## _wp12237 — 4.1 Calibration ## Source details **Canonical URL:** [_wp12237 — 4.1 Calibration](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12237.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12237.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12237.pdf.json) --- ### Calibration overview - Purpose: set parameter values and steady-state targets for the Small Open Economy model with search-matching frictions (Mexico, quarterly). - Key calibration anchors: average international interest rate, consumption-output ratio, working hours, match break-up rate, steady-state unemployment, vacancy flow cost, capital share, matching elasticity and efficiency, bargaining power. ### Calibration targets and parameter values (explicit) - Average international interest rate = 1.74 percent (average of EMBI yields for Mexico over sample period). - σ = 2. - Consumption-gross output ratio: c*/y* = 0.69. - Working hours l = 0.32. - For endogenous hours case: intertemporal (Frisch) elasticity of labor supply = 1.6 implying ν = 1.42. - Breakup rate ψ = 0.06. - Steady-state unemployment rate u* = 8.21 percent (matches Mexico data for 1988−2006). - Steady-state matches formed m* = (1−u*) ψ = 0.055. - Assumed φ(θ)/θ = 0.7 corresponding to average vacancy duration of 45 days. - Recruiting expenditure to GDP ratio κ v* = 0.01; unit cost κ = 0.01 / v* = 0.127. - Capital share ζ = 0.36. - Labor share implied by parameters = 0.63. - Matching elasticity α set to 0.5 (Andolfatto (1994)); bargaining power ξ set equal to α. - Matching efficiency ω computed from steady state: - ω = m* / (u*^α v*^{1−α}) = 0.687 (table excerpt also reports ω = 0.778 in related calibration listings). - Leisure coefficients excerpt: - φ_U: 1.1599 (coefficient of leisure in utility (employed) calculation). - φ_E (unemployed leisure coefficient) excerpted as 0.1915 in the calibration listing. - Other calibration notes from table excerpts: - ξ = 0.5. - ψ = 0.06. - ω reported in parameter list as 0.778. - r: 1.74 (world interest rate EMBI data). - b: -1/3 steady state bond holdings data. ### Shock processes (TFP and interest rate shocks) - Shocks considered: ε_t ≡ [ε_z_t, ε_r_t]′ with ε_z_t denoting TFP shocks and ε_r_t denoting interest rate shocks. - Joint VAR estimated using Solow residuals and EMBI yields for Mexico (EMBI yields cover 1993Q4:2008Q4). - Interest rate series constructed by deflating dollar-denominated EMBI yields by adaptive U.S. inflation. - Interest rate and TFP shocks correlation = −0.8 (significantly negatively correlated). - VAR representation: - ε_t = RHO · ε_{t−1} + e_t, with - RHO = [ 0.61 −0.17 0.19 0.69 ]. - covar(e_t e_t′) = [ 0.0004 −0.00048 −0.00048 0.0009 ]. - Discretization: Tauchen and Hussey (1991) quadrature procedure used to form transition probability matrix and shock realizations. ### Numerical solution and grids - Solution method: nonlinear value function iterations solving the social planner’s problem to preserve nonlinear dynamics and precautionary saving. - Grids used for discretization of endogenous state variables: - bond grid in [−1.0, 4.0] interval with 200 equidistant nodes. - unemployment grid in [0.02, 0.07] interval with 20 equidistant nodes. - Solution robust to number of nodes; decision rules used with decentralized equilibrium conditions to evaluate wage function. ### Wage determination and Nash bargaining (formulae preserved) - Matching technology: M(u_t, v_t) = ω u_t^α v_t^{1−α}. - Market tightness: θ_t = v_t / u_t. - Job-finding probability: φ(θ_t) = ω θ_t^{1−α}. - Employer vacancy fill probability: φ(θ_t)/θ_t. - Hosios efficiency condition imposed: α = ξ. - Wage formula under Nash bargaining (Equation (10)): - w_t = ξ(F_{l,t} + κ θ_t l_t) + (1−ξ) [φ_U H(1) − φ_E H(1−l_t)] / (l_t U′(c_t)). ### Calibration implications for steady state and intuition - From u* and ψ, steady-state matches m* = 0.055. - Given φ(θ)/θ = 0.7 and κ v* = 0.01, unit recruitment cost κ solves to 0.127. - Matching efficiency ω pinned down to match m*, u*, v* (computed value reported: 0.687; parameter list also shows 0.778 in a table excerpt). - Wage depends on marginal product F_{l,t}, market tightness θ_t, leisure valuations φ_E and φ_U, and marginal utility U′(c_t) — tying consumption dynamics and interest rate shocks to wage determination. ### Key calibration numbers retained (quick list) - r = 1.74 percent. - σ = 2. - c*/y* = 0.69. - l = 0.32. - ν = 1.42 (endogenous hours case implication). - ψ = 0.06. - u* = 8.21 percent. - m* = 0.055. - φ(θ)/θ = 0.7. - κ = 0.127. - ζ = 0.36. - α = ξ = 0.5 (baseline), alternative ξ = α = 0.7 used in sensitivity. - ω reported values: 0.687 (steady-state computation) and 0.778 (parameter table excerpt). - Leisure coefficients: φ_U = 1.1599; φ_E (unemployed) ≈ 0.1915. _Italic source: IMF Working Paper — _wp12237 — section 4.1 Calibration (PDF chapter/section)._ ### 4.1 Calibration ........................................................................................................ ### 4.1 Calibration ### Section structure - 4.1 Calibration ............................................................................................................. 15 - 4.2 Solution: Nonlinear Methods ................................................................................. 17 - 4.3 The Model Dynamics ................................................................................................ 18 - 4.4 Main Findings ............................................................................................................ 20 - Canonical SOE-RBC. ...................................................................................... 20 - Search-Matching Model .................................................................................. 21 - 4.5 Sensitivity Analysis ............................................................................................... 24 - 5 Matching efficiency shocks .................................................................................................. 25 - 6 Conclusion ............................................................................................................................ 28 ### Tables (listed) - Table 1: Real earnings ............................................................................................................. 40 - Table 2: Unemployment Rate and Employment ..................................................................... 41 - Table 3: Hours worked: Manufacturing and Aggregate .......................................................... 42 - Table 4: Calibrated Parameters ................................................................................................ 43 - Table 5: Business Cycle Moments .......................................................................................... 44 - Table 6: Sensitivity Analysis ................................................................................................... 45 - Table 7: Matching Efficiency Shocks ...................................................................................... 46 ### Figures (listed) - Figure 1: Sectoral Decomposition of Employment ................................................................. 47 - Figure 2: Limiting Distributions of Endogenous State Variables ........................................... 48 - Figure 3: Impulse Response Functions: Main Macroeconomic Variables .............................. 49 - Figure 4: Impulse Response Functions: Labor Market Variables ........................................... 50 ### Appendixes - A Data Appendix ..................................................................................................................... 32 - B TFP computation .................................................................................................................. 35 - C Decentralized Economy ....................................................................................................... 36 - D Canonical SOE-RBC ........................................................................................................... 39 ### References - References ............................................................................................................................... 29 *Source: _wp12237 - 4.1 Calibration (PDF chapter/section) — canonical source URL: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12237.pdf* ### Introduction ### Introduction ### Motivation and objective - Recent evidence emphasizes the role of labor markets in understanding macroeconomic dynamics specific to emerging market economies (EMEs) including recovery from financial crises and output fluctuations. - The paper aims to fill a gap in the literature by systematically documenting business cycle properties of key labor market variables (real earnings, unemployment, hours worked) for EMEs and comparing them to developed economies, and by illustrating how interactions between labor markets and exogenous driving forces affect macroeconomic fluctuations in an augmented Small Open Economy Real Business Cycle (SOE-RBC) model. - Main exogenous driving forces considered: Total Factor Productivity (TFP) shocks and countercyclical interest rate shocks (the latter as a proxy of financial conditions). ### Key empirical findings - A striking feature of labor markets in EMEs: fluctuations in prices are large while those in quantities are subdued. - Real wages, on average: - Are almost twice as variable as output. - Have a positive correlation with contemporaneous output of 0.38. - Variability of employment is about half the variability of output. - These regularities contrast with developed economies where: - Variability of wages is lower than that of output (for CPI-based definition). - Wages are less procyclical than in EMEs. - Variability of employment is close to that of output. - Robustness checks and additional empirical statistics: - Median standard deviation of real earnings (CPI-deflated) relative to real output: ratio 1.62. - When compared to manufacturing output (more variable than GDP), median real earning variability relative to manufacturing output falls to 1.0 from 1.62. - Nominal wages behave similarly to real wages in being highly variable. - Using the PPI to calculate real earnings yields similar results. - Unemployment and employment correlations with output: - Median correlation of unemployment with output: −0.46. - Median correlation of employment with output: 0.39. - Median standard deviations relative to standard deviation of output: - Unemployment rate: 9.64. - Employment: 0.58. - Hours worked statistics: - Hours worked in manufacturing normalized by the standard deviation of output has a variability of 1.58. - Aggregate hours worked variability approximated similarly is 1.24. - Correlations with output for manufacturing and aggregate hours: 0.57 and 0.47, respectively. - Statistical significance: - Statistics related to earnings in Table 1 are statistically significantly different for EMEs than developed economies (at 5 percent confidence level) as evidenced by small p-values reported in the source. - Differences in unemployment and employment statistics between groups are less significant, except for the standard deviation of employment relative to output. ### Model features and mechanisms - Labor markets and employer-employee relationships are explicitly modeled; wages are determined by Nash bargaining. - Introduces search-matching frictions à la Mortensen and Pissarides (1994) and Pissarides (2001) into a standard SOE-RBC model. - Workers’ outside option depends on labor market tightness, external wealth, and interest rates; therefore it influences wage determination. - Key propagation mechanisms when TFP shocks and countercyclical interest rate shocks interact with search-matching frictions: - Mechanism 1 (firm recruiting and bargaining power): - A high interest rate that accompanies a negative TFP shock reduces the discounted future return on recruiting. - Decline in employer recruiting efforts leads to higher subsequent unemployment rates. - Firms discount future revenues more heavily, increasing firms’ bargaining power; wages decline more than in a Walrasian labor market. - Mechanism 2 (workers’ outside option and consumption/savings effects): - Higher interest rates during recessions decrease consumption and increase savings. - With labor market frictions and unemployment spells, decline in consumption and rise in savings are amplified due to increased future employment uncertainty and decline in permanent income. - Slackened labor market and fall in consumption reduce the attractiveness of non-market activity and lower workers’ outside option, reducing workers’ bargaining power and putting further downward pressure on wages. - Combined effect yields declines in wages and consumption and increases in savings, bringing model implications in line with EME data. ### Quantitative implications and extensions - The interaction of TFP shocks and countercyclical interest rate shocks with search-matching frictions contributes significantly to the joint behavior of consumption, the current account, and wages observed in EMEs. - The model with search-matching frictions amplifies the effect of countercyclical interest rate shocks and brings implications closer to EME regularities on consumption, current account, and wages without resorting to tight working capital constraints. - Baseline model performance and limitations: - Baseline model performs well for many EME business cycle properties but falls short on accounting for the variability of unemployment (Shimer critique). - Illustrative extension: - Incorporating matching efficiency shocks (motivated by labor market observations during Sudden Stop episodes) can bring model implications for unemployment variability closer to data. - Rationale: Sudden Stops generate large sectoral reallocations and differing skill requirements across sectors, which can reduce aggregate matching efficiency and increase unemployment variability; adding matching efficiency shocks helps account for high wage variability and high unemployment variability observed in the data. ### Contributions to the literature - Connects emerging market business cycles literature and search-matching literature by: - Documenting EME labor market stylized facts (especially high real wage variability and subdued quantity variability). - Proposing a labor-market-based amplification/transmission mechanism through search-matching frictions that interacts with TFP and countercyclical interest rate shocks. - Complements earlier EME studies (e.g., Neumeyer and Perri (2005), Uribe and Yue (2006), Aguiar and Gopinath (2007)) by offering an alternative channel—search-matching frictions—through which external shocks affect consumption, real wages, and current account fluctuations, and by doing so without relying on large working capital constraints. - Positions the model as a first-generation MP-type SOE model with Nash bargaining applicable to both existing workers and new hires; notes potential for extensions (heterogeneous agents, endogenous job separation, alternative bargaining concepts) for policy analyses. ### Organization of the paper - Section 2: Documents business cycle properties of key labor market variables for EMEs and developed economies, and provides empirical motivation for matching efficiency shocks. - Section 3: Lays out the model. - Section 4: Explains calibration, solution, and main quantitative findings. - Section 5: Extends the model to analyze matching efficiency shocks. - Section 6: Concludes. *Source: _wp12237 - Introduction* ### 1.77 percent). It is difficult to argue that the public sector employment does not function as ### 3 A Small Open Economy Model with Search-Matching Frictions ### Informal sector, data coverage, and empirical context - OECD (2008) reports that the informal sectors in Hungary, Korea, Mexico and Turkey are quite substantial with the number of employees in informal jobs reaching or exceeding 20 percent of total non-farm employment in all four countries. - These informal-sector ratios appear to be larger than those for the developed small open economies. - For Mexico and Turkey, OECD (2008) documents earnings distributions for formal and informal sectors: - Mexico: standard deviation of earnings in the formal sector is 0.89; in the informal sector is 1.13. - Turkey: standard deviation of earnings in the formal sector is 0.54; in the informal sector is 0.90. - Implication: If the informal sector were included in the earnings analysis, the contrast between EMEs and developed economies would be stronger. - Data coverage comments: - Some EME quantity series (employment, unemployment rate) are constructed from household surveys and thus capture the informal sector. - Earnings data are based on establishment surveys and therefore do not include the informal sector. ### Model setup: agents, matching technology, and market tightness - Framework: labor market search-matching friction nested into a standard SOE-RBC model with an infinitely-lived representative household (employed and unemployed members) and a continuum of identical competitive firms. - Matching technology: M(u_t, v_t) = ω u_t^α v_t^{1−α}, where ω governs matching efficiency, u_t is the unemployment rate, and v_t are vacancies. - Market tightness: θ_t = v_t / u_t. - Vacancy flow cost: κ. - Job finding probability for a searching worker: φ(θ_t) = M(u_t, v_t)/u_t = ω θ_t^{1−α}. - Employer vacancy fill probability: M(u_t, v_t)/v_t = φ(θ_t)/θ_t. - Exogenous match breakup rate: ψ. - Household: large extended family (income pooling) implying planner representation; later decentralized economy wages determined by Nash bargaining. - International bond: one-period, non-state-contingent; interest rate on international bond holdings is exogenous and subject to shocks; financial markets incomplete for hedging aggregate TFP and interest rate shocks. - Aggregate state variables: endogenous {b_t, u_t} and exogenous ε_t = [ε_z_t, ε_r_t] with ε_z_t denoting TFP shocks and ε_r_t denoting interest rate shocks. ### Preferences, production, and labor supply - Utility: - Consumption utility: U(c_t) = c_t^{1−σ}/(1−σ). - Leisure utility: H(1−l_t) = (1−l_t)^{1−ν}/(1−ν). - Per-period utility: U(c_t) + φ_i H(1−l_t), i = E, U for employed and unemployed respectively. - σ denotes CRRA coefficient; 1/ν governs Frisch elasticity of labor supply. - Production: y_t = F[k, (1−u_t) l_t, z_t] = z_t k^ζ [(1−u_t) l_t]^{1−ζ}, where ζ is capital share and z_t = (1 + ε_z_t) z. - Labor indivisibility initially: l_t = l. Extension later endogenizes working hours. - Capital: time-invariant with zero depreciation (to permit global solution by containing state space). ### Social planner’s problem and first-order conditions - State-contingent plan chooses {c_t, b_{t+1}, u_{t+1}, v_t} to maximize: V(b_t, u_t, ε_t) = max_{c_t,b_{t+1},u_{t+1},v_t} U(c_t) + (1−u_t) φ_E H(1−l_t) + u_t φ_U H(1) + β(c_t) E_t V(b_{t+1}, u_{t+1}, ε_{t+1}) subject to: - c_t + b_{t+1} + κ v_t ≤ F(k, (1−u_t) l_t, z_t) + b_t (1 + r_t), - u_{t+1} ≥ [u_t − M(u_t, v_t)] + (1−u_t) ψ, - b_{t+1} ≥ B̄. - Endogenous discount factor for stationarity: β(c_t) = (1 + c_t)^{−γ}. - First-order conditions (optimal choices): - U′(c_t) − μ_t = β(c_t) E_t U′(c_{t+1}) (1 + r_t). (Equation (2)) - U′(c_t) κ = β(c_t) M_{v,t} E_t [ − ∂V(b_{t+1}, u_{t+1}, ε_{t+1}) / ∂u_{t+1} ]. (Equation (3)) - M_{v,t} = (1−α) φ(θ_t)/θ_t. - Envelope condition: surplus from marginal job match: S_t = − ∂V(b_t, u_t, ε_t)/∂u_t = φ_E H(1−l_t) − φ_U H(1) + U′(c_t) F_{l,t} l_t + (1−ψ−M_{u,t}) β(c_t) E_t S_{t+1}, where M_{u,t} = α φ(θ_t). (Equation (4)) ### Wage determination via Nash bargaining - Employer payoff dynamics under free entry: - Recruiting cost equality: κ = φ(θ_t)/θ_t E_t ρ_{t,t+1} J_{t+1}. (Equation (5)) - Transition equation for J_t: J_t = π_t + (1−ψ) E_t ρ_{t,t+1} J_{t+1}, where π_t = F_l(k_t n_t, l_t; z_t) l_t − w_t l_t. (Equation (6)) - Combining yields J_t = F_{l,t} l_t − w_t l_t + (1−ψ) κ θ_t / φ(θ_t). (Equation (7)) - Nash bargaining with worker bargaining power ξ ∈ (0,1): - Joint surplus: J_t U′(c_t) + E_t − U_t = S_t. - Nash solution: J_t = (1−ξ) S_t / U′(c_t). (Equation (8)) - Combining (4) and (8) and imposing Hosios efficiency condition α = ξ yields wage: - w_t = ξ(F_{l,t} + κ θ_t l_t) + (1−ξ) [φ_U H(1) − φ_E H(1−l_t)] / (l_t U′(c_t)). (Equation (10)) - Interpretation: - Wage depends on marginal product F_{l,t} and the value of unemployment/search. - ξ κ θ_t l_t term captures forward-looking expected value of reentering the job market (Equation (11)). - Falling consumption raises marginal utility U′(c_t), reducing the consumption-valued marginal utility of leisure and making workers accept lower wages. - Higher interest rates reduce the value of matches and increase firms’ bargaining power, putting downward pressure on wages. ### 4 Quantitative Analysis — Calibration - Calibration targets and parameter values (Mexico, quarterly): - Average international interest rate = 1.74 percent (average of EMBI yields for Mexico over sample period). - σ = 2. - Consumption-gross output ratio: c*/y* = 0.69 (model has no investment or government spending; subtract fixed amount 1−0.69 from budget constraint to capture those shares). - Working hours l = 0.32 (OECD Annual Hours and Productivity data: average worker in Mexico spent 32 percent of non-sleeping time on market activities). - For endogenous hours case: intertemporal (Frisch) elasticity of labor supply = 1.6 implying ν = 1.42 given utility and working hours. - Breakup rate ψ = 0.06 (based on Bosch and Maloney (2008) range for Mexico). - Steady-state unemployment rate u* set to 8.21 percent to match Mexico data for 1988−2006. - From u* and ψ, steady-state matches formed m* = (1−u*) ψ = 0.055. - Assumed φ(θ)/θ = 0.7 corresponding to average vacancy duration of 45 days. - Recruiting expenditure to GDP ratio κ v* = 0.01; unit cost κ = 0.01 / v* = 0.127. - Capital share ζ = 0.36. - Labor share expression implied by parameters equals 0.63, close to (1−ζ). - Matching elasticity α must equal bargaining power ξ; set α = 0.5 (Andolfatto (1994)). - Calculated matching efficiency ω using steady-state condition: ω = m* / (u*^α v*^{1−α}) = 0.687. - Remaining parameters φ_E and φ_U jointly determined by efficiency condition of labor hours and optimality condition for unemployment. ### Shock processes (TFP and interest rate shocks) - Benchmark shocks: TFP shocks (ε_z) and interest rate shocks (ε_r) as in Neumeyer and Perri (2005) and Uribe and Yue (2006). - Joint VAR estimated using Solow residuals and EMBI yields for Mexico; EMBI yields cover 1993Q4:2008Q4. - Interest rate series constructed by deflating dollar-denominated EMBI yields by adaptive U.S. inflation. - Interest rate and TFP shocks are significantly negatively correlated with correlation −0.8. - VAR shock representation: - ε_t = RHO · ε_{t−1} + e_t, with ε_t ≡ [ε_z, ε_r]′. - RHO = [ 0.61 −0.17 0.19 0.69 ]. - covar(e_t e_t′) = [ 0.0004 −0.00048 −0.00048 0.0009 ]. - Discretization: transition probability matrix and shock realizations obtained using Tauchen and Hussey’s (1991) quadrature procedure and fed into the model. *Source: IMF working paper content (sections 3–4 excerpt).* ### 4.2 Solution: Nonlinear Methods ### 4.2 Solution: Nonlinear Methods ### Solution method and numerical implementation - Solve for the recursive competitive equilibrium using value function iterations to preserve nonlinear dynamics and capture precautionary saving. - Nonlinear solution requires a relatively stylized model due to curse of dimensionality. - First step: solve the social planner’s problem (Equation (1)) using discretization: - bond grid in [-1.0, 4.0] interval with 200 equidistant nodes - unemployment grid in [0.02, 0.07] interval with 20 equidistant nodes - Solution robust to the number of nodes used in each grid. - After deriving decision rules, use decentralized equilibrium conditions to evaluate the wage function. - Solution delivers ergodicity in bond holdings and unemployment distributions. ### Model dynamics and impulse-response scenarios - Impulse responses shown for three shock scenarios in the baseline search-matching model: - negative one-standard-deviation TFP shock (dashed line) - positive one-standard-deviation interest rate shock (dash-dotted line) - both shocks simultaneously (solid line) - Shock correlation setups: - individual shock scenarios: corr(ez_t, er_t)=0 - joint-shock scenario: corr(ez_t, er_t)<0 (as in baseline calibration) - Responses to a negative TFP shock: - firms reduce vacancies, leading to fewer matches and higher unemployment (predetermined by previous period) - equilibrium wage drops - output falls on impact due to lower productivity - households borrow internationally and accumulate debt to smooth consumption - incomplete markets prevent full offset of output decline, so consumption decreases and economy runs a current account deficit - TFP shocks alone cannot account for volatile consumption relative to output and strongly countercyclical current account - Responses to a positive interest rate shock: - households increase savings; current account to GDP ratio increases - higher interest rates make current consumption more expensive relative to future (Equation (2)), so consumers postpone consumption - search-matching frictions amplify saving because lower future employment prospects and large fall in wages boost incentives to save - economy runs a large current account surplus and consumption drops significantly (by six percent) on impact - decline in output is minuscule because TFP unchanged and unemployment increases only marginally - labor market: decline in recruiting, lower job-finding rate, slacker labor market, higher unemployment; firms discount future revenues more and gain bargaining power, pushing wages down - Joint TFP and interest rate shocks: - interest rate shock effect on savings dominates borrowing motive from TFP shock - interaction with search frictions produces higher volatility of consumption relative to output and a strongly countercyclical current account - labor market frictions increase precautionary saving motive and persistence because new matches take time to form; lower lifetime income and stronger precautionary saving amplify consumption fall ### Main findings (model comparisons and statistics) - Baseline empirical regularities for Mexico preserved in data: consumption more variable than income; current account-output ratio strongly countercyclical; wage procyclical and more variable than income; unemployment countercyclical and highly variable. - Canonical SOE-RBC (with GHH preferences): - falls short on EME regularities for consumption and current account - consumption is less variable than output and current account to GDP ratio weakly countercyclical (correlation with output equals−0.13 compared with−0.75 in the data) - yields σ(w)/σ(y)=0.31 and wages perfectly correlated with output - Baseline search-matching model with TFP and countercyclical interest rate shocks: - generates consumption more variable than income - produces wage fluctuations more variable than income - yields a strongly countercyclical current account (correlation of current account with output is−0.46) - main discrepancy: unemployment displays considerably less movement (standard deviation equals 3.24 in the model compared to 14.70 in the data) - Scenario “Only Prod” (only TFP shocks): - consumption less variable than output (ratio σ(c)/σ(y)=0.79) - current account procyclical (correlation with output equals 0.97) - wage variability low: σ(w)/σ(y)=0.83 (compared to 2.22 in the data) - Scenario “Only interest rate shocks”: - interest rate shocks generate higher variability for labor market variables and consumption - output movements are negligible, so σ(y) very small (consumption standard deviation relative to output not reported) - can produce countercyclical vacancies and slightly procyclical unemployment when isolated (reported ρ(y, u) = 0.10, which is actually ρ(y_t, u_{t+1})) - autocorrelation reported: ρ(u, u−1) =−0.10 - Endogenous labor extension: - search-matching model with endogenous labor hours shows consumption declines more for same shocks than canonical RBC - search frictions strengthen precautionary saving and lower expected lifetime income via endogenous persistence - current account becomes more countercyclical in the search model (ρ(y, ca/y) =−0.56) - wages substantially more variable in search-matching model due to combined effects on workers’ outside option and firms’ expected return from a match - model delivers a negative unemployment–vacancy correlation consistent with the Beveridge Curve ### Mechanisms driving results - Two channels for higher wage variability in presence of countercyclical interest rates and TFP shocks: - Firms’ channel: high interest rate + negative TFP reduces discounted future return to recruiting → decline in recruiting efforts → higher unemployment → firms have more bargaining power → larger wage decline. - Workers’ channel: consumption falls and saving rises during downturns (amplified by search frictions) → non-market activity less attractive → workers’ outside option falls and bargaining power declines → wages fall further. - Search-matching frictions are key to: - strengthening precautionary saving motive - increasing persistence (matches take time to form; unemployment declines gradually) - producing a larger decline in consumption and a more countercyclical current account than canonical SOE-RBC _Italic source: IMF Working Paper — section 4.2 (Solution: Nonlinear Methods) and related text._ ### 4.5 Sensitivity Analysis ### 4.5 Sensitivity Analysis ### Sensitivity experiments on search-matching parameters - Baseline focus: parameters related to search-matching frictions. Results summarized in Table 6 (as referenced in source). - Experiment 1 — lower vacancy posting cost κ: - κ reduced from 0.127 to 0.1. - Lower firm search cost → more vacancies posted one period after a negative TFP shock → more rapid reversion of vacancy and unemployment. - Households build less savings because the prospect of searching next period is less adverse → consumption drops less and the current account does not increase as much. - Workers’ threatening point of wage bargaining increases (higher job-finding probability and higher value of leisure in consumption terms) → wage variability relative to output becomes lower. - Experiment 2 — higher natural separation rate ψ: - ψ raised from 6 percent to 8 percent. - Higher ψ decreases the continuation value of being employed (shorter employment duration) and reduces firms’ continuation value of posting a vacancy. - Total surplus from a new match decreases → vacancy responds less to exogenous shocks → unemployment rate becomes less responsive. - Vacancy and unemployment become less variable and more persistent compared to benchmark. - Variabilities of consumption and wage decline, consistent with a slightly more stable labor market. - Experiment 3 — higher matching efficiency ω: - ω raised to 0.85 from 0.778. - More matches for the same pair (u, v) → search friction less severe. - Both consumption and wage become less variable and the current account becomes weakly countercyclical. - Extreme case (matching infinitely efficient): probability of finding a job and filling a vacancy is close to one; unemployed worker still experiences a necessary unemployment spell but only for one period → vacancy and unemployment revert quickly, increasing their variability and reducing unemployment risk. - Faster reversion reduces household need to cut consumption after a negative TFP shock → lower wage reduction due to increased bargaining power. - Experiment 4 — higher workers’ Nash bargaining weight ξ (and corresponding α change): - ξ and α increase from 0.5 to 0.7. - Unemployment rate varies less while vacancy varies more because matching is more sensitive to unemployment and less to vacancy. - Wage determination (Equation (10) referenced): higher workers’ bargaining power moves equilibrium wage closer to the maximum value to a firm of a filled vacancy and further from the minimum necessary for an unemployed worker to join employment. - Overall conclusion from sensitivity exercises: - Results are generally robust to changes in key search-matching parameters. - MP type search frictions appear to better characterize labor markets of EMEs than Walrasian labor markets. ### Matching efficiency shocks (section 5 content included) - Extension: introduce random disturbance ε^ω_t to matching efficiency ω_t such that: - M_t = ω_t u_t^α v_t^(1−α), ω_t = (1 + ε^ω_t) ω. - Economic interpretation: - Fluctuations in ω_t affect number of matches formed for given u_t and v_t. - Matching efficiency shocks capture structural changes, cross-sectoral reallocations, and sectoral segmentation in emerging economies. - Empirical motivation: Sudden Stop episodes often generate costly reallocations across tradable and nontradable sectors (examples noted: Mexico 1994-1995; Chile 1981-84, 1998-99; Colombia 1998-99). - Calibration strategy for matching efficiency shocks (as described): - Standard deviation of the innovation to the matching efficiency shock set to be 10 percent. - Persistence parameter set to 0.6. - Correlation with the innovation to TFP set to 0.5. - ρ_ω and var(e_ω) pinned down to match σ(u) and ρ(y, u). - Other VAR ingredients involving the matching efficiency shock set to zero. - Scenarios analyzed (results reported in Table 7 as referenced): - Column 1: baseline scenario (copied). - Column 2: matching efficiency shocks positively correlated with TFP. - When matching efficiency is low during low TFP, unemployment is eliminated more slowly → more persistent unemployment. - Autocorrelation of unemployment becomes 0.31 versus baseline 0.10. - Variability for unemployment and vacancy become 16.24 and 14.56 compared to baseline 3.24 and 5.59, respectively. - Firms cut vacancies significantly when matching efficiency is low because match probability falls while vacancy cost is constant → vacancies fall dramatically → higher unemployment with one period lag. - Column 3: matching efficiency shocks uncorrelated with TFP. - Main significant difference: correlation of unemployment with output becomes closer to zero (decoupling of matching process from TFP). - Mechanism and implications: - Given steady state unemployment ≈ 8 percent and fixed other factor inputs, a one percentage point rise in unemployment rate leads to only a 0.056 percentage decrease of output (about one twentieth the size of the change in unemployment). - Matching efficiency shocks can generate high relative variability of unemployment (relative to output) without significantly affecting variability of output and consumption. - Empirical and literature notes: - Direct measures of new hires and vacancy rates do not exist for EMEs, making estimation of matching efficiency shocks infeasible with available data. - Andolfatto (1996) (U.S. calibration) found innovations to matching shocks almost ten times those to technology shocks and positive correlation between the two; this motivates exploring positively correlated matching efficiency shocks. - When matching function degenerates to M(u, v) = min(u, v) and u and v do not deviate substantially, probability of finding a job or filling a vacancy approaches one (footnote discussion). ### Quantitative effects and key statistics (preserved exact values and comparisons) - κ: 0.127 → 0.1 (experiment 1). - ψ: 6 percent → 8 percent (experiment 2). - ω: 0.778 → 0.85 (experiment 3). - ξ and α: 0.5 → 0.7 (experiment 4). - Matching efficiency shock calibration: - standard deviation of innovation = 10 percent. - persistence = 0.6. - correlation with TFP innovation = 0.5. - Baseline vs. positively correlated matching efficiency shock scenario: - Autocorrelation of unemployment: baseline 0.10 → scenario 0.31. - Variability of unemployment: baseline 3.24 → scenario 16.24. - Variability of vacancy: baseline 5.59 → scenario 14.56. - Output response to unemployment change: a one percentage point rise in unemployment leads to a 0.056 percentage decrease of output. ### Conclusion (sections 5–6 synthesis) - A SOE-RBC model with countercyclical interest rate shocks and search-matching frictions can account for dynamics of consumption, the current account, and wages simultaneously. - Augmenting the baseline model with matching efficiency shocks brings unemployment variability significantly closer to data. - The interaction between countercyclical interest rates and labor market frictions is important for understanding labor market dynamics and other business cycle features in EMEs. - Framework is amenable to extensions to study political regime changes, labor market regulation, and other issues affecting emerging market labor markets. *Source: IMF working paper content unit _wp12237 - 4.5 Sensitivity Analysis (extracted sections on sensitivity analysis, matching efficiency shocks, and conclusion).* ### References ### _wp12237 - References ### References - [1] Aguiar, Mark and Gita Gopinath (2007), “Emerging Market Business Cycles: The Cycle is the Trend,”Journal of Political Economy, Vol. 115(1), pp 69-102. - [2] Arellano, Cristina, (2008), “Default Risk and Income Fluctuations in Emerging Economies,” American Economic ReviewVol. 98(3), 690-712. - [3] Andolfatto, David (1996), “Business Cycles and Labor-Market Search,”American Economic Review, Vol. 86(1), pp 112-132. - [4] Benjamin, David and Felipe Meza (2008), “Total Factor Productivity and Labor Reallocation: the Case of the Korean 1997 Crisis,” Discussion Paper Series In Economics And Econometrics No. 0701, University of Southampton. - [5] Bergoeing, Raphael, Patrick J. 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(2001) “Equilibrium Unemployment Theory,” 2nd ed., Cambridge, MA: MIT Press. - [32] Pissarides, Christopher A. (1985) “Short-Run Equilibrium Dynamics of Unemployment, Vacancies, and Real Wages,”American Economic Review, Vol. 75(4), pp. 676-690. - [33] Schmitt-Grohe, S and M. Uribe (2003) “Closing Small Open Economy Models”,Journal of International Economics, Vol.61, pp 163-185. - [34] Uribe, Martin and Vivian Z. Yue (2006), “Country Spreads and Emerging Countries: Who Drives Whom?,”Journal of International Economics, Vol 69, pp 6-36. ### Data Appendix (sample, detrending, and data sources) - Sample period: 1976-2007. - Detrending: HP filter with smoothing parameter of 1600. - Deseasonalization: U.S. Census Bureau’s X-12 for series that seemed to have seasonality. - GDP: All data from the International Financial Statistics (IFS). Countries with full-sample data: Australia, Austria, Canada, Finland, France, Israel, Japan, Korea, Norway, Spain, Sweden. Countries with shorter samples: Belgium [1980], Brazil [1991], Chile [1980], Denmark [1977], Ecuador [1991], Hungary [1995], Ireland [1997], Malaysia [1988], Mexico [1980], the Netherlands [1977], New Zealand [1982Q2], the Philippines [1981], Portugal [1977], Turkey [1988]. - Manufacturing Output: Real manufacturing output from Haver Analytics. Full-sample: Australia, Austria, Chile, Norway, Spain. Shorter-sample availability examples: Belgium [1990], Brazil [1991], Canada [1981], Denmark [1985], Ecuador [1990], Finland [1995], Hungary [1997], Ireland [1980], Israel [1990], Mexico [1980], New Zealand [1987Q2], Philippines [1998], Portugal [2000], Sweden [2000], Turkey [1985]. - Aggregate Hours, Manufacturing Hours, Employment: - Hours worked data available only for the manufacturing sector. - Aggregate hours approximated by (hours worked per worker in manufacturing) × (total employment). - Country-specific notes (selection): - Australia, Austria, Canada, Finland, Japan: All series from OECD, available for entire sample. - Brazil: Monthly hours in manufacturing from OECD [1992]; 1987Q1-1991Q4 calculated using Confederation of Industries; civilian employment from Neumeyer and Perri (2005) for 1991-2002; 2003-2007 extrapolated using “formal employment” series from Ministerio do Trabalho e Emprego (MTE). - Chile, Malaysia, The Netherlands, Philippines: No hours-worked data; employment from IFS with various start dates: Netherlands [1984], Chile [1983Q3], the Philippines [1992], Malaysia [1998]. - Ecuador: No hours-worked data; employment short in quarterly frequency (IFS only for 2000-2003) and thus not included in employment statistics. - Hungary: All series from OECD; hours worked per worker in manufacturing from 1984; civilian employment and manufacturing employment from 1992. - Ireland: Weekly hours in manufacturing per worker from OECD (entire sample); number of employees in manufacturing starts 1998, so total manufacturing hours calculable only from 1998. - Israel: Hours in manufacturing from ILO covering entire sample (series named weekly hours actually worked in non-agricultural activities per worker); employment from IFS [1992]; number of employees in manufacturing not available. - Korea: Monthly hours in manufacturing from OECD [1993]; employment data from Korean Statistical Institute [1976]. - Mexico: Employment from Neumeyer and Perri (2005) covering 1987-2001; monthly hours in manufacturing from INEGI [1980] and OECD [1987]; OECD series is an index (2000=100) used in hours-worked statistics; INEGI series in units of hours used to compute approximate aggregate hours; manufacturing employment from INEGI [1987]. - New Zealand: Hours in manufacturing from ILO [1980]; employment from OECD [1985Q4]. - Norway, Sweden: OECD series available for entire sample except manufacturing hours starting 1988Q2 (Norway) and 1987 (Sweden). - Turkey: Total manufacturing hours from OECD [1977]; manufacturing employment and total employment from TURKSTAT [1988Q4] semi-annual in 1988Q4-1999Q4 and quarterly afterwards; semi-annual series interpolated to quarterly via linear interpolation. - Unemployment Rate sources: - From OECD: Austria [1976], Belgium [1976], Brazil [1981], Canada [1976], France [1976], Japan [1976], Korea [1976], Mexico [1987], the Netherlands [1987], Norway [1986], Sweden [1976], Turkey [1976]. - From the Economist Intelligence Unit: Australia [1993], Chile [1993], Ecuador [1998], Finland [1993], Hungary [1994], Ireland [1997Q4], Israel [1996], Malaysia [1998], New Zealand [1993], the Philippines [1993], Spain [1993]. - Earnings: - From OECD: Brazil and Mexico earnings reported both in real and nominal terms; other countries’ earnings deflated by corresponding countries’ CPI. - Coverage: Full-sample for Canada, Denmark, Finland, Germany, Ireland, Japan, Norway, Sweden. Other availability varies: Australia [1983Q4], Belgium [1996], Brazil [1989], France [1996], Hungary [1995], Korea [1992], Mexico [1980], New Zealand [1987], Spain [1981], Turkey [1990]. Nominal earnings for Brazil and Mexico start in 1994Q3 and 1980Q1, respectively. - From ILO: Chile [1982], Israel [1985], the Philippines [2001]. - From IEO: Ecuador [1993]. - Prices: - All CPI data used to deflate earnings from IFS; available for entire sample except Brazil [1980]. - PPI data from Haver Analytics. Full-sample for Australia, Canada, Korea, Spain, Sweden. Other availability varies with country-specific start dates (examples provided in source). ### TFP computation (methodology and parameters) - Production function assumed: Y_t = K_t^α (h_t L_t)^{1−α} A_t. - Capital stock constructed via perpetual inventory: - Law of motion: K_{t+1} = K_t (1−δ) + I_t. - Depreciation rate δ set equal to 0.07. - Initial capital-output ratio in steady state: k = i / (g + δ), where i is steady-state investment-output ratio and g is steady-state growth rate. - Annual investment data from Penn World Tables, version 6.2. - i approximated by country’s average investment-output ratio in the first ten years of the sample. - g approximated by weighted average between world growth (75 percent) and the country’s average growth in the first ten years of the sample. - Initial capital level K_0 obtained by multiplying the three-year average output at the beginning of the sample. - Labor and human capital: - Labor from Penn World Tables (real GDP per worker and real GDP (chain) series). - Human capital h_t constructed as h = e^{φ(E)}, with φ(0) = 0 and φ′(E) equal to the Mincerian return to schooling. - Assumed returns to schooling (same for all countries): 13.4 percent for the first four years, 10.1 percent for the next four, and 6.8 percent for all years above eight years (following Psacharopoulos, 1994). - Years of schooling from Barro-Lee database; linear extrapolations used to complete five-year data. - Output per worker relation: - Y_t / L_t = (K_t / L_t)^α h_t^{1−α} A_t. - Log TFP computed as: ln(A_t) = ln(Y_t) − ln(L_t) + α(ln(k_t) + ln(L_t)) + (1−α) ln(h_t). ### C. Decentralized Economy (search-matching and Nash bargaining) - Setting: Decentralized world where wage sequence determined by Nash Bargaining between workers and firms. Markets for aggregate shocks incomplete; households may partially insure via precautionary savings. - Externalities: - Positive externality for searching workers when firms post more vacancies. - Negative externality for firms as vacancies increase. - Individual household takes hiring probability M/u = φ(θ) as given; firm takes probability of filling vacancy M/v = φ(θ)/θ as given. - Household problem and marginal value of employment: - V_Ht denotes value of representative household at period t. - Value of being employed: E_t; value of being unemployed and searching: U_t. - Relationship: −∂V_Ht/∂u_t = E_t − U_t. (Equation (13)) - Household optimization problem (choice variables c_t, b_{t+1}) subject to budget and employment law of motion; borrowing constraint b_{t+1} ≥ B̄. - Envelope condition expressed for −∂V_Ht/∂u_t including terms φ_E H(1−l) − φ_U H(1) + U′(c_t) w_t l, and continuation terms with β(c_t)E_t. - Firms: - Firms owned by households; discount factor ρ_{t,t+1} = β(c_t) U′(c_{t+1})/U′(c_t). - Firms maximize V_F(u_t, ε_t) over vacancies v_t and subsequent u_{t+1} subject to employment law of motion. - Envelope theorem gives job-creation condition and first-order condition w.r.t. v_t leading to κ = [φ(θ_t)/θ_t] E_t ρ_{t,t+1} ∂V_F(u_{t+1}, ε_{t+1})/∂u_{t+1}. (Equation (14)) - Marginal value of filling a position: −∂V_F/∂u_t = F_{2,t} l_t − w_t l_t + E_t ρ_{t,t+1} ∂V_F(u_{t+1}, ε_{t+1})/∂u_{t+1} (1−ψ). - Define J_t as value of filling a position and Q_t as value of posting a vacancy: −∂V_F/∂u_t = J_t − Q_t. (Equation (15)) - Nash Bargaining: - Employed workers’ bargaining power ξ ∈ (0,1). - Nash problem: max_{w_t} (E_t − U_t)^ξ (J_t − Q_t)^{1−ξ}. - Implication: J_t − Q_t = (1−ξ)/ξ (E_t − U_t)/U′(c_t). (Equation (16)) - Combining equations yields wage formula: w_t = ξ(F_{2,t} + κ θ_t l) + (1−ξ) [φ_U H(1) − φ_E H(1−l)] / [l U′(c_t)] which is the same as Equation (10) in the main text. ### D. Canonical SOE-RBC (social planner representation and calibration) - Recursive social planner’s problem: - V(b_t, ε_t) = max_{c_t, b_{t+1}} u(c_t, l_t) + β(c_t) E_t V(b_{t+1}, ε_{t+1}) - Subject to c_t + b_{t+1} ≤ F(k, l_t, z_t) + b_t (1 + r_t), and b_{t+1} ≥ B̄. - Per-period utility: GHH form u(c_t, l_t) = (c_t − χ l_t^η)^{1−σ} / (1−σ). - η captures labor supply elasticity parameterized via 1/(η−1). - Parameter choices: - Use same preference-related parameters as baseline search-matching model (as documented in Table 4 of the source). - Additional parameter η set to 1.6 following Mendoza (1991) and Aguiar and Gopinath (2007). - Shocks: Same TFP and interest rate shocks as in baseline search-matching framework. ### Selected empirical tables and summary statistics (as reported) - Table 1: Real earnings (selected aggregate statistics) - Emerging Markets mean: 4.64 2.06 0.32 1.18 4.23 5.36 0.16 - Emerging Markets median: 3.68 1.62 0.38 1.00 3.16 4.76 0.09 - Developed Markets mean: 1.19 0.84 0.04 0.45 1.23 2.50 -0.36 - Developed Markets median: 1.54 0.96 0.13 0.46 1.28 2.40 -0.28 - Notes: Table shows standard deviation of real earnings, ratio to output sd, correlation with output, ratio to manufacturing output sd, sd of nominal earnings, sd of real earnings using PPI, and correlation of PPI-based real earnings with output. All series HP-filtered with smoothing parameter 1600. Numbers in parenthesis report p-values for tests of equality of means and medians. - Table 2: Unemployment rate and employment (selected aggregate statistics) - Emerging Markets mean: 11.40 4.92 -0.41 1.42 0.64 0.39 - Emerging Markets median: 9.64 4.43 -0.46 1.26 0.58 0.39 - Developed Markets mean: 8.89 6.56 -0.33 1.25 0.91 0.47 - Developed Markets median: 9.06 6.31 -0.32 1.24 0.88 0.46 - Notes: Table shows standard deviation of unemployment rate, ratio to output sd, correlation with output, and analogous statistics for employment. All series HP-filtered with smoothing parameter 1600. Numbers in parenthesis report p-values for tests of equality of means and medians. - Table 3: Hours worked: manufacturing and aggregate (selected aggregate statistics) - Emerging Markets mean: 3.12 1.51 0.50 2.95 1.23 0.32 - Emerging Markets median: 3.42 1.58 0.57 2.35 1.24 0.47 - Developed Markets mean: 2.72 1.97 0.57 1.79 1.29 0.55 - Developed Markets median: 2.98 1.96 0.68 1.70 1.24 0.65 - Notes: Table shows standard deviation of manufacturing hours, ratio to output sd, correlation with output, and analogous statistics for aggregate hours. All series HP-filtered with smoothing parameter 1600. Numbers in parenthesis report p-values for tests of equality of means and medians. - Table 4: Calibrated Parameters (header and partial entries) - Parameter list begins; example entries: - β = 0.983 steady-state discount factor inverse of gross real interest rate - ν = 3.54 elasticity of leisure Frisch elasticity of labor supply is 0.6 - (Table continues in source with full calibration; only excerpted here.) *Italic: IMF Working Paper content unit: _wp12237 - References* ### 1.1599 coefficient of leisure in utility (employed)calculation ### 1.1599 coefficient of leisure in utility (employed)calculation ### Calibration and parameter values - Leisure coefficients: - φ_U: 1.1599 coefficient of leisure in utility (employed)calculation - 0.1915 coefficient of leisure in utility (unemployed) calculation - Production Technology: - z: total factor productivity normalization - ζ: 0.36 capital’s share in output literature - Search Technology: - ω: 0.778 matching efficiency ω = m* u*^α v*^(1−α) - α: 0.5 elasticity of matching function Petrongolo and Pissarides (2001), Shimer (2004) - κ: 0.127 unit cost of posting vacancy recruiting expenditure as 1% of GDP - ψ: 0.06 natural breakup rate Bosch and Maloney (2008) - ξ: 0.5 bargaining power the same as α - Other: - r: 1.74 world interest rate EMBI data - b: -1/3 steady state bond holdings data - Notes: "This table shows the parameter values used in the analysis." ### Business cycle moments (Table 5) — comparison across models - Description: Columns show moments in the data, RBC (with productivity and countercyclical interest rate shocks; Walrasian labor markets), baseline search-matching model (both TFP and countercyclical interest rate shocks), search-matching only with TFP shocks, and search-matching only with interest rate shocks. The RBC model features a GHH preference; search-matching model features a time-separable CRRA preference. - Key statistics (preserve exact values as listed): - Standard Deviation: - σ(u): 14.70 (Data); n.a. (RBC); 3.24 (Baseline); 2.10 (Only Prod); 3.04 (Only Int Rate); 5.47 (Endog Labor) - σ(v): n.a.; n.a.; 5.59; 3.90; 5.51; 10.3 - σ(θ): n.a.; n.a.; 17.53; 10.34; 15.62; 26.8 - σ(w)/σ(y): 2.22; 0.31; 1.67; 0.83; n.a.; 1.81 - σ(c)/σ(y): 1.26; 0.78; 1.35; 0.79; n.a.; 1.55 - Correlation with y: - ρ(y, ca/y): −0.75 (Data); −0.13; −0.46; 0.97; −0.09; −0.56 - ρ(y, u): −0.78; n.a.; −0.68; −0.26; 0.10; −0.44 - ρ(y, v): n.a.; n.a.; 0.51; 0.16; −0.41; 0.27 - ρ(y, w): 0.56; 1.00; 0.83; 0.82; 0.01; 0.73 - ρ(y, θ): n.a.; n.a.; 0.77; 0.33; 0.16; 0.59 - ρ(u, v): n.a.; n.a.; −0.94; −0.96; −0.95; −0.96 - Autocorrelation: - ρ(c): 0.70; 0.75; 0.60; 0.87; 0.56; 0.64 - ρ(y): 0.75; 0.64; 0.63; 0.67; 1.00; 0.65 - ρ(ca/y): 0.72; 0.41; 0.45; 0.65; 0.45; 0.42 - ρ(u): 0.84; n.a.; 0.67; −0.32; −0.10; −0.35 - ρ(v): n.a.; n.a.; n.a.; −0.65; −0.52; −0.65 - ρ(w): 0.85; 0.64; 0.63; 0.54; 0.34; 0.44 - ρ(θ): n.a.; n.a.; n.a.; 0.09; 0.27; 0.06 - Findings summarized in notes: - In the data: wage is more variable than income; unemployment is countercyclical; consumption is more variable than income; current account-GDP ratio is countercyclical. - The baseline scenario accounts for these regularities reasonably well. ### Sensitivity analysis (Table 6) - Baseline and alternative parameter scenarios: Baseline; κ = 0.1; ψ = 0.08; ω = 0.85; ξ = 0.7 (with ξ = α = 0.7 noted). - Standard Deviation: - σ(y): 2.20; 2.20; 2.21; 2.20; 2.20 - σ(u): 3.24; 3.79; 2.79; 3.71; 1.75 - σ(v): 5.59; 5.86; 4.77; 5.69; 6.62 - σ(θ): 17.53; 23.17; 15.04; 17.91; 9.41 - σ(w)/σ(y): 1.67; 1.64; 1.57; 1.64; 1.82 - σ(c)/σ(y): 1.35; 1.23; 1.30; 1.22; 1.30 - Correlation with y: - ρ(y, ca/y): −0.46; −0.23; −0.53; −0.23; −0.54 - ρ(y, u): −0.68; −0.63; −0.67; −0.66; −0.79 - ρ(y, v): 0.51; 0.48; 0.50; 0.51; 0.66 - ρ(y, w): 0.83; 0.86; 0.82; 0.86; 0.69 - ρ(y, θ): 0.77; 0.79; 0.75; 0.81; 0.75 - ρ(u, v): −0.94; −0.93; −0.94; −0.96; −0.91 - Autocorrelation: - ρ(c): 0.53; 0.52; 0.55; 0.52; 0.58 - ρ(y): 0.65; 0.65; 0.65; 0.65; 0.65 - ρ(ca/y): 0.40; 0.37; 0.40; 0.38; 0.42 - ρ(u): 0.10; −0.06; 0.15; −0.02; 0.56 - ρ(v): −0.33; −0.38; −0.26; −0.35; 0.16 - ρ(w): 0.50; 0.52; 0.51; 0.53; 0.54 - ρ(θ): 0.40; 0.43; 0.42; 0.45; 0.40 - Notes: "This table shows the results of the sensitivity analysis. The columns show the moments of the baseline case and those of the scenarios with κ= 0.1, ψ= 0.08, ω= 0.85, and ξ=α= 0.7." ### Matching efficiency shocks (Table 7) - Scenarios: Baseline; w/ MES ρ(ε_z, ε_ω) = 0.5; ρ(ε_z, ε_ω) = 0 - Standard Deviation: - σ(y): 2.20; 2.37; 2.26 - σ(u): 3.24; 16.24; 15.59 - σ(v): 5.59; 14.56; 13.96 - σ(θ): 17.53; 33.02; 30.31 - σ(w)/σ(y): 1.67; 1.82; 1.77 - σ(c)/σ(y): 1.35; 1.20; 1.27 - Correlation with y: - ρ(y, ca/y): −0.46; −0.20; −0.34 - ρ(y, u): −0.68; −0.57; −0.20 - ρ(y, v): 0.51; −0.01; 0.01 - ρ(y, w): 0.83; 0.88; 0.78 - ρ(y, θ): 0.77; 0.76; 0.49 - ρ(u, v): −0.94; −0.34; −0.29 - Autocorrelation: - ρ(c): 0.53; 0.51; 0.50 - ρ(y): 0.65; 0.68; 0.64 - ρ(ca/y): 0.40; 0.41; 0.37 - ρ(u): 0.10; 0.31; 0.32 - ρ(v): −0.33; −0.32; −0.28 - ρ(w): 0.50; 0.52; 0.51 - ρ(θ): 0.40; 0.50; 0.51 - Notes: "This table shows the results of the setup with shocks to the matching efficiency. The columns show the moments of the baseline case and those of the scenarios with procyclical (ρ(ε_z, ε_ω) = 0.5) and acyclical (ρ(ε_z, ε_ω) = 0) matching efficiency shocks." ### Limiting distributions of endogenous state variables (Figure 1) - Variables plotted: - Bond Distribution (Bond Holdings): x-axis values shown from 0.02 to 0.07 (0.020.0250.030.0350.040.0450.050.0550.060.0650.07) - Unemployment Distribution (Unemployment): x-axis values from −1 to 4 (−1−0.500.511.522.533.54) - Notes: "The charts plot the limiting distributions of bond holdings and unemployment." ### Impulse response functions: main macroeconomic variables (Figure 2) - Shocks analyzed: - one-standard-deviation negative TFP (dashed line) - one-standard-deviation positive interest rate (dash-dotted line) - simultaneous one-standard-deviation negative TFP and positive interest rate shocks (solid line) - Variables and qualitative responses: - Output: With TFP shocks, output falls on impact due to lower productivity. - Consumption: Households borrow from international capital markets and accumulate debt to smooth consumption; with incomplete markets, borrowing cannot entirely offset output decline hence consumption decreases. - Bond Holdings: Households borrow from international capital markets and accumulate debt. - Current Account−Output Ratio: With TFP shocks, the economy runs a current account deficit. In response to a positive interest rate shock, households increase savings, causing an increase in the current account-GDP ratio. - Additional note: The decline in output due to the interest rate shock is minuscule because TFP does not change and unemployment increases only marginally. ### Impulse response functions: labor market variables (Figure 3) - Same shock types as Figure 2. - Labor market responses (qualitative): - Unemployment Rate: Higher interest rate depresses discounted future return to recruiting, leading to a decline in recruiting efforts, a lower job-finding rate, and a slacker labor market with higher unemployment. - Vacancy Rate: Falls in response to interest rate shock (recruiting efforts decline). - Vacancy−Unemployment Ratio: Declines with higher interest rate. - Wage: Higher interest rate leads to a lower wage because value of making a match for firms declines and value of becoming unemployed for workers declines (lower marginal value of becoming unemployed). Firms gain relative bargaining power and workers lose bargaining power, leading to a large fall in wages. - Quantitative statement: "The interest rate shock has quantitatively larger effects on labor market variables particularly on wages." ### Sectoral decomposition of employment (Figure 4) - Charts show: share of tradable goods sector employment relative to nontradable sector employment for Mexico, Colombia, and Chile across indicated years. - Mexico: share of traded goods sector employment series plotted across 1991–2007 period with shaded sudden stop episode(s). - Colombia: series plotted across 1985–1999 period with shaded sudden stop episode(s). - Chile: series plotted across 1980–2006 period with shaded sudden stop episode(s). - Finding: Large depreciation of the real exchange rate during sudden stop episodes drove down the relative price of nontradable goods, leading to massive sectoral reallocations; in Mexico, the employment share of traded goods sector in total employment stopped following a downward trend and even rose somewhat after the crisis. Similar patterns observed in other Sudden Stop episodes as well. *Source: _wp12237 - 1.1599 coefficient of leisure in utility (employed)calculation (PDF chapter/section).* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12237.pdf_