Emerging Market Business Cycles
The Role of Labor Market Frictions

Contributor Notes

Emerging economies are characterized by higher consumption and real wage variability relative to output and a strongly countercyclical current account. A real business cycle model of a small open economy that embeds a Mortensen-Pissarides type of search-matching frictions and countercyclical interest rate shocks can jointly account for these regularities. In the face of countercyclical interest rate shocks, search-matching frictions increase future employment uncertainty, improving workers’ incentive to save and generating a greater response of consumption and the current account. Higher consumption response in turn feeds into larger fluctuations in the workers’ bargaining power while the interest rates shocks lead to variations in the firms’ willingness to hire; both of which contribute to a highly variable real wage.

Abstract

Emerging economies are characterized by higher consumption and real wage variability relative to output and a strongly countercyclical current account. A real business cycle model of a small open economy that embeds a Mortensen-Pissarides type of search-matching frictions and countercyclical interest rate shocks can jointly account for these regularities. In the face of countercyclical interest rate shocks, search-matching frictions increase future employment uncertainty, improving workers’ incentive to save and generating a greater response of consumption and the current account. Higher consumption response in turn feeds into larger fluctuations in the workers’ bargaining power while the interest rates shocks lead to variations in the firms’ willingness to hire; both of which contribute to a highly variable real wage.

1 Introduction

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.1 Despite the rapid development of emerging market business cycle models over the past decade—which, in general, aim to explain large swings in consumption relative to output and countercyclical current account dynamics prevalent in EMEs—we have limited understanding about the labor market dynamics in these countries and their role in business cycle fluctuations.2 To our knowledge, this paper makes the first attempt to fill this gap.

We begin by systematically documenting the business cycle properties of key labor market variables (i.e., real earnings, unemployment, hours worked) for EMEs and comparing them to those of developed economies. Our empirical analysis reveals a striking feature of the labor markets in EMEs: the fluctuations in prices are large while those in quantities are subdued. In particular, real wages, on average, are almost twice as variable as output and have a positive correlation with contemporaneous output (0.38). Conversely, the variability of employment is about half the variability of output. These regularities stand in contrast with the developed economies where variability of wages is lower than that of output, and wages in developed economies are less procyclical than those in emerging economies. Further, the variability of employment in developed economies is close to that of output.3 Combined with the findings of the earlier literature on the importance of the behavior of interest rates in EMEs, our findings suggest that there may be a crucial interaction between the labor market and financial markets in EMEs, which, then, contribute to the salient business cycle characteristics of those economies.4

We then move on to our main objective and illustrate how the interaction between the labor markets and the exogenous driving forces such as Total Factor Productivity (TFP) and interest rate shocks affect (the latter as the proxy of financial conditions) macroeconomic fluctuations in an augmented workhorse Small Open Economy Real Business Cycle (SOE-RBC) model. In our model, labor market conditions and employer-employee relationships are explicitly modeled and wages are determined by Nash bargaining. Examining the interaction between labor markets and financial markets requires moving away from the frictionless spot labor market, where the wage is simply pinned down by the labor productivity. To do so, we incorporate labor search-matching frictions à la Mortensen and Pissarides (1994) (MP) and Pissarides (2001) into an, otherwise, standard SOE-RBC model. Differently from the previous models of EMEs, our setting allows the workers’ outside option—which depends on labor market tightness, external wealth and interest rates—to influence wage determination. Changes in the expected returns to searching induce equilibrium responses in labor market conditions, the effects of which are propagated over time through changes in the stock of unemployment. These changes directly impact household’s saving behavior, lifetime wealth and hence other macroeconomic variables such as wages, consumption and the current account.

We find that the interaction of TFP shocks and countercyclical interest rate shocks with search-matching frictions contributes significantly in driving the joint behavior of consumption, the current account and wages observed in EMEs. Two important forces play a role. First, in the search-matching framework, a high interest rate that accompanies a negative TFP shock reduces the discounted future return on recruiting, leading to a decline in employer recruiting efforts, and higher subsequent unemployment rates. Since future revenues from a match are now discounted at a high rate, firms have less to lose from not making a match, giving rise to more bargaining power for firms. Everything else equal, with more bargaining power for firms, wages decline more than that in a Walrasian labor market. The second force that puts downward pressure on wages in this scenario is a decline in workers’ bargaining power. During recessions, higher interest rates lead to a decrease in consumption and increase in savings. With labor market frictions—which imply that unemployed workers have to take time and necessarily experience an unemployment spell to find a job—the decline in consumption and increase in savings are amplified because of an increase in future employment uncertainty and the associated decline in permanent income. Further, the slackened labor market and a substantial fall in consumption make non-market activity less attractive and lower workers’ outside option, thus their bargaining power. More bargaining power of firms together with less bargaining power of workers put wages down markedly. The decline in wages and consumption together with the increase in savings bring the model implications very much in line with the EME data.5

In our model, we consider TFP and countercyclical interest rate shocks as the main exogenous driving forces motivated by earlier research. Typically, EMEs face an increase in interest rates on external debt due to the rising default risk premium (Neumeyer and Perri, 2005, Uribe and Yue, 2006, Arellano, 2008) when a negative TFP shock hits.6 The higher interest rates make it optimal to postpone consumption and increase savings, partly offsetting the negative effect of lower TFP on saving potentially giving rise to a countercyclical current account.7

Search-matching frictions provide significant improvement in accounting for EME regularities in models with TFP and countercyclical interest rate shocks. Earlier research (Neumeyer and Perri, 2005 and Uribe and Yue, 2006) found that SOE-RBC with TFP and countercyclical interest rate shocks can account for EME regularities especially on consumption and the current account. However, those models needed to resort to tight working capital constraints to account for the high volatility of consumption relative to output and the countercyclicality of the current account (Oviedo, 2005). Further, spot labor markets in those models imply that wages are perfectly correlated with output as they are equal to the marginal product of labor in equilibrium; implying a relatively low wage variability relative to the data. Our model with search-matching frictions amplify the effect of countercyclical interest rate shocks bring the model implications closer to EME regularities on consumption, current account and wages without resorting to working capital constraints.

The improvement we provide with search-matching frictions in accounting for EME regularities in models with TFP and countercyclical is an important step forward in the literature. As Mendoza and Yue (2010) point out, working capital loans, estimated using the observed bank credit to the private sector as a share of output, are rather small in EMEs. In our model, negative TFP shocks coupled with positive interest rate shocks have a lasting effect on the economy via search-matching frictions as the stock of employment does not adjust instantaneously and searching and matching are costly. This gives rise to an increase in unemployment, a fall in permanent wealth, and a higher degree of savings, giving rise to a fall in consumption. The fall in consumption reduces workers’ bargaining power, which then gives rise to a fall in wages by more than would happen with Walrasian labor markets.8 The pressure on wage is further reinforced because firms discount future employment with a higher weight when interest rates are high.

Our baseline model with search-matching frictions performs well in accounting for EME business cycles generally but falls short of accounting for the variability of unemployment. On this front, we inherit the typical drawback of search-matching frictions in line with Shimer’s critique. In an illustrative exercise, we show how incorporating matching efficiency shocks could bring the model implications for unemployment variability closer to data. Our motivation to explore the effects of matching efficiency shocks is based on the labor market observations during Sudden Stop episodes.9 During Sudden Stops, real exchange rate depreciations generate large reallocations across sectors (e.g., from nontradable goods sectors to tradable goods sectors (Kehoe and Ruhl, 2009) and from investment goods sector to consumption goods sector (Benjamin and Meza, 2007)). The different nature and skill requirement of jobs across sectors might make matching more difficult during these periods of massive sectoral reallocations. This difficulty can be captured by a reduction in the technical efficiency of the matching function at the aggregate level. By extending our baseline search-matching model to incorporate these fluctuations, we show that these matching efficiency shocks can help bring the wage variability predicted by the model further closer to data and account for the high variability of unemployment observed in the data.

Our paper connects two strands of literature—the emerging market business cycles literature and the search-matching literature. In the emerging market business cycles literature, Mendoza (1991, 1995) and Correia, Neves and Rebelo (1995) among others provide the early contributions. More recently, Neumeyer and Perri (2005) and Uribe and Yue (2006) study the role of countercyclical interest rate shocks in EMEs that are amplified through the working capital constraints. Aguiar and Gopinath (2007) examines the role of trend growth shocks and argue that these shocks can explain the high variability of consumption relative to output and the countercyclical current account.10 These papers, however, are largely silent about labor market dynamics and our paper complements these studies by proposing an additional mechanism through which external shocks can feed into the variability in consumption and real wages and affect current account fluctuations. As for analyzing labor markets, Li (2009) presents the first contribution on this front by documenting the cyclical wage movements in EMEs. Unlike our setup, Li (2009) considers a hybrid utility function that allows for flexible parameterization of the income effects on labor supply in a spot labor market model to account for the higher variability and procyclicality of wages. In addition, in Li’s framework, interest rate shocks work through a working capital requirement, affecting labor demand directly.

In the closed-economy macroeconomics literature, the MP search-matching model has been widely used to study various employment related issues. Andolfatto (1996) and Merz (1995) were among the first to integrate the search environment into a closed-economy business cycle model with risk-averse agents and document its improved performance in explaining U.S. business cycles. When we introduce search-matching frictions into a small open economy—which is subject to TFP and countercyclical interest rate shocks—an additional propagation mechanism arises because of the interaction between the labor market conditions and interest rate fluctuations. Our model is closely related to the aforementioned closed-economy models and, essentially, is a first-generation MP-type model, in which wages are determined by Nash bargaining and is applied to both existing workers and new hires.11 Considering alternative wage setting could possibly lead to interesting implications. However, our model takes an important first step by deviating from the standard SOE-RBC models. In fact, it can be extended to include heterogeneous agents, endogenous job separation, alternative bargaining concepts to study policy related questions for EMEs such as labor regulation, unemployment insurance, the role of institutions, etc.

The rest of the paper is organized as follows. Section 2 documents the business cycle properties of labor market variables both for emerging economies and developed economies, as well as empirical evidence motivating the matching efficiency shock. Section 3 lays out our model. Section 4 explains our calibration, solution, and main quantitative findings. Section 5 extends the model to analyze matching efficiency shocks. Finally, Section 6 concludes.

2 Empirical Evidence on Emerging Economy Labor Markets

In this section, we document the business cycle properties of key labor market variables, in particular, real earnings, the unemployment rate, and employment level for a group of EMEs.12 In summary, we find that the variability of prices, i.e., real earnings, is strikingly high in EMEs and this kind of variability is absent in quantity variables such as employment, unemployment and hours worked.

Table 1 reports the statistics related to hourly real earnings. The median standard deviation of real earnings, calculated by deflating the nominal earnings by the CPI, is significantly greater than the standard deviation of real output, with the ratio between the two being 1.62. The real earnings are procyclical as evidenced by a correlation of 0.38 with contemporaneous output. To check the robustness of these findings, we also report real earnings variability relative to manufacturing output variability, the nominal earning variability and the real earnings variability calculated by using the PPI deflator. Manufacturing output is more variable than GDP for all countries; therefore, the median real earning variability relative to manufacturing output variability falls to 1.0 from 1.62.13 The nominal wages behave similarly to real wages in the sense that they are highly variable. Finally, when using the PPI to calculate real earnings instead of the CPI, we find similar results.

Table 1:

Real earnings

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Notes: This table shows 1) standard deviation of real earnings, 2) standard deviation of real earnings as a ratio of output standard deviation, 3) correlation of real earnings with output, 4) standard deviation of real earnings as a ratio of manufacturing output standard deviation, 5) standard deviation of nominal earnings, 6) standard deviation of real earnings calculated using the PPI instead of CPI, 7) correlation of real earnings calculated using the PPI with output. All series are HP-filtered using a smoothing parameter of 1600. See Data Appendix for more information about data sources and coverage. The numbers in parenthesis report p-values of Student’s t (for means) and Mann-Whitney (for medians) tests of equality of means and medians of emerging market and developed economy statistics.

The first three columns of Table 2 report the statistics regarding the unemployment rate while the remaining three report those for employment.14 The correlations of these two variables with output deliver consistent results: the median correlation of unemployment with output is -0.46 while that for employment is 0.39. Unemployment appears to have higher variability than employment but note that we are reporting percentage deviations. Since we consider the unemployment rate (as opposed to unemployment), this variable is already normalized by the labor force leading to higher percentage deviations from the mean. The median standard deviation of the unemployment rate is 9.64 while that for employment is 0.58 relative to the standard deviation of output.15

Table 2:

Unemployment rate and employment

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Notes: This table shows 1) standard deviation of unemployment rate, 2) standard deviation of unemployment as a ratio of output standard deviation, 3) correlation of unemployment rate with output, 4) standard deviation of employment, 5) standard deviation of employment as a ratio of output standard deviation, 6) correlation of employment with output. All series are HP-filtered using a smoothing parameter of 1600. See Data Appendix for more information about data sources and coverage. The numbers in parenthesis report p-values of Student’s t (for means) and Mann-Whitney (for medians) tests of equality of means and medians of emerging market and developed economy statistics.

A broad comparison between EMEs and developed economies can be made based on the results reported in the aforementioned tables. The high variability of real earnings emerges as an EME-specific result; this variability for developed economies is lower than real output for the CPI-based definition of real earnings. As for the other definitions, the developed economies also display much lower variability and less procyclicality in their real earnings compared to EMEs. All of the statistics related to earnings reported in Table 1 are statistically significantly different for EMEs than developed economies (at 5 percent confidence level) as evidenced by small p-values reported at the bottom of this table in parentheses. The variabilities of unemployment rate and employment normalized by output variability are somewhat higher in developed countries compared to EMEs as suggested by Table 2. These two variables also are more procyclical in developed economies. Compared to the differences between EMEs and developed countries established for earnings, the differences with regards to unemployment and employment are less significant from a statistical perspective except the standard deviation of employment relative to the standard deviation of output. Hours worked in manufacturing and aggregate hours worked appear to be somewhat more procyclical in developed economies compared to EMEs.

To our knowledge, the only study that provides statistics on labor markets in the emerging market business cycles literature so far is Neumeyer and Perri (2005). Our findings on employment and hours are roughly in line with theirs; they also find that employment and hours are less variable and less correlated with output in EMEs.16 In this paper, we conduct a more comprehensive analysis than Neumeyer and Perri (2005) by reporting real earnings and unemployment rate statistics. In addition, we expand the set of EMEs used in the calculation of employment, unemployment rate, and earnings statistics and we also expand the set of developed countries that is used as a comparison group. Expanding the EME set for hours worked is difficult because the relevant data are available for only a few countries. Nevertheless, we report the comparison of available statistics of working hours in the Appendix.

Some research has suggested that the relatively lower variability in EMEs’ employment statistics could be due to a relatively high portion of employees working in the public sector, given the less variable public sector employment. In particular, Kydland and Zarazaga (2002) argue that public sector employment in Argentina often serves as unemployment insurance. Although Argentina is not included in our sample, this might still be an issue for other EMEs we consider. Therefore, we investigate if there are EMEs that have data on the decomposition of public and private employment. For Turkey, this decomposition is available during 2000-2006 at quarterly frequency.17 We compare the variabilities of the public and private sector employment and find that, contrary to the previous finding mentioned above, public sector employment is in fact more variable (3.12 vs. 1.77 percent). It is difficult to argue that the public sector employment does not function as unemployment insurance in these countries based on seven years of data only for one country, but the limited data do not confirm the initial expectation of the public sector being less variable.

Finally, it is worth noting that an important difference between these two country groups is the size of the informal sector and therefore the size of the working population that is not included in most of our data. In fact, 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.18 These ratios appear to be larger than those for the developed small open economies.19

We argue that the informal sector being larger in EMEs is not detrimental to our empirical analysis. First, part of our data for quantities of EMEs (employment, unemployment rate) are constructed based on household surveys implying that those data would capture the informal sector. Second, although our data on earnings are based on establishment surveys and therefore do not include the informal sector, we conjecture that the difference between these two country groups regarding wages would be even larger if our data were able to capture the informal sector. OECD (2008) documents the earnings distribution of full-time, non-farm employees for the formal and informal sectors for Mexico and Turkey. Based on their estimates of these distributions, we find that earnings in the informal sector are more variable than those in the formal sector. Specifically, the standard deviation of earnings in the formal sector is 0.89 (0.54) while that in the informal sector is 1.13 (0.90) in Mexico (Turkey). Hence, if the informal sector were to be included in our analysis of the earnings, we would have found an even stronger contrast between EMEs and developed economies.

3 A Small Open Economy Model with Search-Matching Frictions

Our framework nests a labor market search-matching friction into an otherwise standard SOE-RBC model. There is an infinitely-lived representative household, which consists of employed workers and unemployed workers at each point in time, and also a continuum of identical competitive firms. Job matches result from a Cobb-Douglas matching technology given by M(ut,vt)=ωutαvt1-α, where ω governs the matching or allocative efficiency, ut and vt stand for the unemployment rate and the vacancies posted by the firms in period t, respectively. The vacancy to unemployment ratio, θt=vtut captures the market tightness. There is a flow cost, κ associated with posting a vacancy, as firms often have to put out job advertisement and undertake screening and reviewing processes. The probability that a searching worker finds a job is ϕ(θt)=M(ut,vt)ut=ωtθt1-α. Correspondingly, the probability that an employer succeeds in filling a vacancy is given by M(ut,vt)vt=ϕ(θt)θt. Existing employer-worker pairs end at an exogenous break-up rate ψ

To keep the analysis simple and allow minimum deviation from the standard SOE-RBC model, we consider a large extended family scenario. That is, even though some family members are employed, and others are searching for a job, they all pool the income together for equal consumption.20 Under this assumption, the household’s optimization problem can be represented by a social planner’s problem. That is, the wage determination is repressed and the social planner maximizes welfare using one-period, non-state contingent international bonds that facilitate the borrowing and lending in the international financial markets. Following the emerging market business cycle literature, we assume that the interest rate on the international bond holdings is exogenous and subject to shocks. Financial markets for hedging against aggregate TFP and interest rate shocks are incomplete. We discuss later in this section how the wage is determined by the Nash bargaining between workers and firms. The full-fledged decentralized economy is described and characterized in the Appendix.

For each period t, the aggregate state is captured by endogenous state variables (bond holdings, bt, and unemployment rate, ut), as well as the vector of exogenous state variables, εt=[εtz,εtr].εtz denotes TFP shocks and εtz denotes interest rate shocks. The set {bt, ut, εt} summarizes the state space of the economy at each point in time.

The representative agent derives utility from consumption and leisure through a time-separable constant relative risk aversion (CRRA) utility function. U(ct)=ct1-σ/(1-σ) denotes the utility derived from consumption, and H(1-lt)=(1-lt)1-v/(1-v) denotes the utility derived from leisure, 1 - lt. σ denotes the CRRA coefficient, and 1/v governs the (Frisch) elasticity of labor supply. The per-period utility function, thereby, is U(ct)+ϕiH(1-lt), i = E,U for employed and unemployed workers respectively, which implies that the value of leisure depends on the employment status.

Population is normalized to one and production is carried out using a Cobb-Douglas production technology, yt=F[k,(1-ut)lt,zt]=ztkζ[(1-ut)lt]1-ζ, where ζ represents the capital share of production. zt denotes the total factor productivity (TFP) and zt=(1+εtz)z. To keep our focus on the dynamics of the extensive margin of labor supply we first follow Hansen (1985) and assume that labor is indivisible, lt = l.21 Once offered a job, workers always supply a fixed amount of labor. In an extension of the model, we endogenize working hours to allow for better comparison with the standard SOE-RBC model.22

In line with some of the small open economy models, e.g., Mendoza and Smith (2006), Durdu and Mendoza (2006), and Durdu et al. (2009), Mendoza and Yue (2012), we assume that the capital stock is time-invariant with zero depreciation. We resort to this strategy mainly to make a global solution possible by containing the size of the state space. Intuitively, in doing so, we restrict the role of interest rate shocks to mainly intertemporal substitution of consumption and savings. Since our main motivation is to explore how the behavior of international borrowing feeds into consumption and wage dynamics, this simplification is not detrimental to our analysis. The so-called “Fisher separation,” which is present in this class of models, induces consumption and borrowing decisions to be largely independent of investment and capital accumulation. To the extent that the output fluctuations due to investment fluctuations can be captured by larger TFP shocks in an environment without investment, we conjecture that shutting down of investment would not distort consumption and debt dynamics significantly.

Social Planner’s Problem. The social planner chooses a state-contingent plan of consumption, bond holdings, unemployment, and vacancies to solve the following optimization problem:

V(bt,ut,εt)=maxct,bt+1,ut+1,vtU(ct)+(1-ut)ϕEH(1-lt)+utϕUH(1)+β(ct)𝔼tV(bt+1,ut+1,εt+1)s.t.ct+bt+1+κvtF(k,(1-ut)lt,zt)+bt(1+rt),(1)ut+1[ut-M(ut,vt)]+(1-ut)ψ,bt+1B.¯

where β(ct) denotes the endogenous discount factor, which we introduce to induce stationarity to bond holdings.23 Using Epstein’s (1983) stationary cardinal utility formulation, this function boils down to β(ct)=(1+ct)-γ, where γ is the elasticity of the rate of time preference.24 The optimal choices of ct, bt+1, ut+1 and vt are as follows:

U(ct)-μt=β(ct)𝔼tU(ct+1)(1+rt),(2)
U(ct)κ=β(ct)Mv,t𝔼t[-V(bt+1,ut+1,εt+1)ut+1],(3)

where μt denotes the multiplier associated with the borrowing constraint and Mυ,t = (1-α) ϕ (θt)/θt. The first equation governs the intertemporal substitution of consumption. The second equation equates the marginal cost of posting an additional vacancy to the marginal benefit, i.e., the discounted future value created by the marginal job match, as a vacancy can only be turned into a job with a one-period lag.

By the Envelope condition, the surplus St that results from the marginal job match is:

St=-V(bt,ut,εt)ut=ϕEH(1-lt)-ϕUH(1)+U(ct)Fl,tlt+(1-ψ-Mu,t)β(ct)𝔼tSt+1,(4)

where Mu,t = αϕ(θt). The first two terms of the right hand side capture the net loss in the utility of leisure to the newly employed worker compared to being unemployed. The third term stands for the contribution to output that results from one more worker measured in marginal utility terms, and the last term measures the continuation value of future employment.

Wage Determination. In the social planner’s problem, wage is absent and the social planner determines and implements the Pareto optimal allocations. In this section, we describe a simple, period-by-period Nash bargaining process, which determines the sequence of wage rates {wt}. A more detailed description of the decentralized economy can be found in the Appendix. For workers, suppose that the value associated with being employed is given by Et, and the value of being unemployed and actively searching for a new job is Ut. For employers, let Jt denote the value of a filled position after making the wage payment. Free-entry indicates that, given the probability of successfully filling a position, ϕ(θt)/θt, employers’ anticipated payoff from a match is completely offset by the recruiting cost:

κ=φ(θt)/θt𝔼tρt,t+1Jt+1(5)

ρ is the stochastic discount factor of the household and is defined as ρt,t+1 = β(ct)U’(ct+1)/U’(ct). The transition equation for Jt is

Jt=πt+(1-ψ)𝔼tρt,t+1Jt+1(6)

where the flow profit of an active job is πt=Fl(ktnt,lt;zt)lt-wtlt. Equations (6) and (5) together imply

Jt=Fl,tlt-wtlt+(1-ψ)κθtϕ(θt).(7)

Assuming that employed workers’ bargaining power is ξ ∊ (0, 1), the matched worker-firm pair negotiates over wage by solving the following Nash bargaining problem:

maxwt(Et-Ut)ξJt1-ξ,

subject to the joint surplus given by JtU’(ct) + Et - Ut = St. The optimal allocation is for the firms and the household to divide the total matching surplus according to the Nash bargaining power of each party Therefore,

Jt=(1-ξ)StU(ct).(8)

Combining Equation (4) with Equation (8), we have

Jt=(1-ξ)U(ct)[ϕEH(1-lt)-ϕUH(1)+U(ct)Fl,tlt]+(1-ψ-αϕ(θt))κθtϕ(θt).(9)

Based on the above Equation (7) and Equation (9) and imposing Hosios’ (1990) efficiency condition, which requires that the bargaining power of firms must correspond to the elasticity of the matching technology with respect to recruiting effort, α = ξ, we have

wt=ξ(Fl,t+κθtlt)+(1-ξ)ϕUH(1)-ϕEH(1-lt)ltU(ct).(10)

Equation (10) suggests that the wage is determined not only by the marginal product of labor Fl,t, but also the value of staying unemployed and searching in the next period. In other words, the wage is a convex combination of the maximum value to a firm that succeeds in activating a job and the minimum value necessary for the household to send an unemployed worker to a new employment relationship. The second term in the first bracket of Equation (10) can be further rewritten as:

ξκθtlt=(1-ξ)ϕ(θt)β(ct)lt𝔼t(Et+1-Ut+1)U(ct+1),(11)

which captures the value of forward-looking aspect of reentering the job market and possibly getting employed in the next period. The last term in Equation (10) is the value of leisure associated with being unemployed in units of marginal consumption. As consumption plunges, the marginal utility of leisure in consumption terms becomes less valuable, and workers are more willing to accept a lower wage to compensate the same amount of hours worked. These two terms together constitute the value of being unemployed, enjoying more leisure, and searching again next period. Also note that when the interest rate rises, firms discount future revenues at a higher rate, thus value of making a match declines. The decline in the value of a match increases firms’ bargaining power putting further downward pressure on the wage.

4 Quantitative Analysis

4.1 Calibration

Parameters. We calibrate our model to quarterly data for Mexico, a representative EME. Given the scarcity of data on labor markets for many of the EMEs including Mexico, we utilize information from other emerging market countries when needed, and also take some of the standard parameter values directly from the existing literature. The implied parameter values are listed in Table 4. The average international interest rate is set to 1.74 percent, the average of Emerging Market Bond Index (EMBI) yields for Mexico over the sample period.25 The risk aversion parameter σ is 2 as commonly used in the literature. We calibrate the consumption-gross output ratio to be c*/y* = 0.69 for Mexico. Since our model does not have investment or government expenditures, we subtract a fixed amount of 1 - 0.69 from the budget constraint to capture the share of investment and government expenditures in output. According to the OECD Annual Hours and Productivity data, an average worker in Mexico spent 32 percent of their non-sleeping time on market activities. Therefore, the working hours l is set to 0.32. For the case with endogenous labor hours, the intertemporal (Frish) elasticity of labor supply is set to 1.6, which is commonly used in SOE-RBC models (Mendoza, 1991; Aguiar and Gopinath, 2007). Given our utility function and steady state working hours, this would imply v = 1.42.

Table 3:

Hours worked: manufacturing and aggregate

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Notes: This table shows 1) standard deviation of hours worked in manufacturing, 2) standard deviation of hours worked in manufacturing as a ratio of output standard deviation, 3) correlation of hours worked in manufacturing with output, 4) standard deviation of aggregate hours worked, 5) standard deviation of aggregate hours worked as a ratio of output standard deviation, 6) correlation of aggregate hours worked with output. All series are HP-filtered using a smoothing parameter of 1600. See Data Appendix for more information about data sources and coverage. The numbers in parenthesis report p-values of Student’s t(for means) and Mann-Whitney (for medians) tests of equality of means and medians of emerging market and developed economy statistics.
Table 4:

Calibrated Parameters

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Notes: This table shows the parameter values used in the analysis.

We set the natural breakup rate, ψ, to 0.06, based on the range of estimates provided in Bosch and Maloney (2008) for Mexico. Using the unemployment rate data for Mexico for the period 1988 − 2006, we set the steady-state unemployment rate to 8.21 percent so that the mean unemployment rate in the stochastic steady state matches the average unemployment rate in the data.26 Combining this information with the natural breakup rate implies a steady state value of 0.055 for matches formed, m* = (1 - u*)ψ. Due to a lack of evidence on the probability that a vacant position becomes an active job by the end of the quarter, we assume job finding rate, ϕ(θ)θ=0.7—corresponding to an average vacancy duration of 45 days—slightly lower than Andolfatto (1996).

In our baseline experiment, the recruiting expenditure to GDP ratio, κv* is assumed to be as small as 0.01, which is in line with Andolfatto (1994). The unit cost of posting a vacancy becomes κ = 0.01/v* = 0.127. We set the capital share parameter ζ to 0.36 following the SOE-RBC literature. To be more precise, in a search economy, the labor’s share of output is given by (1-ζ) - [1 - (1 - σ)β(ct)]κv*/(β(ct)σ). Our parameters imply this expression to be 0.63, very similar to the standard value in the literature and also to (1 - ζ).

The elasticity of the matching rate with respect to aggregate unemployment rate, α needs to be the same as the bargaining power ξ, in order for the wages implied by Nash bargaining to support the allocations obtained from the social planner’s problem. We follow Andolfatto (1994) and set α to 0.5. Given the values for v*, m*, u*, and α, we can calculate the matching efficiency parameter, ω, using the steady state condition ω=m*u*αυ*(1-α)=0.687. The remaining parameters φE and φU are jointly determined by the efficiency condition of labor hours and the optimality condition for unemployment.

Shock processes. In the benchmark case, we consider TFP shocks and interest rate shocks as in Neumeyer and Perri (2005) and Uribe and Yue (2006). We estimate a joint VAR process using the TFP and international interest rate for Mexico, in particular, Solow residuals and EMBI yields.27 We construct interest rate series by deflating the dollar denominated EMBI yields by adaptive U.S. inflation.28 We then feed in the corresponding transition probability matrix and shock realizations using Tauchen and Hussey’s (1991) quadrature procedure to our model. EMEs typically face relatively variable and countercyclical real interest rates mainly due to the default risk that is negatively correlated with output (see Neumeyer and Perri, 2005, Uribe and Yue, 2006). In our calibration, interest rate and TFP shocks are significantly negatively correlated with a correlation of -0.8.

The VAR representation of the shock processes and their estimates are summarized below:

ϵt=RHOϵt-1+et,(12)

where

ϵt[ϵzϵr],RHO=[ρzρz,rρr,zρr],et[etzetr].RHO=[0.61-0.170.190.69],covar(etet)=[0.0004-0.00048-0.000480.0009].

4.2 Solution: Nonlinear Methods

We solve for the recursive competitive equilibrium using value function iterations. This solution method preserves the nonlinear dynamics of the model which is important to capture precautionary saving. A nonlinear solution method, however, forces us to keep our model relatively stylized due to curse of dimensionality.

As a first step in our solution algorithm, we solve for the social planner’s problem (Equation (1)) discretizing the bond grid in [-1.0, 4.0] interval with 200 equidistant nodes and the unemployment grid in [0.02, 0.07] interval with 20 equidistant nodes. Our solution is robust to the number of nodes used in each grid. Once we derive the decision rules, we use the decentralized equilibrium conditions to evaluate the wage function.

Figure 1 shows the limiting distributions of bond holdings and unemployment in the baseline model with search-matching frictions. As these graphs illustrate, the solution delivers ergodicity in both of these dimensions.

Figure 1:
Figure 1:

Limiting Distributions of Endogenous State Variables

Citation: IMF Working Papers 2012, 237; 10.5089/9781475511208.001.A001

Notes: The charts plot the limiting distributions of bond holdings and unemployment.

4.3 The Model Dynamics

Impulse responses of main aggregate variables to exogenous shocks help develop intuition about the key mechanism of our model. Figures 2 and 3 plot the impulse responses to a negative one-standard-deviation TFP shock (dashed line), a positive one-standard-deviation interest rate shock (dash-dotted line) and a case that incorporates both of these shocks at the same time (solid line) in our baseline search-matching model. In order to add no other impetus to responses, individual shocks scenarios feature zero correlation in the innovations to TFP shocks and interest rate shocks: corr(etz,etr)=0. The scenario with both of the shocks, however, features corr(etz,etr)<0, as estimated in our baseline calibration.

Figure 2:
Figure 2:

Impulse Response Functions: Main Macroeconomic Variables

Citation: IMF Working Papers 2012, 237; 10.5089/9781475511208.001.A001

Notes: The figures show the impulse responses of main macroeconomic variables in response to one-standard-deviation negative TFP (dashed line), one-standard-deviation positive interest rate (dash-dotted line), and simultaneous one-standard-deviation negative TFP and positive interest rate shocks (solid line) in our baseline model with search-matching frictions. With TFP shocks, output falls on impact due to lower productivity. Households borrow from the international capital markets and accumulate debt to smooth consumption. With incomplete markets, the borrowing from abroad cannot entirely offset the decline in output hence, consumption decreases and 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. The decline in output as a result of the interest rate shock is minuscule because TFP does not change and unemployment increases only marginally.
Figure 3:
Figure 3:

Impulse Response Functions: Labor Market Variables

Citation: IMF Working Papers 2012, 237; 10.5089/9781475511208.001.A001

Notes: The figures show the impulse responses of main macroeconomic variables in response to one-standard-deviation negative TFP (dashed line), one-standard-deviation positive interest rate (dash-dotted line), and simultaneous one-standard-deviation negative TFP and positive interest rate shocks (solid line) in our baseline model with search-matching frictions. Higher interest rate depresses the 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. The higher interest rate leads to a lower wage because value of making a match for the firms declines and value of becoming unemployed for the workers also declines (with low level of consumption marginal value of becoming unemployed falls). In return, firms have more and workers have less bargaining power, leading to a large fall in wages. The interest rate shock has quantitatively larger effects on labor market variables particularly on wages.

In response to the negative TFP shock, on impact, firms reduce vacancies created, leading to fewer matches—as the current unemployment rate is predetermined in the previous period—and consequently causing a higher unemployment rate in the following period.29 With slackened labor market and less attractive outside option of non-market activities, equilibrium wage drops. Output falls on impact due to lower productivity. In order to smooth consumption, households borrow from the international capital markets and accumulate debt. Due to markets for aggregate shocks being incomplete, the borrowing from abroad cannot entirely offset the decline in output hence, consumption decreases and the economy runs a current account deficit. Similar to the standard SOE-RBC models—where interest rates are acyclical or constant—TFP shocks alone cannot account for volatile consumption relative to output and strongly countercyclical current account.

Interest rate shocks affect the optimal bond holdings and the current account to GDP ratio differently from TFP shocks. In particular, in response to a positive interest rate shock, households increase savings, causing an increase in current account to GDP ratio. This is because higher interest rates imply that current consumption is more expensive relative to future consumption (Equation (2)) and make it optimal for consumers to postpone consumption and increase saving. The increase in saving is further amplified because of search-matching frictions. With lower future employment prospects (as discussed next) and a large fall in wages, workers’ incentives to save for future is boosted. As a result, the economy runs a large current account surplus and consumption drops significantly (by six percent) on impact. The decline in output as a result of the interest rate shock is minuscule because TFP does not change and unemployment increases only marginally.30

Figure 3 shows that equilibrium responses of labor market variables to the positive interest rate shock are qualitatively similar to the corresponding responses to the negative TFP shock. Higher interest rate depresses the discounted future return to recruiting (Equations (2) and (6)). The immediate effect is a decline in recruiting efforts, a lower job-finding rate, and a slacker labor market with higher unemployment. Equation (10) on wage determination suggests that since with the higher interest rate, firms discount future revenues with a higher weight, they have less to lose not making a match, which also, in turn, increases their bargaining power in the wage negotiation process, putting downward pressure on wages. The immediate effect is a deterioration in labor market conditions, a lower value of unemployment from the perspective of workers, and a lower value of creating a match from the perspective of firms. Also a low level of consumption in bad times due to higher interest rate leads to an increase in the marginal utility of consumption that reduces the net gain of leaving the negotiation process and enjoying more leisure. The higher bargaining power of firms and lower bargaining power of workers imply a large drop in wages. Overall, the interest rate shock has quantitatively larger effects on labor market variables particularly on wages.

When both interest rate and TFP shocks hit the economy simultaneously, the effect of interest rate shock on savings dominates the incentives to borrow to smooth consumption in the face of a negative TFP shock. Interacting with the search frictions, the joint driving forces of interest rate and TFP shocks lead to a higher volatility of consumption relative to output and strongly countercyclical current account. Labor market frictions play an important role in driving these dynamics. First, search-matching frictions imply that workers, once laid off, have to go through a necessary spell of unemployment and the changes in the vacancies are only reflected in employment with a lag. The prospect of higher unemployment strengthens the precautionary saving motive in the search environment. Second, it takes time for output to recover when the economy is hit by a negative shock. This means that the lower life-time income is even lower due to the search frictions. The large drop in the permanent income and stronger precautionary saving incentive lead to a large fall in consumption.

To sum, our experiments show that TFP shocks play an important role in generating realistic output responses which interest rate shocks alone cannot achieve. However, the interest rate shocks are necessary to generate consumption to respond more than output, to generate real wage to respond more than output, and to generate current account dynamics consistent with those observed in emerging markets. Search-matching frictions in this environment provide the necessary propagation by strengthening the precautionary savings motive, and increasing persistence since new matches take time to form and unemployment declines only gradually.

4.4 Main Findings

Table 5 reports the statistics describing the cyclical behavior of the Mexican economy, the moments in the canonical SOE-RBC economy, and in our baseline search economy. All model economies are subject to correlated TFP and interest rate shocks estimated except those in columns 4-5 where we shut down one shock at a time to isolate the importance of each shock. The model with endogenous labor reported in the last column features endogenous labor choice. We introduce endogenous labor mainly to examine if the main differences between our baseline search-matching model and the canonical SOE-RBC model depends on the difference in the behavior of intensive margin. Note that our baseline search-matching model features indivisible labor whereas the canonical SOE-RBC model features endogenous labor.

Table 5:

Business Cycle Moments

article image
Notes: This table shows the business cycle moments. The columns show the moments in the data, in the RBC model with both productivity and countercyclical interest rate shocks but Walrasian labor markets, in the baseline search-matching model with both TFP and countercyclical interest rate shocks, the search-matching model only with TFP shocks, and the search-matching model only with interest rate shocks. The RBC model features a GHH preference, whereas search-matching model features a time-separable CRRA preference. This table shows that 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.

The first column of Table 5 suggests that the salient features of EME business cycles are preserved in the Mexican data.31 In particular, consumption is more variable than income, and the current account-output ratio is strongly countercyclical. As for the labor market variables, as thoroughly discussed in Section 2, wage is procyclical and more variable than income, and unemployment is countercyclical and highly variable. Unfortunately, due to data limitations, we are not able to obtain an empirical measure for vacancies in Mexico, and thus cannot compare our model against data in this dimension.

Canonical SOE-RBC. We consider a canonical RBC model in which we feed in the same TFP and interest rate shock processes as in our baseline search-matching model. We study a spot labor market economy with Greenwood, Hercowitz and Huffman (1988) (GHH) preferences. With GHH preferences, we allow the canonical SOE-RBC model the “best chance” in replicating the Mexican data, because the GHH preferences appear crucial in replicating small open economy business cycles (see Correia et al. 1995).

As shown in column two of Table 5, the SOE-RBC model falls short of explaining the key emerging market regularities regarding consumption and the current account. In particular, consumption is less variable than output and the current account to GDP ratio is only weakly countercyclical (correlation with output equals -0.13 compared with -0.75 in the data). Even in the presence of interest rate shocks, assuming a reasonable value of the intertemporal elasticity, the intertemporal substitution effect is not sufficient to cause a response of consumption that exceeds the response of output. This is also because the SOE-RBC model we consider here does not include working capital constraints. And, as shown by Oviedo (2005), the RBC model with interest rate shocks can quantitatively explain regularities on consumption and the current account simultaneously only when the variability of interest rate shocks is high and the impact of interest rate shocks is amplified through a working capital constraint. Also note that the RBC model with GHH preferences falls short of accounting for wage dynamics. It yields wages that are significantly less variable than those in the data (σ(w)/σ(y)=0.31) and perfectly correlated with output, as the wage is tightly connected to the marginal product of labor in a spot labor market.

Search-Matching Model with TFP and countercyclical interest rate shocks. Our baseline model with search-matching frictions, TFP and countercyclical interes rate shocks is able to replicate the cyclical behavior of the Mexican macroeconomic aggregates. It generates a consumption profile that is more variable than income, wage fluctuations that are more variable than income and a strongly countercyclical current account (note that correlation of current account with output is −0.46), all which are consistent with the observed patterns in the data. The main discrepancy between the baseline model and data is the unemployment displaying considerably less movement (standard deviation equals 3.24 in the model compared to 14.70 in the data). In the next section, we extend our model to incorporate matching efficiency shocks—which reflect the “allocative disturbances” and discuss how this extension helps us bring the model predictions closer to data with regards to employment.

We identify two important channels through which the interaction of TFP shocks and countercyclical interest rate shocks with search-matching frictions contributes to accounting for the behavior of wages observed in EMEs. The first channel operates through firms’ hiring incentives and bargaining power. In the search-matching environment, a high interest rate coupled with a negative TFP shock reduces the discounted future return on recruiting. This leads to a decline in employer recruiting efforts, and higher subsequent unemployment rates. Since future revenues from a match are now discounted at a high rate, firms have less to lose from not making a match, giving rise to more bargaining power for firms. More bargaining power for firms implies a larger wage decline.

The second channel that puts downward pressure on wages in this scenario is a decline in workers’ bargaining power. Consumptions falls while saving increases during downturns due to higher interest rates. This decline in consumption and increase in savings are higher in presence of labor market frictions as workers face an increase in future employment uncertainty and an associated decline in permanent income. The decline in consumption make non-market activity less attractive and lower workers’ outside option, thus their bargaining power. Overall, more bargaining power of firms together with less bargaining power of workers push wages down during downturns. Quantitatively, this higher wage variability is large as we show in Table 5.

The “Only Prod” column reports the results of a scenario in which only aggregate productivity shocks are prevalent. In this case, external adjustments are useful for consumption smoothing: households borrow and save to prevent large fluctuations in consumption. Thus, the model generates less variable consumption (the ratio of standard deviation of consumption to standard deviation of output equals 0.79) and strongly procyclical current account adjustments (correlation with output equals 0.97). The model with only TFP shocks also cannot account for volatile wage movements (the ratio of standard deviation of wage to standard deviation of output equals 0.83, compared to 2.22 in the data), because borrowing from international capital markets provides a cushion for consumption and the worker’s outside option does not fluctuate as much in the wage bargaining in response to TFP shocks.

The “Only interest rate shocks” column shows that interest rate shocks contribute to generating higher variability for the labor market variables as well as consumption. As also shown in Figure 2, compared to TFP shocks of the same magnitude, interest rate shocks drive large fluctuations in consumption, as it directly affects intertemporal decision of consuming and saving, but has little impact on output.32 As a result of negligible movements of output in response to interest rate shocks, the standard deviation of output is very small and hence we do not report the consumption standard deviation relative to output.

As for the labor market dynamics, this setup with only interest rate shocks generates countercyclical vacancies and slightly procyclical unemployment that appears at odds with the data. The positive correlation of unemployment with output seems puzzling at first sight. If there are no TFP shocks and the only source of output fluctuations is changes in employment, it seems counterintuitive to have higher output when unemployment is high. This puzzle is resolved when we consider that the correlation reported in Table 5, ρ(y,u) = 0.10 is in fact ρ(yt, ut+1), that is, the correlation of the choice of unemployment at time t + 1 with output at time t. In the production function however, yt = F(k,(1–ut)l;zt). Therefore yt would be perfectly negatively correlated with ut but its correlation with ut+1 would be the negative of the autocorrelation of u. As reported in Table 5, ρ(u, u–1) = -0.10 while ρ(y, u) = 0.10.

To demonstrate that the different business cycle dynamics generated by the search-matching model compared to the standard RBC model comes from the endogenous transmission mechanism instead of the difference in labor supply elasticities, we extend our baseline model to include endogenous labor hours and fix the elasticity of working hours to be the same as in the standard RBC case. The results are reported in Column “Endog Labor.” In the “RBC” column in Table 5, the model generates a weakly countercyclical current account (–0.13) and lower variability of consumption relative to output implying that in the face of a negative TFP shock and higher interest rates, the household increases savings, but overall, the decrease in consumption is not larger than the decline in output. With a large adjustment in the labor supply, wage variability remains low and consumption is less variable than income. In contrast, in our search-matching model with endogenous labor hours, consumption declines more in response to the same set of shocks. This comes from two effects of labor market frictions: the strengthened precautionary saving motive and lower expected life-time income due to endogenous persistence built into the responses. The large drop in consumption reflects a significant increase in saving (in the form of accumulating foreign bonds), thus the current account becomes more countercyclical in our search model (ρ(y, ca/y) = −0.56) than the canonical RBC.

The variability of consumption generated in our search-matching model (both indivisible labor and endogenous labor hours) leads to a larger decline in wages. Since the equilibrium wage is a convex combination of marginal product of labor and the value of remaining unemployed and searching in the next period, a low consumption in bad times leads to an increase in the marginal utility of consumption that reduces the net gain of leaving the negotiation process and enjoying more leisure. A much tighter job market during the downturn makes it harder to find a job in the following periods, lowering workers’ threatening point in the wage bargaining. Wage variability is further reinforced by the variations in firms’ expected return from a match due to variations in the interest rate. Overall, wages are significantly more variable in the search-matching model. In addition, the fact that the value of being unemployed is not perfectly correlated with output leads to a lower procyclicality of wages in the search-matching model, which constitutes another improvement to the prototype SOE-RBC models. The model also does a good job in delivering a negative unemployment and vacancy rate correlation, consistent with the “Beveridge Curve”.33

4.5 Sensitivity Analysis

We now discuss our sensitivity analysis that focuses on the importance of parameters related to the search-matching frictions. The results are presented in Table 6. First, we reduce the unit cost of posting a vacancy, k, from 0.127 to 0.1. As the search cost of firms is lowered, more vacancies would be posted one period after a negative TFP shock, inducing more rapid reversion of the vacancy and consequently, unemployment. Since the prospect of being unemployed and searching in the next period is not as bad as in the baseline case, the household builds less savings. Hence, consumption drops less and the current account does not increase as much. In addition, compared to the baseline scenario, workers’ threatening point of wage bargaining becomes higher due to the higher possibility of finding a job in the following period and a higher value of leisure in consumption terms. Therefore, wage variability relative to that of output becomes lower.

Table 6:

Sensitivity Analysis

article image
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.

In the second experiment, we raise the natural separation rate, ψ, from 6 percent to 8 percent. Similar to the previous sensitivity analysis, raising ψ decreases the workers’ continuation value of being currently employed as the employment duration becomes shorter. For the firm, the continuation value of posting a vacancy is also reduced as an existing match may end with a higher probability. Ceteris paribus, the total surplus from a successful new match decreases with the higher natural breakup rate. Hence, vacancy responds less to exogenous shocks, and consequently, unemployment rate also becomes less responsive. Both vacancy and unemployment becomes less variable and more persistent compared to the benchmark case. Consistent with the slightly more stable labor market, the variabilities of consumption and wage decline.

Next, we examine the importance of the matching efficiency parameter, ω, by raising it to 0.85 from 0.778. In this case, more matches are formed for the same pair of unemployment and vacancy, which implies that the search friction becomes less severe. The results indicate that both consumption and wage become less variable and the current account becomes weakly countercyclical. In an extreme case when matching is infinitely efficient, the probability of finding a job and filling a vacancy is close to one.34 An unemployed worker would still experience a necessary unemployment spell but only for one period. Therefore, vacancy and unemployment both revert quickly, increasing the variability of both variables and reducing the risk of unemployment. As a consequence, the household does not need to reduce its consumption as much in response to a negative TFP shock, which, in turn, implies a lower wage reduction than in the benchmark scenario due to the increased bargaining power.

Finally, we examine the importance of the workers’ Nash bargaining weight, ξ. In order for the decentralized equilibrium to be the first best, the elasticity of matching function with respect to unemployment, α, also has to change accordingly with ξ. As shown in the last column of Table 5, when ξ and α increase from 0.5 to 0.7, unemployment rate varies less while vacancy varies more. This is because matching is more sensitive to unemployment and less so to vacancy. Moreover, as shown in the wage determination in Equation (10), as workers’ bargaining power increases, the equilibrium wage gets closer to the maximum value to a firm of a filled vacancy and moves further away from the minimum value necessary for an unemployed worker to join a new employment relationship. Overall, these sensitivity exercises show that our results are generally robust to the changes in the key search-matching parameters. Hence, MP type search frictions appear to better characterize the labor markets of EMEs than the Walrasian labor markets.

5 Matching Efficiency Shocks

In our baseline model, the allocative or matching efficiency, ω, is a fixed parameter. In this section, we explore the quantitative implications of introducing a random disturbance ϵtω to the matching efficiency. More specifically, we add shocks εω to our matching function Mt=wtutαvt1-α,ωt=(1+ϵtω)ω.. For a given pair of ut and vt, fluctuations in ωt affect the number of matches formed. These matching efficiency shocks could be allowed to interact with the other fundamental shocks as in Andolfatto (1996).35 We consider these shocks and their interaction with the other shocks of the economy to be particularly relevant for emerging economies, as these countries often experience structural changes and cross-sectoral reallocations during large economic fluctuations. Moreover, the labor markets tend to be more segmented across sectors in developing countries (see Agenor and Montiel (2008)). In fact, resources are often not instantaneously mobile or perfectly substitutable across different sectors. Even within sectors but across establishments, different jobs involve various skills and may require specific training. If the aggregate shocks affect different sectors in an asymmetric way, the difficulties associated with searching and matching with jobs from different sectors can be interpreted as an efficiency loss at the aggregate level.

Empirically, matching efficiency shocks can be motivated by the following observations regarding the Sudden Stop episodes. Kehoe and Ruhl (2009) document that substantial reallocations, which are often costly, take place from nontradable to tradable goods sectors following Sudden Stops. For example, in the aftermath of the Mexican crisis in 1994-1995, massive sectoral reallocations took place as the depreciation of real exchange rate drove down the relative price of nontradable goods. In the case of Mexico, the employment share of traded goods sector in total employment stopped following a downward sloping trend and even rose somewhat after the crisis. Figure 4 shows that similar patterns of cross-sectoral allocations are observed in other Sudden Stop episodes: e.g., Chile 1981-84, 1998-99 and Colombia 1998-99.36,37 Moreover, Benjamin and Meza (2007) argue that the Sudden Stops raise the cost of imported intermediate input in the investment sector and often lead to reallocation of labor from the investment sector to the consumption sector suggesting that there are differential effects on the labor variables across sectors. We study the potential impact of matching efficiency shock on the business cycle variables when matching across sectors are inherently more difficult than matching within sectors.

Figure 4:
Figure 4:

Sectoral Decomposition of Employment

Citation: IMF Working Papers 2012, 237; 10.5089/9781475511208.001.A001

Notes: These charts show the share of the tradable sector employment relative to the nontradable sector employment. Shaded areas show the corresponding sudden stop episodes in respective countries. The large depreciation of the real exchange rate in those countries drove down the relative price of nontradable goods, which in turn led to a massive sectoral reallocations; in Mexico, the employment share of traded goods sector in total employment stopped following a downward sloping trend and even rose somewhat after the crisis. Similar patterns of cross-sectoral allocations are observed in other Sudden Stop episodes as well.

Unfortunately, data on the direct measures of new hires and vacancy rate do not exist for emerging economies, making it impossible to estimate matching efficiency shocks. However, Andolfatto (1996) estimates a joint VAR(1) process of productivity shocks and matching efficiency shocks using the U.S. data and shows that the innovations to the matching shock is almost ten times the innovations to the technology shock and these two shocks are positively correlated. In line with this observation, we experiment with matching efficiency shocks that are positively correlated with TFP shocks. That is, at the aggregate level, times of high matching efficiency are associated with economic expansions and periods of low reallocation efficiency are accompanied by economic downturns. Our calibration strategy with regards to the matching efficiency shocks is to pin down ρω and var(eω) in order to match σ(u) and ρ(y, u). Specifically, the standard deviation of the innovation to the matching efficiency shock is set to be 10 percent with a persistence parameter of 0.6, and the correlation with the innovation to TFP is 0.5.38 Other ingredients of the VAR involving the matching efficiency shock were set to zero.

The results with matching efficiency shocks are presented in Table 7. The first column copies the baseline scenario results, the second column reports the findings of the scenario with matching efficiency shocks that are positively correlated with TFP and finally the last column documents the case with uncorrelated matching efficiency shocks. In the positively correlated matching efficiency shock scenario, since the matching efficiency is likely to be low when TFP is low, as discussed before, the stock of unemployment can be eliminated at a slower pace. This generates a more persistent unemployment (notice that the autocorrelation of unemployment (0.31) is higher than the baseline case (0.10)) and a significantly higher variability for unemployment and vacancy (16.24 and 14.56 compared to 3.24 and 5.59 in the baseline case). If the matching efficiency is low, the firms cut vacancies significantly because the probability of forming a match is smaller while the cost of keeping the vacancy is constant. Hence, vacancies fall dramatically leading to higher unemployment with one period lag. In the scenario with uncorrelated matching efficiency shocks, the only significant difference is with regard to the correlation of unemployment with output that becomes closer to zero. This is intuitive as the uncorrelated matching efficiency shocks lead to a decoupling of the matching process from the TFP process.

Table 7:

Matching Efficiency Shocks

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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(εz, εw) = 0.5) and acyclical (ρ(εz, εw) = 0) matching efficiency shocks.

The conventional search models of closed economies have difficulty in generating the high unemployment rate variability found in the data, unless the replacement rate is high.39 In our model extended to include matching efficiency shocks, an adverse matching efficiency shock directly reduces the job creation rate and leads to higher unemployment rate for the following period. Given that the steady state level of unemployment is about 8 percent and the other factor inputs are fixed, a one percentage point rise of unemployment rate leads to only a 0.056 percentage decrease of output, which is about one twentieth the size of the change in unemployment. This implies that the matching efficiency shock, itself, can lead to high relative variability of unemployment rate (relative to output) without affecting the variability of output and consumption significantly.

6 Conclusion

A SOE-RBC model featuring countercyclical interest rate shocks and search-matching frictions can perform well in accounting for the dynamics of consumption, the current account and the wages simultaneously. Quantitative results showed that our model improved upon the standard RBC model in many dimensions, underscoring the dynamic interaction of search-matching frictions along with countercyclical interest rates in accounting for EME stylized facts. As an illustrative extension, we augmented our baseline model to include shocks to the matching efficiency. With this feature, we showed that the model brought the unemployment variability significantly closer to data.

Exploring emerging market labor market dynamics using general equilibrium models is ripe for further research. This paper showed how far the modeling of the transitions from unemployment-employment (extensive margin) takes us in terms of explaining the key regularities. Our paper emphasizes the interaction between countercyclical interest rates and labor market frictions in understanding the labor market dynamics and other business cycle features. Our framework can be extended to investigate the effect of political regime changes on labor markets, the role of labor market regulation.

Emerging Market Business Cycles: The Role of Labor Market Frictions
Author: Ms. Emine Boz, Ceyhun Bora Durdu, and Ms. Nan Li