profit condition, raising the cost of credit for bank-dependent private firms by approximately twice the deposit rate increase (0.7pp loan rate rise for 0.4pp deposit rate rise in the model).

business dynamism channel : the extensive margin of the paper’s mechanism — rising top income shares increase loan rates, which increase private firm exit rates and the rate of private-to-public firm transitions, reducing firm entry and contributing to documented trends of falling startup rates and declining business dynamism in the US since 1980.

On the Nature of Entrepreneurship

Mon, 01 Jan 0001 00:00:00 +0000

This paper uses a novel longitudinal administrative dataset drawn from U.S. Internal Revenue Service (IRS) and Social Security Administration (SSA) records to characterize income dynamics and the determinants of entrepreneurial entry for pass-through business owners — sole proprietors, partners, and S corporation owners — who collectively account for over 50 percent of all U.S. business net income. The sample covers 2000–2015 and includes up to 1.3 billion person-year observations for individuals aged 25–65. The authors construct balanced panels using birth cohorts 1950–1975, impute education (college attainment) and skill (cognitive, interpersonal, manual) via machine-learning classifiers trained on CPS and O*NET data, and estimate life-cycle income profiles using a three-component model that separates individual fixed effects, group-specific time effects, and group-cohort-specific age effects.

The paper’s central departure from prior work is coverage of the full income distribution, including the high-earning right tail that household surveys such as the CPS misrepresent due to top-coding and small samples. When the IRS and CPS samples are compared on a consistent classification basis, median self-employment income is lower in the IRS data at all ages, consistent with the survey literature’s emphasis on the “typical” self-employed individual. However, mean incomes diverge sharply: the IRS shows mean self-employment income rising from $23 thousand at age 25 to $93 thousand at age 55, whereas the CPS (with incorporated owners reclassified) shows a rise from only $41 thousand to $73 thousand. Roughly 80 percent of self-employment income in the IRS data accrues to individuals above the $100 thousand threshold, compared to 42–53 percent in the CPS. The IRS-CPS gap is dominated by the right tail and concentrated in professional services and health care. For paid-employed individuals, the IRS and CPS medians and means are close at all ages, confirming the discrepancy is specific to self-employment.

The life-cycle estimation finds that individuals who have “tried self-employment” — a group earning virtually all self-employment income — start at similar average incomes to primarily paid-employed peers at age 25 but reach $134 thousand by age 55, compared with $79 thousand for paid-employed peers with the same observable characteristics. Age effects for the self-employed are 63 percent higher than for the paid-employed at age 26 and remain elevated until age 55. Time effects show dramatically greater cyclical volatility for the self-employed: income growth declined by $9,655 (2008) and $8,785 (2009) for the self-employed versus $373 and $1,583 for paid-employed in the same years, concentrated in real estate and construction.

On the determinants of entry, the paper finds: (i) no evidence that house-price appreciation raises entry rates, contra collateral-constraint hypotheses; (ii) most entrants have lower asset incomes than future entrants with the same characteristics, arguing against a liquid-wealth precondition; (iii) most entrants have higher prior labor income than future entrants, consistent with entry being driven by on-the-job experience rather than fallback from low-paid work; (iv) almost all founders report positive individual tax income in their first year of operation despite negative business net income and no external debt financing. Self-employed income growth exhibits greater dispersion — a 10th-to-90th percentile range roughly 2.5 times wider than for the paid-employed — and a Kelly skewness about 0.1 higher. A standard consumption-risk model calibrated with household-finance estimates of risk aversion rationalizes the patterns if individuals are insured against the most adverse downside shocks. Entry and exit rates are stable across the sample period, including the Great Recession, and the entrepreneurship share does not decline.

The subgroup congruent with non-pecuniary motivation — primarily self-employed individuals earning less than paid-employed peers with matching characteristics — comprises roughly 57 percent of primarily self-employed by count but earns only 16 percent of total self-employment income.

Q1: Why do IRS and CPS data give such different pictures of self-employment income? The CPS suffers from top-coding of high incomes and small samples that underrepresent high earners in key industries. The IRS-CPS mean income gap for the self-employed is dominated by the right tail: in the main IRS sample, individuals above the $100 thousand threshold earn roughly 80 percent of all self-employment income, versus 42 percent in the comparable CPS sample. The average income of top earners above $100 thousand is $355 thousand in the IRS versus $218 thousand in the CPS. The gap is concentrated in professional services and health care and persists across all income thresholds and sample definitions tested. No analogous discrepancy exists for paid-employed individuals, where IRS and CPS medians and means are close at all ages.

Q2: What does the comparison look like at the median versus the mean? At the median, IRS self-employment income is lower than both CPS samples at all ages, with the gap largest for younger owners and those with incorporated businesses — a pattern consistent with the survey-based “self-employment discount” narrative. At the mean, the IRS shows much higher income at older ages: by age 55, IRS mean self-employment income is $93 thousand versus $73 thousand in the CPS sample that includes reclassified incorporated-owner wages. The divergence arises because the mean is sensitive to the right tail, which the CPS systematically underrepresents.

Q3: How does the paper estimate life-cycle income profiles while separating age, time, and cohort effects? Individual income is decomposed into an individual fixed effect (permanent latent ability and preferences), a group-specific time effect (business-cycle fluctuations common to a group), and a group-cohort-specific age effect (life-cycle income growth). Identification exploits the overlapping cohort structure of the 16-year panel: age effects are assumed equal across cohort bins of size at least two, allowing time and age effects to be separately identified. The model is estimated in levels rather than logs to accommodate business losses. Groups are defined as a Cartesian product of 32,256 subgroups based on education, three skill dimensions, industry (21 two-digit NAICS codes), demographics (gender, cohort, marital status, children), and employment-status history.

Q4: What are the headline life-cycle income profile findings for self- versus paid-employed? Among the “primarily employed” group, those who have tried self-employment and those who are primarily paid-employed have similar average incomes at age 25. By age 55 the self-employed reach an estimated $134 thousand (2012 dollars) versus $79 thousand for paid-employed peers with identical observable characteristics. The estimated age effect for the self-employed is 63 percent higher than for the paid-employed at age 26 and remains higher through age 55. These gaps would widen further if incomes were adjusted upward for the BEA-estimated net misreporting rates of 46 percent for unincorporated owners and 14 percent for S corporation owners.

Q5: How large is the group consistent with non-pecuniary motivation, and how much income does it earn? The non-pecuniary subgroup — primarily self-employed individuals (at least 12 years in self-employment) who earn less on average than primarily paid-employed peers matched on gender, education, skills, and other characteristics — is numerically larger, comprising approximately 57 percent of primarily self-employed by count. However, this group earns only 16 percent of total self-employment income. Adjusting for paid-employed fringe benefits and self-employed income misreporting can change the group’s size but does not alter the finding that it accounts for a small income share. The paper concludes that non-pecuniary motives may guide occupational choice for many individuals but are not the driver of the typical dollar earned in self-employment.

Q6: How does idiosyncratic income risk compare between self- and paid-employed? Self-employed income changes are substantially more dispersed: the 10th-to-90th percentile range of income growth is roughly 2.5 times wider for the self-employed than for the paid-employed. Income changes for the self-employed are also more right-skewed, with a Kelly skewness difference of approximately 0.1. When a standard consumption-risk model — augmented with a lower bound on consumption growth to allow for external insurance — is parameterized with risk-aversion estimates from the household finance literature, the observed patterns are rationalized if individuals are insured against the most adverse downside shocks, i.e., the attractive aspect of self-employment is large potential upside with insured downside.

Q7: What happened to self-employed income and exit rates during the Great Recession? Time effects show steep income growth declines for the self-employed of -$9,655 in 2008 and -$8,785 in 2009, compared with much more modest declines of -$373 and -$1,583 for paid-employed peers. The aggregate income declines are concentrated in cyclically sensitive self-employed subgroups in real estate and construction, with their paid-employed counterparts experiencing only modest declines. Despite these large income shocks, exit rates from self-employment showed little change during the Great Recession, either in aggregate or in the cyclically sensitive sectors. Entry rates were likewise stable, and the share of entrepreneurs in the population did not decline over the full sample period.

Q8: Does the evidence support collateral constraints as a binding barrier to entrepreneurial entry? No. The paper tests the hypothesis, standard in the liquidity-constraints literature, that entry rates should be higher for homeowners experiencing house-price appreciation (which raises collateral value). The IRS data do not support this prediction. Separately, comparing asset incomes (interest, dividends, capital gains) of current entrants and future entrants with the same characteristics, the paper finds that most current entrants have lower asset incomes and less liquid wealth than those who switch later, which also argues against a liquid-wealth precondition for entry.

Q9: What does prior labor income reveal about why people enter self-employment? Current entrants have higher prior labor income than matched future entrants with the same characteristics, indicating they enter with accumulated on-the-job experience rather than being pushed into self-employment as a fallback after failure in paid work. This is consistent with self-employment being a deliberate, experience-driven career transition for most entrants rather than a last resort for low earners. The paper interprets this as positive evidence for the role of experience-based human capital in driving entrepreneurial choice.

Q10: How do founders finance startup costs if most have negative business net income in early years? Almost all founders in the sample report positive income on their personal (individual) tax form in the first year of operation, even though most report negative business net income and carry no external debt financing. This pattern suggests founders rely on personal income sources — prior savings, part-time paid employment, or spousal income — to cover startup costs rather than external debt, implying that formal credit-market financing constraints are not the primary barrier to entry for most entrants in the sample.

Q11: What are the scope conditions and key limitations? The sample covers pass-through owners (sole proprietors, partners, S corporation owners) and excludes C corporation shareholders, whose entrepreneurial income does not flow to individual returns until distributed. Income measures exclude most employer fringe benefits; capital gains are excluded from self-employment income, and the authors note their inclusion would strengthen the main findings. The analysis covers 2000–2015 for cohorts born 1950–1975, and income is reported before taxes and transfers. Baseline estimates are not adjusted for misreporting, though BEA-implied adjustments of 46 percent for unincorporated owners and 14 percent for S corporation owners would widen the income gaps further.

Pass-through business owner: An individual who owns a sole proprietorship, partnership, or S corporation, such that business net income flows directly onto the owner’s personal tax return; excludes C corporation shareholders whose income appears only upon dividend or capital-gains distributions.

Tried self-employment: The paper’s primary self-employed comparison group within the “primarily employed” category — individuals with any years in self-employment (including frequent switchers and those with most years in self-employment) — who collectively earn virtually all self-employment income.

Group-specific age effect: The paper’s estimate of how individual income changes with age within a defined subgroup (determined by education, skill, industry, demographics, and employment history), identified by exploiting overlapping birth cohorts in the 16-year panel and separated from individual fixed effects and business-cycle time effects.

Primarily employed: Individuals with at least 12 of 16 sample years in either self- or paid-employment, with at most one intermediate year of non-employment; the paper’s main analytical focus for life-cycle income comparisons.

SOI Databank: The Statistics of Income Databank, a de-identified balanced panel combining SSA demographic records with IRS tax filing data for all living U.S. individuals with a Social Security number over 1996–2015; the paper’s primary data source providing Schedule C, K-1, W-2, and related filing information.

Kelly skewness: A robust measure of distributional asymmetry used by the paper to characterize income growth; the paper reports that Kelly skewness of self-employed income changes exceeds that of paid-employed by approximately 0.1, indicating greater right-skewness in self-employment income dynamics.

Non-pecuniary motivation subgroup: Primarily self-employed individuals who earn less on average than primarily paid-employed peers matched on observable characteristics, taken by the paper as consistent with non-wage job amenities (autonomy, flexibility) driving occupational choice; found to be 57 percent of primarily self-employed by count but earning only 16 percent of total self-employment income.

Present Bias Amplifies the Household Balance-Sheet Channels of Macroeconomic Policy

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Summary

Maxted, Laibson, and Moll study fiscal and monetary policy in a partial-equilibrium heterogeneous-agent model in which homeowners have present-biased time preferences (Instantaneous Gratification preferences, the continuous-time limit of quasi-hyperbolic discounting) and naive beliefs, alongside a liquid savings account, an illiquid home, and access to credit card and mortgage debt. Because present bias substantially increases households’ marginal propensity to consume — in the calibrated model the quarterly MPC rises from 4% under exponential discounting to 14% under present bias, and the quarterly marginal propensity for expenditure (MPX) rises from 13% to 30% — present bias powerfully increases the effect of fiscal stimulus. Present bias also amplifies the overall effect of expansionary monetary policy, but at the same time slows down the speed of monetary transmission: interest rate cuts incentivize households to conduct cash-out refinances, which become targeted liquidity injections to households near the liquidity constraint who have especially high MPCs, but present bias with naive beliefs also introduces a motive for households to procrastinate on refinancing their mortgage, which substantially slows the speed at which this channel operates. A noteworthy feature of the model is that present bias amplifies the direct effect of monetary policy on household consumption while simultaneously delivering larger MPCs — a combination that is in contrast to standard heterogeneous-agent models, where modeling choices that amplify MPCs typically deliver smaller consumption responses to interest rate changes. The calibrated present-biased economy also replicates several empirical regularities that are difficult to match with exponential discounting: high-cost credit card borrowing by homeowners, empirically plausible cash-out behavior and loan-to-value ratios, and refinancing inertia.

Layer 2 — Q&A

Q: What is the core modeling innovation and why is it needed? A: The paper introduces naive Instantaneous Gratification (IG) preferences — the continuous-time limit of quasi-hyperbolic (beta-delta) discounting — into a two-asset heterogeneous-agent model with a liquid savings account and illiquid home equity accessible via mortgage refinancing. The naivete assumption (households do not foresee their own future present bias) is essential because it generates procrastination: naive households perpetually intend to refinance “soon” but keep delaying. A model with exponential discounting that merely sets parameters to match empirical MPCs would not generate procrastination behavior, and would require implausible interest rate calibrations (very low credit card rates or very high illiquid asset returns) to simultaneously match low liquid wealth accumulation and high credit card borrowing. Present bias with interest rates taken from the data resolves both issues.

Q: What are the key quantitative MPC results and why do they matter for fiscal policy? A: In the exponential discounting benchmark, the quarterly MPC is 4% and the quarterly MPX (which includes nondurables and durables) is 13%. Under the present-bias benchmark, the MPC rises to 14% and the MPX rises to 30%. The empirical literature estimates quarterly nondurable spending responses on the order of 15%–25%, and total expenditure responses typically two to three times larger, so the present-biased model is substantially more consistent with the data. Because fiscal stimulus (modeled as an unexpected one-time lump-sum payment, financed by a flow income tax) operates through household spending propensities, the higher MPCs and MPXs under present bias directly and powerfully increase the aggregate consumption response to fiscal policy relative to the exponential benchmark.

Q: How does present bias amplify the effect of monetary policy? A: Interest rate cuts incentivize households to conduct cash-out refinances — they borrow against accumulated home equity, converting illiquid home equity into liquid wealth. Because this liquidity is targeted to households who are near their borrowing constraint (and thus have especially high MPCs), the aggregate consumption response to a given rate cut is amplified. Crucially, present bias amplifies this channel beyond the exponential benchmark precisely because higher MPCs mean each dollar of liquidity injected generates more consumption. This stands in contrast to the standard result in the heterogeneous-agent literature (Auclert 2019; Olivi 2017; Kaplan, Moll, and Violante 2018) that MPC-amplifying modeling choices reduce the consumption response to interest rate changes because MPC enters the substitution effect with a negative sign in standard one-asset models. The two-asset structure with home equity and the cash-out refinance channel breaks this trade-off.

Q: How does present bias slow the speed of monetary transmission? A: Present bias with naive beliefs introduces a motive for households to procrastinate on refinancing their mortgage. Refinancing is an immediate-cost, delayed-reward task: it requires the borrower to spend weeks gathering documents, filling out paperwork, and negotiating with lenders, with benefits (lower mortgage payments or extracted home equity) accruing afterward. Naive present-biased households discount current effort costs very heavily relative to future benefits, so they delay, all the while (counterfactually) believing they will complete the task in the near future. This procrastination substantially slows down the speed at which the cash-out refinance channel of monetary policy operates: even though a rate cut eventually incentivizes households to refinance and extract equity, the timing of that response is stretched out relative to what exponential discounters would do.

Q: What is the role of naive beliefs versus sophisticated (partially or fully aware) present bias? A: Naivete is necessary to generate procrastination from small effort costs. A fully sophisticated present-biased household (one who correctly anticipates its own future self-control problems) would not indefinitely defer a task it correctly anticipates will keep being deferred. The paper extends the analysis to partial and full sophistication in Online Appendix D.5. The key takeaway is that procrastination — and thus the speed-reduction effect on monetary transmission — is driven by at least partial naivete. The MPC-amplification and fiscal-policy amplification results are more robust across sophistication levels.

Q: What empirical regularities does the present-biased calibration match that the exponential model cannot easily match? A: The present-biased economy replicates: (1) empirically plausible levels of high-cost credit card debt held simultaneously with home equity (a puzzle under exponential discounting); (2) cash-out behavior and loan-to-value ratios consistent with data; (3) a buildup of liquidity-constrained households consistent with empirical propensities to spend out of credit card limit increases (Gross and Souleles 2002; Agarwal et al. 2018); (4) consumption function discontinuities at the borrowing constraint consistent with Ganong and Noel (2019); (5) MPCs and MPXs that remain elevated for large shocks (Fagereng, Holm, and Natvik 2021); (6) the intertemporal MPC profile consistent with Auclert, Rognlie, and Straub (2018); (7) differential MPCs out of liquid versus illiquid transfers (Ganong and Noel 2020); and (8) refinancing inertia — the proclivity for households to delay refinancing when financially optimal (Keys, Pope, and Pope 2016; Johnson, Meier, and Toubia 2019; Andersen et al. 2020).

Q: What is the model’s scope — what does it abstract from? A: The model is set in partial equilibrium, so general equilibrium effects (e.g., endogenous interest rate responses, aggregate demand externalities) are not captured; the authors describe their results as inputs for a fuller general equilibrium analysis. The model focuses on homeowners (two-thirds of U.S. housing units), abstracting from renters. House prices are fixed (consistent with their slow movement over short horizons), with an extension to house price shocks in Online Appendix D.2.1. The model does not allow for home equity lines of credit, second mortgages, or reverse mortgages, because these products are more commonly used when interest rates are rising, and the paper focuses on the stimulative effect of rate cuts. The interest rate in the model is a long rate (e.g., 10-year TIPS), with the implicit assumption that the Federal Reserve implements the necessary short-rate adjustments.

Q: How does the present-biased model compare to the standard HANK picture on the monetary-MPC trade-off? A: In standard one-asset heterogeneous-agent models, a household’s MPC is a sufficient statistic that enters the substitution effect of interest rate changes with a negative sign — so modeling choices that raise MPCs reduce monetary policy effectiveness. The present-biased two-asset model breaks this result: because interest rate cuts trigger cash-out refinances that inject liquidity targeted to high-MPC households near the constraint, higher MPCs translate into larger, not smaller, aggregate consumption responses to monetary policy. Present bias therefore simultaneously amplifies fiscal policy (via higher MPCs) and amplifies the overall effect of monetary policy (via the targeted liquidity channel), while introducing the procrastination-driven speed reduction as the offsetting cost.

Key Concepts

Present bias (Instantaneous Gratification preferences): The paper uses “present bias” to refer to quasi-hyperbolic discounting. In the continuous-time limit (Instantaneous Gratification, or IG, preferences, following Harris and Laibson 2013), the current self discounts all future selves by factor β < 1, while exponential discounting of the future (rate ρ) applies from any future vantage point. This creates a discontinuity in the discount function at t = 0 whenever β < 1. Setting β = 1 recovers standard exponential discounting.

Naive beliefs: Households do not foresee their own future present bias. The current self believes all future selves will be exponential discounters (β = 1), even though this belief is incorrect. Naivete is what transforms present bias into procrastination: the household perpetually expects its future self to complete effortful tasks, but each future self faces the same bias.

Cash-out refinance channel: When market interest rates fall, households have an incentive to refinance their fixed-rate mortgage, locking in a lower interest rate. If the household has accumulated home equity (illiquid), it can simultaneously borrow against that equity — a cash-out refinance — converting illiquid home equity into liquid wealth. In the model, this acts as a targeted liquidity injection to households near their borrowing constraint (who have high MPCs), amplifying the aggregate consumption response to rate cuts.

Procrastination motive: Present bias introduces a motive to procrastinate on immediate-cost, delayed-reward tasks such as mortgage refinancing. The effort and paperwork costs of refinancing are borne immediately, while the financial benefits accrue over time. A naive present-biased household heavily discounts the current effort cost relative to future benefits, leading it to defer refinancing repeatedly. This substantially slows the speed at which the cash-out refinance channel of monetary policy operates.

Marginal propensity to consume (MPC) vs. marginal propensity for expenditure (MPX): The paper distinguishes the quarterly MPC (response of nondurable consumption to a one-unit cash transfer) from the quarterly MPX (which also includes durables). Under exponential discounting, MPC = 4% and MPX = 13%; under the present-bias benchmark, MPC = 14% and MPX = 30%. The higher MPXs are more consistent with empirical estimates (quarterly nondurable responses of 15%–25%; total spending responses two to three times larger).

Refinancing inertia: The empirical regularity that households delay mortgage refinancing even when it is financially optimal to do so. The paper provides a theoretical foundation for this behavior through the procrastination motive generated by naive present bias combined with the small effort cost of refinancing.

Summary based on LSE Research Online published version. AI-assisted, human review pending.

The housing wealth effect: Quasi-experimental evidence

Mon, 01 Jan 0001 00:00:00 +0000

This paper estimates a causal housing wealth effect on consumption using a quasi-natural experiment in Stockholm, Sweden. The identification exploits an unanticipated political decision — announced in September 2007 — to renew the operating contract of Bromma Airport through 2038, reversing a long-standing expectation of closure by 2011. Because the decision resulted from opaque political bargaining and was widely characterized as a political coup by opposition parties, the announcement was genuinely unexpected. The negative externality of continued airport operations (primarily aircraft noise exceeding 70 decibels within a mapped contour) capitalized locally into house prices within one quarter of the announcement. Using difference-in-differences on all single-family house transactions in Stockholm Municipality from 2004 to 2012, the authors estimate a house price decline of 19.4 percent for dwellings within 1,000 meters of the noise contour relative to those farther away (t-statistics above 5; robust to control variables and sample period). Co-op apartment prices show no statistically significant response, consistent with greater structural noise insulation in multi-story concrete buildings.

The consumption outcome is new car purchases, observed at quarterly frequency in a registry-based household panel covering all Stockholm residents, with balance sheet information (loan-to-value ratios, bank deposits, mortgage types) and GIS-located residences. The paper focuses on the intensive margin — the log value of new cars purchased conditional on a purchase — since no effect is found on the extensive margin (probability of buying). A two-sample IV approach yields a short-run elasticity of 0.39: homeowners near the noise contour reduce the value of new cars purchased by 7.7–8.5 log points relative to homeowners farther away. Converting to a marginal propensity for expenditures (MPX): conditional on purchasing a new car, the car MPX is 2.5 cents per dollar of housing wealth lost; scaling by the annual new-car purchase rate of 0.049 per household yields an aggregate new-car MPX of 0.12 cents per dollar per year. Including a symmetry assumption for used cars raises the overall car MPX to 0.38 cents per dollar per year.

Heterogeneity analysis reveals that the collateral channel dominates the pure wealth channel. Homeowners with loan-to-value ratios above 50 percent respond almost twice as strongly as those below (elasticities of 0.526 versus 0.269). Homeowners with below-median bank deposits respond with an elasticity of 0.694, roughly five times larger than those with larger deposits. The financing data show that 47 percent of a new car’s value is financed with credit on average, of which 71 percent takes the form of mortgage debt; however, households with high LTV ratios borrow one-third less per dollar of car value, almost entirely through reduced mortgage use.

A calibrated life-cycle model (quarterly, ages 30–85, Cobb-Douglas preferences over non-durables and cars, long-term fixed-rate mortgage, adjustment costs for cars and mortgages, information friction) replicates the empirical findings. In simulation, a 19.4 percent permanent house-price shock reduces new car values purchased by 6.1 log points on average over the first four quarters, implying an elasticity of 0.31 and a new-car MPX of 0.20 cents per dollar — close to the empirical 0.12 cents and within the 95 percent confidence interval. The model decomposes the response: the collateral effect accounts for 93 percent of the car MPX and 83 percent of the total MPX in the first four quarters; the pure wealth effect accounts for the remainder. The model further shows that full information awareness would roughly double the one-year response, and that smaller shock magnitudes, shorter measurement windows, and crisis-era credit conditions (where more households are already at borrowing limits) each amplify estimated MPXs — helping account for the wide range of estimates (0.12 to 2.3 cents per dollar) in prior literature.

The identification is validated by dose-response monotonicity with distance to the noise contour, placebo tests showing no response for apartment owners or renters, and absence of income effects or differential moving behavior in the treatment group.

Q: What is the quasi-experiment and why is it well-suited for identifying housing wealth effects? A: The Stockholm municipality unexpectedly renewed Bromma Airport’s operating contract through 2038 in September 2007, reversing a broadly held expectation that the airport would close by 2011. The decision emerged from closed-door political negotiations and was denounced as a political coup by opposition parties, making it genuinely unanticipated. Because the shock is geographically contained within the airport’s noise contour, it is unrelated to macroeconomic conditions and unlikely to generate general equilibrium feedback. The authors also verify that no differential income effects, tax changes, or other policies affected the treatment versus control groups over the study window.

Q: How large is the estimated house price effect, and how precisely is it measured? A: Dwellings within 1,000 meters of the noise contour experienced a price decline of 19.4 percent relative to dwellings farther away (baseline estimate, longer sample period). The estimate is highly significant with t-statistics above 5 in all specifications and is robust to the inclusion of rich property-level controls; adding controls changes the pre-crisis estimate only trivially (from -21.4 to -21.3 percent). Co-op apartment prices show no statistically significant response across all specifications, consistent with better structural insulation of multi-story concrete buildings.

Q: What is the main consumption response finding? A: Homeowners near the noise contour reduce the log value of new cars purchased by 7.7–8.5 log points relative to homeowners farther away (reduced form, intensive margin). There is no detectable effect on the extensive margin — the probability of purchasing a new car changes by only 0.029 percentage points per quarter against a baseline of approximately 1.2 percent per quarter. Two-sample IV yields an elasticity of 0.39 (statistically significant at 1 percent), meaning a 1 percent decline in house prices leads to a 0.39 percent reduction in new car values among purchasers.

Q: What does the elasticity of 0.39 imply for the marginal propensity to spend on cars? A: Conditional on purchasing a new car, the car MPX is 2.5 cents per dollar of housing wealth lost (calculated as 0.393 × 19.4% × SEK 250,000 average car value, divided by SEK 774,060 housing wealth loss). Scaling by the annual new-car purchase frequency of 0.049 per household yields an aggregate new-car MPX of 0.12 cents per dollar per year. Assuming an equal response for used cars, the overall car MPX is 0.38 cents per dollar per year. These estimates are substantially smaller than Mian et al. (2013)’s 1.8–2.3 cents per dollar, a discrepancy the model helps explain.

Q: What is the role of the loan-to-value ratio in shaping the consumption response? A: Homeowners with LTV ratios above 50 percent respond almost twice as strongly (elasticity 0.526) as those with LTV below 50 percent (elasticity 0.269). The financing data confirm the mechanism: on average 71 percent of car-purchase borrowing takes the form of mortgage debt, but households with high LTV ratios borrow one-third less per dollar of car value, with the difference almost entirely attributable to reduced mortgage use. This pattern is consistent with binding borrowing constraints preventing high-LTV households from extracting home equity for collateral.

Q: What is the role of liquid savings (bank deposits) in the response? A: Homeowners with bank deposits below the median respond with an elasticity of 0.694, roughly five times larger than homeowners with larger deposits (elasticity approximately 0.139). This heterogeneity is consistent with deposits serving as a buffer stock that allows wealthier households to smooth consumption without altering borrowing behavior after a wealth shock.

Q: What does the quantitative model find about the relative importance of the collateral channel versus the pure wealth effect? A: In the first four quarters following the shock, the collateral effect accounts for 93 percent of the car MPX response and 83 percent of the total expenditure MPX; the pure wealth effect accounts for only 7.5 percent of car MPX and 19 percent of total MPX over the same horizon. Over a longer horizon of 20 quarters, the collateral channel remains dominant at 69 percent of the car baseline, while the wealth effect rises to 32 percent. For non-durable consumption, the short-run collateral effect is 81 percent and the wealth effect is 19 percent.

Q: How does the model match the empirical estimates? A: Simulating a permanent 19.4 percent house-price shock for 200,000 household pairs, the model produces a 6.1 log point average reduction in new car values over the first four quarters, corresponding to an elasticity of 0.31 and a new-car MPX of 0.20 cents per dollar. The empirical estimate is 0.12 cents, and the model value falls within the empirical 95 percent confidence interval. The model also replicates the pattern of no extensive-margin response in the short run and a gradual build-up in the non-durable consumption response (maximum elasticity of 0.079 reached only after ten quarters).

Q: Why is the short-run response concentrated in cars rather than non-durables? A: The paper establishes an intertemporal smoothing mechanism for durables analogous to McKay and Wieland (2021): households delay or bring forward lumpy durable purchases in response to shocks to borrowing capacity. Although cars represent only 5.5 percent of total consumption in the model (Cobb-Douglas expenditure share), they account for 45–72 percent of the total expenditure response in the first four quarters after the house-price shock. The non-durable consumption response builds slowly and reaches its maximum after about ten quarters.

Q: What factors does the model identify as explanations for the wide range of MPX estimates across studies? A: Three factors are identified. First, shock magnitude: larger shocks produce smaller partial-equilibrium MPXs because more households hit borrowing constraints; across shock sizes from -30 to +20 percent, car and total MPXs can range from 1 to 2 cents per dollar. Second, measurement period: short-run (1-year) MPXs exceed long-run (3-year) MPXs, especially for durable goods. Third, the state of the economy: in a crisis-era bust following credit-fueled boom, many more households are constrained when prices fall, amplifying MPXs; Guerrieri and Iacoviello (2017) report car elasticities of 0.24 in the boom phase and 0.49 in the bust phase of the US financial crisis.

Q: What is the role of the information friction in the model? A: Because the quasi-experiment occurred in “normal times” just before the global financial crisis became acute, the authors argue that households were not immediately aware of the house-price shock; they only update their perceived housing wealth when they attempt to adjust their mortgage, trade cars, or receive a random information update. Under full information awareness, the one-year MPX would be approximately twice as large, and the one-year total MPX could be as much as three times as large (with a car MPX of 3 cents per dollar and total MPX well above 6 cents per dollar under full information with small positive shocks). The information friction thus attenuates the estimated MPX relative to a world of full information.

Q: What placebo and robustness tests support the identification? A: Co-op apartment owners show no statistically significant price or consumption response, consistent with their structural insulation from aircraft noise. Renters also show no consumption response. The dose-response test confirms a monotone relationship between distance to the noise contour and both house price and car expenditure effects. Income effects are absent (Figure B.2), and there is no differential probability of moving in either the short or long run. Tax reforms benefited both groups equally and had already been announced before the quasi-experiment.

Q: How does this study’s identification strategy compare to instrumental variable approaches using housing supply elasticity? A: Supply elasticity IV approaches (Mian et al. 2013; Aladangady 2017; Kaplan et al. 2020) rely on regional variation in construction constraints and must assume that consumption demand factors are either observed or uncorrelated with supply elasticity — an assumption critiqued by Davidoff (2016). This paper’s identification exploits an exogenous change in a local negative externality, yielding a geographically granular shock unrelated to macroeconomic conditions and free from general equilibrium feedback. The result is interpretable as a partial equilibrium housing wealth effect in the sense of Berger et al. (2018) and Guren et al. (2020).

Housing wealth effect: The causal effect of a change in housing wealth on household consumption expenditure, decomposed in this paper into a pure wealth channel (change in lifetime resources) and a collateral channel (change in borrowing capacity via home equity).

Marginal propensity for expenditures (MPX): The change in spending per dollar change in housing wealth; distinct from the marginal propensity to consume (MPC) because spending on durables may be lumpy and differ from the flow of consumption services. The paper distinguishes the car MPX conditional on purchase (2.5 cents per dollar), the aggregate new-car MPX (0.12 cents per dollar per year), and the total expenditure MPX.

Collateral channel: The mechanism by which a decline in house prices reduces homeowners’ borrowing capacity — because the house serves as collateral for mortgage debt — thereby tightening credit constraints and reducing spending, independent of any change in permanent income. The model assigns 93 percent of the short-run car MPX to this channel.

Two-sample instrumental variable (TSIV): The empirical strategy of Angrist and Krueger (1992) used here to estimate the consumption elasticity: the house-price first stage is estimated in one sample (transaction data), and the reduced-form consumption effect is estimated in a second sample (household panel), with the IV elasticity computed as the ratio.

Information friction: The assumption in the model that households do not immediately observe the spatial divergence in house prices; they update their perceived housing wealth only when they attempt to adjust their mortgage, trade a durable good, or receive a random information shock. This friction attenuates the short-run consumption response and is calibrated to “normal times” conditions.

Noise contour: The geographic boundary around Bromma Airport within which properties are regularly exposed to noise levels of at least 70 decibels, as adjudicated by the Swedish Land and Environment Court. Properties within 1,000 meters of this contour define the treatment group.

Intertemporal smoothing of durables: The pattern, documented in the model and complementary to McKay and Wieland (2021), whereby households adjust lumpy durable purchases (cars) rapidly in response to changes in borrowing capacity, so that durables account for a disproportionately large share of the total expenditure response in the short run (45–72 percent in the first four quarters despite a 5.5 percent Cobb-Douglas expenditure share).

E60 | Macro Paper Warehouse

Bridging micro and macro production functions: The fiscal multiplier of infrastructure investment

Layer 1 — Overview

Layer 2 — Q&A

Key Concepts

Income Inequality and Job Creation

In depth

Q1. Why does the portfolio composition of saving matter more than the aggregate savings rate?

Q2. Why are small firms disproportionately harmed by higher loan rates?

Q3. How is the pre-determined share IV constructed and why does it satisfy the exclusion restriction?

Q4. What explains the aggregate output decline when private firms have higher marginal products?

Q5. How does rising inequality amplify its own effect through welfare and further portfolio reallocation?

Q6. What fraction of US macroeconomic trends since 1980 can the channel explain?

Q7. What happens to firm entry and exit under rising inequality?

Q8. Why do deposits account for such a large share of bank liabilities and why can’t banks substitute easily?

Key concepts

On the Nature of Entrepreneurship

Present Bias Amplifies the Household Balance-Sheet Channels of Macroeconomic Policy

Layer 1 — Summary

Layer 2 — Q&A

Key Concepts

The housing wealth effect: Quasi-experimental evidence