Bank Of Greece Sa · ATHEX:TELL
Bank Of Greece Sa — Investor Presentation (September 2022)
75 slides from Bank Of Greece Sa's investor presentation, Sep 30, 2022
Slide 1: Firm Cyclicality and Financial Frictions
Firm Cyclicality and Financial Frictions Alex Clymo Filip Rozsypal 6th annual Workshop of ESCB Cluster 2 Athens, 30 September 2022 The views presented in this paper are our own and do not represent the views of Danmarks Nationalbank
Slide 2: This paper
This paper 1 Empirics, SIZE × AGE: • Different patterns in levels, growth rates and cyclicality both real and financial variables • Effects of leverage on growth rate and cyclicality 2 Model with firm heterogeneity and financial frictions • Standard borrowing contraint is not able to match the data
Slide 3: Literature
Literature • Financial frictions as amplification mechanism: Bernanke and Gertler (1989); Gertler and Gilchrist (1994); Bernanke et al. (1999); Crouzet and Mehrotra (2020) • Cyclicality by size: Gertler and Gilchrist (1994); Khan and Thomas (2013); Gavazza et al. (2018) vs Moscarini and Postel-Vinay
Slide 4: Data
Data Sources and coverage • Administrative micro-level datasets, 2001-2018 • Tax information from SKAT + survey by Statistics Denmark • 90,000 firms per year, 1.25M firm-year observations • Variables: • employment, sales, value added,... • debt, assets, equity • All non-finance sectors • All firm si
Slide 5: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 4 / 17
Slide 6: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets 4 / 17
Slide 7: Cyclicality of employment
Cyclicality of employment Only size emp X X gi,t = αj + βj gtY 1i∈Ij + γl + δl gtY 1i∈Sl + εi,t j l 1 0.9 0.8 0.7 0-3 4-8 9-19 0.6 20+ 0.5 0.4 0.3 0-30 30-60 60-90 90+ size bins (similar framework to Crouzet and Mehrotra (2020)) 5 / 17
Slide 8: Cyclicality of employment
Cyclicality of employment Additive size and age emp X X X gi,t = αj + βj gtY 1i∈Ij + αk + βk gtY 1i∈Ak + γl + δl gtY 1i∈Sl + εi,t j k l 2.5 2 1.5 1 0.5 0-3 4-8 0 9-19 20+ -0.5 0-30 30-60 60-90 90+ size bins (similar framework to Dinlersoz et al. (2018)) 6 / 17
Slide 9: Cyclicality of employment
Cyclicality of employment emp XX X gi,t = αj,k + βj,k gtY 1i∈Ij 1i∈Ak + γl + δl gtY 1i∈Sl + εi,t j k l 7 / 17
Slide 10: Cyclicality of employment
Cyclicality of employment emp(fte) 3.0 0-3 2.5 2.0 1.5 1.0 0.5 0.0 0-30 30-60 60-90 90+ size bins • Entrants: higher over all, falls with size sales assets, debt 7 / 17
Slide 11: Cyclicality of employment
Cyclicality of employment emp(fte) 3.0 0-3 4-8 9-19 2.5 20+ 2.0 1.5 1.0 0.5 0.0 0-30 30-60 60-90 90+ size bins • Entrants: higher over all, falls with size • Everybody else: increases with size sales assets, debt 7 / 17
Slide 12: Cyclicality of employment
Cyclicality of employment emp(fte) 3.0 0-3 4-8 9-19 2.5 20+ 2.0 1.5 1.0 0.5 0.0 0-30 30-60 60-90 90+ size bins • Entrants: higher over all, falls with size • Everybody else: increases with size ⇒ large firms are much more alike than small firms sales assets, debt 7 / 17
Slide 13: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets 8 / 17
Slide 14: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 8 / 17
Slide 15: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 2 Document the size x age heterogeneity in the dist
Slide 16: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 2 Document the size x age heterogeneity in the dist
Slide 17: Level and growth rate of Leverage
Level and growth rate of Leverage 0.85 0.02 0-3 0-3 4-8 0.015 4-8 0.8 9-19 9-19 20+ 0.01 20+ 0.75 0.005 0.7 0 -0.005 0.65 -0.01 0.6 -0.015 0.55 -0.02 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins • Debt/Asset ratio is generally falling with age, • Both debt and assets growing ⇒ asset
Slide 18: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 2 Document the size x age heterogeneity in the dist
Slide 19: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 2 Document the size x age heterogeneity in the dist
Slide 20: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 2 Document the size x age heterogeneity in the dist
Slide 21: Empirical results overview
Empirical results overview Goal: recover AGE × SIZE interaction 1 Cyclicality of sales, employment, debt and assets • conditional on size: young firms more cyclical than old • conditional on age: large more cyclical than small (apart from entrants) 2 Document the size x age heterogeneity in the dist
Slide 22: Model introduction
Model introduction Questions: • What model features are needed match “age × size” distributions? (levels, growth rates, cyclicality) • What are the effects of different policies in such a model? 11 / 17
Slide 23: Model introduction
Model introduction Questions: • What model features are needed match “age × size” distributions? (levels, growth rates, cyclicality) • What are the effects of different policies in such a model? Heterogeous firm model with financial frictions 11 / 17
Slide 24: Model introduction
Model introduction Questions: • What model features are needed match “age × size” distributions? (levels, growth rates, cyclicality) • What are the effects of different policies in such a model? Heterogeous firm model with financial frictions + heterogeneity in returns to scale 11 / 17
Slide 25: Model introduction
Model introduction Questions: • What model features are needed match “age × size” distributions? (levels, growth rates, cyclicality) • What are the effects of different policies in such a model? Heterogeous firm model with financial frictions + heterogeneity in returns to scale + starting net worth,
Slide 26: Model introduction
Model introduction Questions: • What model features are needed match “age × size” distributions? (levels, growth rates, cyclicality) • What are the effects of different policies in such a model? Heterogeous firm model with financial frictions + heterogeneity in returns to scale + starting net worth,
Slide 27: Model - firm problem
Model - firm problem • Production function: qi = zi f (kI , li )ηi R 1 • Aggregate output Q = 0G qiθ di θ −1/(1−θ) ⇒ i-th firm demand: qi = pi Q • Profit function: n o π = max q θ Q 1−θ − wl • Leontief production function f (k , l) = min k, αl implies ∗ l (k ) = αk π(k, s, g) = z θ k ηθ Q 1−θ − αwk.
Slide 28: Model - firm shocks
Model - firm shocks • Heterogeneous productivity: z ≡ z(s, q) = zsS zgG • z S : firm ”quality” → contributes to size dispersion • z G : age component → penalty for entrants • Timing of shocks: • at entry: • zsS and η (currently perfectly correlated) • every period: • age specific exogenous exit • tr
Slide 29: Model experiments
Model experiments 1 Simple steady-state focused model does not match the data ”Steady-state calibration” • setting: • no heterogeneity in rts • entrant productivity penalty • uniform initial net worth • finding: no combination of MIT shocks to colateral constraint, interest rate and tfp can replicat
Slide 30: Model experiments
Model experiments 1 Simple steady-state focused model does not match the data ”Steady-state calibration” • setting: • no heterogeneity in rts • entrant productivity penalty • uniform initial net worth • finding: no combination of MIT shocks to colateral constraint, interest rate and tfp can replicat
Slide 31: Model experiments
Model experiments 1 Simple steady-state focused model does not match the data ”Steady-state calibration” • setting: • no heterogeneity in rts • entrant productivity penalty • uniform initial net worth • finding: no combination of MIT shocks to colateral constraint, interest rate and tfp can replicat
Slide 32: Policy experiments - Labor subsidy
Policy experiments - Labor subsidy Output (Y) Coefficients: SS Cali Coefficients: BC Cali 1.04 SS cali 1 1 1.03 BC cali 0.8 0.8 1.02 0.6 0.6 0-3 1.01 0.4 4-8 0.4 0-3 9-19 0.2 0.2 4-8 1 20+ 9-19 0 0 20+ 0.99 0 1 2 3 4 5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ time (years) size bins size bins • SS c
Slide 33: Policy experiments - Labor subsidy
Policy experiments - Labor subsidy Output (Y) Coefficients: SS Cali Coefficients: BC Cali 1.04 SS cali 1 1 1.03 BC cali 0.8 0.8 1.02 0.6 0.6 0-3 1.01 0.4 4-8 0.4 0-3 9-19 0.2 0.2 4-8 1 20+ 9-19 0 0 20+ 0.99 0 1 2 3 4 5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ time (years) size bins size bins • SS c
Slide 34: Policy experiments - Labor subsidy
Policy experiments - Labor subsidy Output (Y) Coefficients: SS Cali Coefficients: BC Cali 1.04 SS cali 1 1 1.03 BC cali 0.8 0.8 1.02 0.6 0.6 0-3 1.01 0.4 4-8 0.4 0-3 9-19 0.2 0.2 4-8 1 20+ 9-19 0 0 20+ 0.99 0 1 2 3 4 5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ time (years) size bins size bins • SS c
Slide 35: Policy experiments - Debt relief
Policy experiments - Debt relief Output (Y) Coefficients: SS Cali Coefficients: BC Cali 1.03 25 25 SS cali 0-3 0-3 BC cali 20 4-8 20 4-8 9-19 9-19 1.02 15 20+ 15 20+ 10 10 1.01 5 5 0 0 1 -5 -5 0 1 2 3 4 5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ time (years) size bins size bins • SS calibration muc
Slide 36: Policy experiments - Debt relief
Policy experiments - Debt relief Output (Y) Coefficients: SS Cali Coefficients: BC Cali 1.03 25 25 SS cali 0-3 0-3 BC cali 20 4-8 20 4-8 9-19 9-19 1.02 15 20+ 15 20+ 10 10 1.01 5 5 0 0 1 -5 -5 0 1 2 3 4 5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ time (years) size bins size bins • SS calibration muc
Slide 37: Conclusion
Conclusion 1 Empirics: Size is not a perfect proxy for age and vice versa • Size gradient of cyclicality depends on age • in terms of cyclicality, large firms are more alike than small firms 2 Model • financial frictions make young firms highly responsive to shocks • but firms grow out of financial
Slide 38: Literature
Literature Andersen, S. G. and Rozsypal, F. (2021). What can old firms tell us about the effect of age on firm size. working paper. Begenau, J. and Salomao, J. (2018). Firm Financing over the Business Cycle. The Review of Financial Studies, 32(4):1235–1274. Bernanke, B. and Gertler, M. (1989). Agenc
Slide 39: Data
Data Averages of Variables of Interest by Age and Size Age groups Size groups 0-3 4-8 9-19 20+ 0-30 30-60 60-90 90+ Employment 7.7 12.2 17.5 26.2 1.6 4.0 11.2 115.9 sales 17435 28038 45910 93294 4219 9333 25012 320649 Assets 18705 32859 56870 128151 10115 20451 24029 360309 Debt 10595 17615 30204 69
Slide 40: Data
Data Number of observations by size and age Age 0 [1,5) [5,10) [10,15) [15,20) [20,25) 25+ all emp<50 0.98 0.98 0.96 0.94 0.91 0.9 0.84 0.94 emp>=50 0.02 0.02 0.04 0.06 0.09 0.10 0.16 0.06 size(0-30) 0.46 0.41 0.35 0.30 0.26 0.26 0.23 0.33 size(30-60) 0.25 0.28 0.26 0.24 0.23 0.23 0.19 0.25 size(60-
Slide 41: Regression framework
Regression framework Goal: recover AGE × SIZE interaction 21 / 17
Slide 42: Regression framework
Regression framework Goal: recover AGE × SIZE interaction • A: age groups (0-3, 4-7, 8-19, 20+) • I: employment groups (percentile cutoffs: 30,60,90,95) details 21 / 17
Slide 43: Regression framework
Regression framework Goal: recover AGE × SIZE interaction for levels, growth rates, XX Xi,t = αj,k 1i∈Ij 1i∈Ak + εi,t j k • A: age groups (0-3, 4-7, 8-19, 20+) • I: employment groups (percentile cutoffs: 30,60,90,95) details • Xi,t : i − th firm variable of interest 21 / 17
Slide 44: Regression framework
Regression framework Goal: recover AGE × SIZE interaction for levels, growth rates, cyclicality, XX Xi,t = αj,k 1i∈Ij 1i∈Ak + εi,t j k X XX gi,t = αj,k + βj,k gtY 1i∈Ij 1i∈Ak + εi,t j k • A: age groups (0-3, 4-7, 8-19, 20+) • I: employment groups (percentile cutoffs: 30,60,90,95) details • Xi,t : i
Slide 45: Regression framework
Regression framework Goal: recover AGE × SIZE interaction for levels, growth rates, cyclicality, effect of leverage XX Xi,t = αj,k 1i∈Ij 1i∈Ak + εi,t j k X XX gi,t = αj,k + βj,k gtY 1i∈Ij 1i∈Ak + εi,t j k X XX gi,t = αj,k + βj,k gtY 1i∈Ij 1i∈Ak + εi,t j k X + (ωm + ψm yt )1i∈DAm m • A: age groups (0
Slide 46: Regression framework
Regression framework Goal: recover AGE × SIZE interaction for levels, growth rates, cyclicality, effect of leverage XX X Xi,t = αj,k 1i∈Ij 1i∈Ak + γl 1i∈Sl + εi,t j k l X XX X gi,t = αj,k + βj,k gtY 1i∈Ij 1i∈Ak + γl + δl gtY 1i∈Sl + εi,t j k l X XX X gi,t = αj,k + βj,k gtY 1i∈Ij 1i∈Ak + γl + δl gtY
Slide 47: Average growth rate of sales
Average growth rate of sales Basic moments g2_turn 1.8 1.6 1.4 1.2 1 age bins 0.8 0-3 0.6 4-8 9-19 0.4 20+ 0.2 0-30 30-60 60-90 90+ size bins back 22 / 17
Slide 48: Average growth rate of assets
Average growth rate of assets Basic moments g2_assets 2.5 age bins 2 0-3 4-8 9-19 20+ 1.5 1 0.5 0 0-30 30-60 60-90 90+ size bins back 23 / 17
Slide 49: Size thresholds (by number of workers)
Size Thresholds and Number of Firms in Different Age Bins 10 4 40 2.8 35 30 0-3 Size thresholds (by number of workers) 2.6 4-8 25 9-19 Number of firms by age group 20 2.4 20+ 17 14 2.2 10 2 8 6 1.8 4 1.6 3 1.4 2 1.2 2000 2005 2010 2015 2000 2005 2010 2015 2020 year year (a) Size thresholds (log scal
Slide 50: Basic moments
Basic moments Figure: Average levels and growth rates by size and age 12 4.5 11 4 10.5 11 3.5 10 3 9.5 10 2.5 9 2 8.5 9 1.5 8 0-3 0-3 0-3 8 1 7.5 4-8 4-8 4-8 9-19 9-19 9-19 0.5 7 20+ 20+ 20+ 7 0 6.5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins size bins (a) (log
Slide 51: Basic moments
Basic moments Figure: Average levels and growth rates by size and age 12 4.5 11 4 10.5 11 3.5 10 3 9.5 10 2.5 9 2 8.5 9 1.5 8 0-3 0-3 0-3 8 1 7.5 4-8 4-8 4-8 9-19 9-19 9-19 0.5 7 20+ 20+ 20+ 7 0 6.5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins size bins (a) (log
Slide 52: Predicted cyclicality
Predicted cyclicality Sales 2 0-3 4-8 9-19 1.5 20+ 1 0.5 0 0-30 30-60 size bins Same pattern: • Entrants: higher cyclicality over all, cyclicality falls with size • Everybody else: cyclicality increases with size back 27 / 17
Slide 53: Predicted cyclicality
Predicted cyclicality Assets, Debt 2 2 0-3 0-3 4-8 4-8 9-19 9-19 1.5 20+ 1.5 20+ 1 1 0.5 0.5 0 0 0-30 30-60 60-90 90+ 0-30 30-60 size bins size bins Same pattern: • entrants more cyclical • entrants’ cyclicality decreasing in size • for everybody else cyclicality is (weakly) increasing with size bac
Slide 54: Basic moments
Basic moments Levels of employment, sales and assets 4.5 12 11 4 10.5 3.5 11 10 3 9.5 10 2.5 9 2 8.5 9 1.5 8 0-3 0-3 0-3 1 8 7.5 4-8 4-8 4-8 9-19 9-19 9-19 0.5 7 20+ 20+ 20+ 0 7 6.5 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins size bins 29 / 17
Slide 55: Basic moments
Basic moments Growth rates of employment, sales and assets g2_emp_fte g2_turn g2_assets 2 2.5 1.8 age bins 1.5 1.6 2 0-3 4-8 1 1.4 9-19 20+ 1.5 1.2 0.5 1 1 age bins age bins 0 0.8 0-3 0-3 4-8 0.6 4-8 9-19 9-19 0.5 -0.5 20+ 0.4 20+ -1 0.2 0 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 9
Slide 56: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) y 1.528*** 1.717*** 1.301*** 1.473*** 1.289*** 1.224*** (5.25) (5.70) (4.30) (4.80) (4.54) (4.1
Slide 57: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 58: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 59: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 60: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 61: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 62: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 63: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 64: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 65: Effects of Leverage
Effects of Leverage (1) (2) (3) (4) (5) (6) • Growth rate Constant Sales 0.012* Sales 0.007 Employment -0.009 Employment -0.043*** Assets Assets 0.026*** 0.014* (1.99) (1.16) (-1.44) (-6.69) (4.40) (2.31) • Emp: ∩ y 1.528*** 1.717*** (5.25) (5.70) 1.301*** (4.30) 1.473*** (4.80) 1.289*** 1.224*** (4
Slide 66: Steady-state calibration details
Steady-state calibration details • targets: • s-type to target size distribution • age-dependent exogenous exit rate to target age distribution (Andersen and Rozsypal, 2021) • size x age distribution: • initial net worth of entrants (n0 ) to target size of entrants • superstar productivity z ∗ : ave
Slide 67: Cyclical calibration details
Cyclical calibration details • targets: relative cyclicality by size and age, size of the recession, growth rate of young-small firms • calibration instruments: two shocks + two features = 9 new parameters • productivity penalty of entrants y1G < 1 to match average size of 0-aged firms • only financ
Slide 68: Model equations
Model equations • final good manufacturer: R 1 G θ θ • production function Q = qi di 0 R 1 R G θ θ G • profits π = qi di − 0 pi qi di 0 • FOC qi = pi− Q • zero profits Q = G pi qi di R 0 • aggregation accounting • final goods resource constraint: Q = C + I + M • aggregate output Y = C + I + G • inte
Slide 69: Model calibration
Model Calibration Interpretation Value Source r Discount rate 0.0202 2% yearly real interest rate z Productivity distribution - See text ηz Returns to scale distribution - See text ζz Exit rates - See text θ Substitution across varieties 0.9 10% markup in frictionless model α Labor-capital ratio in
Slide 70: Model results
Model results Firm evolution by age Average employment Average leverage Fraction constrained 70 3 1 prod 1 (~lowest 30%) prod 2 (~next 30%) 0.9 60 prod 3 (~next 30%) 2.5 prod 4 (~top 10%) 0.8 50 0.7 2 0.6 40 1.5 0.5 30 0.4 1 20 0.3 0.2 0.5 10 0.1 0 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 age age
Slide 71: Model results
Model results Basic model Figure: Cyclicality of employment 2.0 2.0 2.0 10.0 8.0 1.5 1.5 1.5 6.0 1.0 1.0 1.0 4.0 0.5 0.5 0.5 0-3 2.0 4-8 9-19 0.0 20+ 0.0 0.0 0.0 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins size bins size bins (a) Collateral
Slide 72: Model results
Model results Full model Figure: Cyclicality of employment 2.0 2.0 15.0 4.0 1.5 1.5 3.0 10.0 1.0 1.0 2.0 0.5 0.5 0-3 5.0 4-8 1.0 9-19 20+ 0.0 0.0 0.0 0.0 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins size bins size bins (a) Het. ηs (b) Het. n
Slide 73: Steady-state calibration details
Steady-state calibration details • targets: • s-type to target size distribution • age-dependent exogenous exit rate to target age distribution (Andersen and Rozsypal, 2021) • size x age distribution: • initial net worth of entrants (n0 ) to target size of entrants • superstar productivity z ∗ : ave
Slide 74: Cyclical calibration details
Cyclical calibration details • targets: relative cyclicality by size and age, size of the recession, growth rate of young-small firms • calibration instruments: two shocks + two features = 9 new parameters • productivity penalty of entrants y1G < 1 to match average size of 0-aged firms • only financ
Slide 75: Model results
Model results Growth rates Figure: Average growth rate of employment 0.4 0.4 0.4 0-3 4-8 0.3 0.3 0.3 9-19 20+ 0.2 0.2 0.2 0.1 0.1 0.1 0.0 0.0 0.0 -0.1 -0.1 -0.1 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ 0-30 30-60 60-90 90+ size bins size bins size bins (a) Basic model (b) Full model (c) Data back 4
Bank Of Greece — Investor Presentation (September 2022) on 6ix