## _wp1578 - References

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### Major research questions and approach
- Research question:
  - How does a countercyclical macroprudential policy that reduces credit fluctuations over the business cycle affect labor market and aggregate dynamics in emerging economies where formal and informal credit markets interact with labor market structure?
- Method:
  - Small open economy real business cycle model with financial and labor market frictions, featuring two production sectors (salaried firms with access to formal financing and self-employed firms reliant on informal input credit), matching firms, capital producers, and Nash bargaining over wages and the self-employment capital rental rate.
- Key modeling innovation:
  - Endogenous interaction between salaried firms’ choice of the fraction of capital used internally (ωS,t) and the supply of capital to matching firms (input credit) that enables self-employment entry.
- Policy implementation in model:
  - Countercyclical Pigovian tax τS,t on the salaried-sector return on capital:
    - R S,t = [ s( Q S,t−1 k S,t / nw S,t ) R t−1 ] τ S,t
    - τ S,t = exp [ η S ( b S,t−1 / b S − 1 ) ], with η S ≥ 0; η S calibrated so that volatility of credit bS is halved in policy experiments.

### Stylized facts motivating the model
- Self-employment shares:
  - between 20 to 50 percent of total employment in many Latin American economies.
- Employment cyclical patterns:
  - Self-employment and entry into self-employment from unemployment are countercyclical; salaried employment differs in financing and cyclicality.

### Model structure and key mechanisms
- Agents and markets:
  - salaried firms (BGG entrepreneurs), households, matching firms, capital producers.
- Financing distinction:
  - salaried firms use formal borrowing subject to an external finance premium; self-employed individuals require matched capital (input credit) from matching firms and lack access to formal finance.
- Matching and search:
  - Cobb-Douglas matching functions in labor and capital markets; capital market tightness θSE,t = vSE,t/kM,t affects self-employment entry probability f(θSE,t).
- Bargaining outcomes determined by Nash bargaining:
  - wages wS,t depend on marginal product of labor and entry probabilities;
  - capital rental rate rSE,t depends on sectoral conditions.
- Input-credit–labor market channel:
  - salaried firms’ decision to retain purchased capital internally (ωS,t) directly affects capital available to matching firms and thus self-employment entry.

### Calibration and numerical environment (Mexico benchmark; quarterly)
- Key parameter values (stated exactly as in source):
  - Capital share in salaried sector: 0.32.
  - Subjective discount factor β = 0.985.
  - Depreciation rate δ = 0.025.
  - Salaried separation rate ρS = 0.05.
  - Self-employment separation rate ρSE = 0.02.
  - Bargaining powers χS and χSE = 0.50.
  - Survival probability of salaried firms φ = 0.93.
  - Steady-state foreign interest rate = 1.015.
  - CRRA parameter σ = 2.
  - Self-employment productivity normalized to 1.
  - Debt-to-output steady-state target: 30 percent.
  - Government spending to total output target: 10.2 percent.
  - Salaried vacancy posting cost calibrated to represent 3.5 percent of wages.
  - Capital search cost parameter ψSE set to three months of wages.
  - Convexity of capital search cost ηSE = 1.1.
  - Elasticity of external finance premium νS set to match leverage ratios (as in calibration).
- Second-moment calibration targets (stated exactly):
  - Relative volatility of consumption to total investment: 1.13 and 2.78 respectively (presented as targets in calibration).
  - Volatility of total output: 2.39.
  - Contemporaneous correlation between leverage and output: -0.30.
- Data/sample and simulation:
  - Data for Mexico used from 1993Q1 to 2007Q4; HP filter smoothing parameter 1600.
  - Model simulation: 2,100 periods, remove first 100 periods; apply HP filter with smoothing parameter 1600.

### Main quantitative findings (no-policy baseline)
- Reproduced empirical patterns (productivity shocks as sole driver):
  - countercyclicality of leverage and interest rates,
  - countercyclicality of the current account-output ratio,
  - countercyclicality of unemployment and self-employment,
  - countercyclicality of the transition probability from unemployment to self-employment,
  - high unemployment persistence.
- Impact of adding net worth shocks:
  - improves fit for cyclicality of interest rates and the cyclical correlation between output and transition into self-employment and between output and the current account-output ratio.
- Importance of capital search frictions (input credit channel):
  - A model variant without capital search frictions fails to generate:
    - countercyclical self-employment,
    - countercyclical leverage and interest rates,
    - relative volatility of consumption greater than one,
    - countercyclical current account-output ratio,
    - persistence of unemployment consistent with the data.

### Effects of countercyclical macroprudential policy (policy calibrated to halve credit volatility)
- General equilibrium intuition:
  - Policy reduces the rise in the external finance premium during downturns (and raises it in booms).
  - Lower rise in borrowing costs leads salaried firms to contract less and to keep a larger fraction of purchased capital in-house (ωS,t falls by less).
  - Smaller reallocation of capital to matching firms reduces availability of input credit for prospective self-employed individuals, weakening the countercyclicality of self-employment entry.
- Response to a negative aggregate productivity shock (policy vs. ηS = 0):
  - smaller contraction on impact and faster recovery of investment;
  - total output and consumption are less persistent under policy (quantitatively small differences);
  - salaried output contraction is less persistent;
  - self-employment output contraction becomes substantially more persistent under policy;
  - unemployment exhibits a larger and more persistent rise under policy because the weaker expansion (or smaller contraction) of capital available to self-employment reduces countercyclical self-employment entry and generates longer-lasting contractions in self-employment.
  - Net effect: policy reduces volatility/persistence in salaried sector but amplifies unemployment dynamics through input-credit–labor market link.
- Response to a negative salaried-firm net worth shock (policy vs. no-policy):
  - No-policy case:
    - net worth shock raises desired borrowed funds and external finance premium, reduces salaried capital demand, induces reallocation of capital to self-employment, increases self-employment entry and initially reduces unemployment (but lowers consumption and total output since salaried output > 70 percent of total).
  - With active policy:
    - policy limits rise in desired borrowed funds, but can put upward pressure on the external finance premium after the shock, leading to:
      - sharper contractions in salaried employment, output, investment, and total output;
      - larger reallocation of capital toward self-employment and a larger expansion in self-employment and self-employment output;
      - ultimately, sharper unemployment fluctuations under policy than without it.
    - Conclusion: policy amplifies fluctuations in most aggregates in response to net worth shocks.
- Cross-shock summary:
  - Policy reduces consumption volatility in response to productivity shocks only modestly; aggregate gains are limited and tend to disappear with household heterogeneity.
  - Policy tends to increase labor market and aggregate volatility in response to net worth shocks.
  - Policy amplifies unemployment fluctuations regardless of shock type because of the input-credit–self-employment channel.

### Robustness and additional experiments
- Self-employment productivity shocks:
  - Negative shock reduces supply of capital to self-employed, raises salaried employment/output, reduces self-employment; introducing policy reduces the drop in capital supply and self-employment but increases investment contraction and total output volatility.
  - Policy can reduce unemployment variability in this shock scenario because it mitigates the fall in self-employment.
- Shocks to efficiency of financial intermediation:
  - Active policy reduces contraction in borrowed funds and leads to smaller reductions in salaried output, employment, investment, and consumption, but reduces reallocation to self-employment and increases unemployment volatility.
- Foreign interest rate shocks:
  - Introducing foreign interest rate shocks worsens the model’s fit to labor market cyclicality and can generate counterfactual employment dynamics; financial frictions in the model suffice to capture several emerging-economy business-cycle features without foreign interest rate shocks.
- Household heterogeneity:
  - Two-household extension preserves main model facts.
  - Countercyclical policy produces asymmetric effects on household consumption volatilities that offset in aggregate, so aggregate consumption volatility remains virtually unchanged relative to no-policy scenario.
  - Main conclusion on adverse impact of policy on unemployment persists.
- Caveat on net worth shocks and matching efficiency:
  - If negative net worth shocks also reduce capital-matching efficiency, the expansion of self-employment observed in the baseline net worth experiment would be attenuated and unemployment could instead increase after the shock.

### Policy implications and recommendations
- Key tradeoff identified:
  - Countercyclical macroprudential policy that stabilizes formal credit and salaried-sector activity can reduce volatility in salaried output and investment but may amplify unemployment volatility by weakening countercyclical self-employment dynamics through reduced availability of input credit.
- Quantitative assessment:
  - Quantitative gains in aggregate stabilization from the policy are limited in the benchmark scenarios, particularly for consumption, and they may vanish under household heterogeneity.
- Recommended complementarities and further exploration:
  - Combining cyclical macroprudential policies with targeted labor market interventions may mitigate adverse employment outcomes.
  - Exploration of interactions with monetary policy and targeted policies toward capital flows/tradable sector is recommended for future work.

### Conclusion (exact framing from source)
- The presence of informal input credit relationships linking salaried firms (with formal financing) and self-employed firms (without formal financing) is crucial in determining the transmission of cyclical macroprudential policy to employment and aggregate dynamics in emerging economies.
- Cyclical macroprudential policy can yield limited aggregate gains but may generate additional labor market volatility; policy complementarities (for example, between macroprudential regulation and active labor market interventions) may be worth exploring.

*Source: _wp1578 - References . . . (PDF chapter/section)*

### References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### _wp1578 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### Major research questions and approach
- Research question: How does a countercyclical macroprudential policy that reduces credit fluctuations over the business cycle affect labor market and aggregate dynamics in emerging economies where formal and informal credit markets interact with labor market structure?
- Method: Small open economy real business cycle model with financial and labor market frictions, featuring two production sectors (salaried firms with access to formal financing and self-employed firms reliant on informal input credit), matching firms, capital producers, and Nash bargaining over wages and the self-employment capital rental rate.
- Key modeling innovation: Endogenous interaction between salaried firms’ choice of the fraction of capital used internally (ωS,t) and the supply of capital to matching firms (input credit) that enables self-employment entry.

### Stylized facts motivating the model
- Self-employment shares: between 20 to 50 percent of total employment in many Latin American economies.
- Employment cyclical patterns: Self-employment and entry into self-employment from unemployment are countercyclical; salaried employment differs in financing and cyclicality.

### Model structure and key mechanisms
- Agents: salaried firms (BGG entrepreneurs), households, matching firms, capital producers.
- Financing distinction: salaried firms use formal borrowing subject to an external finance premium; self-employed individuals require matched capital (input credit) from matching firms and lack access to formal finance.
- Matching and search: Cobb-Douglas matching functions in labor and capital markets; capital market tightness θSE,t = vSE,t/kM,t affects self-employment entry probability f(θSE,t).
- Nash bargaining determines:
  - wages wS,t (depends on marginal product of labor and probability of entering self-employment),
  - capital rental rate rSE,t (depends on both sectoral conditions).
- Countercyclical macroprudential policy implemented as a Pigovian tax τS,t on the salaried-sector return on capital:
  - R S,t = [ s( Q S,t−1 k S,t / nw S,t ) R t−1 ] τ S,t
  - τ S,t = exp [ η S ( b S,t−1 / b S − 1 ) ], with η S ≥ 0; η S calibrated so that volatility of credit bS is halved in policy experiments.

### Calibration and numerical environment
- Benchmark country: Mexico.
- Time period: a quarter.
- Key parameter values (stated exactly as in source):
  - Capital share in salaried sector: 0.32.
  - Subjective discount factor β = 0.985.
  - Depreciation rate δ = 0.025.
  - Salaried separation rate ρS = 0.05.
  - Self-employment separation rate ρSE = 0.02.
  - Bargaining powers χS and χSE = 0.50.
  - Survival probability of salaried firms φ = 0.93.
  - Steady-state foreign interest rate = 1.015.
  - CRRA parameter σ = 2.
  - Self-employment productivity normalized to 1.
  - Debt-to-output steady-state target: 30 percent.
  - Government spending to total output target: 10.2 percent.
  - Salaried vacancy posting cost calibrated to represent 3.5 percent of wages.
  - Capital search cost parameter ψSE set to three months of wages.
  - Convexity of capital search cost ηSE = 1.1.
  - Elasticity of external finance premium νS set to match leverage ratios (as in calibration).
- Second-moment calibration targets (stated exactly):
  - Relative volatility of consumption to total investment: 1.13 and 2.78 respectively (presented as targets in calibration).
  - Volatility of total output: 2.39.
  - Contemporaneous correlation between leverage and output: -0.30.
- Data/sample and simulation details:
  - Data for Mexico used from 1993Q1 to 2007Q4; HP filter smoothing parameter 1600.
  - Model simulation: 2,100 periods, remove first 100 periods; apply HP filter with smoothing parameter 1600.

### Main quantitative findings (no-policy baseline)
- The model with productivity shocks as sole driver qualitatively replicates:
  - countercyclicality of leverage and interest rates,
  - countercyclicality of the current account-output ratio,
  - countercyclicality of unemployment and self-employment,
  - countercyclicality of the transition probability from unemployment to self-employment,
  - high unemployment persistence.
- Adding net worth shocks improves fit for cyclicality of interest rates and the cyclical correlation between output and transition into self-employment and between output and the current account-output ratio.
- A model variant without capital search frictions (no input credit channel) fails to generate:
  - countercyclical self-employment,
  - countercyclical leverage and interest rates,
  - relative volatility of consumption greater than one,
  - countercyclical current account-output ratio,
  - persistence of unemployment consistent with the data.

### Effects of countercyclical macroprudential policy (policy that halves credit volatility)
- General equilibrium intuition:
  - Policy reduces the rise in the external finance premium during downturns (and raises it in booms).
  - Lower rise in borrowing costs leads salaried firms to contract less and to keep a larger fraction of purchased capital in-house (ωS,t falls by less).
  - Smaller reallocation of capital to matching firms reduces availability of input credit for prospective self-employed individuals, weakening the countercyclicality of self-employment entry.
- Response to a negative aggregate productivity shock:
  - Policy outcomes (compared to ηS = 0):
    - smaller contraction on impact and faster recovery of investment;
    - total output and consumption are less persistent under policy (quantitatively small differences);
    - salaried output contraction is less persistent;
    - self-employment output contraction becomes substantially more persistent under policy;
    - unemployment exhibits a larger and more persistent rise under policy because the weaker expansion (or smaller contraction) of capital available to self-employment reduces countercyclical self-employment entry and generates longer-lasting contractions in self-employment.
  - Net effect: policy reduces volatility/persistence in salaried sector but amplifies unemployment dynamics through input-credit–labor market link.
- Response to a negative salaried-firm net worth shock:
  - No-policy case: net worth shock raises desired borrowed funds and external finance premium, reduces salaried capital demand, induces reallocation of capital to self-employment, increases self-employment entry and initially reduces unemployment (but lowers consumption and total output since salaried output > 70 percent of total).
  - With active policy: policy limits rise in desired borrowed funds, but can put upward pressure on the external finance premium after the shock, leading to:
    - sharper contractions in salaried employment, output, investment, and total output;
    - larger reallocation of capital toward self-employment and a larger expansion in self-employment and self-employment output;
    - ultimately, sharper unemployment fluctuations under policy than without it.
  - Conclusion: policy amplifies fluctuations in most aggregates in response to net worth shocks.
- Across shock types:
  - Policy reduces consumption volatility in response to productivity shocks only modestly; aggregate gains are limited and tend to disappear with household heterogeneity.
  - Policy tends to increase labor market and aggregate volatility in response to net worth shocks.
  - Policy amplifies unemployment fluctuations regardless of shock type because of the input-credit–self-employment channel.

### Robustness and additional experiments
- Self-employment productivity shocks:
  - Negative shock to self-employment productivity reduces supply of capital to self-employed, raises salaried employment/output, reduces self-employment; introducing policy reduces the drop in capital supply and self-employment but increases investment contraction and total output volatility.
  - Policy can reduce unemployment variability in this shock scenario because it mitigates the fall in self-employment.
- Shocks to efficiency of financial intermediation:
  - Active policy reduces contraction in borrowed funds and leads to smaller reductions in salaried output, employment, investment, and consumption, but reduces reallocation to self-employment and increases unemployment volatility (similar channel as productivity shocks).
- Foreign interest rate shocks:
  - Introducing foreign interest rate shocks worsens the model’s fit to labor market cyclicality and can generate counterfactual employment dynamics; financial frictions in the model suffice to capture several emerging-economy business-cycle features without foreign interest rate shocks.
- Household heterogeneity:
  - Two-household extension preserves main model facts.
  - Countercyclical policy produces asymmetric effects on household consumption volatilities that offset in aggregate, so aggregate consumption volatility remains virtually unchanged relative to no-policy scenario.
  - Main conclusion on adverse impact of policy on unemployment persists.
- Caveat on net worth shocks and matching efficiency:
  - If negative net worth shocks also reduce capital-matching efficiency, the expansion of self-employment observed in the baseline net worth experiment would be attenuated and unemployment could instead increase after the shock.
  - The model notes that allowing matching efficiency to be positively correlated with net worth shocks produces this effect.

### Policy implications and recommendations
- Key tradeoff identified: Countercyclical macroprudential policy that stabilizes formal credit and salaried-sector activity can reduce volatility in salaried output and investment but may amplify unemployment volatility by weakening countercyclical self-employment dynamics through reduced availability of input credit.
- Quantitative gains in aggregate stabilization from the policy are limited in the benchmark scenarios, particularly for consumption, and they may vanish under household heterogeneity.
- Complementarities suggested: Combining cyclical macroprudential policies with targeted labor market interventions may mitigate adverse employment outcomes; exploration of interactions with monetary policy and targeted policies toward capital flows/tradable sector is recommended for future work.

### Conclusion (exact framing from source)
- The presence of informal input credit relationships linking salaried firms (with formal financing) and self-employed firms (without formal financing) is crucial in determining the transmission of cyclical macroprudential policy to employment and aggregate dynamics in emerging economies.
- Cyclical macroprudential policy can yield limited aggregate gains but may generate additional labor market volatility; policy complementarities (for example, between macroprudential regulation and active labor market interventions) may be worth exploring.

*Source: _wp1578 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . (PDF chapter/section)*

### REFERENCES

### _wp1578 - REFERENCES

### References inventory
- The document lists references [1] through [55], including working papers, journal articles, memos, and World Bank/IDB/OECD reports cited throughout the study. Notable citation entries include:
  - [1] Adjemian et al. 2011, “Dynare: Reference Manual, Version 4," Dynare Working Papers, 1, CEPREMAP.
  - [2] Aguiar and Gopinath. 2007, “Emerging Market Business Cycles: The Cycle is the Trend," Journal of Political Economy, Vol. 115, No. 1, pp. 69-102.
  - [7] Bernanke, Gertler, and Gilchrist. 1999, “The Financial Accelerator in a Quantitative Business Cycle Framework," Handbook of Macroeconomics, Vol. 1, Chapter 21, pp. 1341-1393.
  - [33] Gilchrist and Zakrajšek. 2011, “Monetary Policy and Credit Supply Shocks," IMF Economic Review, Vol. 59, pp. 195-232.
  - [37] Jácome, Nier, and Imam. 2012, “Building Blocks for Effective Macroprudential Policies in Latin America: Institutional Considerations," IMF Working Paper WP/12/183.
  - [45] Medina and Roldós. 2014, “Monetary and Macroprudential Policies to Manage Capital Flows," IMF Working Paper WP/14/30.
- References cover themes such as financial frictions, macroprudential policy, trade credit, informal employment, firm finance, and small open economy DSGE modelling.

### Stylized facts (Appendix A.1)
- Table 1 — Distribution of Employment in Select Countries (self-employment is percent of non-agricultural employment; annual average 2000–2007):
  - Argentina: Salaried 74.7; Self-Employment 25.3
  - Brazil: Salaried 64.3; Self-Employment 35.7
  - Colombia: Salaried 50.7; Self-Employment 49.3
  - Mexico: Salaried 70.7; Self-Employment 29.3
  - Philippines: Salaried 67.6; Self-Employment 32.4
  - United States: Salaried 92.5; Self-Employment 7.5
  - Norway: Salaried 93.3; Self-Employment 6.7
- Table 2 — Consequences from Limited Access to External Formal Financing for Small Firms in Latin America (Percent of Entrepreneurs):
  - Reduced Scale: 56.0
  - Search for Partners: 11.0
  - Search for Support from Suppliers or Customers: 51.0
  - Delay in Launching Enterprise: 32.0
- Table 3 — Percent of Small Entrepreneurs Using Informal Financing in Latin America:
  - Financing from Suppliers: Startup Year 32.0; Early Years 36.6
  - Financing via Purchase of Second-Hand Machinery and Equipment: Startup Year 27.5; Early Years 20.6
  - Financing from Customers: Startup Year 18.0; Early Years 19.1

### Model specification (Appendix A.2)
- Value functions and Nash bargaining formulation (expressions preserved as in source):
  - Value of a worker employed in the salaried sector:
    - W_{S,t} = w_{S,t} + E_t Ξ_{t+1|t} { (1−ρ_S) W_{S,t+1} + ρ_S W_{U,t+1} }.
  - Value of self-employment:
    - W_{SE,t} = (z_{SE,t} − r_{SE,t}) + E_t Ξ_{t+1|t} { (1−ρ_{SE}) W_{SE,t+1} + ρ_{SE} W_{U,t+1} }.
  - Value of unemployment:
    - W_{U,t} = b + E_t Ξ_{t+1|t} { (1−ρ_S) f(θ_{S,t}) W_{S,t+1} + (1−ρ_{SE}) v^u_{SE,t} f(θ_{SE,t}) W_{SE,t+1} + [1 − (1−ρ_S) f(θ_{S,t}) − (1−ρ_{SE}) v^u_{SE,t} f(θ_{SE,t})] W_{U,t+1} }.
  - Firm values:
    - J_{S,t} = p_{n,t} − w_{S,t} + E_t Ξ_{t+1|t} { (1−ρ_S) J_{S,t+1} }.
    - J_{SE,t} = r_{SE,t} + (ρ_{SE} − δ) + E_t Ξ_{t+1|t} { (1−ρ_{SE}) J_{SE,t+1} }.
  - Nash bargaining problems:
    - max_{w_{S,t}} { (W_{S,t} − W_{U,t})^{χ_S} (J_{S,t})^{1−χ_S} }.
    - max_{r_{SE,t}} { (W_{SE,t} − W_{U,t})^{χ_{SE}} (J_{SE,t} − J^u_{k,t})^{1−χ_{SE}} }.
  - J^u_{k,t} ≡ 1 − δ.

- Competitive equilibrium conditions include matching and transition equations, capital pricing and law of motion, resource constraint, and Euler conditions. Representative equations from the model (as listed in source) include:
  - n_{S,t+1} = (1−ρ_S)(n_{S,t} + v_{S,t} q(θ_{S,t})), (17)
  - ψ_S q(θ_{S,t}) = (1−ρ_S) E_t Ξ_{t+1|t} { p_{n,t+1} − w_{S,t+1} + ψ_S q(θ_{S,t+1}) }, (18)/(27)
  - k_{S,t+1} = (1−δ) k_{S,t} + Φ(i_{S,t}/k_{S,t}) k_{S,t}, (30)
  - Q_{S,t} = [Φ'(i_{S,t}/k_{S,t})]^{−1}, (31)
  - u_c(c_t) = E_t β [R_t u_c(c_{t+1})], (32)
  - Resource constraint (excerpt): y_t = c_t + κ(v_{SE,t}) + ψ_S v_{S,t} + (1−φ_v)(1−φ) V_{S,t} + i_{S,t} − (ρ_{SE} − δ) n_{SE,t} + b^*_t−1 / R^*_t−1 − b^*_t + ... (34)

### Calibration details (Appendix A.3 and A.5)
- Benchmark parametrization (selected parameters and sources):
  - α_S = 0.32 (Capital Share, Salaried Sector) — DSGE Literature
  - b0 (Unemployment Insurance) = No Unempl. Benefits
  - β = 0.985 (Discount Factor) — DSGE Literature
  - δ = 0.025 (Capital Depreciation Rate) — DSGE Literature
  - ρ_S = 0.05 (Salaried Separation Rate) — Bosch, Maloney (2007)
  - ρ_{SE} = 0.02 (SE Separation Rate) — Bosch, Maloney (2007)
  - η_b = 0.050 (Elasticity of Foreign Debt)
  - η_{SE} = 1.10 (Curvature of Capital Search Cost) — Krause and Lubik (2010)
  - χ_S = 0.50; χ_{SE} = 0.50 (Bargaining powers)
  - ξ = 0.50 (Matching Elasticity)
  - φ = 0.93 (Survival Rate, BGG Salaried Firms)
  - R^* = 1.015 (Foreign Interest Rate)
  - z_{SE} = 1 (Self-Employment Productivity, normalization)

- Calibrated parameters (targets and values, Table 5 / Table 7 excerpts):
  - b^* = 0.950 (Steady State Foreign Debt; target b^*/4y = 0.30)
  - g = 0.081 (Steady State Gov. Spending; target g/y = 0.102)
  - M_S = 0.154 (Salaried Matching Efficiency; target n_S = 0.72)
  - M_{SE} = 0.081 (SE Matching Efficiency; target n_{SE} = 0.23)
  - ν_S = 0.070 (EFP Elasticity; target Leverage Ratio of 1.73)
  - φ_v = 0.050 (Fraction of nw_S, Exiting Firms; target 1 percent of wages)
  - ψ_S = 0.020 (Salaried Vacancy Cost; target 3.5 percent of wages)
  - ψ_{SE} = 0.573 (Project Posting Cost; target 3 months of wages)
  - ρ_z = 0.970 (Autocorrelation of z)
  - σ_z = 0.0185 (Standard Dev. of z) in the model with only productivity shocks
  - φ_k = 8.82 (Investment Adjustment Cost) in the model with only productivity shocks
  - φ_k = 9.900 (Investment Adjustment Cost) reported in Table 5 for full benchmark calibration

### Main results and business-cycle statistics (Appendix A.4)
- Targeted moments (Table 6 — Data vs. Model):
  - σ_y (volatility of total output): Data 2.39; Model with z shocks 2.39; Model with z and z_{nw} shocks 2.39; Model with No Capital Search 2.39
  - σ_c/σ_y (relative volatility of consumption): Data 1.14; Model with z shocks 1.16; Model with z and z_{nw} shocks 1.16; Model with No Capital Search 0.49
  - σ_i/σ_y (relative volatility of investment): Data 2.78; Model variations: 2.78 across columns shown
  - corr(lev_t, y_t) (targeted): Data −0.30; Model with z shocks −0.31; Model with z and z_{nw} shocks 0.08 (No Capital Search column blank for this entry)
- Non-targeted moments (selected, Table 6):
  - σ_u/σ_y: Data 6.28; Model with z shocks 0.33; Model with z and z_{nw} shocks 0.37; Model with No Capital Search 0.89
  - σ_R: Data 0.34; Model values 0.04, 0.04, 0.20 respectively
  - corr(ca_t/y_t, y_t): Data −0.47; Model values −0.96, −0.62, 0.30
  - corr(R_t, y_t): Data −0.35; Model values −0.19, −0.23, 0.44
  - corr(u_t, y_t): Data −0.85; Model values −0.67, −0.68, −0.57
  - corr(n_{SE,t}, y_t): Data −0.45; Model values −0.45, −0.33, 0.43
  - corr(y_t, y_{t−1}): Data 0.85; Model values 0.72, 0.75, 0.77
  - corr(u_t, u_{t−1}): Data 0.88; Model values 0.81, 0.83, −0.19

### Impulse-response illustrations (Appendix A.4 Figures)
- Figures show model responses (percent deviations from steady state) to:
  - Negative aggregate productivity shock (Figure 1): responses plotted for Total Output, Salaried Output, Self-Employment Output, Investment, Consumption, Capital Supply to SE, Salaried Employment, Self-Employment, Unemployment, Salaried Vacancies, Borrowed Funds, Net Worth; two policy scenarios are illustrated in the figures’ legend: No Policy and Macroprudential Policy.
  - Negative net worth shock (Figure 2): similar set of variables plotted; comparison of No Policy and Macroprudential Policy.
  - Negative aggregate productivity shock — benchmark model with household heterogeneity (Figure 3): same variables plotted with No Policy and Macroprudential Policy comparisons.

*Source: _wp1578 - REFERENCES (Appendix A content and bibliographic references as provided in the source PDF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1578.pdf_