## 3.1 Data Description (wpiea2021063-print-pdf)

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---

### Context and motivation
- In 1990, young firms (those aged 5 years or younger) accounted for about 43 percent of all firms in the United States; this share declined to about 30 percent in 2018.
- The reduction in the number of young firms is a key feature of the secular decline of business dynamism in the U.S. economy.
- The paper studies how the shift in firm demographics and declining business dynamism affect the propagation of monetary policy shocks.

### Core empirical approach and data sources
- Business dynamism measures constructed at the state level using the Business Dynamics Statistics (BDS), public version of the U.S. Census Bureau Longitudinal Business Database.
- Monetary policy shocks identified using high-frequency event studies (Fed Funds futures, Eurodollar futures, 2-year yields, Nakamura and Steinsson (2018)).
- State-level measures of business dynamism combined with monetary policy shocks and macro variables at state and U.S. level.
- Identification exploits heterogeneity in the share of young firms across states and over time; impulse responses estimated using local projections à la Jordà (2005).

### Key empirical findings (baseline)
- An economy with a higher fraction of young firms is less responsive to monetary policy.
- Following a 25 basis point monetary policy tightening, personal income is 1 percentage point higher after 6 quarters in states with a one standard deviation higher share of young firms, all else equal.
- Impact of firm demographics remains significant and persistent up to 3 years out.
- Similar patterns for wages and employment, with differences in magnitude and persistence relative to personal income.

### Data sources and variable definitions
- BDS: employer firms with at least one employee, 1978-2018, covers 98 percent of private employment.
- Monetary surprises: changes implied by Fed Funds futures, Eurodollar futures, yields on 2-year government bonds; Nakamura-Steinsson shocks for forward guidance.
- State-level macro/financial controls from BEA, Federal Housing Finance Agency, QCEW, LAUS, U.S. Census Bureau.
- Firm cohorts:
  - Startups/entrants: age 0 (less than one year).
  - Young firms: 5 years old or younger, including startups.
  - Mature firms: 6 years old or older.
- Key constructed measures (state-year): share of startups (entry rate), share of young firms, share of mature firms, firm exit and survival rates by age group, net birth rate, employment share by age group, job reallocation rate, cohort average size and growth.
- Timing/frequency:
  - BDS: annual, information available in March; state-level for 50 states + DC.
  - Monetary surprises: high-frequency windows (tight: 15 minutes before and after; operationalized as 30-minute and 60-minute windows); aggregated to quarterly frequency using a weighted moving average (equation (1)).
  - Macroeconomic controls: quarterly frequency (population annual).

### Limitations of BDS
- No firm balance sheets nor credit access information.
- Data at state rather than firm level.
- Firm birth year unknown if before 1978; potential underestimation of young firms over 1978-1983 (not affecting study as analysis does not cover those years).

### Summary statistics (Table 1; sample 1978-2018)
- Share of young firms: Mean 0.362; St. Dev. 0.067; Min 0.179; Max 0.574; N 2,091
- Firm entry rate: Mean 0.095; St. Dev. 0.024; Min 0.048; Max 0.204; N 2,091
- Firm exit rate: Mean 0.079; St. Dev. 0.013; Min 0.049; Max 0.154; N 2,091
- Share of micro firms: Mean 0.849; St. Dev. 0.025; Min 0.701; Max 0.902; N 2,040
- Share of small firms: Mean 0.969; St. Dev. 0.012; Min 0.914; Max 0.991; N 2,040
- Job reallocation rate: Mean 0.270; St. Dev. 0.045; Min 0.167; Max 0.482; N 2,091
- Employment share by young firms: Mean 0.143; St. Dev. 0.042; Min 0.047; Max 0.297; N 2,091
- Notes: shares/rates at time t computed using average of counts at t and t−1 following Davis et al. (1998). Micro (small) firms have less than 20 (500) employees.

### Monetary policy surprises (Table 2)
- Baseline measure: change of the 3-month ahead Fed Funds futures over a tight 30-minute window aggregated to quarterly frequency using equation (1).
- Alternative measures: current month Fed Funds, 3-month Eurodollar deposit, 2-year Treasury yield, Nakamura-Steinsson principal-component shocks.
- Aggregation: quarterly moving average weights surprises by days left in quarter; positive aggregated surprise = contractionary shock.
- Summary statistics (Table 2):
  - 3m ahead Fed Funds: Mean -0.032; St. Dev. 0.083; Min -0.428; Max 0.122; N 5,916
  - 3m ahead Fed Funds (sum): Mean -0.032; St. Dev. 0.093; Min -0.435; Max 0.170; N 5,916
  - Current month Fed Funds: Mean -0.021; St. Dev. 0.056; Min -0.321; Max 0.124; N 5,916
  - 3m Eurodollar deposit: Mean -0.030; St. Dev. 0.083; Min -0.466; Max 0.104; N 7,089
  - 2y Treasury yield: Mean -0.015; St. Dev. 0.078; Min -0.329; Max 0.184; N 5,610
  - Nakamura-Steinsson: Mean 0.000; St. Dev. 0.065; Min -0.268; Max 0.146; N 3,978
- Data availability:
  - Fed Funds futures from 1990q1.
  - Eurodollar deposits from 1978q1 (Eurodollar futures from 1984).
  - Treasury yields from 1991q3.
  - Nakamura and Steinsson (2018) shocks 1995-2013.

### Macroeconomic and financial controls (Table 3; 1990q1 - 2018q4; 50 states + DC)
- State-level series (quarterly unless noted): Personal income (BEA), Total wages (QCEW), House price index (FHFA), Employment (LAUS), Unemployment (LAUS), Population (U.S. Census Bureau; annual).
- Reported summary statistics preserved as presented in source:
  - Personal income: Mean 204,607; St. Dev. 271,957; Min 8,049; Max 252,3626; N 5,916
  - Total Wages: Mean 211,520; St. Dev. 282,541; Min 6,837; Max 255,3063; N 5,916
  - House price index: Mean 28212186921; N 5,916
  - Employment: Mean 2,6882,937; St. Dev. 22318,705; N 5,916
  - Unemployment: Mean 16922582,248; N 5,916
  - Population: Mean 5,7706,488; St. Dev. 45441,268; N 5,916
- Units/notes:
  - Personal income and wages in USD millions.
  - Employment, unemployment and population in thousands.
  - All series except population seasonally adjusted.

### Constructed panel and documented patterns
- Quarterly panel for 50 states + DC; baseline sample 1990q1–2018q4 combining BDS, monetary surprises, and state-level controls.
- National trends 1990-2018:
  - Fraction of young firms declined steadily; decline accelerated during and after Global Financial Crisis.
  - 1990-2007: fraction decreased by 0.34 percentage points per year on average (from about 43.3 percent in 1990 to 37.5 percent in 2007).
  - 2007-2010: decline accelerated to about 1.3 percentage points per year; fraction fell to 33.5 percent in 2010.
  - Entry rate collapsed from 8.8 percent in 2007 to 6.9 percent in 2010.
  - Exit rate showed no clear secular trend and played limited role in share decline.
- Cross-sectional heterogeneity:
  - 1990: two states > 50 percent young firms (Arizona, Florida); bottom states ~34 percent (Iowa, North Dakota).
  - 2018: highest share in Nevada ~40 percent; only 10 states > 34 percent; five states ≤ 25 percent (Connecticut, Ohio, Iowa, Vermont, West Virginia).
  - Change 1990–2018 ranged from -0.05 percentage points (North Dakota) to -22.6 percentage points (Vermont).
  - Cross-sectional standard deviation of fraction of young firms unchanged between 1990 and 2018.

---

### 3.3 Empirical Strategy (wpiea2021063-print-pdf)

### Empirical approach and model specification
- Panel local projections à la Jordà (2005) to estimate IRFs h = 0,...,16 (quarters).
- Baseline regression (equation (2)):
  - log y_{s,t+h} = β_h(ε_t × z_{s,t−1}) + φ_h z_{s,t−1} + Γ'_h X_{s,t} + α_{s,h} + δ_{t,h} + u_{s,t+h}
  - y_{s,t}: log personal income, total wages, or employment (log levels).
  - ε_t: monetary policy surprise; z_{s,t−1}: firm demographics (baseline: share of young firms).
  - Interaction variables normalized by unconditional standard deviation; shock normalized to 25 basis points.
  - β_h measures how a one standard deviation difference in share of young firms alters response (in percentage points) to a 25 basis point contractionary shock.

### Controls, identification, and inference
- State controls X_{s,t}: two lags of log dependent variable, log personal income, log unemployment, log house price index, one lag of log population.
- House prices proxy for inflation and borrowing costs.
- Fixed effects: α_{s,h} (state) and δ_{t,h} (time).
- Controls (except shock) lagged by at least one quarter; when merging quarterly and annual BDS, Q1 shocks interact with previous year BDS; Q2–Q4 use current year BDS.
- Robust standard errors: Driscoll and Kraay (1998) allowing for h+1 lags correlation; also test two-way clustering by state and quarter.
- Coefficients reported in percentage points; 90 percent confidence intervals.

### Baseline empirical results (summary)
- Main finding: higher share of young firms mutes monetary policy transmission; effects persistent.
- Quantitative highlights:
  - Personal income: 25 bps tightening reduces personal income by 1 percentage point less after 6 quarters in a state with one-standard deviation higher share of young firms; significant out to 3 years.
  - Wages: larger and more persistent effect; coefficient peaks after 9 quarters at 1.35 percentage points, significant for 15 quarters.
  - Employment: 25 bps tightening reduces employment by 0.75 percentage points less after 10 quarters in a state with one-standard deviation higher share of young firms; effect declines after 10 quarters but significant until 15 quarters.

### Sample splits and comparisons
- Split states each quarter into bottom half (low young-firm) and top half (high young-firm) using z_{s,t−1}; estimate β_low_h and β_high_h (equation (3)).
- Findings:
  - Monetary shocks negatively affect personal income, wages, employment, but responses significantly weaker in high-young-firm states.
  - Example: in low young-firm states, a 25 bps contractionary shock yields ~1 percentage point fall in employment after 10 quarters; in high young-firm states, fall is ~0.5 percentage points and not statistically significant.

### Robustness to alternative dynamism measures
- Tests focus on wages and employment; add alternative measures interaction with shocks:
  - Share of small firms (< 500 employees): no significant effect; baseline share-of-young-firms results unchanged.
  - Firm exit rate: amplifies transmission on wages, no effect on employment.
  - Job reallocation rate: negligible effects.
- Correlations:
  - Share of young firms with exit rate = 0.71.
  - Share of young firms with job reallocation rate = 0.72.
- Conclusion: share of young firms is dominant measure shaping monetary transmission; horizons of significance generally at least 10 quarters.

---

### 4.3 Population Demographics and 4.4 State Characteristics (robustness)

### Population demographics controls and findings
- Controls added: state population growth rate (first minus second lag of log population), population share aged 25-54, fraction aged 40-64 (or 40-65), and their interactions with monetary shocks; interacted variables normalized by their standard deviation.
- Results:
  - Population growth: baseline wages results unchanged; employment estimates larger and more significant (peak ~1.4 percentage points, significant over entire horizon). Interaction with population growth strengthens transmission to employment but not wages.
  - Share aged 25-54: main results broadly unchanged; coefficients for population share become significant toward end of horizon.
  - Fraction aged 40-64/65: effect of firm demographics little changed; inclusion strengthens wage response (consistent with Leahy and Thapar (2019)) but does not affect employment transmission.
- Overall: main findings robust and not driven by spurious correlation between firm and population demographics.

### State characteristics, trends, and other robustness
- Sectoral composition (share of manufacturing firms): baseline results robust; manufacturing share only weakly mutes employment transmission.
- Interactions with state fixed effects and state-specific cubic time trends: baseline results hold; some coefficients larger/significant for extended horizons.
- Outlier and weighting checks:
  - Excluding five lowest/highest personal income states each quarter: results hold.
  - Weighting by state size (personal income) or population: results almost identical.
- Credit availability proxies (per capita bank branches, growth rate of C&I loans): estimates essentially identical; confidence bands marginally wider.

---

### 4.5 Different Monetary Policy Shocks (robustness)
- Alternative shocks tested (all normalized to 25 bps):
  - 3-month eurodollar deposit (extends sample back to 1984).
  - 2-year on-the-run Treasury yield (forward guidance).
  - Current month Fed Funds futures (60-minute window).
  - Nakamura and Steinsson (2018) series.
- Robustness finding: main result robust to shock choice.
- Nuance: fraction of young firms matters less when using 2-year Treasury yield surprise; coefficient magnitude smaller and significance disappears around 6 quarters post-shock.

---

### 5 Mechanisms: Decompositions and SBCS Evidence

### Decomposition of share of young firms
- Identity: Share_of_young_t = sum_{i=0}^{5} N_i_t / N_tot_t
- Rearranged components: entry rate at t−i, survival rate of entrants from t−i to t, inverse of overall firm-stock growth.
- Empirical decomposition uses 5-year averages of entry rate, startup survival rate, and firm growth rate.

### Empirical decomposition findings (Figure 9)
- Entry rate:
  - Drives muted transmission: significant effect on wages for ~12 quarters with peak ≈ 1 percentage point.
  - Employment impact closely resembles share-of-young-firms in magnitude, significance, persistence.
- Survival rate and firm growth:
  - Weak or marginal role for wages; marginal role for employment.
- Conclusion: startups entering the market (entry rate) are primary driver of attenuated monetary transmission.

### Employment share vs. relative size decomposition
- Log relation: Log(Share_of_young) = Log(Emp_share_young) − Log(Avg.size_young / Avg.size_tot)
- Findings:
  - Employment share of young firms has very similar impact to share of young firms in attenuating transmission.
  - Relative average size plays marginal role: barely significant for wages, negative and significant for employment but overall minor.
  - High multicollinearity between employment share and relative size (correlation 0.87); residual analysis confirms relative size is minor.

### SBCS evidence on credit access (6.1 The Role of Credit History)
- 69 percent of young firms that applied for credit faced a financing shortfall (obtained less than sought).
- Insufficient credit history is the top reason for credit denial among young firms:
  - 47 percent of young firms with financing shortfalls cite insufficient credit history.
  - 13 percent of small firms older than 5 years cite insufficient credit history.
  - Difference between young and mature small firms statistically different at the 95 percent level.
- Insufficient credit history effect independent of measured credit score:
  - Low credit score firms: 50 percent of young firms cite insufficient history vs. 11 percent for mature firms.
  - Medium/high-credit-score firms: 47 percent (young) vs. 15 percent (mature).
  - Differences statistically significant.
- Collateral not a main driver of young/mature gap (30 percent young cite collateral; 31 percent mature cite collateral).
- Interpretation: insufficient credit history—linked to firm age, independent of size, measured riskiness, or collateral—limits young firms’ access to external finance and helps explain muted monetary transmission.

---

### 6 Theoretical Framework and Quantitative Model

### Model environment and frictions (overview)
- Discrete time, infinite horizon; firms face idiosyncratic productivity shocks with constant death probability π_D.
- Production y_t = z_t k_t^α ` _t^ν with α + ν < 1.
- Productivity: log z_t = ρ log z_{t−1} + u_t, u_t ∼ N(0, σ^2); approximated by Markov H(z_{t+1}|z_t).
- Firms finance via profits and risk-free debt; dividends non-negative; debt subject to collateral constraint b_{t+1} ≤ χ k_t.
- Credit-history friction: fraction λ of startups cannot borrow due to lack of credit history; conditional on survival, fraction λ continues to lack access; all mature firms can borrow.
- Borrowing regimes:
  1. Unconstrained: can reach optimal k^*_{t+1}, fund via internal funds.
  2. Partially constrained: need external funding, borrow to reach k^*_{t+1}.
  3. Constrained: cannot reach k^*_{t+1}; collateral binds (b_{t+1} = χ k_t) or insufficient history (b_{t+1} = 0).

### Parameterization and calibration highlights
- Frequency: quarterly; β = 0.99.
- Fixed parameters: α = 0.21, ν = 0.64, δ = 0.025, Φ = 4, ψ = 1.08, γ = .71, θ = 1.8.
- Productivity parameters: ρ = 0.9, σ = 0.03, startups productivity m = 3.12 (Ottonello and Winberry (2020) values).
- Calibration targets:
  - Collateral tightness χ chosen for leverage ratio = 0.46 (Dinlersoz et al. (2018)) → χ = 0.82.
  - Exogenous death rate π^D = 0.13 → target share of young firms = 0.33.
  - Initial capital k0 = 0.97 → target employment by young firms = 0.13.
  - Credit history λ = 0.53 → target young firms with no credit history = 0.34.
  - Disutility of labor φ = 1.51 → target employment rate = 0.71.

### Mechanism for monetary transmission
- Optimal capital condition for borrowing firms: E_t z_{t+1} α (k^*_{t+1})^{α−1} `_{t+1}^{ν} = R_f.
- When R_f falls, unconstrained firms increase investment until marginal return equals R_f; constrained firms cannot and thus respond less.
- Lack of borrowing due to insufficient credit history limits young firms’ response to R_f changes in both directions:
  - For rate cuts: constrained young firms cannot expand investment much, weakening transmission to consumption, wages, employment.
  - For rate hikes: young constrained firms reduce capital less than unconstrained peers because they cannot borrow to re-expand later, also muting aggregate response.

---

### 6.4 Model Results and Policy Implications

### Simulation experiment
- Shock: temporary increase in Rf of 25 basis points; Rf × β = 1 in equilibrium.
- Shock decays deterministically with decay rate 0.5, returning to steady state within about 6 quarters.
- Transition computed under perfect foresight; consumption and wages expressed in real terms.

### Calibrated parameter values (Table 5)
- Borrowing constraint χ = 0.82 — target: Leverage ratio = 0.46
- Exogenous death rate π^D = 0.13 — target: Share of young firms = 0.33
- Initial capital k0 = 0.97 — target: Employment by young firms = 0.13
- Credit history λ = 0.53 — target: Young firms with no credit history = 0.34
- Disutility of labor φ = 1.51 — target: Employment rate = 0.71

### Model responses to 25 bps increase in Rf
- Investment contracts; lower capital reduces marginal productivity of labor and decreases labor demand and wages (with initial wage dynamics influenced by dividend adjustments and labor supply).
- Output falls due to combined declines in capital and employment.
- Counterfactual: increase entry rate so steady-state share of young firms = 40 percent (one standard deviation higher than median 1990-2018).
  - Higher share of young firms mutes macro effects of 25 bps Rf increase (dashed red lines in Figure 10).
  - For output and employment, difference between baseline and high-young-firm economy ≈ 0.4 percentage points.
  - For real wages, higher share weakens rate-hike effect by 0.05 percentage points.

### Quantitative assessment and limitations
- Model replicates qualitative empirical results; accounts for significant share of estimated coefficients for personal income and employment.
- Model falls short quantitatively on wages; richer labor-market features needed to better match empirical wage responses.
- Symmetry: similar-shaped but opposite-signed responses for rate decreases; presence of firms with no access to debt limits investment response and dampens changes in consumption, wages, employment.

### Identified mechanisms and policy implications
- Empirical and theoretical evidence point to two key channels weakening monetary transmission:
  - Entry rate (startups entering the market) — main driver.
  - Employment share of young firms.
- Policy implications and suggested further work:
  - Changes in firm demographics (entry rates, age structure) can alter monetary policy transmission, affecting central bank ability to provide accommodation—relevant given potential Covid-19 impacts.
  - Suggested theoretical extensions:
    - Richer model with risky firms and endogenous exit to assess role of frictions.
    - Embed a New Keynesian block to study pass-through to prices.
    - Extend empirical analysis to other countries to test external validity.
  - Ultimate goal: understand why young firms respond less to monetary policy shocks and how to optimally incorporate these results in central bank decision-making.

*Source: wpiea2021063-print-pdf — excerpted sections 3.1, 3.3, 4.3–4.5, 5, 6.1, 6.2, 6.4*

### 3.1  Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   7

### 3.1  Data Description

### Context and motivation
- In 1990, young firms (those aged 5 years or younger) accounted for about 43 percent of all firms in the United States; this share declined to about 30 percent in 2018.
- The reduction in the number of young firms is a key feature of the secular decline of business dynamism in the U.S. economy.
- The paper studies how the shift in firm demographics and declining business dynamism affect the propagation of monetary policy shocks.

### Core empirical approach and data sources
- Measures of business dynamism are constructed at the state level using the newly released and redesigned Business Dynamics Statistics (BDS), the publicly available version of the U.S. Census Bureau Longitudinal Business Database.
- Monetary policy shocks are identified using high-frequency event studies.
- State-level measures of business dynamism are combined with monetary policy shocks and macroeconomic variables at both the state and U.S. level.
- Identification exploits heterogeneity in the share of young firms across U.S. states and over time, controlling for a wide set of state-level and aggregate variables, both observable and unobservable.
- Impulse response functions to monetary policy shocks are estimated using local projections à la Jordà (2005).

### Key empirical findings (baseline)
- An economy with a higher fraction of young firms is less responsive to monetary policy.
- Following a 25 basis point monetary policy tightening, personal income is 1 percentage point higher after 6 quarters in states with a one standard deviation higher share of young firms, all else equal.
- The impact of firm demographics remains significant and persistent up to 3 years out.
- Similar patterns are found for wages and employment, with differences in magnitude and persistence relative to personal income.

### Robustness and additional empirical checks
- The role of firm demographics is tested across different, closely related measures of business dynamism.
- The main findings are robust to controlling for population demographics; evidence is provided that results are not driven by a spurious correlation between firm and population demographics.
- Results are essentially unchanged when controlling for:
  - sectoral composition of business activity,
  - state-specific time trends and unobservable characteristics,
  - outlier states.
- Sensitivity checks using different monetary policy shock series show the main results are largely unaffected.

### Investigation of drivers within firm demographics
- The share of young firms reflects: entry rate of new firms, survival rate of young firms, and the overall growth rate of existing businesses.
- The entry rate's impact on monetary policy transmission closely resembles that of the share of young firms in magnitude, persistence, and statistical significance—suggesting startups entering the market are a key driver.
- When decomposed by potential mechanisms (employment share of young firms vs. relative size of young firms):
  - The employment share by young firms has a very similar impact to the share of young firms.
  - The relative size of young firms plays a minor role.

### Theoretical interpretation and model ingredients (overview)
- A heterogeneous-firm model with financial frictions is developed where some young firms lack access to external financing due to insufficient credit history.
- The external financing constraint for young firms is supported by the Federal Reserve Banks’ Small Business Credit Survey (SBCS, Federal Reserve Banks (2017)), which identifies insufficient credit history as the main reason behind young firms’ financing shortfalls relative to older firms comparable on multiple dimensions.
- In the model:
  - Young firms without access to credit rely on dividends to fund investment and are less responsive to reductions in the risk-free interest rate.
  - In response to a temporary rate hike, young firms that cannot issue debt reduce their capital stock by less than unconstrained peers because they anticipate future borrowing constraints; this reduces aggregate sensitivity to interest rate changes.
- Calibrated to literature parameters and key moments of firm demographics, the model replicates the empirical result that increases in the risk-free interest rate have smaller effects on consumption, employment, and wages as the fraction of young firms increases.

### Organization of the paper (section roadmap)
- Section 2: Literature review.
- Section 3: Data and empirical methodology.
- Section 4: Empirical findings and robustness.
- Section 5: Potential channels behind main results.
- Section 6: Heterogeneous-firm model to interpret findings.
- Section 7: Conclusions.

*Source: wpiea2021063-print-pdf — 3.1 Data Description (excerpt).*

### 3.1  Data Description

### 3.1  Data Description

### Data sources
- Business Dynamics Statistics (BDS): publicly available version of the U.S. Census Bureau Longitudinal Business Database, covers employer firms with at least one employee over the period 1978-2018 and covers 98 percent of private employment.
- High-frequency event-study measures of U.S. monetary policy surprises: changes in rates implied by Fed Funds futures, Eurodollar futures, and yields on 2-year government bonds; also Nakamura and Steinsson (2018) shocks capturing “forward guidance.”
- State-level macroeconomic and financial variables from multiple official sources: BEA, Federal Housing Finance Agency, QCEW, LAUS, and U.S. Census Bureau.

### Variable construction and definitions
- Firm cohorts:
  - Startups/entrants: less than one year old (age 0).
  - Young firms: 5 years old or younger, including startups.
  - Mature firms: 6 years old or older.
- Demographic and dynamism measures (computed at state and year):
  - Share of startups (entry rate), share of young firms, share of mature firms (fractions of total firms).
  - Firm exit rate and survival rate by age group.
  - Net birth rate = entry rate − overall exit rate at the state level.
  - Labor dynamics: employment share by age group; net and gross job creation and job destruction rates by age group.
  - Job reallocation rate = sum of job creation and destruction rates in excess of net job creation rate (i.e., job creation + job destruction − |net job creation| as described).
  - Average size of each cohort and cohort growth over time.
- Timing and frequency:
  - BDS: annual frequency, reports information available in March of each year; state-level data for the 50 U.S. states plus the District of Columbia.
  - Monetary surprises: high-frequency windows (tight: 15 minutes before and after; or operationalized as 30-minute and 60-minute windows for aggregation as noted) aggregated to quarterly frequency using the weighted moving average in equation (1).
  - Macroeconomic controls: quarterly frequency (population annual).

### Limitations of BDS noted
- Does not include firms’ balance sheets nor information on credit market access.
- Data available at the state rather than the firm level.
- Firm birth year unknown if it took place before 1978; potential underestimation of young firms over 1978-1983 (stated not to affect the study because analysis does not cover those years).

### Summary statistics of business dynamism (Table 1)
- Share of young firms: Mean 0.362; St. Dev. 0.067; Min 0.179; Max 0.574; N 2,091
- Firm entry rate: Mean 0.095; St. Dev. 0.024; Min 0.048; Max 0.204; N 2,091
- Firm exit rate: Mean 0.079; St. Dev. 0.013; Min 0.049; Max 0.154; N 2,091
- Share of micro firms: Mean 0.849; St. Dev. 0.025; Min 0.701; Max 0.902; N 2,040
- Share of small firms: Mean 0.969; St. Dev. 0.012; Min 0.914; Max 0.991; N 2,040
- Job reallocation rate: Mean 0.270; St. Dev. 0.045; Min 0.167; Max 0.482; N 2,091
- Employment share by young firms: Mean 0.143; St. Dev. 0.042; Min 0.047; Max 0.297; N 2,091
- Notes on construction: sample covers 1978-2018; shares and rates at time t are computed using the average of the number of firms (employment for job reallocation and employment share of young firms) for times t and t−1, following Davis et al. (1998). Micro (small) firms have less than 20 (500) employees.

### Normalization for empirical analysis
- Measures of business dynamism are normalized by dividing by the corresponding unconditional standard deviation to facilitate interpretation of coefficients (as explained in Section 3.3).

### Monetary policy surprises: measures and summary statistics (Table 2)
- Baseline measure: change of the 3-month ahead Fed Funds futures over a tight window of 30 minutes aggregated to quarterly frequency using equation (1).
- Alternative measures: current month Fed Funds, 3-month Eurodollar deposit, 2-year Treasury yield, and Nakamura-Steinsson principal-component shocks.
- Aggregation formula (quarterly moving average): equation (1) — weights surprises by number of days left between the FOMC announcement and the end of the quarter; assigns higher weight to surprises observed at the beginning of the quarter and to surprises at the end of the previous quarter.
- Interpretation: positive value of aggregated surprise corresponds to a contractionary monetary policy shock.
- Summary statistics (Table 2):
  - 3m ahead Fed Funds: Mean -0.032; St. Dev. 0.083; Min -0.428; Max 0.122; N 5,916
  - 3m ahead Fed Funds (sum): Mean -0.032; St. Dev. 0.093; Min -0.435; Max 0.170; N 5,916
  - Current month Fed Funds: Mean -0.021; St. Dev. 0.056; Min -0.321; Max 0.124; N 5,916
  - 3m Eurodollar deposit: Mean -0.030; St. Dev. 0.083; Min -0.466; Max 0.104; N 7,089
  - 2y Treasury yield: Mean -0.015; St. Dev. 0.078; Min -0.329; Max 0.184; N 5,610
  - Nakamura-Steinsson: Mean 0.000; St. Dev. 0.065; Min -0.268; Max 0.146; N 3,978
- Data availability windows noted:
  - Fed Funds futures: available from 1990q1.
  - Eurodollar deposits: available from 1978q1 (Eurodollar futures data beginning 1984 as discussed).
  - Treasury yields: available from 1991q3.
  - Nakamura and Steinsson (2018) shocks available for 1995-2013.
- Rationale for baseline choice (3-month ahead Fed Funds, 30-minute window):
  - Captures surprises relative to conventional policy and near-term forward guidance, relevant during zero lower bound periods.
  - Longer-horizon futures less sensitive to small timing-related surprises.
  - Tight window reduces confounding factors.

### Macroeconomic and financial controls (Table 3)
- State-level series used (quarterly unless noted):
  - Personal income (BEA), Total wages (QCEW), House price index (Federal Housing Finance Agency), Employment (LAUS), Unemployment (LAUS), Population (U.S. Census Bureau; annual).
- Summary statistics (Table 3; period 1990q1 - 2018q4; 50 states + DC):
  - Personal income: Mean 204,607; St. Dev. 271,957; Min 8,049; Max 252,3626; N 5,916
  - Total Wages: Mean 211,520; St. Dev. 282,541; Min 6,837; Max 255,3063; N 5,916
  - House price index: Mean 28212186921; N 5,916 (table-formatting in source—values preserved exactly as presented)
  - Employment: Mean 2,6882,937; St. Dev. 22318,705; N 5,916 (table-formatting in source—values preserved exactly as presented)
  - Unemployment: Mean 16922582,248; N 5,916 (table-formatting in source—values preserved exactly as presented)
  - Population: Mean 5,7706,488; St. Dev. 45441,268; N 5,916 (table-formatting in source—values preserved exactly as presented)
- Units and notes:
  - Personal income and wages are in USD millions.
  - Employment, unemployment and population are in thousands of people.
  - All series, except for population, are seasonally adjusted.
  - House price index is a weighted sales index of single-family house prices based on mortgage transactions purchased or securitized by Fannie Mae or Freddie Mac.
  - QCEW total compensation includes bonuses, stock options, and other gratuities.
  - LAUS data derive from the Current Population Survey (CPS).

### Constructed panel dataset and sample
- Quarterly-frequency panel including all 50 U.S. states plus the District of Columbia.
- Baseline sample spans the period from 1990q1 to 2018q4.
- Dataset combines business dynamism measures (BDS), monetary policy surprises, and state-level macroeconomic and demographic controls.
- Data sources are public.

### Declining business dynamism: documented patterns (summary of findings)
- National trends (1990-2018):
  - Fraction of young firms exhibited a steady decline over 30 years; decline accelerated during and after the Global Financial Crisis.
  - During 1990-2007: fraction of young firms decreased by 0.34 percentage points per year on average, from about 43.3 percent in 1990 to 37.5 percent in 2007.
  - In 2007-2010: decline accelerated to about 1.3 percentage points per year, bringing fraction of young firms to 33.5 percent in 2010.
  - Entry rate collapsed from 8.8 percent in 2007 to 6.9 percent in 2010.
  - Exit rate did not present a clear secular trend and played a limited role in the decline of the share of young firms.
- Cross-sectional heterogeneity across states:
  - 1990: two states had fraction of young firms > 50 percent (Arizona and Florida); bottom states (Iowa and North Dakota) were about 34 percent.
  - 2018: highest share of young firms observed in Nevada at about 40 percent; only 10 states had fraction of young firms > 34 percent (Arizona, California, Colorado, Florida, Georgia, Nevada, Idaho, Texas, Utah, Washington).
  - 2018: five states had fraction of young firms ≤ 25 percent (Connecticut, Ohio, Iowa, Vermont, West Virginia).
  - Change in fraction of young firms from 1990 to 2018 varied widely: range from -0.05 percentage points in North Dakota to -22.6 percentage points in Vermont.
  - Cross-sectional standard deviation of fraction of young firms is the same in 1990 and 2018.
- Distributional notes:
  - Mean and median values of shares are very close, indicating measures are not driven by outlier states.
  - Substantial variation in business dynamism across both time and states supports empirical strategy exploiting time and cross-sectional variation.

*Source: IMF working paper chapter 3.1 "Data Description" from wpiea2021063-print-pdf.*

### 3.3  Empirical Strategy

### 3.3 Empirical Strategy

### Empirical approach
- Use panel local projections à la Jordà (2005) to produce impulse response functions (IRFs) over the medium run, avoiding VAR restrictions.
- Monetary policy shock identified using high-frequency event studies; benchmark uses the quarterly moving average of shocks to the rate implied by the 3-month ahead Fed Funds futures contract (equation (1)).
- Monetary policy shock normalized to 25 basis points to aid interpretation (rescaling does not affect distribution).

### Model specification
- Baseline specification (equation (2)):
  - log y_{s,t+h} = β_h(ε_t × z_{s,t−1}) + φ_h z_{s,t−1} + Γ'_h X_{s,t} + α_{s,h} + δ_{t,h} + u_{s,t+h}
  - s and t denote state and time; h ≥ 0 indexes forecast horizon.
  - Dependent variable y_{s,t} is the log of personal income, total wages, or employment (all in log levels).
  - ε_t is the monetary policy surprise; z_{s,t} is firm demographics (baseline: share of young firms).
  - Interaction variables (e.g., share of young firms) normalized by dividing by their standard deviation.
  - Main coefficient β_h measures how a one standard deviation difference in the share of young firms alters the response (in percentage points) to a 25 basis point contractionary monetary policy shock.

### Variables, controls, and identification
- Dependent variables: personal income (nominal), total wages, employment.
- Firm demographics baseline measure: share of young firms (firms aged 5 and under / total firms in each U.S. state).
- State-level controls X_{s,t}:
  - Two lags of the log dependent variable,
  - log personal income,
  - log unemployment,
  - log house price index,
  - one lag of log population.
- House prices included as proxy for inflation and to control for borrowing costs and financial frictions.
- Fixed effects: α_{s,h} (state) and δ_{t,h} (time) to control for permanent state differences and national aggregate conditions.
- To mitigate endogeneity and recursiveness concerns, all control variables (except monetary shock) are lagged by at least one quarter.
  - When merging quarterly and annual data (BDS), monetary policy shocks in Q1 are interacted with previous year BDS; Q2–Q4 use current year BDS.
- Robust standard errors: Driscoll and Kraay (1998) allowing for h+1 lags of the dependent variable to be correlated; also test two-way clustering at state and quarter levels.

### Estimation horizons and inference
- IRFs estimated for horizons h = 0,...,16 (16 quarters, short to medium term).
- Coefficients reported in percentage points; 90 percent confidence intervals obtained using Driscoll-Kraay errors.
- Interpretation of β_h sign:
  - Monetary tightening typically reduces activity; a positive β_h implies higher share of young firms weakens (mutes) transmission.
  - A negative β_h implies higher share of young firms strengthens transmission.

### Baseline results (Figure 4 summary)
- Main finding: firm demographics matter for monetary policy transmission; effects are persistent and indicate weaker transmission in states with more startups.
- Quantitative results:
  - Personal income:
    - A 25 basis point tightening reduces personal income by 1 percentage point less after 6 quarters in a state with a one-standard deviation higher share of young firms.
    - Effect remains significant out to 3 years.
  - Wages:
    - Effect is larger and more persistent than for personal income.
    - Coefficient peaks after 9 quarters at 1.35 percentage points and remains statistically significant for 15 quarters.
  - Employment:
    - A 25 basis point tightening reduces employment by 0.75 percentage points less after 10 quarters in a state with a one-standard deviation higher share of young firms.
    - Effect starts declining after 10 quarters but remains significant until 15 quarters.

### Sample split and comparison of IRFs (equation (3) and Figure 5)
- Split sample into young-firm and old-firm states each quarter:
  - D_low_{s,t} = 1 if state in bottom half of distribution of z_{s,t−1} (young-firm state).
- Specification includes cubic time trend f(t) and U.S.-level macro-financial controls C_t (two lags of log PCE price index, log real GDP, log unemployment, log Commodity Research Bureau spot commodity index, and level of Fed Funds rate); time fixed effects dropped.
- β_low_h and β_high_h measure transmission in bottom 25 states and top 26 states by share of young firms (distribution evaluated each quarter).
- Findings:
  - Monetary shocks negatively affect personal income, wages, and employment, but responses are significantly weaker in states with higher fraction of young firms.
  - IRFs for top-half firm-age states are generally weaker and often not statistically significant (except some marginal employment responses).
  - Example magnitudes:
    - In low young-firm states, a 25 basis point contractionary shock produces a fall in employment of about 1 percentage point after 10 quarters.
    - In high young-firm states, the decrease is about 0.5 percentage points and not statistically significant.

### Robustness: alternative measures of business dynamism (Figure 6)
- Focus on wages and employment due to similar size/shape with personal income and direct link to firm choices.
- Tests add alternative measures and their interactions with monetary shocks to baseline:
  - Share of small firms (firms with less than 500 employees):
    - Including share of small firms does not affect magnitude or significance of baseline share-of-young-firms results.
    - Share of small firms has no significant effect on transmission.
    - Similar results for micro (< 20 employees), medium (500–999 employees), and large (1000+ employees) firm shares (not shown).
  - Firm exit rate:
    - Exit rate significantly amplifies the transmission of monetary policy on wages (larger coefficients), but has no effect for employment.
  - Job reallocation rate:
    - Job reallocation rate has negligible effects.
- Correlations in sample:
  - Correlation of share of young firms with exit rate = 0.71.
  - Correlation of share of young firms with job reallocation rate = 0.72.
- Overall: share of young firms remains the dominant business dynamism measure shaping monetary policy transmission; alternative measures do not materially alter the main findings. The horizon over which estimates differ from zero shortens in some robustness tests but generally remains at least 10 quarters.

*Italic: Source — 3.3 Empirical Strategy, wpiea2021063-print-pdf*

### 4.3  Population Demographics

### 4.3 Population Demographics

### Role of population demographics in robustness checks
- Baseline specification already includes the lag of the (log) state population.
- Additional state-level population demographics are added together with their interactions with the monetary policy shock; the interacted variables are normalized by dividing the variable by its standard deviation.
- The size of the monetary policy shock is normalized to 25 basis points; coefficients are reported in percentage points and for 16 quarters. Confidence intervals are 90 percent and calculated using Driscoll-Kraay errors. All dependent variables (wages and employment) are in log levels.

### Population growth (Hopenhayn et al. (2018) motivation)
- Added controls: state population growth rate and its interaction with monetary policy shocks (state population growth rate controlled as the difference between the first and second lag of the log population).
- Findings:
  - Baseline results for wages remain unchanged both quantitatively and qualitatively.
  - Estimates for employment become larger and more statistically significant; peak response is around 1.4 percentage points and is statistically different from zero over the entire forecast horizon.
  - Interaction between monetary policy surprises and population growth rate:
    - Never significantly different from zero for wages.
    - Points to a significant strengthening of the monetary policy transmission to employment.

### Share of prime-age (25-54) population (Karahan et al. (2019); Pugsley and Sahin (2019) motivation)
- Added controls: population share aged 25-54 and its interaction with monetary policy shocks.
- Findings:
  - Confirms robustness of main results: impact of the share of young firms on monetary policy transmission is broadly unchanged in magnitude and significance compared to baseline.
  - Population share of prime-age workers matters more than population growth rate: corresponding coefficients become statistically different from zero toward the end of the horizon window.

### Share of middle-aged population (40-64 / 40-65)
- Added controls: fraction of people aged between 40 and 64 years (text also references 40 and 65 years).
- Findings:
  - Despite a significant and negative correlation between the share of young firms and the fraction of middle-aged people across U.S. states, the effect of firm demographics on monetary policy transmission is little changed when adding this control.
  - Inclusion of the fraction of people between 40 and 65 years generates a stronger response for wages (consistent with Leahy and Thapar (2019)).
  - Differently from Leahy and Thapar (2019), the fraction of people between 40 and 65 years does not matter for transmission to employment.

### Overall conclusion from population-demographics robustness
- Figure 7 provides compelling evidence that the main findings are robust and not due to a spurious correlation between firm and population demographics.
- Although firm and population demographics are closely linked, the role of the share of young firms in influencing monetary policy transmission is largely unaffected by population demographics.

_Italic: Source — wpiea2021063-print-pdf - 4.3 Population Demographics_

### 4.4 State Characteristics and Trends

### Sectoral composition (share of manufacturing firms)
- Added control: share of manufacturing firms from BDS and its interaction with monetary policy shocks.
- Findings:
  - Baseline results are robust in magnitude and statistical significance.
  - Share of manufacturing firms only weakly mutes transmission of monetary policy for employment.

### Unobservable state characteristics (state fixed effects)
- Added interactions between monetary policy shocks and state fixed effects.
- Findings:
  - Baseline results hold and are sometimes strengthened.
  - Share of young firms continues to dampen monetary policy transmission; coefficients become larger and significant for about 12 quarters for wages and for the entire horizon for employment.

### State-specific secular trends
- Added control: state-specific cubic time trend (time dummies already included to control for common U.S. trends).
- Findings:
  - For employment, coefficient of interest is similar to previous robustness exercises.
  - For wages, interaction of share of young firms and monetary policy shock is significant only for the first 5 quarters and is smaller in size.

### Influence of state outliers and weighting by state size
- Exclusion tests: in each quarter exclude the five states with the lowest personal income and then the five with the highest; results continue to hold.
- Weighted estimation: specification (2) weighted by state’s relative size using personal income each quarter; state size does not affect baseline results.
- Note: Almost identical results when removing or weighing states based on relative population rather than personal income.

### Credit availability and dynamics
- Added controls: per capita number of bank branches (FDIC) and growth rate of commercial and industrial bank loans by state.
- Findings:
  - Estimates essentially identical to baseline; confidence bands widen marginally.

_Italic: Source — wpiea2021063-print-pdf - 4.3 Population Demographics_

### 4.5 Different Monetary Policy Shocks

### Alternative monetary shock measures considered
- Four alternatives:
  - 3-month eurodollar deposit (allows sample extension back to 1984).
  - 2-year on-the-run Treasury yield (captures forward guidance component).
  - Change in current month Fed Funds futures contract around a wide 60-minute window.
  - Series constructed by Nakamura and Steinsson (2018) (captures “forward guidance”; considers surprises around scheduled FOMC meetings only).
- All shock series normalized to correspond to a 25 basis point tightening.

### Robustness findings
- Main result is robust to the choice of monetary shocks.
- Notable nuance:
  - Fraction of young firms seems to matter less when using the surprise in the 2-year on-the-run Treasury yield: estimated coefficient magnitude becomes smaller and significance disappears around 6 quarters after the initial shock.

_Italic: Source — wpiea2021063-print-pdf - 4.3 Population Demographics_

### 5 Possible Mechanisms

### Decomposition of share of young firms (definitions and algebra)
- Share of young firms:
  - Share_of_young_t = sum_{i=0}^{5} N_i_t / N_tot_t
  - Where N_i_t is number of businesses of age i in year t and N_tot_t is total firms in year t.
- Alternative rearrangement:
  - N_i_t / N_tot_t = (N_0_{t−i} / N_tot_{t−i}) × (N_i_t / N_0_{t−i}) × (N_tot_t / N_tot_{t−i})^{−1}
  - Components: entry rate at t−i (N_0_{t−i}/N_tot_{t−i}), survival rate of entrants from t−i to t (N_i_t/N_0_{t−i}), inverse of overall growth rate of stock of firms.

### Empirical decomposition using 5-year averages
- In baseline specification, fraction of young firms is replaced by average values over the last 5 years of:
  - Entry rate.
  - Startup survival rate.
  - Firm growth rate.

### Entry vs survival vs firm growth: empirical findings (Figure 9, panels (a)-(b))
- Entry rate:
  - Effect on monetary policy transmission to wages: statistically significant for about 12 quarters with a peak value around 1 percentage point.
  - Effect on employment: strong dependence on entry rate; impact closely resembles that of the share of young firms in magnitude, statistical significance, and persistence.
- Survival rate and firm growth rate:
  - Do not seem to matter for transmission to wages (weakly statistically significant estimates).
  - Play a marginal role for employment.
- Conclusion: Number of startups entering the market (entry rate) drives the muting of monetary policy effects, more so than survival rate or growth in stock of firms.

### Decomposition into employment share and relative size (equations (6) and (7))
- Alternative decomposition:
  - Share_of_young_t = (E_y_t / E_tot_t) × (E_tot_t / N_tot_t) × (E_y_t / N_y_t)^{−1}
  - Log form: Log(Share_of_young_t) = Log(Emp_share_young) − Log(Avg.size_young / Avg.size_tot)
  - Interpretation: log fraction of young firms equals log employment share of young firms minus log of relative average size.
  - A large share of young firms can reflect a large employment share of young firms, small relative size of young firms, or both.

### Empirical findings from employment-share / relative-size decomposition (Figure 9, panel (c))
- Employment share of young firms (solid blue line):
  - Plays a very similar role to the share of young firms in attenuating monetary policy transmission.
- Relative average size (dashed red line):
  - Barely significant for response of wages.
  - Negative and significant for employment.
  - Overall, relative average size plays a marginal role compared to employment share.
- Additional note on multicollinearity:
  - High correlation between the two RHS variables in equation (7): correlation is 0.87.
  - Regression of log share of young firms on log employment share yields residuals (opposite sign) interpreted as portion of relative average size orthogonal to employment share; results confirm relative average size is minor compared to employment share.

### Two main mechanism conclusions
- Among components that make up the share of young firms, the entry rate is the main driver explaining the muted response of the economy to monetary policy shocks.
  - Implication: Between two states with the same share of young firms, monetary policy is likely less effective in the state where the fraction of startups is higher (as opposed to the state where startups exit at a slower pace).
- Transmission of monetary policy weakens as the share of employees in young businesses increases; the relative size of young firms plays a marginal role in weakening monetary shocks.

_Italic: Source — wpiea2021063-print-pdf - 4.3 Population Demographics_

### 6.1  The Role of Credit History

### 6.1 The Role of Credit History

### Empirical findings from the SBCS on young firms' access to credit
- 69 percent of young firms that applied for credit faced a financing shortfall (obtained less than the amount sought).
- Insufficient credit history is the most reported reason for credit denial:
  - 47 percent of young firms that experienced financing shortfalls cite insufficient credit history.
  - 13 percent of small firms older than 5 years cite insufficient credit history.
  - The gap between young and mature small firms on this margin is large and statistically different at the 95 percent level.
- The role of insufficient credit history does not depend on measured credit score:
  - Among low credit score firms, 50 percent of young firms cite insufficient credit history as a reason for credit denial versus 11 percent for mature firms.
  - For medium- and high-credit-score firms the corresponding shares are 47 percent and 15 percent, respectively.
  - In both cases the differences are statistically significant.
- Collateral appears not to drive the young/mature gap:
  - 30 percent of young firms report lack of sufficient collateral as reason for credit denial.
  - 31 percent of mature small firms report lack of sufficient collateral.
- Interpretation:
  - The SBCS evidence indicates that insufficient credit history—linked by construction to firm age and independent of firm size, measured riskiness, or availability of collateral—plays an important role in explaining young firms’ difficulties accessing credit.
  - This friction helps explain empirical findings that a higher share of young firms weakens the effects of monetary policy shocks on macroeconomic variables; the entry rate matters more than the relative size of young firms.

*Source: wpiea2021063-print-pdf - 6.1 The Role of Credit History*

---

### 6.2 Theoretical Framework

### Model environment and key features
- Time and agents:
  - Discrete time, infinite horizon economy with infinitely lived households and firms.
  - Firms face idiosyncratic productivity shocks and a constant death probability.
  - Available financing: profits and risk-free debt. Abstract from aggregate uncertainty.
- Firm production and productivity:
  - Production: y_t = z_t k_t^α ` _t^ν , with α + ν < 1 (decreasing returns to scale).
  - Productivity: log z_t = ρ log z_{t−1} + u_t, with u_t ∼ N(0, σ^2); approximated by a Markov process H(z_{t+1} | z_t) over [z, z̄].
- Labor and wages:
  - Firms hire labor at wage w_t; wage rigidity modeled as staggered wage setting: w_t = γ w_{t−1} + (1−γ) w_t^*.
- Capital accumulation and adjustment costs:
  - Capital price q_t; capital predetermined one period ahead and depreciates at rate δ.
  - Convex investment adjustment costs ψ( k_{t+1}/k_t − (1−δ) )^2.
- Entry, exit, and firm age groups:
  - New entrants receive initial capital k_0 and draw productivity from μ_ent(z) ∼ logN( −mσ(1−ρ^2)^{−2}, σ^2/(1−ρ^2) ).
  - At end of period a share π_D ∈ (0,1) of firms exits; mass of entrants equals exiting firms to keep firm mass constant.
  - Young firms = age 0 to 2 periods (entrants + firms in last two periods that survived); mature firms = age ≥ 3 periods.
- Credit-history friction:
  - A fraction λ ∈ [0,1] of startups cannot borrow today due to lack of credit history.
  - Conditional on survival, fraction λ of these firms continues to lack access; (1−λ) gains access. All mature firms can borrow.
- Borrowing constraints:
  - Debt must satisfy a no-default condition (risk-free) and a collateral constraint b_{t+1} ≤ χ k_t with χ ≥ 0.
  - Dividends must be non-negative (d_t ≥ 0); no new equity issuance.

### Timing within a period
- (i) Mass π_D of new firms enters.
- (ii) Firms draw idiosyncratic productivity: mature/young from H(z_t | z_{t−1}), entrants from μ_ent(z_t).
- (iii) Young firms draw credit history shock: with probability (1−λ) a startup can borrow; a fraction (1−λ) of firms aged 1 and 2 that were previously unable to borrow can now borrow. All firms aged 3+ can borrow.
- (iv) Firms hire labor, produce, and repay outstanding debt b_t at gross rate R_f.
- (v) Exit shock: with probability π_D firm exits, transferring profits and undepreciated capital to households.
- (vi) Continuing firms purchase k_{t+1}, financed through nominal debt b_{t+1} or internal funds; remaining resources paid as dividends.

### Firm value and borrowing feasibility
- Firm static profit: π(z,k) = max_{`} { z k^α `^ν − w ` }, with labor policy `^D(z,k).
- Borrowing feasibility threshold (no-default) requires:
  - π(z,k′) + (1−δ) q′ k′ − R_f b(k′) = 0.
- Mature firm value function V(z,k,b) (Bellman) incorporates exit probability π_D, production net of debt expenses, investment adjustment costs, capital price q, and expectation over future V given H.
- Borrowing constraints in optimization:
  - b′ ≤ min{ χ k, b(k′) }
  - Dividends non-negativity and no-default conditions bind choices of k′ and b′.

### Financing regimes and implications for monetary policy transmission
- Firm categories by debt policy:
  1. Unconstrained firms: can select k^*_{t+1} and fund via internal funds by cutting dividends to non-negative value; indifferent across debt choices as long as b_{t+1} ≤ b(k^*_{t+1}).
  2. Firms that achieve k^*_{t+1} but require external funding: use all internal funds and borrow remainder b_{t+1} = k^*_{t+1} − d_t.
  3. Constrained firms: cannot reach k^*_{t+1} because internal resources insufficient and borrowing restricted:
     - If collateral binds: b_{t+1} = χ k_t.
     - If insufficient credit history (young firms): b_{t+1} = 0.
- Response to a temporary interest rate cut:
  - Equation characterizing optimal capital for a borrowing firm:
    - E_t z_{t+1} α (k^*_{t+1})^{α−1} `_{t+1}^{ν} = R_f.
  - Firms optimally increase investment until expected marginal return equals R_f; constrained firms cannot reach that level.
  - As share of constrained firms rises, the effects of an interest rate reduction weaken; in the extreme (no firm can borrow) investment can increase only by reducing dividends, muting monetary policy impact.
- Response to a temporary interest rate increase:
  - Firms reduce capital; borrowing constraints less likely to bind, but lack of credit history still mutes young firms’ reductions in capital because they anticipate future recovery and cannot borrow to expand later—so young firms reduce capital less than firms with access to external financing.
- Overall mechanism:
  - Lack of access to credit due to insufficient credit history reduces young firms’ sensitivity to interest rate changes in both directions, consistent with empirical evidence.

### Parametrization highlights (calibration targets and fixed parameters)
- Frequency: quarterly; set β = 0.99.
- Production and preference parameters fixed:
  - α = 0.21, ν = 0.64, δ = 0.025, Φ = 4, ψ = 1.08, γ = .71, θ = 1.8.
  - Frisch elasticity of labor supply implied = 0.54.
- Productivity shock parameters taken from Ottonello and Winberry (2020): ρ = 0.9, σ = 0.03, startups productivity m = 3.12.
- Calibration targets:
  - Disutility of labor φ chosen to generate employment rate ≈ 70 percent (average 1990–2018).
  - Collateral tightness chosen to target leverage ratio = 0.46 (Dinlersoz et al. (2018)).
  - Empirical SBCS target: share of young firms citing insufficient credit history = 0.47 (34 percentage points larger than mature firms). Choose λ = 0.53 so that 34 percent of young firms cannot issue debt due to lack of credit history.
  - Firm demographics targets from BDS: entry rate set so share of young firms = 0.34; initial capital of startups set to match share of employment by young firms = 0.13.

*Source: wpiea2021063-print-pdf - 6.1 The Role of Credit History*

### 6.4  Results

### 6.4  Results

### Simulation setup and shock specification
- The experiment simulates a change in the risk-free rate Rf by changing the discount factor because in equilibrium Rf × β = 1.
- The simulated shock is an increase in the interest rate Rf of 25 basis points.
- The shock decays back to zero following a deterministic decaying process. The decay rate equals 0.5 and implies that the interest rate returns to its steady state value within about 6 quarters.
- Given no aggregate uncertainty, transition paths from and to the steady state are computed under perfect foresight.
- Consumption and wages are expressed in real terms in the model results.

### Calibration (fitted parameters from Table 5)
- Borrowing constraint χ = 0.82 — target: Leverage ratio = 0.46
- Exogenous death rate π^D = 0.13 — target: Share of young firms = 0.33
- Initial capital k0 = 0.97 — target: Employment by young firms = 0.13
- Credit history λ = 0.53 — target: Young firms with no credit history = 0.34
- Disutility of labor φ = 1.51 — target: Employment rate = 0.71
- Notes: the value of the leverage ratio comes from Dinlersoz et al. (2018). The share of young firms and their employment share are computed using BDS data. The share of young firms that face financing shortfall because of insufficient credit history is taken from the SBCS. The employment rate is expressed as a ratio of the population aged 15-64 and provided by the BLS.

### Model responses to a 25bps temporary increase in the risk-free rate
- Core impulse responses plotted: investment, output, wage, and employment.
- Primary transmission:
  - Investment contracts following the rate increase.
  - Lower capital reduces marginal productivity of labor, decreasing labor demand and wages (wages initially increase due to firms cutting investment and paying more dividends, which decreases households' marginal utility of consumption and affects labor supply).
  - Combined decreases in capital and employment cause a fall in output.
- The model produces qualitatively consistent responses with the empirical analysis in earlier sections.

### Role of young firms in monetary transmission
- Counterfactual exercise: increase the entry rate so the steady-state share of young firms equals 40 percent (one standard deviation higher than its median value over 1990-2018).
- Results when share of young firms = 40 percent:
  - The macroeconomic effects of the temporary 25bps increase in Rf are smaller (dashed red lines in Figure 10), indicating a higher share of young firms mutes the impact of the interest rate shock.
  - For output and employment, the difference between baseline and high-young-firm economies amounts to about 0.4 percentage points.
  - For real wages, a higher share of young firms weakens the effect of a rate hike by 0.05 percentage points.

### Quantitative assessment and limitations
- The difference in response between the baseline and the higher-share-of-young-firms economy accounts for a significant share of the estimated coefficient reported for personal income and employment in the empirical Figure 4.
- The model is more distant from empirical evidence for wages, indicating the need for a richer model to better capture labor market responses to monetary policy shocks.
- Similar responses (in shape and magnitude but opposite sign) are obtained for a decrease in the interest rate. In that case, the presence of firms with no access to debt limits the response of investment, which dampens changes in consumption, wages, and employment.

### Mechanisms identified
- Young firms are more likely to face external financing shortfalls because of insufficient credit history; this friction limits investment responses to interest rate changes.
- Two key channels through which weaker transmission operates empirically: the entry rate and the share of employment by young firms.

### Policy implications and directions for future work
- Changes in firm demographics (entry rates and age structure) can alter monetary policy transmission and thus affect the central bank’s ability to provide monetary accommodation, particularly relevant given potential Covid-19 impacts on firm demographics.
- Suggested theoretical extensions to improve policy relevance:
  - Develop a richer model including risky firms with endogenous exit to assess the role of different frictions more precisely.
  - Embed a New Keynesian block to study how firm demographics affect monetary policy transmission to prices.
  - Extend empirical analysis to other countries to test international applicability of results.
- Ultimate goals: understand why young firms respond less to monetary policy shocks and how to optimally incorporate these results in central bank decision-making.

*Source: 6.4 Results, wpiea2021063-print-pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021063-print-pdf.pdf_