## 1 Introduction (wpiea2021170-print-pdf) ## Source details **Canonical URL:** [1 Introduction (wpiea2021170-print-pdf)](https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021170-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2021/english/wpiea2021170-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2021/english/wpiea2021170-print-pdf.pdf.json) --- ### Overview and research question - Puzzle: output across advanced and emerging economies recovered much more slowly than expected after the Global Financial Crisis (GFC). - Main goal: understand mechanics of slow recoveries with focus on the role of financial frictions and investment dynamics in the aftermath of crises. - Alternative hypothesis: tighter financial conditions constrain investment, and because investment can embody technological change (capital-embodied technological change), investment slumps can depress measured total factor productivity (TFP) in the medium term, producing persistent output losses. ### Empirical motivation (stylized facts) - Four country cases (Brazil, France, South Korea, US) show permanent output losses relative to pre-crisis trend accompanied by persistent reductions in TFP; R&D did not uniformly fall and in many cases continued on pre-crisis trends. - Key observed co-movements: investment dynamics are correlated with TFP dynamics; declines in investment are associated with declines in TFP during and after the GFC. ### Empirical strategy and main empirical findings - Three empirical approaches: - Cross-country distributions of deviations from pre-crisis trends (2000–2008 trend; post-crisis deviations 2015–2017). - Univariate autoregressive panel analysis following Cerra and Saxena (2008) to estimate impulse responses of levels after banking crises. - Cross-country regressions linking medium-term TFP losses (average 2015–2017 deviation from pre-crisis trend) to early investment and financial variables (average 2008–2010 deviations from trend). - Distributional evidence: - Sample sizes: 24 countries with a banking crisis (Laeven and Valencia (2013) database) and 168 countries without a banking crisis. - Distributions for crisis countries are shifted left for investment, output, and productivity relative to non-crisis countries; R&D distribution shows no notable difference between samples. - Impulse-response (univariate panel) results (levels, annual frequency): - Output dropped 7 percent initially and remained persistently depressed for 10 years in response to a banking crisis shock. - TFP declined around 5 percent. - Investment exhibits a persistent contraction of around 20 percent after 10 years. - Credit (domestic credit to the private sector by banks) falls nearly 40 percent over the medium to long run. - Regression (medium-term determinants of TFP) — key quantified relationships: - A 1 percent loss of investment (average 2008–2010 deviation from trend) leads to 0.5 percent loss of TFP in the medium term. - The drop in credit (domestic credit to the private sector by banks) has a significant impact on medium-term productivity loss. - Losses in R&D do not have a significant effect on mid-term productivity after a financial crisis in single-factor regressions and regressions with multiple controls. - Selected coefficients and model statistics (preserving source values and significance indicators): - Table 1 (Medium-term TFP Losses and Investment): - inv0810,ave loss: 0.529** (Model 1) - inv0810,ave loss: 0.601* (Model 2) - credit0810,ave loss: -0.115* (Model 2) - Constant examples: -0.038** ; -0.040** ; -0.055** ; -0.098** ; -0.046** ; -0.043* - R-squared (selected): 0.107 ; 0.052 ; 0.000 ; 0.007 ; 0.005 ; 0.369 - Observations row as presented in the source: 10710476508035 - Table 2 (Medium-term TFP Loss and Equipment Investment): - equip0810,ave loss: 0.187** (Model 1) - equip0810,ave loss: 0.303 (Model 2) - credit0810,ave loss: -0.115* (Model 1) - Constant examples: -0.018 ; -0.040** ; -0.055** ; -0.098** ; -0.046** ; -0.020 - R-squared (selected): 0.107 ; 0.052 ; 0.000 ; 0.007 ; 0.005 ; 0.340 - Observations row as presented in the source: 10710476508035 - Standard errors reported in parentheses in source tables; significance markers: ** p<0.01, * p<0.05. - Dependent variable in both tables: Deviations of TFP from pre-crisis trend during 2015-2017. ### Figures and empirical visuals referenced - Figure 1: Deviations from Pre-crisis Trend: US, Korea, Brazil, and France. - Figure 2: Distribution of Deviations from Pre-crisis Trend. - Figure 3: Empirical Impulse Response Functions. - Figure 4: Model-based Impulse Response Functions. - Figure 5: Financial Crises and Hysteresis Effects in the US. - Figure 6: Sensitivity Analysis. - Figure 7: Financial Crises and Hysteresis Effects in the Emerging Economies. - Figure 8: Financial Policies and Hysteresis Effects. --- ### Model framework and quantitative implications ### Model summary - Model type: closed-economy real business cycle model with flexible prices extended by: - Financial accelerator mechanism à la Bernanke et al. (1999) where firm-level financial frictions amplify shocks through investment channels. - Capital-embodied technological change (Greenwood et al., 1997): investment raises both physical capital and capital quality, increasing measured TFP. - Agents and structure: - Households: supply labor, consume, save via deposits, receive wages, deposit returns, lump-sum transfers, and firm profits; preference shock ξ_Pt follows AR(1): log ξ_Pt = ρ_P log ξ_Pt−1 + ε_Pt. - Entrepreneurs: produce output using capital from capital goods producers and labor; finance projects with net worth and borrowing from financial intermediaries. - Financial intermediaries: accept deposits and lend to entrepreneurs; a state-contingent spread can model macroprudential policy in simulations. - Capital goods producers and production structure include capital-embodied technological change. - Key household first-order conditions (excerpt): - Euler equation: E_t[ξ_Pt β E_t u′(C_t+1) / u′(C_t) R_t+1] = 1. - Labor supply: W_t = u_{c,t} / u_{l,t}. ### Quantitative and policy implications (summarized results) - The model replicates key dynamics of output, investment, and TFP for advanced and emerging economies after the GFC only when both frictions (financial accelerator + capital-embodied technological change) are included. - Financial policies: - Macroprudential policies modeled as a state-contingent spread on borrowing can stabilize financial intermediation and investment in the short run and reduce medium-term TFP losses. - Contribution to literature: - Provides an alternative to R&D-driven endogenous growth explanations for hysteresis following financial crises by emphasizing investment-driven capital quality effects and financial frictions. - Links short-run financial amplification to medium-term supply-side losses through capital-embodied technological change. --- ### 3.2 Entrepreneurs (wpiea2021170-print-pdf) ### Problem setup and balance sheet - Entrepreneurs finance capital goods K_{i,t+1} with net worth N_{i,t+1} and borrowing B_{i,t+1}. - Balance sheet: Q_t K_{i,t+1} = N_{i,t+1} + B_{i,t+1}, where Q_t is the price of capital. - Borrowing occurs at t−1: entrepreneurs borrow B_t from a financial intermediary at gross interest rate Z_t. - After risks materialize, gross revenue is ω_i R_{k,t} Q_{t-1} K_t. ### Idiosyncratic risk and returns - Return to capital for entrepreneur i: ω_i R_{k,t}, with ω_i following log-normal distribution: - ln ω ∼ N(−σ_ω^2 / 2, σ_ω^2). - Mean: E[ω] = 1; cdf: F(ω). ### Entrepreneurs' profit-maximization and lending condition - Entrepreneurs solve: - max_{K_t, ω_t} E_{t−1} ∫_{ω_t}^{∞} [ω R_{k,t} Q_{t−1} K_t − Z_t B_t] dF(ω) - Budget constraint (zero-profit condition of lenders): - R_t (Q_{t−1} K_t − N_t) = [Γ(ω_t) − μ G(ω_t)] R_{k,t} Q_{t−1} K_t - Definitions: - Γ(ω_t) ≡ ∫_{0}^{ω} f(ω) dω + ω ∫_{ω}^{∞} f(ω) dω. - μ G(ω_t) ≡ μ ∫_{0}^{ω} ω f(ω) dω. - Interpretation: - Left-hand side: opportunity cost of lending, R_t B_t = R_t (Q_{t−1} K_t − N_t). - Right-hand side: net returns from risky lending (Γ(ω_t) is gross return for lenders; μ G(ω_t) expected monitoring costs for bankrupt entrepreneurs with ω < ω_t). ### Equilibrium relationships and returns - In perfect competition in financial markets, lending at the risk-free rate equals net returns from risky loans; budget constraint holds with equality. - Equilibrium relationship between external finance premium and leverage ratio: - E{R_{k,t+1} / R_{t+1}} = s( Q_t K_{i,t+1} / N_{i,t+1} ). - Return on capital defined as: - R_{k,t} = X_t + (1 − δ) Q_t / Q_{t−1}, - where marginal productivity of capital X_t = α Y_t / K_t. ### Entrepreneur outcomes, failure, and net worth dynamics - A fraction (1−γ) of entrepreneurs fail and consume entrepreneurial profit C^e_t = (1−γ) V_t. - V_t (entrepreneurial profit) given by: - V_t = R_{k,t} Q_{t-1} K_t − ( R_t + μ ∫_{0}^{ω_t} dF(ω) R_{k,t} Q_{t-1} K_t / (Q_{t-1} K_t − N_t) ) (Q_{t-1} K_t − N_t). - V_t is gross return on capital less cost of servicing debt by solvent firms and total monitoring costs. - Surviving entrepreneurs (fraction γ) reinvest profits into net worth: - N_t = γ V_t + W^e − ξ^N_t, - where W^e is a "start up" lump transfer from households to new entrepreneurs and ξ^N_t is a net worth shock. - Net worth shock process: - log ξ^N_t = ρ_N log ξ^N_{t−1} + ε^N_t. --- *Source: wpiea2021170-print-pdf.* ### 1. Introduction ........................................................................................................ ### 1 Introduction ### Overview and research question - Puzzle: output across advanced and emerging economies recovered much more slowly than expected after the Global Financial Crisis (GFC). - Main goal: understand mechanics of slow recoveries with focus on the role of financial frictions and investment dynamics in the aftermath of crises. - Alternative hypothesis developed: tighter financial conditions constrain investment, and because investment can embody technological change (capital-embodied technological change), investment slumps can depress measured total factor productivity (TFP) in the medium term, producing persistent output losses. ### Empirical motivation (stylized facts) - Four country cases (Brazil, France, South Korea, US) show permanent output losses relative to pre-crisis trend accompanied by persistent reductions in TFP; R&D did not uniformly fall and in many cases continued on pre-crisis trends. - Key observed co-movements: investment dynamics are correlated with TFP dynamics; declines in investment are associated with declines in TFP during and after the GFC. ### Empirical strategy and main empirical findings - Three empirical approaches: - Cross-country distributions of deviations from pre-crisis trends (2000–2008 trend; post-crisis deviations 2015–2017). - Univariate autoregressive panel analysis following Cerra and Saxena (2008) to estimate impulse responses of levels after banking crises. - Cross-country regressions linking medium-term TFP losses (average 2015–2017 deviation from pre-crisis trend) to early investment and financial variables (average 2008–2010 deviations from trend). - Distributional evidence: - Sample sizes: 24 countries with a banking crisis (Laeven and Valencia (2013) database) and 168 countries without a banking crisis. - Distributions for crisis countries are shifted left for investment, output, and productivity relative to non-crisis countries; R&D distribution shows no notable difference between samples. - Impulse-response (univariate panel) results (levels, annual frequency): - Output dropped 7 percent initially and remained persistently depressed for 10 years in response to a banking crisis shock. - TFP declined around 5 percent. - Investment exhibits a persistent contraction of around 20 percent after 10 years. - Credit (domestic credit to the private sector by banks) falls nearly 40 percent over the medium to long run. - Regression (medium-term determinants of TFP) — key results summarized qualitatively and quantitatively: - A 1 percent loss of investment (average 2008–2010 deviation from trend) leads to 0.5 percent loss of TFP in the medium term. - The drop in credit (domestic credit to the private sector by banks) has a significant impact on medium-term productivity loss. - Losses in R&D do not have a significant effect on mid-term productivity after a financial crisis in single-factor regressions and regressions with multiple controls. - Selected coefficients from reported tables (preserving source values and significance indicators): - Table 1 (Medium-term TFP Losses and Investment): - inv0810,ave loss: 0.529** (Model 1), 0.601* (Model 2) - credit0810,ave loss: -0.115* (Model 2) - Constant examples: -0.038** ; -0.040** ; -0.055** ; -0.098** ; -0.046** ; -0.043* - R-squared (selected): 0.107 ; 0.052 ; 0.000 ; 0.007 ; 0.005 ; 0.369 - Table 2 (Medium-term TFP Loss and Equipment Investment): - equip0810,ave loss: 0.187** (Model 1), 0.303 (Model 2) - credit0810,ave loss: -0.115* (Model 1) - Constant examples: -0.018 ; -0.040** ; -0.055** ; -0.098** ; -0.046** ; -0.020 - R-squared (selected): 0.107 ; 0.052 ; 0.000 ; 0.007 ; 0.005 ; 0.340 - Standard errors in parentheses; significance markers: ** p<0.01, * p<0.05. - Dependent variable in both tables: Deviations of TFP from pre-crisis trend during 2015-2017. - Observations rows as presented in the source (Table 1): 10710476508035; (Table 2): 10710476508035. ### Model framework (DSGE model summary) - Model type: closed-economy real business cycle model with flexible prices extended by: - Financial accelerator mechanism à la Bernanke et al. (1999) where firm-level financial frictions amplify shocks through investment channels. - Capital-embodied technological change (Greenwood et al., 1997): investment raises both physical capital and capital quality, increasing measured TFP. - Agents and structure: - Households: supply labor, consume, save via deposits, receive wages, deposit returns, lump-sum transfers, and firm profits; preference shock ξ_Pt follows AR(1): log ξ_Pt = ρ_P log ξ_Pt−1 + ε_Pt. - Entrepreneurs: produce output using capital from capital goods producers and labor; finance projects with net worth and borrowing from financial intermediaries. - Financial intermediaries: accept deposits and lend to entrepreneurs; a state-contingent spread can model macroprudential policy in simulations. - Capital goods producers and production structure include capital-embodied technological change. - Key first-order conditions (excerpt for households): - Euler equation: E_t[ξ_Pt β E_t u′(C_t+1) / u′(C_t) R_t+1] = 1. - Labor supply: W_t = u_{c,t} / u_{l,t}. ### Quantitative and policy implications (summarized results) - Model replicates key dynamics of output, investment, and TFP for advanced and emerging economies after the GFC when both frictions (financial accelerator + capital-embodied technological change) are included. - Financial policies: - Macroprudential policies modeled as a state-contingent spread on borrowing can stabilize financial intermediation and investment in the short run and reduce medium-term TFP losses. - Contribution to literature: - Provides an alternative to R&D-driven endogenous growth explanations for hysteresis following financial crises by emphasizing investment-driven capital quality effects and financial frictions. - Links short-run financial amplification to medium-term supply-side losses through capital-embodied technological change. *Source: wpiea2021170-print-pdf - 1. Introduction.* ### 3.2 Entrepreneurs ### 3.2 Entrepreneurs ### Problem setup and balance sheet - Entrepreneurs finance capital goods K_{i,t+1} with net worth N_{i,t+1} and borrowing B_{i,t+1}. Balance sheet: - Q_t K_{i,t+1} = N_{i,t+1} + B_{i,t+1}, where Q_t is the price of capital. - Borrowing occurs at t−1: entrepreneurs borrow B_t from a financial intermediary at gross interest rate Z_t. - After risks materialize, gross revenue is ω_i R_{k,t} Q_{t-1} K_t. ### Idiosyncratic risk and returns - Return to capital for entrepreneur i: ω_i R_{k,t}, with ω_i following log-normal distribution: - ln ω ∼ N(−σ_ω^2 / 2, σ_ω^2). - This process has mean E[ω] = 1 and cdf F(ω). ### Entrepreneurs' profit-maximization problem - Entrepreneurs solve: - max_{K_t, ω_t} E_{t−1} ∫_{ω_t}^{∞} [ω R_{k,t} Q_{t−1} K_t − Z_t B_t] dF(ω) - Budget constraint (zero-profit condition of lenders): - R_t (Q_{t−1} K_t − N_t) = [Γ(ω_t) − μ G(ω_t)] R_{k,t} Q_{t−1} K_t - Definitions: - Γ(ω_t) ≡ ∫_{0}^{ω} f(ω) dω + ω ∫_{ω}^{∞} f(ω) dω. - μ G(ω_t) ≡ μ ∫_{0}^{ω} ω f(ω) dω. - Interpretation: - Left-hand side: opportunity cost of lending, R_t B_t = R_t (Q_{t−1} K_t − N_t). - Right-hand side: net returns from risky lending. - Γ(ω_t): gross return for lenders. - μ G(ω_t): expected monitoring costs to verify entrepreneurs that go bankrupt (ω < ω_t). ### Equilibrium relationships and returns - In perfect competition in financial markets, lending at the risk-free rate equals net returns from risky loans; budget constraint holds with equality. - Equilibrium relationship between external finance premium and leverage ratio: - E{R_{k,t+1} / R_{t+1}} = s( Q_t K_{i,t+1} / N_{i,t+1} ). - Return on capital defined as: - R_{k,t} = X_t + (1 − δ) Q_t / Q_{t−1}, - where marginal productivity of capital X_t = α Y_t / K_t. ### Entrepreneur outcomes, failure, and net worth dynamics - A fraction (1−γ) of entrepreneurs fail and consume entrepreneurial profit C^e_t = (1−γ) V_t. - V_t (entrepreneurial profit) given by: - V_t = R_{k,t} Q_{t−1} K_t − ( R_t + μ ∫_{0}^{ω_t} dF(ω) R_{k,t} Q_{t−1} K_t / (Q_{t−1} K_t − N_t) ) (Q_{t−1} K_t − N_t). - V_t is gross return on capital less cost of servicing debt by solvent firms and total monitoring costs. - Entrepreneurs who survive (fraction γ) reinvest profits into net worth: - N_t = γ V_t + W^e − ξ^N_t, - where W^e is a "start up" lump transfer from households to new entrepreneurs and ξ^N_t is a net worth shock. - Net worth shock follows AR(1): - log ξ^N_t = ρ_N log ξ^N_{t−1} + ε^N_t. *Source: wpiea2021170-print-pdf - 3.2 Entrepreneurs* ### References ### References (wpiea2021170-print-pdf) ### Key cited works - Ball, L. (2014). Long-term damage from the great recession in oecd countries. European Journal of Economics and Economic Policies: Intervention, 11(2):149–160. - Bernanke, B. S., Gertler, M., and Gilchrist, S. (1999). The financial accelerator in a quantitative business cycle framework. Handbook of macroeconomics, 1:1341–1393. - Cerra, M. V. and Saxena, M. S. C. (2017). Booms, crises, and recoveries: A new paradigm of the business cycle and its policy implications. International Monetary Fund. - Cerra, V., Fatás, A., and Saxena, S. (2021). Hysteresis and business cycles. Journal of Economic Literature, forthcoming. - Cerra, V. and Saxena, S. C. (2008). Growth dynamics: the myth of economic recovery. American Economic Review, 98(1):439–57. - Fatás, A. and Mihov, I. (2013). Policy volatility, institutions, and economic growth. Review of Economics and Statistics, 95(2):362–376. - Greenwood, J., Hercowitz, Z., and Krusell, P. (1997). Long-run implications of investment-specific technological change. The American economic review, pages 342–362. - IMF (2010). World economic outlook: Recovery, risk, and rebalancing. World Economic Outlook. - IMF (2018). World economic outlook: Challenges to steady growth. World Economic Outlook. - Jermann, U. and Quadrini, V. (2012). Macroeconomic effects of financial shocks. American Economic Review, 102(1):238–71. - Laeven, L. and Valencia, F. (2013). Systemic banking crises database. IMF Economic Review, 61(2):225–270. - Laeven, M. L. and Valencia, M. F. (2018). Systemic banking crises revisited. International Monetary Fund. - Rawdanowicz, L., Bouis, R., Inaba, K.-I., and Christensen, A. K. (2014). Secular stagnation: evidence and implications for economic policy. - Reifschneider, D., Wascher, W., and Wilcox, D. (2015). Aggregate supply in the united states: recent developments and implications for the conduct of monetary policy. IMF Economic Review, 63(1):71–109. - Reinhart, C. M. and Rogoff, K. S. (2009). This time is different: Eight centuries of financial folly. princeton university press. - Reinhart, C. M. and Rogoff, K. S. (2014). Recovery from financial crises: Evidence from 100 episodes. American Economic Review, 104(5):50–55. - Stadler, G. W. (1986). Real versus monetary business cycle theory and the statistical characteristics of output fluctuations. Economics Letters, 22(1):51–54. - Stadler, G. W. (1990). Business cycle models with endogenous technology. The American Economic Review, pages 763–778. - Stiglitz, J. E. (1993). Endogenous growth and cycles. Working Paper 4286, National Bureau of Economic Research. ### Thematic concentration in the references - Financial crises, systemic banking crises, and crisis databases (Laeven and Valencia 2013; Laeven and Valencia 2018). - Hysteresis, long-term output losses, and growth dynamics after recessions and crises (Ball 2014; Cerra and Saxena 2008; Cerra, Fatás, and Saxena 2021). - Financial accelerator and macro-financial linkages (Bernanke, Gertler, and Gilchrist 1999; Jermann and Quadrini 2012). - Policy implications: secular stagnation, policy volatility, aggregate supply, and monetary policy conduct (Rawdanowicz et al. 2014; Fatás and Mihov 2013; Reifschneider, Wascher, and Wilcox 2015). - Long-run drivers: investment-specific technological change and endogenous technology (Greenwood, Hercowitz, and Krusell 1997; Stadler 1990; Stiglitz 1993). - Historical syntheses and cross-episode evidence on recoveries (Reinhart and Rogoff 2009; Reinhart and Rogoff 2014). ### Reference usage implications for the chapter - Empirical foundation draws on crisis databases and World Economic Outlook data. - Theoretical framing integrates financial accelerator mechanisms and endogenous-technology growth models. - Policy discussion likely informed by works on policy volatility, secular stagnation, and aggregate supply developments. ### Figures referenced in the section - Figure 1: Deviations from Pre-crisis Trend: US, Korea, Brazil, and France - Source: IMF World Economic Outlook; and authors’ calculations - Note: The blue lines are pre-crisis linear trends estimated from filtered (Hodrick-Prescott filter) series between 2000 and 2008 and are extrapolated linearly thereafter. 2008 log variables normalized to zero. - Figure 2: Distribution of Deviations from Pre-crisis Trend - Source: Laeven and Valencia (2013); IMF World Economic Outlook; and authors’ calculations - Note: Distribution of average percent deviations in years 2015-2017 from pre-crisis trend. The deviations from pre-crisis trend are calculated by detrending each variable using a linear trend estimated for the sample period 2000-2008. The blue line represents the kernel density distribution of the countries that experienced a crisis and the red line represents the distribution of the non-crisis sample. - Figure 3: Empirical Impulse Response Functions - Source: IMF World Economic Outlook; and authors’ calculations - Figure 4: Model-based Impulse Response Functions - Figure 5: Financial Crises and Hysteresis Effects in the US - Figure 6: Sensitivity Analysis - Figure 7: Financial Crises and Hysteresis Effects in the Emerging Economies - Figure 8: Financial Policies and Hysteresis Effects *Content unit: wpiea2021170-print-pdf - References* --- _Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021170-print-pdf.pdf_