L25 | Macro Paper Warehouse

Heterogeneous innovations and growth under imperfect technology spillovers

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

Layer 1 — Overview

Research Question. Jo and Kim ask two related questions: (1) How do firms use different types of innovation when learning others’ technology takes time? (2) How does this process alter the aggregate implications of firm innovation, particularly in the context of increasing competition?

Model. The paper develops a discrete-time infinite-horizon endogenous growth model with multi-product firms pursuing two types of innovation — “own-innovation” (improving existing product quality) and “creative destruction” (entering new product markets by displacing incumbents) — subject to a novel friction called “imperfect technology spillovers.” The friction takes the specific form of lagged learning: creative destruction builds on the one-period-lagged technology of the target market’s incumbent, while only the incumbent can observe the current frontier technology level. This one-period lag creates a technology gap (Δ = q_t / q_{t−1}) between the incumbent’s frontier and the level available to rivals. Four possible technology gap values arise in equilibrium: Δ₁ = 1 (no gap), Δ₂ = λ (one successful own-innovation), Δ₃ = η (one successful creative destruction), and Δ₄ = η/λ. The step sizes satisfy λ² > η > λ, meaning a single creative destruction improves quality more than a single own-innovation, but two consecutive own-innovations dominate a single creative destruction.

Key Mechanisms. The learning friction generates two novel mechanisms. First, the “market-protection effect”: incumbents with a technology advantage (Δ > 1) intensify own-innovation to widen the gap and protect their product lines when competitive pressure rises. Formally, own-innovation probability is highest for Δ₂ products and declines monotonically (z₂ > z₃ > z₄ > z₁), and ∂z₂/∂x > ∂z₃/∂x > 0 while ∂z₁/∂x < 0, conditional on value coefficients. Second, the “technological barrier effect”: higher overall own-innovation and creative destruction intensity widens the average technology gap across products, reducing rivals’ conditional probability of successfully taking over a product market. This is distinct from the standard Schumpeterian effect (lower expected future profits) and from the escape-competition effect in step-by-step models (which apply only to neck-and-neck, single-product firms).

Data and Empirical Strategy. The empirical analysis combines the USPTO PatentsView database, the Longitudinal Business Database (LBD), the Longitudinal Firm Trade Transactions Database (LFTTD), the Census of Manufactures (CMF), Compustat, and NBER-CES data, covering the universe of U.S. patenting firms from 1976 to 2016, with main analyses from 1982 to 2007. Own-innovation is proxied by the self-citation ratio of patents (the ratio of self-citations to total backward citations); creative destruction by new products added and low-self-citation patents. Exogenous competitive pressure comes from China’s WTO accession in 2001, instrumented by the industry-level NTR tariff gap (the gap between non-NTR and NTR rates in 1999) following Pierce and Schott (2016).

Empirical Findings. Pre-shock (1982–1999): patents with lower self-citation ratios (closer to creative destruction) have significantly longer backward citation gaps (coefficient −2.29 to −2.59, p < 0.01 across specifications), confirming that learning others’ technology takes more time. Creative-destruction-type patents also have higher market value (Kogan et al. stock return measure) and scientific value (forward citations), with self-citation ratio negatively associated with both (e.g., coefficient on self-citation for market value: −0.289 without firm FE; −0.110 with firm FE, p < 0.01). Conditional on patenting, higher self-citation ratios are negatively associated with employment growth (coefficient −0.256, p < 0.05), number of industries added (−0.158, p < 0.05), and products added (−0.274, p < 0.01).

Post-shock (DID): foreign competition had no statistically significant effect on overall patent counts, but firms with above-average innovation intensity in industries with high NTR gaps significantly increased their self-citation ratio — indicating a shift toward own-innovation. The triple-interaction coefficient is 0.795 (p < 0.01) with baseline controls. For a firm with average lagged innovation intensity (0.18) in an industry with an average NTR gap (0.291), this corresponds to a 4.2 percentage point increase in the seven-year growth rate of the self-citation ratio, representing a 15.0% increase relative to the average growth rate of 28.2 percentage points. Consistent with the technological barrier effect, firm entry rates are lower in industries with higher TFPR-skewness-based technological barriers (coefficient −0.012 to −0.016, p < 0.05).

Quantitative Analysis. Calibrated to the U.S. manufacturing sector in 1992, the model matches six target moments including average number of products (2.3), products added (0.3), firm entry rate (7.6%), average productivity growth (1.9%), high-growth-firm employment growth (22.5%), and import penetration (15.3%). Creative destruction contributes approximately 1.88 times more to growth per unit than own-innovation (step size ratio 0.075/0.04). The aggregate R&D-to-sales ratio (untargeted) is 4.6% in the model vs. 4.1% in data.

A counterfactual increasing outside entrants by 83% (matching the rise in import penetration from 15.3% to 25.1% between 1992 and 2007) generates a 1.51% increase in aggregate creative destruction arrival rate x, but firm-level creative destruction probability falls 1.33% and startup creative destruction also falls 1.33%. The aggregate R&D-to-sales ratio falls 1.6% and creative destruction R&D intensity falls 1.2%. Average domestic productivity growth declines 11.0%, with growth from creative destruction falling 13.0% and growth from domestic startups falling 1.7%. The total mass of domestic firms falls 6.4%.

In economies with creative destruction costs 80 times higher than the U.S. baseline, the same competitive pressure shock raises rather than lowers total R&D (by 1.0%), but domestic growth still falls 9.7%, because the marginal decline in creative destruction impedes the growth contribution and firm entry even when aggregate innovation spending rises.

Layer 2 — Q&A

Q1: What is the key friction that distinguishes this model from the existing multi-product firm literature (e.g., Klette and Kortum 2004; Akcigit and Kerr 2018)?

A: The key friction is “imperfect technology spillovers,” modeled as lagged learning: creative destruction can only build on the one-period-lagged technology of the target product (q_{j,t−1}), while the product’s current owner observes the frontier technology (q_{j,t}). In models without this friction — such as Akcigit and Kerr (2018) — rivals can instantly learn and copy frontier technology, so firms have no technological advantage and cannot protect their markets. In the current model, own-innovation by the incumbent widens the gap between q_{j,t} and q_{j,t−1}, creating a barrier that a rival must overcome even after successful creative destruction. This makes own-innovation an endogenous function of the technology gap, a feature absent from existing multi-product firm frameworks.

Q2: Why does the model predict that own-innovation increases with the technology gap up to a point, then decreases?

A: From Corollary 1, the ordering z₂ > z₃ > z₄ > z₁ reflects competing forces. Products with gap Δ₂ = λ gain the most from additional own-innovation in terms of reducing the probability of losing the product line (equation 2), so own-innovation is highest there. Products with Δ₃ = η or Δ₄ = η/λ already have substantial technological advantages from prior creative destruction, so the marginal value of own-innovation in reducing market loss probability is lower. Products with Δ₁ = 1 have no advantage at all: if a rival succeeds in creative destruction, the incumbent loses the product regardless of own-innovation (equation 1), so z₁ is lowest. Beyond a certain gap level, the incumbent is sufficiently protected that additional own-innovation has diminishing returns in deterrence.

Q3: What is the market-protection effect formally, and for which products is it strongest?

A: The market-protection effect (Corollary 2) is the positive response of a firm’s own-innovation to an increase in the aggregate creative destruction arrival rate x, conditional on the value coefficients A₁ and A₂ being fixed. It is strongest for products with Δ₂ = λ (∂z₂/∂x is the largest and positive), positive but weaker for Δ₃ = η (∂z₃/∂x > 0), of ambiguous sign for Δ₄ = η/λ, and negative for Δ₁ = 1 (∂z₁/∂x < 0). The asymmetry reflects the asymmetric payoff to own-innovation across gap levels: for Δ₂ products, successful own-innovation can turn a losing situation into a winning one because it shifts the technology gap from Δ₁ to Δ₂ from the rival’s perspective, effectively defeating the rival’s creative destruction attempt. This mechanism provides a micro-foundation for why frontier firms (like Google or NVIDIA) keep innovating intensely despite their technological leads, a pattern the standard step-by-step model cannot explain.

Q4: What is the technological barrier effect and how does it differ from the Schumpeterian effect?

A: The technological barrier effect refers to the reduction in rivals’ incentive for creative destruction caused by an increase in the average technology gap across product lines. When incumbents do more own-innovation or when outside firms do more creative destruction, the distribution of technology gaps shifts rightward (density at Δ₁ falls; density at Δ₂, Δ₃, Δ₄ rises). This raises the average technology barrier rivals must overcome to successfully take over a product market, reducing the conditional takeover probability x^{takeover} and the expected value of creative destruction B. In the U.S. counterfactual, the technological barrier effect accounts for 17.0% of the total change in the aggregate creative destruction rate x and 15.0% of the change in startup creative destruction x_e. In contrast, the Schumpeterian effect refers to the reduction in expected future profits from owning a product due to increased displacement risk (through the value coefficient A₂), a mechanism present in standard quality-ladder models. Both operate simultaneously but the technological barrier effect is a novel feature of this framework.

Q5: How is own-innovation vs. creative destruction measured empirically, and what validates this measure?

A: The self-citation ratio (the share of a patent’s backward citations that cite the same assignee’s earlier patents) is used as the primary measure: a higher ratio indicates greater reliance on the firm’s own prior knowledge, hence a higher probability that the innovation improves an existing product line (own-innovation). This is validated empirically in three ways. First, patents with lower self-citation ratios have significantly larger backward citation gaps (coefficient −2.29 to −2.59 across fixed-effect specifications on 728,721 observations), consistent with creative destruction requiring more time to learn others’ technology. Second, lower self-citation patents have higher market value and scientific value (forward citations), consistent with η > λ (creative destruction contributes more per event to quality). Third, firm-level regressions show that lower self-citation ratios are associated with higher employment growth, more products added, and more industries entered, consistent with creative destruction contributing more to firm expansion.

Q6: How does the DID identification strategy work, and what are the main results?

A: The identification exploits the removal of trade policy uncertainty (TPU) after China’s WTO accession in 2001. The treatment variable is the industry-level NTR gap (the gap between non-NTR and NTR tariff rates in 1999): industries with larger gaps experienced a larger reduction in uncertainty and thus a greater increase in Chinese import competition. The DID compares patenting firms across periods (1992–1999 vs. 2000–2007) and across high- vs. low-NTR-gap industries, with a triple interaction for firm-level innovation intensity (lagged five-year average patents per employee, normalized within two-digit NAICS). The main finding (Table 4): the NTR gap × Post interaction has no significant effect on overall patent counts (coefficient 0.238 without controls, standard error 0.237), but the triple interaction (NTR gap × Post × innovation intensity) has a positive and significant effect on the growth rate of the self-citation ratio (0.732 without controls, p < 0.05; 0.795 with baseline controls, p < 0.01). This implies that innovation-intensive firms in high-competition industries shifted their composition toward own-innovation, while overall patenting was unchanged — consistent with an offsetting rise in own-innovation and fall in creative destruction.

Q7: What are the aggregate growth effects of increasing competitive pressure in the calibrated model?

A: Using an 83% increase in outside entrants (matching the 1992–2007 rise in import penetration from 15.3% to 25.1%), average domestic productivity growth falls 11.0%. Decomposing: growth from domestic own-innovation falls 11.4%, growth from domestic creative destruction falls 13.0%, and growth from domestic startups falls 1.7% (Table 9). The aggregate R&D-to-sales ratio falls 1.6% and the creative destruction R&D intensity falls 1.2%, indicating that the decline in creative destruction R&D outweighs the rise in own-innovation R&D. The total mass of domestic firms falls 6.4% and the average number of products per firm falls 5.5%.

Q8: How do results differ in economies with high creative destruction costs vs. the U.S.?

A: When creative destruction costs (χ̃) are set 80 times higher than the U.S. baseline, the initial equilibrium has much lower creative destruction: R&D-to-sales ratio is 1.39% (vs. 4.58% in U.S.), creative destruction R&D intensity is 8.6% (vs. 63.9%), average number of products is 1.0 (vs. 2.3), and average domestic productivity growth is 1.4% (vs. 1.9%). Under the same competition shock, total R&D actually rises by 1.0% in this high-CD-cost economy (because own-innovation increases more than creative destruction falls, given the already low baseline of creative destruction), in contrast to the −1.6% in the U.S. However, domestic growth still falls 9.7% even in this economy, driven by reductions in creative destruction by incumbents and startups combined with a decline in the mass of domestic incumbents. This result holds even with a fixed firm mass (Table E5), confirming the mechanism is not solely due to entry/exit dynamics.

Q9: What is the technological barrier effect’s quantitative contribution to the decline in creative destruction?

A: In the U.S. counterfactual (Table 8 and associated decomposition), 17.0% of the total change in the aggregate creative destruction arrival rate x and 15.0% of the total change in startup creative destruction x_e are attributable specifically to the technological barrier effect — that is, to the shift in the technology gap distribution µ(Δℓ) holding all else equal. The conditional takeover probability x^{takeover} declines from 73.2% to 73.0%. The density at Δ₁ (the easiest gap to overcome) falls 0.4%, while densities at Δ₃ and Δ₄ rise 1.1% and 1.4% respectively, driven by increased creative destruction by outside firms and intensified own-innovation by incumbents.

Q10: What are the policy implications the paper draws from its framework?

A: The paper argues that policies evaluating innovation should account for composition, not just aggregate R&D levels or patent counts. Increased overall innovation driven by defensive own-innovation contributes less to economic growth than creative destruction and restricts firm entry — so it is less beneficial than it appears. In low-creativity economies (e.g., European economies with high regulatory barriers to creative destruction), increased foreign competition may raise aggregate R&D while still lowering domestic growth, misleading policymakers who track only total innovation spending. The model also suggests that the mixed empirical findings in the competition-innovation literature (Aghion et al. 2005; Bloom et al. 2016; Autor et al. 2020) can be reconciled by accounting for compositional shifts: the net effect of competition on total innovation is ambiguous because it raises own-innovation for technologically advantaged firms while reducing creative destruction for all firms.

Key Concepts

Imperfect Technology Spillovers: The novel friction introduced in this paper, modeled as lagged learning: firms attempting creative destruction can only access the one-period-lagged technology of the target product market (q_{j,t−1}), while the incumbent product owner observes and can improve from the current frontier (q_{j,t}). This asymmetry creates a persistent technological advantage for incumbents and enables strategic defensive innovation.

Own-Innovation: R&D investment by a firm to improve the quality of its existing product lines. Successful own-innovation raises product quality by a step size λ > 1. Own-innovation does not require learning others’ technology and, in the model, constitutes the incumbents’ defensive margin against creative destruction. At the aggregate level, it contributes more to total growth than creative destruction because it succeeds more frequently, but per successful event it contributes less (λ < η).

Creative Destruction: R&D investment enabling a firm to enter a new product market by displacing the incumbent. Successful creative destruction improves the lagged quality of the target product by a step size η > λ, where λ² > η > λ. It requires learning the incumbent’s one-period-lagged technology, takes longer to develop (evidenced empirically by longer backward citation gaps), and contributes more to firm growth and product expansion per event than own-innovation.

Technology Gap (Δ): The ratio of a product’s current-period technology to its previous-period technology (Δ_{j,t} = q_{j,t}/q_{j,t−1}). This gap summarizes the technological advantage the incumbent holds in a product market under imperfect spillovers. Four values are possible in equilibrium: Δ₁ = 1, Δ₂ = λ, Δ₃ = η, Δ₄ = η/λ. The gap determines both the incumbent’s own-innovation incentive and the rival’s probability of successfully completing a product takeover conditional on creative destruction.

Market-Protection Effect: The mechanism by which incumbents with a technological advantage (Δ > 1) increase own-innovation in response to heightened competitive pressure (an increase in the aggregate creative destruction arrival rate x). This effect is maximized for products with Δ₂ = λ and positive but diminishing for Δ₃. It is absent for Δ₁ = 1 products (where own-innovation cannot prevent displacement) and is formally distinct from the escape-competition effect in step-by-step innovation models, which applies only to neck-and-neck single-product firms.

Technological Barrier Effect: The reduction in rivals’ incentive for creative destruction caused by an increase in the average technology gap across the economy’s product lines. When incumbents intensify own-innovation and/or when outside creative destruction increases, the distribution of technology gaps shifts toward higher Δ values, reducing the conditional probability that a rival successfully takes over any given product market. This feedback mechanism endogenously suppresses creative destruction and firm entry beyond what the Schumpeterian effect alone would predict.

Self-Citation Ratio: The share of a patent’s backward citations that cite patents previously owned by the same firm. Used in the paper as a continuous proxy for the likelihood that a patent represents own-innovation vs. creative destruction: a ratio of 1 (100% self-citations) implies 100% probability of own-innovation; a ratio of 0 implies 100% probability of creative destruction. This measure follows Akcigit and Kerr (2018) and is validated in the paper against learning time, quality, and firm growth outcomes.

NTR Gap (Trade Policy Uncertainty Shock): The industry-level difference between non-NTR (column 2) and NTR (column 1) U.S. tariff rates in 1999, used as an instrument for the exogenous increase in Chinese competitive pressure following China’s WTO accession and the U.S. granting of Permanent Normal Trade Relations (PNTR) in 2002. Industries with larger NTR gaps experienced a greater reduction in trade policy uncertainty and thus a larger increase in competitive pressure from foreign firms.

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.