Labor Force Participation, Interest Rate Shocks, and Unemployment Dynamics in Emerging Economies∗ Alan Finkelstein Shapiro† Tufts University March 16, 2017

Abstract Emerging economies (EMEs) have highly volatile unemployment and real wages. Standard models with interest rate shocks can generate higher unemployment volatility, but still fall quantitatively short of matching the empirical volatility of unemployment. A small open economy search model with endogenous participation and self-employment—a feature of EMEs—generates 90 percent of the volatility of unemployment in the data, highly volatile wages, and quantitatively-consistent cyclical aggregate dynamics amid productivity and interest rate shocks of plausible magnitudes. Endogenous participation amplifies shocks and plays a critical role in overcoming a key limitation of standard search models for EMEs. JEL Classification: E24, E32, E44, F41 Keywords: Emerging economies, business cycles, unemployment volatility, search frictions, labor force participation.

∗

I thank Brendan Epstein and Sanjay Chugh for useful comments discussions. Any errors are my own. Department of Economics, Tufts University, Braker Hall, 8 Upper Campus Road, Medford, MA 02155. E-mail: Alan.Finkelstein [email protected]. †

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Introduction

Recent work has shown that emerging economies (EMEs) face high unemployment volatility, that this high volatility occurs within a context of highly volatile real wages, and that interest rate shocks can contribute to the volatility of unemployment and wages in these economies (Li, 2011; Boz, Durdu, and Li, 2015).1 Related studies have also stressed the relevance of the EME labor market structure—specifically, the prevalence of self-employment or informal employment (Table 1)—for aggregate fluctuations.2 However, from a quantitative standpoint, the volatility of unemployment implied by existing small-open-economy (SOE) search models continues to fall considerably short of its empirical counterpart, even amid interest rate shocks. Thus, the well-known limitation of standard search models for advanced economies (Shimer, 2005; Hall, 2005; and Hagedorn and Manovskii, 2008) extends to EMEs. Identifying the factors that explain the magnitude of unemployment fluctuations is crucial for better understanding business cycle dynamics and the impact of policy in EMEs. In this paper, I use Mexico as a representative EME to show that, once we incorporate the cyclical movements of labor force participation in the data, a SOE RBC search framework that embodies the EME employment structure can quantitatively generate more than 90 percent of the volatility of unemployment in the data. This result emerges amid a conventional calibration that features standard TFP and interest rate shocks of plausible magnitudes.3 The model’s ability to quantitatively replicate the variability of unemployment in the data stands in contrast with existing models that reproduce only a fraction of the volatility in the data under otherwise similar shocks. Moreover, the high volatility of unemployment in the model takes place against a backdrop of empirically- and quantitatively-factual volatile real wages and cyclical dynamics for a host of other labor market and macroeconomic variables (i.e., strongly countercyclical unemployment and self-employment, high relative investment, and a countercyclical trade balance).

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For evidence on nominal wage rigidities in EMEs, see Schmitt-Groh´e and Uribe (2016). See Fern´andez and Meza (2015), Finkelstein Shapiro (2014), and Finkelstein Shapiro and Mandelman (2016), among others. 3 I choose Mexico because the country has been extensively studied in both the EME business cycle literature and the literature on EME labor markets (see, for example, Bosch and Maloney, 2008; Lama and Urrutia, 2011; Finkelstein Shapiro, 2014; Boz, Durdu, and Li, 2015; Fern´andez and Meza, 2015; Finkelstein Shapiro and Mandelman, 2016; among others). 2

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Table 1: Volatility of Unemployment Rate and Real Wages and Average Self-Employment in Emerging Economies

Country

Argentina Brazil Chile Colombia Ecuador Korea Malaysia Mexico Peru Philippines South Africa Thailand Turkey

Unemployment Rate Volatility (Standard Deviation) 8.51 9.81 12.2 7.56 12.5 9.28 8.81 15.9 8.66 14.2 4.17 25.5 10.7

Real Wage Volatility (Standard Deviation) 6.92 1.77 7.16 3.63 5.20 1.53 10.43

Average Self-Employment (% of Non-Agricultural Employment) 24.9 32.3 28.9 51.3 47.6 31.8 24.9 34.9 51.7 47.4 15.8 57.1 41.8

Notes: Author’s calculations (unemployment volatility), Boz, Durdu, and Li (2015) (real wage volatility, subject to data availability; period coverage varies by country), and OECD (2009) (self-employment). Similar facts hold if we consider the relative volatility of unemployment. See the Appendix for details about the sources and time coverage for unemployment volatility and self-employment, where coverage varies depending on the country, and Boz, Durdu, and Li (2015) for coverage on wage volatility. The volatility measure is given by the standard deviation of the cyclical component of the variable, where the latter is computed using the Hodrick-Prescott (HP) filter with smoothing parameter 1600. Average self-employment corresponds to average self-employment expressed as a percent of total non-agricultural employment from 2000 to 2007, obtained from OECD (2009). See Boz, Durdu, and Li (2015) for similar facts on unemployment volatility in EMEs.

The framework I use is a modified version of Finkelstein Shapiro and Mandelman (2016) and features two production firms—salaried firms and self-employed firms—and two agents— households (who own production firms) and capital producers. Capital producers accumulate and decide how to allocate their (existing) capital stock between salaried firms—who interact with capital producers in frictionless (spot) capital rental markets—and potential self-employed firms—who interact with capital producers through matching (frictional) markets. Salaried firms rent capital from capital producers and hire workers in frictional labor markets. Households make salaried and self-employment labor force participation decisions, where self-employment searchers successfully exit unemployment to operate self-employed firms only if a successful capital match with capital producers occurs. Existing evidence highlights the relative difficulty that small (self-employed) firms face in obtaining external financing from formal credit markets in EMEs (Global Financial Development Report, 2014).4 Instead of modeling financial frictions for salaried (larger) firms, which adds unnec4

Table A5 in the Appendix shows that informal firms—defined as firms which are not registered with government authorities, most of which are self-employed or micro and small firms—have little access, if any, to formal credit (of note, these firms account, on average, for about 70 percent of firms in EMEs). As a result, informal firms rely on alternative financing sources, including input credit from suppliers and resources from

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essary complexity, I interpret the asymmetry in frictions in capital markets between salaried and self-employed firms as reflecting the relative difficulty of these firms in obtaining resources compared to salaried firms (Section 2 below briefly discusses how matching markets are consistent with existing evidence and why matching frictions matter). The intuition behind the model’s success is as follows. Consider an adverse (TFP or interest rate) shock to the economy. Total labor force participation, salaried employment, investment, consumption, wages, and output all contract, whereas unemployment and selfemployment rise. These cyclical dynamics are consistent with those observed around recessions in EMEs. Amid the shock, households react to the fall in salaried employment conditions by reallocating their non-employed members’ search activity away from salaried work and towards self-employment (in recessions, the latter becomes a better outside option in relative terms; also, the expansion of search for self-employment contributes to producing the correct cyclical correlation of unemployment and output in the data). Households’ ability to explicitly make sectoral participation decisions amplifies the response of salaried employment, investment, wages, and output to shocks relative to a model without such margin as the reallocation of individuals in the labor force further reduces firms’ job-filling probabilities and raises the effective cost of posting vacancies. The sharper response of vacancies also affects salaried capital demand and eventually translates into a larger contraction in investment as salaried firms account for the bulk of capital demand. Interest rate shocks are particularly relevant because they are important contributors to consumption dynamics, and the behavior of consumption influences both households’ and firms’ discounting of the future via movements in the stochastic discount factor. The latter affects firms’ hiring and capital demand decisions, but more importantly households’ participation decisions as well. After an interest rate shock, households respond by altering their allocation of searchers. This reallocation affects firms’ job-filling probabilities and makes firms’ decisions more sensitive to shocks over and above what movements in firms’ discounting would imply absent endogenous participation. This amplifies the economy’s response to a given set of shocks in the benchmark model. Ultimately, this implies that in equilibrium and for identically-sized disturbances, interest rate shocks will produce much family and friends. Formal (registered) firms also face credit constraints but have relatively better access to formal credit (see the evidence in Tables A5 for all firms, and Tables A6 and A7 for formal firms only in the Appendix).

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sharper fluctuations in unemployment (and wages) relative to both productivity shocks and to models without endogenous participation. Of note, since participation is procyclical, a strong response of participation after a shock can generate counterfactual movements in unemployment. The presence of countercyclical self-employment, which is consistent with the data, limits the otherwise strong procyclicality of participation and delivers a particularly good empirical fit, not only in absolute terms but also relative to simpler model alternatives that abstract from self-employment or labor force participation. Furthermore, by influencing workers’ outside options, self-employment makes vacancy postings more sensitive and further amplifies the impact of shocks, ultimately leading to sharper (and therefore more factual) unemployment movements relative to models where self-employment and labor force participation are absent. All told, this makes self-employment, along with labor force participation, an important ingredient for quantitatively matching the data. My work is related to existing work that tries to explain the high volatility of unemployment in the data (Shimer, 2005; Hall, 2005; Krause and Lubik, 2006; Hagedorn and Manovskii, 2008; among others, for the U.S.; Boz, Durdu, and Li, 2015, in EMEs). It contributes to the business cycle literature on EMEs (Neumeyer and Perri, 2005; Uribe and Yue, 2006; Chang and Fern´andez, 2013) and their labor markets (Lama and Urrutia, 2011; Li, 2011; Finkelstein Shapiro, 2014; Fern´andez and Meza, 2015; Boz et al., 2015, Schmitt-Groh´e and Uribe, 2016), and to the search literature that incorporates richer features of the labor market, including labor force participation (T¨ uzemen, 2012, for the U.S.; Finkelstein Shapiro and Mandelman, 2016, for EMEs).5 Closest to my interest on unemployment volatility are Boz, Durdu, and Li (2015). They are the first to stress the relevance of interest rate shocks for unemployment and wage volatility in EMEs by using a standard SOE labor search framework. While interest rate shocks do appear to be relevant for EME labor market dynamics, standard models with these shocks generate roughly 1/4 of the observed volatility of unemployment in the data. In contrast, the mechanism I put forth can replicate more than 90 percent of the volatility 5

Other papers that model the rich structure of labor markets in EMEs in a business cycle context include Epstein and Finkelstein Shapiro (2017a, 2017b) and Finkelstein Shapiro and Gonz´alez G´omez (2016). In particular, the latter two suggest that microfounded financial frictions in an EME context may play a limited role in generating high unemployment volatility. Among the aforementioned studies, Li (2011) and Fern´ andez and Meza (2015) are the only papers based on a Walrasian labor market. Also, Schmitt-Groh´e and Uribe (2016) focus on nominal wage rigidities and a notion of unemployment in a model without search-based unemployment.

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in the data under a plausible calibration. Thus, my main contribution relative to their work and the existing literature is to highlight a plausible, microfounded amplification mechanism rooted in endogenous participation and the interaction between sectoral participation and self-employment—two margins that Boz et al. (2015) abstract from—that can quantitatively explain the bulk of the volatility of unemployment (and wages) in the data and simultaneously generate factual aggregate dynamics in EMEs. As such, I illustrate how the combination of interest rate shocks and a more factual EME employment structure overcomes a key limitation that standard search models face in quantitatively replicating the high volatility of unemployment in EMEs. More broadly, my findings suggest that labor force participation movements play an important role in the amplification and propagation of shocks and in explaining labor market dynamics in EMEs. At the same time, the labor market structure of these economies should be adequately taken into account to comprehensively match other EME stylized facts. The model structure I rely on is based on Finkelstein Shapiro and Mandelman (2016). There are three main differences relative to their work. First, my main focus is on the role of interest rate shocks and key features of labor markets for quantitatively explaining the volatility of unemployment in EMEs. In contrast, Finkelstein Shapiro and Mandelman (2016) study how the cyclicality of remittances affects employment and business cycles and abstract from the role of interest rate shocks. Second, I abstract from remittance fluctuations as they are not critical for the mechanisms I stress.6 Third, I decentralize the capital accumulation and allocation process by distinguishing between capital producers and salaried firms. This modification accommodates a more general input-output structure and proves to be nontrivial in quantitatively replicating key features of labor market dynamics—including the countercyclicality of self-employment and unemployment in the data—amid interest rate shocks. This modification also unambiguously provides a better quantitative fit with the data.7 As such, the framework I present captures a more comprehensive set of business cycle 6

While remittances are very volatile and partially contribute to the volatility of unemployment, they cannot quantitatively explain the latter in the data, suggesting that other shocks and mechanisms may be at play (Finkelstein Shapiro and Mandelman, 2016). 7 In Finkelstein Shapiro and Mandelman (2016), salaried firms accumulate capital internally and then attempt to match any unused capital with potential self-employed individuals. The separation between capital suppliers and firms in my framework is not critical for qualitatively matching the main facts in the absence of interest rate shocks. This explains why the model in Finkelstein Shapiro and Mandelman (2016) provides a reasonable fit with the data with respect to sectoral employment in the absence of interest rate shocks.

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facts relative to Finkelstein Shapiro and Mandelman (2016). The main contributions of the paper are twofold. First, I show that quantitatively capturing the cyclical dynamics of labor force participation plays a critical role in generating quantitatively-factual unemployment volatility in a typical EME, suggesting that labor force participation decisions may be important for understanding unemployment dynamics in EMEs. Second, I highlight how a combination of well-known features of EMEs—mainly interest rate shocks and the employment structure amid endogenous participation, both of which had thus far been studied in isolation—can plausibly explain the quantitative cyclical behavior of unemployment while simultaneously and successfully capturing other well-known business cycle regularities in EMEs. More broadly, I present a framework that represents a clear quantitative improvement on the labor market front relative to existing search models that sheds light on important features of EMEs that can explain the data. The rest of the paper is structured as follows. Section 2 presents the model. Section 3 provides details regarding the calibration. Section 4 presents the quantitative analysis and discusses different extensions and robustness experiments. Section 5 concludes.

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The Model

There are two types of production firms—salaried firms and self-employed (owner-only) firms— and two agents—households (who own salaried and self-employed firms) and capitalsupplying entrepreneurs (I refer to these entrepreneurs as capital producers). Each agent has a unit mass. Each period, capital producers choose future capital and decide how to allocate their current capital stock between renting it to salaried firms—this takes place via frictionless markets—and matching it with potential self-employed firms—this takes place via matching markets. Newly matched capital with self-employed firms today becomes productive tomorrow.8 The use of matching markets is relevant for two reasons. First, it is consistent with evidence on small firms’ heavier dependence on input-based supplier credit—which is rooted in long-term relationships with suppliers and is rarely tied to the provision of collateral—as one of the main sources of external financing (IDB, 2005; Beck and Demirg¨ u¸c-Kunt, 2006; Beck, Demirg¨ u¸c-Kunt, and Maksimovic, 2008; Ayyagari, Demirg¨ u¸c8

See Kurmann (2014) for an environment with frictional capital markets and Walrasian labor markets.

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Kunt, and Maksimovic. 2012; Allen et al., 2012; IFC, 2010a, 2010b, 2013).9 Furthermore, relative to larger (salaried) firms, self-employed firms face more frictions and external finance constraints such that the asymmetry in frictions between salaried and self-employed firms captures this fact tractably. Second, as shown in existing theoretical work, the inclusion of capital matching frictions to model self-employment in EMEs plays a central role in generating the countercyclicality of self-employment in the data (Finkelstein Shapiro, 2014; Finkelstein Shapiro and Mandelman, 2016).10 Households are comprised of a large measure of members. The latter can be: unemployed and searching for either salaried employment or self-employment; working as salaried workers; working as self-employed individuals; or outside of the labor force. Households explicitly choose the measure of members looking for salaried employment or self-employment and desired employment in each firm category—that is, sectoral (and therefore aggregate) labor force participation is endogenous. The sum of all employed individuals and all searchers (regardless of employment category) represents the total labor force. Salaried and self-employed firms produce an identical good with differing technologies. Salaried firms use salaried labor and capital to produce. They demand capital from capital producers and post (costly) vacancies to attract salaried workers. In turn, each self-employed individual uses a single unit of matched capital from capital producers and an inelasticallysupplied unit of his own labor to produce. Thus, the measure of capital in self-employment is also the measure of self-employed individuals (Finkelstein Shapiro, 2014; Finkelstein Shapiro and Mandelman, 2016). An additional note on capital search frictions: while standard collateral constraints seem, in principle, a natural way to model frictional self-employment, these constraints would not 9

According to IFC data, only 20 percent of firms in EMEs, the majority of which are salaried and larger firms, have access to external financing from formal financial intermediaries. In Mexico, Pav´ on (2010) documents that close to 70 percent of external financing for micro and small firms—most of which are owneronly—comes from relationships with input suppliers. In a cross-country survey that encompasses several countries in Latin America and Asia, close to 50 percent of small entrepreneurs cited searching for input suppliers to obtain resources as a way to overcome the availability of formal financing (IDB, 2005). Epstein and Finkelstein Shapiro (2017) and Finkelstein Shapiro and Mandelman (2016), and Finkelstein Shapiro and Gonz´alez G´omez (2016) present similar evidence on small firms’ reliance on input credit relationships in EMEs, where this evidence provides empirical support for the use of capital search frictions. Also, the fact that micro and small (owner-only) firms in EMEs rely heavily on input credit relationships with suppliers and not on credit from formal financial institutions, as is the case in more advanced economies where credit access for smaller firms is more prevalent, explains my focus on EMEs. 10 See Bosch and Maloney (2008) and Fern´andez and Meza (2015) for evidence on the countercyclicality of self-employment in EMEs.

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be able to generate the countercyclicality of self-employment in the data since collateral constraints become tighter during recessions, thereby preventing countercyclical self-employment entry from unemployment as observed in the data (see Bosch and Maloney, 2008). Hence the focus on capital search frictions. Importantly, collateral constraints require having pledgable collateral. The latter is very difficult to come by among the self-employed since (1) the majority of the self-employed in EMEs are informal and lack appropriate documentation and records that facilitate access to formal (bank) credit, and (2) the contracting, institutional, legal environments needed to sustain collateral registries remains underdeveloped.11 As a result, the self-employed need to devote resources to search for alternative sources of external financing, including input suppliers.

2.1

Capital Producers

Capital-supplying entrepreneurs (or input suppliers) choose consumption ck,t , capital accumulation kt+1 , the share of capital rented to salaried firms ωt , and desired capital in P t self-employed firms ne,t+1 to maximize E0 ∞ t=0 β u(ck,t ) subject to the budget constraint ck,t = rs,t ωt kt + re,t n e,t − i t + [(ρe − δ)ne,t − (1 − ρe )qe,t (1 − ωt )kt ] ,

(1)

the evolution of total capital kt+1 = (1 − δ) kt + it ,

(2)

and the perceived evolution of capital in self-employed firms ne,t+1 = (1 − ρe ) [ne,t + qe,t (1 − ωt ) kt ] ,

(3)

where u′ (·) > 0, u′′ (·) < 0. rs,t denotes the capital rental rate for salaried firms (determined in competitive markets), ωt kt is the amount of total capital kt rented to salaried firms, re,t is the capital rental rate for self-employed firms (which, as a result of search frictions, is determined via Nash bargaining), and it is total investment. The first term inside the brackets in the budget constraint, (ρe − δ)ne , captures the (depreciated) capital that returns to capital producers when capital relationships with self-employed firms end with exogenous 11

For recent work on the introduction of moveable assets as collateral, see Campello and Larrain (2016).

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probability ρe . The second term captures the fact that any capital supplied for matching with new self-employed firms, (1 − ωt )kt , is successfully matched with endogenous probability qe,t (defined further below). This capital becomes productive next period with probability (1−ρe ), and cannot be used for consumption or future capital accumulation once matched. (1 − ωt )kt represents input credit to the self-employed. All told, from the capital producers’ perspective, new capital matches are given by (1 − ρe ) (1 − ωt ) kt qe,t and therefore the perceived evolution of capital in self-employed firms ne,t+1 shows that these new matches add to the future stock of capital in self-employment ne,t+1 (given the assumption of one unit of matched capital per self-employed, therefore, they also add to the measure of future self-employed individuals). Finally, since ωt is a choice variable, the allocation of capital between salaried and potential self-employed firms responds contemporaneously to shocks. Optimal total capital accumulation and the allocation of capital between salaried and new self-employed firms are characterized by 1 = Et Ξkt+1|t {rs,t+1 + (1 − δ)} ,

(4)

and   rs,t + (1 − ρe ) qe,t rs,t+1 + (1 − ρe ) qe,t+1 e k e = (1 − ρ ) Et Ξt+1|t re,t+1 + (ρ − δ) + , qe,t qe,t+1

(5)

where Ξkt+1|t ≡ βu′ (ck,t+1 )/u′ (ck,t). The first equation is a standard capital Euler equation that equates the marginal cost of accumulating a unit of capital to the expected marginal benefit of supplying that unit of capital to salaried firms, where the latter is effectively given by the expected rental rate of capital to salaried firms and the value of a unit of capital net of depreciation. The second equation amounts to a self-employment capital supply condition. The left-hand-side denotes the expected marginal cost of devoting an additional unit of capital to matching with potential self-employed individuals. This is given by the opportunity cost of that unit of capital (i.e., the return from renting that unit of capital to salaried firms) as well as a term that captures the fact that matched capital is committed to self-employed firms and remains idle right after being matched until it becomes productive next period. The right-hand-side is the expected marginal benefit of a new capital match. The latter is given by the Nash rental rate that the capital producer would obtain next

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period, the net benefit of recovering a separated unit of capital from the self-employment sector next period, and the continuation value of the capital relationship.12

2.2

Salaried Production

Salaried firms demand capital ks,t , post vacancies vs,t , and choose desired salaried employment ns,t+1 to maximize

E0

∞ X

Ξht|0 [zt F (ns,t , ks,t) − wst ns,t − rs,t ks,t − ψvs,t ] ,

t=0

subject to the perceived evolution of salaried employment ns,t+1 = (1 − ρs ) [ns,t + vs,t qs,t ] ,

(6)

where F (·) is a constant-returns-to-scale production function, ψ is the exogenous flow cost of posting vacancies, qs,t is the endogenous job-filling probability (defined below), and rs,tks,t is the cost of renting capital. The solution to the salaried firm’s problem yields standard capital demand and job creation conditions: rs,t = zt Fks (ns,t , ks,t),

(7)

  ψ ψ s h = (1 − ρ ) Et Ξt+1|t zt+1 Fns ,t+1 − ws,t+1 + , qs,t qs,t+1

(8)

and

The capital demand equation equates the capital rental rate to the marginal product of salaried-firm capital; the job creation condition equates the expected marginal cost of posting a vacancy to the expected marginal benefit. Note that in equilibrium ks,t = ωt kt .13 12

As shown below, in equilibrium, rs is equal to the marginal product of salaried-firm capital, so these conditions are similar to the ones presented in Finkelstein Shapiro and Mandelman (2016), except for the difference in stochastic discount factors between production firms and capital producers (recall that households and capital producers are separate agents). 13 This implies that ks,t responds contemporaneously to shocks since ωt is a choice for capital producers in period t.

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2.3

Households and Self-Employment

There is a representative household with a large number of members and perfect consumption insurance within the household. Members can be: searching for salaried employment ss , searching for capital to become self-employed se , working in salaried firms ns , working in self-employment ne , or outside the labor force. Normalizing the total population to 1, let lf pt denote total labor force participation (also the labor force participation rate), where lf pt = ss,t +se,t +ns,t +ne,t . Also, the total unemployment (employment) level is st ≡ se,t +ss,t (nt ≡ ne,t + ns,t ) and the unemployment rate is ut ≡ st /lf pt . Households choose consumption ch,t, the measure of self-employed and salaried searchers se,t and ss,t , desired sectoral employment ne,t+1 and ns,t+1 , and foreign debt b∗t to maximize ∞ X E0 β t [u(ch,t ) − h(ss,t + ns,t ) − g(se,t + ne,t )] , t=0

subject to the budget constraint ch,t + Rt−1 b∗t−1 = b∗t + ws,t ns,t + (zt − re,t )ne,t + Πs,t ,

(9)

and the perceived evolution of self-employment and salaried employment ns,t+1 = (1 − ρs )[ns,t + ss,t fs,t ],

(10)

ne,t+1 = (1 − ρe )[ne,t + se,t fe,t ].

(11)

and

The subutility functions for consumption and sectoral participation satisfy u′ (·) > 0, u′′ (·) < 0, h′ (·) > 0, h′′ (·) > 0, g ′(·) > 0, g ′′ (·) > 0. ws,t is the real salaried wage rate (determined via Nash bargaining), Rt = Rt∗ + Θ(b∗t − b∗ ) is the gross country real interest rate, where Θ(b∗t − b∗ ) is a portfolio adjustment cost function needed to avoid non-stationarity in the stock of foreign debt, and Rt∗ is the exogenous foreign interest rate (Schmitt-Groh´e and Uribe, 2003). Each self-employed individual receives (zt − re,t ) in real income, where zt denotes exogenous aggregate productivity. Πs,t represents salaried-firm lump-sum profits. Turning to the evolution of sectoral employment, ρs is the exogenous salaried separation probability, fe,t is the household’s endogenous probability of finding capital for self-employment, and fs,t 11

is the endogenous salaried job-finding probability (both defined further below). I abstract from any exogenous income while being unemployed since the majority of EMEs do not have unemployment insurance schemes.14 Optimal allocations are characterized by a standard consumption-savings Euler equation u′ (ch,t ) = βEt Rt u′ (ch,t+1 ),

(12)

and participation decisions for salaried workers and self-employed individuals:

and

    h′t+1 1 1 h′t s h = (1 − ρ )Et Ξt+1|t ws,t+1 − 1 − , u′ (ch,t ) fs,t fs,t+1 u′ (ch,t+1 )

(13)

    ′ gt+1 gt′ 1 1 e h = (1 − ρ )Et Ξt+1|t zt+1 − re,t+1 − 1 − , u′ (ch,t) fe,t fe,t+1 u′ (ch,t+1 )

(14)

where Ξht+1|t ≡ βu′ (ch,t+1 )/u′ (ch,t ), and h′t and gt′ denote the partial derivatives of the disutility from salaried participation and the disutility from self-employment participation, respectively. The salaried participation condition equates the expected marginal cost of searching for salaried employment—given by the marginal disutility from searching, adjusted for the job-finding probability—to the expected marginal benefit—given by the expected wage (net of the disutility from participation) and the continuation value from staying in salaried employment. The self-employment participation condition equates the expected marginal cost of searching for capital for self-employment—given by the disutility from searching for capital, adjusted by the probability of a capital match—to the expected marginal benefit— given by the expected net individual self-employment income (that is, net of the disutility from participation), plus the continuation value of staying self-employed.

2.4

Matching Processes

Let m(ss,t , vs,t ) and m(se,t , (1 − ωt )kt ) be standard constant-returns-to-scale labor and (capital) matching functions that bring together salaried searchers ss and vacancies vs (selfemployment searchers se and available capital for self-employment (1 − ω)k). The en14

That is, the contemporaneous value of unemployment in zero.

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dogenous salaried matching probabilities are given by qs,t = q(θs,t ) = m(ss,t , vs,t )/vs,t and fs,t = f (θs,t ) = m(ss,t , vs,t )/ss,t where salaried market tightness is θs,t = vs,t /ss,t . The corresponding capital matching probabilities are qe,t = q(θe,t ) = m(se,t , (1 − ωt )kt )/(1 − ωt )kt and fe,t = f (θe,t ) = m(se,t , (1 − ωt )kt )/se,t where capital market tightness θe,t = se,t /(1 − ωt )kt .

2.5

Price Determination and Market Clearing

The Nash wage and self-employment capital rental rates are determined by bilateral Nash bargaining between households and salaried firms and households and capital producers, respectively. The details regarding the value functions and the Nash bargaining process are presented in the Appendix for expositional brevity. The Nash wage and capital rental rate are given by: ws,t

 h′t = νzt Fns (ns,t , ks,t) + (1 − ν) ′ , u (ch,t ) 

(15)

and re,t

 = (1 − ν) zt +

gt′ ′ u (ch,t )



1 −1 fe,t





 r s,t −ν , qe,t

(16)

where ν is the (common) bargaining power of salaried workers and self-employed individuals.15 Intuitively, the Nash wage depends on a convex combination of the marginal product ′

of salaried labor and the disutility cost from participating in the labor market h′t /u (ch,t ) (recalling the optimal labor force participation decision, this depends on market tightness via the job-finding probability fs,t ). In particular, an increase in salaried searchers implies a higher disutility from participation, which generates upward pressure on wages as household searchers need to be compensated for the incurred participation costs. Analogously, the Nash capital rental rate depends positively on aggregate productivity and negatively on the household’s effective disutility from participation. Furthermore, the Nash rental rate depends negatively on the salaried capital rental rate. Intuitively, for a given level of the capital producer’s capital stock, a higher r s implies that a larger share of the total capital stock is available for matching with potential self-employed individuals. The greater availability of capital for self-employment all else equal reduces the self-employed’s cost from renting capital in frictional markets.16 A higher qe,t implies that less capital is available for 15

There is no available data that points to potential differences in bargaining powers between salaried workers and the self-employed. Also, introducing such differences does not change the main conclusions in the paper. As such, I assume the same bargaining power for workers and self-employed individuals. 16 Recall that in equilibrium rs,t = zt Fks (ns,t , ks,t ) and ks,t = ωt kt .

13

matching with self-employed individuals relative to the demand for capital, which makes matched capital more expensive for self-employed individuals. Finally, total output is given by the sum of salaried and self-employment output, yt = ys,t + ye,t . Total consumption is ct ≡ ch,t + ck,t . The aggregate resource constraint of the ∗ economy is yt = ct + ψvs,t + it + b∗t−1 Rt−1 − b∗t .

3

Calibration

Functional Forms and Shocks The utility function for households and capital producers is u(c) = c1−σ /(1 − σ), σ > 0. The matching functions are Cobb-Douglas: m(vs,t , ss,t ) = 1−ξ Ms sξs,t vs,t and m(se,t , (1 − ωt )kt ) = Me sξe,t ((1 − ωt )kt )1−ξ , where Ms and Me denote sec-

toral matching efficiency in salaried work and self-employment, respectively. The salaried a production function is F (ns,t , ks,t) = n1−α s,t ks,t , 0 < α < 1. The disutility of salaried and

self-employment participation are given by h(ns,t + ss,t ) = λ (ns,t + ss,t )1+1/φ /(1 + 1/φ) and g(ne,t + se,t ) = λ (ne,t + se,t )1+1/φ /(1 + 1/φ) where λ, φ > 0 (Arseneau and Chugh, 2012; Finkelstein Shapiro and Mandelman, 2016). The foreign debt adjustment cost is Φ (b∗t − b∗ ) = ηb [exp(b∗t − b∗ ) − 1], with ηb > 0. Both aggregate productivity and the foreign interest rate follow independent AR(1) processes in logs: ln(xt ) = (1 − ρx) ) ln(x) + ρx ln(xt−1 ) + εxt , where 0 < ρx < 1 and εxt ˜N(0, σx ) for x = z, R∗ . Parameters from Literature The time period is a quarter. I calibrate the model to Mexico, an EME whose labor market has been studied more extensively due to the availability and quality of data on labor flows.17 I set the relative risk aversion parameter σ = 2, the depreciation rate δ = 0.025, and the capital share α = 0.32, all standard values in the literature. I normalize steady-state exogenous aggregate productivity z = 1. The exogenous separation rates are set to ρs = 0.05 and ρe = 0.02, in line with evidence for Mexico (Bosch and Maloney, 2008). The foreign-debt adjustment parameter ηb = 0.001, a small number that does not affect aggregate dynamics (Garc´ıa-Cicco, Pancrazi, and Uribe, 2010; Chang and Fern´andez, 2013). Alternative small values do not affect the main results. The steady state gross foreign interest rate R∗ = 1.1015 (Fern´andez and Meza, 2015). The persistence 17

See, for example, Bosch and Maloney (2008); Lama and Urrutia (2011); Finkelstein Shapiro (2014); Boz, Durdu, and Li (2015); Fern´andez and Meza (2015); Finkelstein Shapiro and Mandelman (2016).

14

of the exogenous processes are ρz = 0.94 and ρR∗ = 0.70, which are consistent with those used in related literature (see, for example, Aguiar and Gopinath, 2007; Neumeyer and Perri, 2005; Boz, Durdu, and Li, 2015).18 Calibrated Parameters Following the search literature, I assume that the bargaining power and the matching elasticity are equal (ν = ξ). Parameters λ, ψ, Me , Ms , ν(= ξ), b∗ , φ, σz , σR∗ are then chosen to match targets consistent with Mexican data: a steady-state labor force participation rate of 0.60, an exogenous cost per vacancy of 3.5 percent of wages, a steadystate share of self-employment in the labor force of 0.23, a steady-state job-finding probability of 0.75, a steady-state share of total consumption in GDP of 0.68, a steady-state foreign debt-GDP ratio equal to 0.30, a volatility of labor force participation of 0.865, a volatility of output of 2.294, and a volatility of consumption of 2.729.19 The resulting parameter values are: λ = 9.9994, ψ = 0.0493, Me = 0.0415, Ms = 0.0233, ν = ξ = 0.2269, b∗ = 1.45, φ = 0.712, σz = 0.00937, σR∗ = 0.017775. Of note, the magnitude of productivity and interest rate shocks is consistent with existing literature on EME business cycles and within the range of values in other studies for Mexico (Lama and Urrutia, 2011; Boz, Durdu, and Li, 2015). Also, note that the standard deviation of productivity shocks is relatively small compared to the volatility of output in the data (2.294). This is partly a reflection of the model’s amplification mechanism rooted in endogenous participation, which allows the model to generate factual aggregate dynamics under plausible shock magnitudes for aggregates productivity and interest rates. Notably, the resulting elasticity of labor force participation, which is given by φ and is chosen to match the volatility of labor force participation in the data, is smaller than one. Therefore, the model’s success in generating high unemployment volatility does not depend on having a high elasticity of labor force participation.20 18

Of note, the value for ρR∗ is consistent with the value obtained by estimating an AR(1) process using data on real U.S. interest rates (as proxied by the 3-month U.S. Treasury bill adjusted for inflation) from 1993Q1 to 2014Q4 (our sample period for other moments). 19 These last two volatility targets are obtained using NIPA Mexican data from 1993Q1 to 2014Q4; the volatility of participation is based on available data from Mexico’s current employment survey, ENOE. This survey spans a shorter time period since it replaced the original employment survey, ENEU. 20 Note that this elasticity is different from the Frisch elasticity of labor supply since the model only includes the extensive margin of labor. However, the fact that this elasticity is smaller than one is still noteworthy as it implies that the model does not need implausible parameter values to quantitatively generate factual dynamics.

15

4

Quantitative Analysis

For future reference, Table 2 presents relevant calibrated parameter values for the benchmark model as well as two alternative model versions—a model with endogenous participation but no self-employment and a model with neither endogenous participation nor self-employment. I use these alternative specifications to assess the advantages and limitations of the benchmark model.21 Note that I use the same calibration targets across all models, implying that the calibrated parameter values will naturally differ across models. The main conclusions from Figure 1 and Table 3 (presented further below) regarding the benchmark model’s performance vis-`a-vis other models hold equally well if I use the same calibrated parameter values across all models. Table 2. Calibrated Parameters in Benchmark Model and Alternative Models

4.1

Calibration

Parameter

Parameter Value, Benchmark Model

Parameter Value, No Self-Empl. (SE)

Target lf p = 0.60 ψ = 0.035w f (θs ) = 0.75 ne /lf p = 0.23 c/y = 0.68 σlf p = 0.865 σy = 2.294 σc = 2.729

λ ψ Ms Me ν=ξ φ σz σR∗

9.9994 0.0493 0.0415 0.0233 0.2269 0.712 0.00937 0.017775

5.9971 0.0510 0.0300 − 0.2566 0.447 0.014974 0.01674

Parameter Value, No SE and No Endog. Participation − 0.0510 0.0300 − 0.2566 − 0.016479 0.016195

Intuition: Impulse Response Functions

To understand the intuition behind the main results I present further below, Figure 1 plots impulse response functions to an adverse interest rate shock for: (1) the benchmark model (solid blue line); (2) the model with endogenous participation but no self-employment (dashed red line); and (3) the model that abstracts from both self-employment and labor force participation (i.e., a standard search model; green line with markers). I present the impulse response functions to an aggregate productivity shock, which are qualitatively similar to those for interest rate shocks, in Figure A1 in the Appendix. The general intuition carries through to the case of productivity shocks. As noted earlier, since the calibration strategy I adopt involves setting σz and σR∗ such that each model reproduces the same volatility of output and consumption in the data, I standardize the impulse response functions by the standard deviation of the corresponding shock for each model. This makes the impulse 21

The parameters borrowed from existing literature remain the same across models.

16

responses across models readily comparable and makes the amplification mechanisms in the benchmark model more transparent given that the shocks across models are of the same magnitude. Figure 1: Response to an Adverse Interest Rate Shock: Benchmark, No LFP, No SE and No LFP

% Dev. from SS

Total Output

Agg. Consumption

Investment

0.5

0

2

0

−0.5

0

−0.5

−1

−2

−1

0

10

20

30

−1.5

0

10

% Dev. from SS

Unemployment

30

−4

Vacancies

5

20

0

0

−5

−20

0

10

20

30

Labor Force Participation 0.5

0

−10

0

10

20

30

−40

0

% Dev. from SS

Wage

10

20

30

−0.5

0

Salaried Employment

0 −1

10

20

30

Salaried Searchers

1

10

0

0

−1

−10

−2 −3 −4

0

10

20

30

Self−Employment % Dev. from SS

20

−2

0

10

20

30

0

Self−Employment Searchers

0.4

10

0.3

10

20

30

Interest Rate 1

5

0.2

0.5 0

0.1 0

−20

0

10

20

30

−5

0

Quarters

10

20

30

0

0

Quarters Benchmark

No SE

10

20

30

Quarters No SE, No LFP

Figure 1 shows that endogenous labor force participation, by itself, amplifies the response of labor market variables, investment, and output to interest rate shocks. A similar claim holds for productivity shocks, but as I discuss below, the response is larger under interest rate disturbances. Furthermore, the interaction between endogenous participation and (frictional) self-employment—a central element of the benchmark model—amplifies these re17

sponses further. Of note, unemployment in the benchmark model is particularly responsive to interest rate shocks, much more so relative to version (3), and more factual than version (2) (where unemployment initially falls considerably as a result of the sharp contraction in participation). Intuitively, an exogenous increase in interest rates pushes households to sharply reduce consumption, which lowers households’ stochastic discount factor. All else equal, the latter reduces salaried firms’ incentive to demand capital and hire workers, which puts downward pressure on wages. The latter reduces the value of searching for salaried employment, thereby pushing households to reduce the measure of salaried searchers. The fall in salaried participation—which all else equal sharply reduces salaried firms’ job-filling probability and therefore raises the expected marginal cost of posting vacancies—implies that salaried firms’ vacancy posting decisions become much more sensitive relative to an economy where endogenous participation is absent. The sharper response of vacancies and capital demand eventually translates into a larger contraction in investment as salaried firms account for the bulk of capital demand. The lower demand for capital by salaried firms implies that, relative to trend, there is more idle capital and therefore more capital available for matching with potential self-employed individuals. All else equal, this increases households’ perceived probability of finding capital. Coupled with the fall in salaried employment opportunities, households optimally reallocate their searchers away from salaried search into self-employment search. The rise in the latter puts upward pressure on both unemployment and labor force participation. Ultimately, participation contracts initially and eventually returns back to trend, consistent with its procyclicality in the data (Finkelstein Shapiro and Mandelman, 2016). The peculiar fact that unemployment initially contracts but subsequently rebounds sharply as the shock subsides and salaried searchers enter the labor force in both the benchmark model and the model without self-employment is not unique to the framework I present. In fact, this result is common in search models with endogenous participation that capture the procyclicality of participation (T¨ uzemen, 2012; Finkelstein Shapiro and Mandelman, 2016).22 22

The intuition is as follows: an adverse shock reduces wages and pushes households to reduce search for employment. In turn, this puts downward pressure on unemployment and explains why unemployment initially falls if participation is factually procyclical (as is the case in this model, see Table 3). The presence of self-employment partially offsets this as search for resources needed for self-employment increases during recessions, thereby putting upward pressure on unemployment (see Finkelstein Shapiro and Mandelman, 2016, for similar intuition).

18

Importantly, the sharp subsequent rise in unemployment—driven by both the recovery in salaried searchers and the sharper contraction in salaried employment—allows the model to successfully generate the countercyclicality of unemployment in the data, as shown in Table 3 further below. Moreover, note that the countercyclicality of self-employment improves salaried workers’ outside options during the downturn, which all else equal puts upward pressure on wages and therefore pushes salaried firms to reduce vacancies by more relative to an economy where self-employment is absent. As such, the presence of self-employment further amplifies the impact of the shock on vacancies (and salaried employment) and capital demand via changes in salaried workers’ outside options. This interacts with the response of salaried searchers, and hence labor force participation, ultimately leading to sharper (and therefore more factual) unemployment movements relative to a model where self-employment and labor force participation are absent. Interest rate shocks are particularly relevant because they are important contributors to consumption dynamics, and the behavior of consumption influences both households’ and firms’ discounting of the future via movements in the stochastic discount factor.23 The latter affects firms’ hiring and capital demand decisions, but more importantly households’ participation decisions as well. After a shock, households respond by altering their allocation of searchers. This reallocation affects firms’ job-filling probabilities and makes firms’ decisions more sensitive to shocks over and above what movements in firms’ discounting would imply absent endogenous participation, thereby amplifying the economy’s response to a given set of shocks in the benchmark model. Ultimately, this implies that in equilibrium and for identically-sized disturbances, interest rate shocks will produce much sharper fluctuations in unemployment (and wages) relative to both productivity shocks and to models without participation. Of note, since participation is procyclical, a strong response of participation after a shock can in principle generate counterfactual movements in unemployment. The presence of countercyclical self-employment, which is consistent with the data (see Table 3 below), limits the otherwise strong procyclicality of participation and delivers a particularly good empirical fit, not only in absolute terms but also relative to simpler model alternatives that abstract from self-employment or labor force participation. Furthermore, by influencing workers’ outside 23 This can be seen by comparing the response of consumption under productivity vs. interest rate shocks for shocks of the same magnitude, as presented in Figure 1 above and Figure 1A in the Appendix.

19

options, self-employment makes vacancy postings more sensitive and further amplifies the impact of shocks, ultimately leading to sharper (and therefore more factual) unemployment movements relative to models where self-employment and labor force participation are absent. As I show below, this makes self-employment, along with labor force participation, an important ingredient for quantitatively matching the data.

4.2

Business Cycle Statistics

Table 3 presents the main results. It compares a comprehensive set of empirical second moments to:24 (1) the benchmark model (”Benchmark Model”); (2) a version of (1) without interest rate shocks (”No IR Shocks”); (3) a version of the benchmark model with no selfemployment (”No SE”) (this version continues to have endogenous participation, but only one employment type); (4) a version of (3) without interest rate shocks (”No SE, No IR Shocks”); (5) a version of the benchmark model that abstracts from both self-employment and labor force participation (that is, this is a standard one-sector SOE RBC model with labor search frictions) (”No SE, No LFP”); and (6) a version of (5) without interest rate shocks (”No SE No LFP, No IR Shocks”) (data on vacancies is not available for the majority of EMEs). For this experiment, all parameter values borrowed from existing literature are common across models. Also, I use the same calibration targets for each model to test how well each model can replicate non-targeted moments under the same calibrated economy. As stated earlier, this implies that the volatility of the shock processes as well as other calibrated parameter values will naturally differ across models in order to match the same targets. Importantly, Table A4 in the Appendix shows a similar table to Table 3 where the alternative versions of the benchmark model are simulated using the same volatility for the shock processes obtained from the calibration of the benchmark model and applied across all alternative models. The results in Table A4 confirms that the benchmark model continues to outperform the simpler alternatives under the same parameter values.25 Of note, considering 24

The empirical second moments for the main macro aggregates are based on data spanning 1993Q1 to 2014Q4. All relevant data series are logged (when appropriate) and HP-filtered with smoothing parameter 1600. 25 Calibration details for all alternatives to the benchmark model are presented in the Appendix, as well as in Table 2 for the models with interest rate shocks. Table A4 in the Appendix also showcases the amplification mechanism that arises from having endogenous participation and frictional self-employment.

20

salaried output as the measure of output in the data does not change the main conclusions either.26 Table 3: Data vs. Benchmark Model and Model Alternatives

Targeted Moments

Data

Benchmark Model

No IR Shocks

No SE

σy,t σc,t σlf p,t Non-Targeted Moments σc,t σinv,t σu,t σv,t corr(yt , ct ) corr(yt , invt ) corr(yt , ut ) corr(yt , tbt /yt )

No SE, No LFP

(3) 2.294 2.729 0.865

No SE, No IR Shocks (4) 2.294 − 0.865

(5) 2.294 2.729 −

No SE, No LFP, No IR Shocks (6) 2.294 − −

2.294 2.729 0.865

(1) 2.294 2.729 0.865

(2) 2.294 − 0.865

2.729 6.470 15.90 − 0.952 0.911 −0.802 −0.685

− 6.086 14.76 40.62 0.602 0.902 −0.630 −0.093

0.546 4.326 14.92 18.11 0.952 0.999 −0.001 0.994

− 3.583 14.77 19.28 0.416 0.999 −0.245 0.299

0.652 3.612 10.67 11.69 0.967 0.999 0.069 0.994

− 3.540 5.322 7.329 0.416 0.999 −0.298 0.304

1.068 3.541 1.655 1.892 0.984 0.999 −0.694 0.984

σw,t σne ,t corr(yt , wt ) corr(yt , ne,t ) corr(yt , lf pt ) corr(yt , Rt )

5.200 2.901 0.560 −0.346 0.507 −0.300

7.155 0.783 0.601 −0.510 0.428 −0.491

1.651 1.064 0.958 −0.708 0.774 0.470

5.925 − 0.482 − 0.351 −0.152

1.753 − 0.975 − 0.904 0.274

6.062 − 0.434 − − −0.036

2.460 − 0.999 − − −0.135

mod data σu,t /σu,t Elasticity of P articipation φ

− −

0.928 0.712

0.938 2.603

0.929 0.447

0.671 2.687

0.335 −

0.104 −

Notes: σx denotes the standard deviation of variable x. All relevant series are logged (when appropriate) and HP-filtered using a smoothing parameter of 1600. SE (LFP) refers to self-employment (labor force participation) and IR refers to interest rate. All second moments are based on data from 1993Q1 to 2014Q4 unless otherwise noted. The volatility and cyclical correlation of wages is from Boz, Durdu, and Li (2015). There is no available data for vacancies in Mexico. The stylized facts for self-employment and labor force participation are based on data from Mexico’s labor force survey for period 2000Q2 to 2010Q4. The sample period is restricted to post-2000 data due to changes in the labor force survey methodology in the early 2000s. However, Bosch and Maloney’s (2008) empirical analysis suggests that the same quantitative patterns for self-employment and labor force participation hold using data going back to 1987Q1 and ending with the mod change in methodology in the early 2000s. σu,t refers to the volatility of unemployment in the model. 26

The bulk of self-employment is considered informal sector employment, and as such self-employment output could be categorized as informal sector output as well. The United Nations provides countries with guidelines on how to incorporate informal sector activity estimates into their national accounts (United Nations, 2008). Mexico has incorporated such estimates into its national accounts since 1993. The steadystate share of self-employment output in total output generated by the model is consistent with the share of informal sector activity included in Mexico’s national accounts.

21

A Note on the Cyclicality of Self-Employment and Participation The general mechanism via which self-employment generates factual unemployment fluctuations in the presence of endogenous labor force participation was highlighted in Finkelstein Shapiro and Mandelman (2016) and naturally carries through in this paper. For completeness, I briefly explain how this mechanism operates.27 Consider an adverse shock (be it a productivity or foreign interest rate shock). The shock pushes salaried firms to reduce vacancy postings and capital demand. As a result, capital for potential use in the salaried sector becomes idle and capital producers reallocate their existing capital stock away from renting it to salaried firms and into matching it with potential self-employed individuals. Households respond to the fall in salaried employment prospects by reallocating their searchers away from salaried search and into search for capital needed for self-employment. Importantly, this generates a sharp fall in salaried searchers, which puts downward pressure on unemployment (and labor force participation). Conversely, the rise in self-employment searchers puts upward pressure on unemployment (and participation).28 In addition, under any plausible calibration, the increased availability of existing (idle) capital as a result of the fall in salaried capital demand dominates the increase in demand arising from more searchers looking for capital for self-employment. This causes a rise in the ease with which searchers can move into self-employment (i.e., the transition probability from unemployment to self-employment increases, consistent with evidence from Bosch and Maloney, 2008, for EMEs). This ultimately leads to a countercyclical expansion in self-employment (in line with the data). Of note, the behavior of self-employment searchers is more forceful given the relative ease with which they can find capital and the large drop in salaried employment opportunities. This allows the model to generate countercyclical fluctuations in unemployment while simultaneously producing procyclical aggregate labor force participation, where the latter is driven by the dynamics in salaried searchers and workers in the aftermath of adverse shocks. Summary of Main Results Table 3 shows that, under a calibration that replicates the volatility of consumption and labor force participation in the data, the benchmark model is quantitatively consistent with a comprehensive set of non-targeted second moments in 27

For more on the mechanisms that replicate the countercyclicality of self-employment in an environment without labor force participation, see Finkelstein Shapiro (2014). 28 Recall that the total labor force and the unemployment rate are given by lf p = se + ss + ne + ns and u = (se + ss )/lf p, respectively.

22

the data. The most noteworthy result is that the benchmark model captures 92 percent of the volatility in the data in the presence of considerable (and factual) wage volatility, strongly countercyclical unemployment and self-employment, a (qualitative albeit quantitatively small) countercyclical trade balance-output ratio, and a cyclical correlation of labor force participation consistent with the data, among other relevant moments.29 Table A3 in the Appendix shows that introducing correlated shocks brings the model much closer to matching the cyclicality of the trade balance while providing an even better fit with the data on virtually all fronts. Therefore, a relatively low countercyclicality in the trade balanceoutput ratio in the baseline calibration is not crucial for generating a very good model fit with the data. The last two rows of Table 3 show the ratio of model-generated unemployment volatility mod data to the empirical volatility (i.e., a value for σu,t /σu,t close 1 implies that the model can

replicate the volatility in the data), and the associated elasticity of participation parameter φ. Importantly, the models with endogenous participation (columns (1) and (3)) generate mod data σu,t /σu,t > 0.90 without requiring elasticities of participation greater than 1. Abstract-

ing from interest rate shocks implies that the benchmark model and the model without self-employment but with endogenous participation can still generate high unemployment volatility close to the data. However, they both require high participation elasticities, which are less plausible. Moreover, while these models can in fact generate high unemployment volatility, the fit with respect to other non-targeted moments is significantly worse. Two comments are in order. First, recall that the contemporaneous value of unemployment is zero. Thus, the results in Table 3 show that the model-generated volatility of unemployment does not depend on having a value of unemployment that is close to individual labor earnings (see, for example, Hagedorn and Manovskii, 2008). Second, the fact that the benchmark model produces higher wage volatility relative to the data is unlikely to be an issue. Indeed, due to data limitations, high-frequency wage data for EMEs is generally available for the formal sector only (see Li, 2011; Boz, Durdu, and Li, 2015). Therefore, the volatility reported in Table 3 is based on formal-sector wage data only. Wages and earnings in the informal sector tend to be more volatile than those in the formal sector and therefore true average salaried wages (that is, average wages based on both formal and informal sector 29

While not reported, the volatility of the population outside the labor force in the data is 1.300. The benchmark model produces a volatility of 1.297.

23

wages) are likely to be even more volatile than what existing evidence suggests since informal employment accounts for at least 50 percent of total employment in EMEs (Bacchetta, Bustamante, and Ernst, 2009). Since my model does not distinguish between formal and informal salaried employment, the high model-generated volatility of wages relative to the data is not per se a limitation of the model. In fact, amid this high real wage volatility, it makes the good fit of the model-generated volatility of unemployment with the data all the more noteworthy (especially since, as is well known from standard search models, highly flexible Nash wages dampen the variability of unemployment). Overall, the model quantitatively captures a comprehensive set of stylized facts surprisingly well. Model Alternatives and Interest Rate Shocks Abstracting from interest rate shocks in the benchmark model implies that the volatility of consumption is lower than the volatility of output—a well-known result from the EME business cycle literature (compare columns numbered (1) and (2) in Table 3).30 Also, the fact that interest rate shocks are important for generating high wage volatility is consistent with the findings in Boz, Durdu, and Li (2015). Importantly, note that the absence of these shocks does not imply that unemployment volatility in the benchmark model is lower. Surprisingly, unemployment volatility remains as high as in the model without such shocks, though note that several non-targeted moments worsen relative to the benchmark model (in particular, the cyclical correlation of unemployment, self-employment, labor force participation, and country interest rates). This reflects the key role of endogenous sectoral participation alongside frictional self-employment in amplifying shocks. Initially, this may seem to downplay the role of interest rate shocks in producing high labor market volatility. However, recall that we recalibrate each model that has endogenous participation to match the volatility of participation in the data. Of note, though, as suggested by the last row of Table 3, models without interest rate shocks require very high (and therefore less plausible) elasticities of participation to match this target (2.603 versus 0.712 in the benchmark model).31 If we simply shut down the interest rate shocks (which 30

Recall that the volatility of interest rate shocks is calibrated to match the volatility of consumption. As such, consumption volatility is no longer a targeted moment in columns (2), (4), and (6). 31 As noted in the Appendix, this model alternative also requires more volatile TFP shocks to match the volatility of output in the data when compared to the benchmark model (indeed, σz = 0.00937 in the benchmark model versus σz = 0.014984 in a model without self-employment). This suggests the presence of a non-trivial amplification mechanism embedded in the benchmark model.

24

naturally reduces the volatility of consumption) without recalibrating the model to match the volatility of participation, we would still capture the cyclicality of key labor market variables, but the volatility of unemployment, wages, and more importantly participation would be considerably lower (see column (4) of Table A2 in the Appendix). I explore this in detail below, but these results confirm that the variability of participation appears to be crucial in explaining unemployment movements, and interest rate shocks are important insofar as they allow the model to better replicate factual dynamics for wages and consumption, but also the counteryclicality of unemployment, amid endogenous participation. Also, the absence of interest rate shocks and its implications for matching data is most notable in the cyclical correlation between unemployment and output, which becomes almost zero. This is due to the fact that, without interest rate shocks self-employment is too countercyclical relative to the data when we match the volatility of participation, which contributes to generating acyclical unemployment. The fit with respect to other relevant moments also deteriorates considerably (see column (2) in Table 3).32 All told, these results highlight the relevance of foreign interest rate shocks for wage volatility previously stressed by Boz, Durdu, and Li (2015). More importantly though, and relative to their work, the results in Table 3 point to the role of such shocks in combination with endogenous labor force participation and self-employment for quantitatively matching the volatility of unemployment alongside a comprehensive set of facts for both the labor market and other macro aggregates. Self-Employment and Unemployment Volatility To assess the relevance of self-employment, compare the benchmark model (column (1)) to a version of the same model without selfemployment (column (3)) in Table 2 (recall that all models are calibrated to match the same volatility of participation and consumption). Comparison of columns (3) and (5) confirms the powerful amplification mechanism rooted in endogenous participation. Indeed, the model with participation but without self-employment continues to produce high unemployment volatility—specifically, it produces 94 percent of the volatility in the data—alongside high wage volatility. However, this same model falls short of generating the strong countercycli32

The fact that endogenous participation by itself generates higher unemployment volatility relative to output in the absence of interest rate shocks is consistent with the findings in Finkelstein Shapiro and Mandelman (2016). In their work, however, the volatility of unemployment falls quantitatively short of the one observed in the data since their model generates relatively low volatility of participation.

25

cality of unemployment in both the data and the benchmark model. Other shortcomings of the model without self-employment include: a low procyclicality of consumption, lower investment volatility, a procyclical trade balance-output ratio, and stronger procyclicality in labor force participation, among others. Abstracting from both self-employment and interest rate shocks lowers the model-generated volatility of unemployment, wages, and consumption; it makes unemployment acyclical, and raises the procyclicality of labor force participation even more relative to the data. From a comprehensive perspective, the fit of this model with respect to both the data and the benchmark model (with and without foreign interest rate shocks) is generally worse. These results are in line with the importance of self-employment in generating factual dynamics in the presence of labor force participation (Finkelstein Shapiro and Mandelman, 2016). Moreover, comparison of the volatility of unemployment in the benchmark model without interest rate shocks (column (2)) to the volatility in the model without self-employment and no interest rate shocks (column (4)) shows that frictional self-employment contributes to unemployment volatility in a non-negligible way. This is easily explained by the fact that, absent interest rate shocks, self-employment (and therefore search for self-employment) is considerably more volatile in the absence of interest rate shocks. This, in turn, contributes to generating higher unemployment volatility. However, recall that the latter is purely due to the fact that the model versions in columns (3) and (4) require a high (and less empirically plausible) elasticity of participation to match the volatility of participation in the data. This is not the case in the benchmark model. All told, comparison of columns (1) and (2) versus (3) and (4) give additional validity to a framework with frictional self-employment.33 Finally, compare the benchmark model (column (1)) to a version of the model with neither self-employment nor labor force participation (column (5)). The latter produces countercyclical unemployment but generates roughly one third of the volatility of unemployment in the data. A model with neither self-employment nor endogenous participation fairs quantitatively worse than the benchmark model (the only exception being the volatility of wages, which the simpler model matches surprisingly well, with the caveat that the empirical wage volatility is based on formal-sector wages only). 33

Table A2 in the Appendix compares the benchmark model to a version of the same model without frictional self-employment. The overall model fit of the benchmark model still outperforms other model alternatives.

26

All told, we conclude that the benchmark model quantitatively outperforms simpler models on virtually all fronts. The most noteworthy result is that the benchmark model can generate unemployment volatility that is exceedingly close to the data amid highly volatile real wages (as in the data), as well as other second moments that are quantitatively consistent with the evidence. The results in Table 3 also suggest a key interaction between labor force participation and interest rate shocks that contributes to the model’s quantitative success. Indeed, as noted earlier, the presence of interest rate shocks allows the benchmark model to generate high unemployment volatility without requiring a high elasticity of participation (as such, amid interest rate shocks, the benchmark model does not need extreme and therefore less plausible parameterizations to match the data). For completeness, Table A3 in the Appendix shows that introducing correlated productivity and interest rate shocks (see, for example, Neumeyer and Perri, 2005, or Lama and Urrutia, 2011) improves the fit of the benchmark model not only with respect to the countercyclicality of the trade balance-output ratio but also other moments. More importantly, this modification does not change the fact that, from a comprehensive perspective, the benchmark model outperforms the empirical fit of the alternative, simpler models that the benchmark model is compared to. Interest Rate Shocks and the Volatility of Participation To highlight the role of the volatility of labor force participation in reproducing the volatility of unemployment in the data, Table 4 considers a version of the benchmark model where I reduce the elasticity of participation parameter φ. This exercise artificially reduces the volatility of participation. As such, the volatility of participation is no longer a targeted moment (recall Table 2). For ease of comparison, columns (1) and (2) of Table 4 reproduce the results from the benchmark model (recall that this model matches the volatility of participation with a value of φ = 0.712), and the same model without the interest rate shocks from Table 3. Column (3) in Table 4 shows a version of the benchmark model that is recalibrated using a lower value of φ = 0.50, which almost halves the volatility of participation (this model continues to match all other calibration targets in the baseline calibration). In turn, column (4) presents a version of column (3) where in addition to lowering φ I shut down the interest rate shocks. Comparison of columns (1) and (3) shows that the variability of labor force participation plays a key role in quantitatively matching the volatility of 27

unemployment. In fact, if the volatility of participation is only roughly 50 percent of the one in the data (and in the benchmark model under the baseline calibration), the volatility of unemployment is almost halved relative to the benchmark model that does match the variability of participation. Moreover, once we match the latter, the benchmark model provides a better overall fit with respect to other second moments of interest. The intuition is simple: if the elasticity of participation is smaller, households’ decisions over participation will be less responsive to changes in the expected marginal benefits of participating in the labor market as a result of interest-rate-driven fluctuations in their discounting of the future. This, in turn, implies smaller fluctuations in firms’ decisions over hiring, which ultimately results in smoother unemployment fluctuations. Table 4: Benchmark Model and Sensitivity to Volatility of Labor Force Participation

Targeted Moments

Data

σy,t σc,t σlf p,t Non-Targeted Moments σlf p,t σc,t σinv,t σu,t σv,t corr(yt , ct ) corr(yt , invt ) corr(yt , ut ) corr(yt , tbt /yt )

2.294 2.729 0.865

σw,t σne ,t corr(yt , wt ) corr(yt , ne,t ) corr(yt , lf pt ) corr(yt , Rt )

Benchmark Model (φ = 0.712)

Benchmark Model, Lower φ (φ = 0.50)

(1) 2.294 2.729 0.865

Benchmark No IR Shocks (φ = 0.712) (2) 2.294 − 0.865

(3) 2.294 2.729 −

Benchmark Model, Lower φ (φ = 0.50) and No IR Shocks (4) 2.294 − −

0.865 2.729 6.470 15.90 − 0.952 0.911 −0.802 −0.685

− − 6.086 14.76 40.62 0.602 0.902 −0.630 −0.093

− 0.546 4.326 14.92 18.11 0.952 0.999 −0.001 0.994

0.492 − 6.280 8.340 30.33 0.499 0.834 −0.580 0.021

0.097 0.712 4.219 2.160 5.819 0.977 0.999 −0.696 0.995

5.200 2.901 0.560 −0.346 0.507 −0.300

7.155 0.783 0.601 −0.510 0.428 −0.491

1.651 1.064 0.958 −0.708 0.774 0.470

7.113 0.416 0.526 −0.427 0.285 −0.316

2.269 0.195 0.995 −0.382 0.331 0.117

Notes: σx denotes the standard deviation of variable x. All relevant series are logged (when appropriate) and HP-filtered using a smoothing parameter of 1600. SE (LFP) refers to self-employment (labor force participation) and IR refers to interest rate. All second moments are based on data from 1993Q1 to 2014Q4 unless otherwise noted. The volatility and cyclical correlation of wages is from Boz, Durdu, and Li (2015). There is no available data for vacancies in Mexico. The stylized facts for self-employment and labor force participation are based on data from Mexico’s labor force survey for period 2000Q2 to 2010Q4. The sample period is restricted to post-2000 data due to changes in the labor force survey methodology in the early 2000s. However, Bosch and Maloney’s (2008) empirical analysis suggests that the same quantitative patterns for self-employment and labor force participation hold using data going back to 1987Q1 and ending with the change in methodology in the early 2000s.

Comparison of columns (2) and (4), where I shut down the interest rate shocks, shows an 28

even more striking result with respect to the sources of unemployment volatility and, more importantly, the joint presence of interest rate shocks and participation: without interest rate shocks and with lower volatility in participation, the model generates only roughly 14 percent of the volatility in unemployment in the data.34 Finally, Table 4 confirms that interest rate shocks are critical for generating highly volatile wages, regardless of the volatility of participation. All told, the importance of matching the volatility of participation for generating quantitatively factual unemployment volatility remains. In turn, interest rate shocks allow the model to generate high wage volatility as well as a better overall fit with the data amid empirically-factual cyclical movements in labor force participation. Thus, the joint presence of endogenous participation, self-employment, and interest rate shocks provides a powerful and empirically-factual combination of characteristics inherent to EMEs that provide an excellent fit with the data across several fronts. Relation to Existing Literature and New Insights As stated earlier, Boz, Durdu, and Li (2015) show that interest rate shocks contribute to higher wage volatility. The results in Table 3 regarding the relevance of these shocks for wage dynamics confirm their findings. Table 3 shows that factual movements in labor force participation, by themselves, can explain a considerable share of the variability of unemployment without necessarily relying on interest rate shocks (even though the latter help in matching other second moments better, as shown in columns (2) and (3) in Table 3). As such, a key contribution relative to Boz et al. (2015) is to stress the role of endogenous participation amid search frictions—a microfounded mechanism in the labor market—in quantitatively explaining unemployment fluctuations, where interest rate shocks are important insofar as they generate high wage volatility and allow a more factual cyclical correlation between unemployment and output, among other things. Importantly, while interest rate shocks of a plausible magnitude do increase the volatility of unemployment in standard search models, absent endogenous participation, such shocks are insufficient for quantitatively generating, and therefore explaining, the volatility of unemployment in the data. Accounting for endogenous participation decisions overcomes this limitation in standard models. In their robustness experiments, Finkelstein Shapiro and Mandelman (2016), show that 34

Once again, this is consistent with Boz, Durdu, and Li’s (2015) quantitative findings regarding the relevance of interest rate shocks for unemployment volatility in a standard search model.

29

introducing shocks to firms’ wage costs that are calibrated to match the volatility of wages in the data can generate factual movements in the population outside of the labor force, which in turn contribute to much higher unemployment volatility relative to their baseline model without such shocks.35 My results are related to theirs insofar as both my findings and theirs emphasize the fact that quantitatively capturing the volatility of labor force participation (or, equivalently, the cyclical movements of the population outside the labor force) plays a key role in generating the large unemployment fluctuations observed in the data. Importantly though, while these wage cost shocks are useful in determining whether wage volatility is important for matching other relevant moments, these shocks are difficult to pinpoint in the data, and are not a well-established characteristic of EMEs. Conversely, interest rate shocks are easily observable and well-known to play a role in EME business cycles. Moreover, under a disciplined and plausible calibration, the model I present can generate unemployment volatility that is even closer to its empirical counterpart while at the same time providing an excellent fit with respect to other variables of interest. This represents a non-negligible, plausible, and quantitative improvement across several fronts relative to the model fit in Finkelstein Shapiro and Mandelman (2016) and others. All told, the new insights relative to existing work—which are responsible for explaining why the model can replicate the bulk of the volatility of unemployment in the data and simpler models face limitations in doing so—are twofold. First, the responsiveness of households’ participation decisions to shocks prevalent in EMEs is crucial and must be consistent with the variability of participation in the data in order to generate high unemployment volatility close to the data (of note, the benchmark model amid interest rate shocks does not require an excessively high elasticity of participation to be consistent with the cyclical dynamics of participation). Second, interest rate shocks are not crucial for explaining the volatility of unemployment in the data in the presence of quantitatively-factual participation dynamics, but these shocks are indeed important for replicating the volatility of unemployment while simultaneously reproducing a comprehensive number of other second moments in the data. Thus, both model assumptions regarding the presence/absence of endogenous participation (and, to a lesser extent for matching the volatility of unemployment, self-employment) and an appropriate (but plausible) calibration that can replicate the variability of participation 35

With such shocks, alongside remittance and TFP shocks, their model can capture roughly 75 percent of the volatility of unemployment in the data.

30

are essential for quantitatively matching the data in a comprehensive way.

4.3

Additional Experiments and Robustness

Firm Ownership Structure Table A1 in the Appendix and the accompanying discussion illustrate the relevance of separating capital producers from salaried firms—a subtle but relevant modification that distinguishes the model I use from Finkelstein Shapiro and Mandelman (2016)—by exploring alternative assumptions about salaried firm ownership. In short, the firm ownership structure I adopt implies a considerable better fit of the benchmark model relative to a model where capital producers own salaried firms. A similar comment applies to a scenario where households own both salaried firms and capital producers. Capital Search and Lower Average Self-Employment Table A2 in the Appendix and the accompanying discussion confirm the relevance of capital search in order to match a comprehensive set of facts in EME labor markets by comparing the benchmark model to a model without capital search (but with self-employment). The importance of capital search for replicating the cyclical dynamics of self-employment was already discussed in a closedeconomy context in Finkelstein Shapiro (2014), and in studying the role of cyclical movements in remittances amid endogenous participation in Finkelstein Shapiro and Mandelman (2016). The results in Table A2 confirm that capital search continues to be of key relevance to match sectoral labor market dynamics, as suggested by existing work, in a context with endogenous participation and interest rate shocks. Turning to the differences between EMEs and advanced economies, the latter tend to have much lower average (steady-state) self-employment shares. To determine the implications of differences in average self-employment shares and for illustrative purposes, I conduct an experiment where I reduce the steady state self-employment share from 23 to 10 percent of the labor force in the benchmark model.36 As shown in column (4) of Table A2 in the Appendix, the resulting economy exhibits lower output, investment, unemployment, and wage volatility, as well as a procyclical trade balance-output ratio relative to the benchmark economy under 36

The details are presented in the Appendix. For this experiment, I change the calibration target for capital matching efficiency to reflect a lower steady-state self-employment share while holding all other calibrated parameters at their original values. Changing other parameters that may affect self-employment directly does not alter the main conclusions. Importantly, I do not shut down the interest rate shocks, implying that this economy continues to exhibit high consumption volatility as a result of the shocks. See the discussion accompanying Table A2 in the Appendix for more details.

31

the baseline calibration. All these facts are consistent with the data as advanced economies— economies with lower average self-employment—tend to be less volatile. Thus, the model is also consistent with cross-country facts regarding business cycle volatility in EMEs relative to advanced economies.

5

Conclusion

It is well known that standard search models face limitations in replicating the high volatility of unemployment in U.S. data. Evidence suggests that emerging economies (EMEs) also exhibit high unemployment volatility, and do so amid highly volatile real wages. Recent work has highlighted the role of interest rate shocks in contributing to labor market fluctuations, but standard small open economy search models that incorporate these shocks still fall short of quantitatively replicating the empirical volatility of unemployment in EMEs. I show that introducing endogenous participation alongside frictional self-employment—a prevalent feature of EME labor markets—into a standard SOE RBC model with productivity and interest rate shocks can replicate more than 90 percent of the empirical volatility of unemployment in a representative EME, Mexico, even amid empirically-factual highly volatile wages. The model is calibrated to match the variability of labor force participation, which proves key to quantitatively capturing the cyclical variability of unemployment. Moreover, the presence of self-employment allows the model to generate empirically-factual labor market dynamics. The model I propose not only matches key facts on EME business cycles and labor market dynamics surprisingly well under a conventional parameterization with plausible shock magnitudes, but also provides a better overall fit relative to alternative frameworks that abstract from self-employment and endogenous labor force participation. The combination of the latter and interest rate shocks introduces a powerful amplification mechanism that is responsible for the model’s ability to replicate the bulk of the variability of unemployment in the data while simultaneously generating quantitatively-factual labor market and aggregate dynamics. These findings suggest that labor force participation decisions may be critical for better understanding labor market dynamics and the amplification and propagation of shocks in EMEs.

32

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] Allen, Franklin, Elena Carletti, Jun Qian, and Patricio Valenzuela. 2013. ”Financial Intermediation, Markets, and Alternative Financial Sectors,” Handbook of the Economics of Finance, Volume 2, Part A, pp. 759-798. [3] Arseneau, David M., and Sanjay K. Chugh. 2012. “Tax Smoothing in Frictional Labor Markets,” Journal of Political Economy, Vol. 120(5), pp. 926-985. [4] Ayyagari, Meghana, Asli Demirg¨ u¸c-Kunt, Asli, and Vojislav Maksimovic. 2012. ”Financing of Firms in Developing Countries: Lessons from Research,” Policy Research Working Paper 6036, The World Bank: Washington, D.C. [5] Bacchetta, Marc, Juana P. Bustamante, and Ekkehard Ernst. 2009. ”Globalization and Informal Jobs in Developing Countries,” A Joint Study of the International Labour Office and the Secretariat of the World Trade Organization, International Labour Office, Geneva, Switzerland. [6] Beck, Thorsten and Asli Demirg¨ u¸c-Kunt. 2006. “Small and Medium-Size Enterprises: Access to Finance as a Growth Constraint,” Journal of Banking & Finance, 30, pp. 2931-2943. [7] Beck, Thorsten, Asli Demirg¨ u¸c-Kunt, and Vojislav Maksimovic. 2008. “Financing Patterns around the World: Are Small Firms Different?”Journal of Financial Economics, Vol. 89(3), pp. 467–487. [8] Bosch, Mariano and William Maloney. 2008. “Cyclical Movements in Unemployment and Informality in Developing Countries,” IZA Discussion Paper No. 3514. [9] Boz, Emine, Ceyhun Bora Durdu, and Nan Li. 2015. ”Emerging Market Business Cycles: The Role of Labor Market Frictions,” Journal of Money Credit and Banking, Vol. 47(1), pp. 31-72. [10] Campello, Murillo, and Mauricio Larrain. 2016. ”Enlarging the Contracting Space: Collateral Menus, Access to Credit, and Economic Activity,” Review of Financial Studies, Vol. 29(2), pp. 349-383. [11] Chang, Roberto, and Andr´es Fern´andez. 2013. ”On the Sources of Aggregate Fluctuations in Emerging Economies,” International Economic Review, Vol. 54(4), pp. 1265– 1293. [12] Epstein, Brendan, and Alan Finkelstein Shapiro. 2017a. ”Firm and Employment Heterogeneity, Capital Allocation, and Countercyclical Labor Market Policies,” Journal of Development Economics, Vol. 127, pp. 25-41. [13] Epstein, Brendan, and Alan Finkelstein Shapiro. 2017b. ”Financial Development, Employment Heterogeneity, and Sectoral Dynamics,” mimeo.

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[14] Epstein, Brendan, Alan Finkelstein Shapiro, and Andr´es Gonz´alez G´omez. 2016. ”Global Financial Risk, Domestic Financial Access, and Unemployment Dynamics,” mimeo. [15] Fern´andez, Andr´es, and Felipe Meza. 2015. “Informal Employment and Business Cycles in Emerging Economies: The Case of Mexico,” Review of Economic Dynamics, Vol. 18, pp. 381-405. [16] Finkelstein Shapiro, Alan. 2014. ”Self-Employment and Business Cycle Persistence: Does the Composition of Employment Matter for Economic Recoveries?” Journal of Economic Dynamics and Control, Vol. 46, September 2014, pp. 200-218. [17] Finkelstein Shapiro, Alan, and Andr´es Gonz´alez G´omez. 2016. “Credit Market Imperfections, Labor Markets, and Business Cycles in Emerging Economies,” mimeo. [18] Finkelstein Shapiro, Alan, and Federico S. Mandelman. 2016. ”Remittances, Entrepreneurship, and Employment Dynamics over the Business Cycle,” Journal of International Economics, Vol. 105, pp. 184-199. [19] Garc´ıa-Cicco, Javier, Roberto Pancrazi, and Martin Uribe. 2010. ”Real Business Cycles in Emerging Countries?” American Economic Review, Vol. 100(5), pp. 2510-2531. [20] Global Financial Development Report. 2014. ”Financial Inclusion,” Global Financial Development Report 2014, The World Bank Group: Washington D.C. [21] Hagedorn, Marcus, and Iourii Manovskii. 2008. ”The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited,” American Economic Review, Vol. 98, pp. 1692–1706. [22] Hall, Robert. 2005. ”Employment Fluctuations with Equilibrium Wage Stickiness,” American Economic Review, Vol. 95, pp. 50–65. [23] IDB. 2005. “Developing Entrepreneurship: Experience in Latin America and Worldwide,” Edited by Hugo Kantis, with collaboration of Pablo Angelelli and Virginia Moori Koenig, Inter-American Development Bank: Washington D.C. [24] IFC. 2010a. “Scaling-Up SME Access to Financial Services in the Developing World,” Financial Inclusion Experts Group, SME Finance Sub-Group, International Finance Corporation. [25] IFC. 2010b. ”The SME Banking Knowledge Guide,” International Finance Corporation: Washington D.C. [26] IFC. 2013. ”Closing the Credit Gap for Formal and Informal Micro, Small, and Medium Enterprises,” IFC Advisory Services, Access to Finance, International Finance Corporation: Washington D.C. [27] Krause, Michael U., and Thomas A. Lubik. 2006. ”The Cyclical Upgrading of Labor and On-the-Job Search,” Labour Economics, 13(4), pp. 459-477. [28] Kurmann, Andr´e. 2014. ”Holdups and Overinvestment in Capital Markets,” Journal of Economic Theory, Vol. 151, pp. 88-113.

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[29] Lama, Ruy, and Carlos Urrutia. 2011. ”Employment Protection and Business Cycles in Emerging Economies,” IMF Working Paper WP/11/293. [30] Levy, Santiago. 2007. “Can Social Programs Reduce Productivity and Growth? A Hypothesis for Mexico,” IPC Working Paper Series Number 37, Gerald R. Ford School of Public Policy, University of Michigan. [31] Li, Nan. 2011. ”CyclicalWage Movements in EmergingMarkets: The Role of Interest Rates,” Review of Economic Dynamics, Vol. 14, pp. 686–704. [32] Neumeyer, Pablo A., and Fabrizio Perri. 2005. “Business Cycles in Emerging Economies: The Role of Interest Rates,” Journal of Monetary Economics, 52(2), pp. 345–380. [33] OECD. 2009. “Overview: Data on Informal Employment and Self-Employment,” in Is Informal Normal? Towards More and Better Jobs in Developing Countries, OECD Development Centre, Ed. Johannes P. J¨ utting and Juan R. de Laiglesia. [34] Pav´on, Lilianne. 2010. ”Financiamiento a las Microempresas y las Pymes en M´exico (2000-2009),” Serie Financiamiento del Desarrollo 226, CEPAL. [35] Shimer, Robert. 2005. ”The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” American Economic Review, Vol. 95(1), pp. 25-49. [36] Schmitt-Groh´e, Stephanie, and Mart´ın Uribe. 2003. “Closing Small Open Economy Models,” Journal ot International Economics, Vol. 61(1), pp. 163-185. [37] Schmitt-Groh´e, Stephanie, and Mart´ın Uribe. 2016. “Downward Nominal Wage Rigidity, Currency Pegs, and Involuntary Unemployment,” Journal of Political Economy, Vol. 124(5), pp. 1466-1514. [38] T¨ uzemen, Didem. 2012. ”Labor Market Dynamics with Endogenous Labor Force Participation and On-the-Job Search,” Federal Reserve Bank of Kansas City Working Paper 12-07. [39] United Nations .2008. ”Non-Observed Economy in National Accounts : Survey of Country Practices,” United Nations Economic Commission for Europe. [40] Uribe, Martin, and Vivian Z. Yue. 2006. “Country Spreads and Emerging Countries: Who Drives Whom?” Journal of International Economics, Vol. 69, pp. 6-36.

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A

Appendix

A.1

Data Details and Sources

Unemployment rate: Argentina (Instituto Nacional de Estad´ıstica y Censos, 2002Q4-2014Q4), Brazil (Instituto Brasileiro de Geografia e Estadistica, 1996Q1-2014Q4), Chile (Instituto Nacional de Estad´ıstica, 1986Q2-2014Q4), Colombia (DANE, 2001Q1-2014Q4), Ecuador (Banco Central del Ecuador, 2003Q1-2014Q4), Korea (Statistics Korea, 1999Q3-2014Q4), Malaysia (Department of Statistics Malaysia, 1998Q1-2014Q4), Mexico (INEGI, 1993Q12014Q4), Peru (Banco Central de la Reserva del Per´ u, 2001Q3-2014Q4), Philippines (National Statistics Office of Philippines, 1995Q1-2014Q4), South Africa (Statistics South Africa, 2000Q3-2014Q4), Thailand (Bank of Thailand, 2001Q1-2014Q4), and Turkey (Turkish Statistical Institute, 1990Q1-2014Q4). Real Wage Volatility: obtained from Boz, Durdu, and Li (2015). Data coverage varies by country. Self-Employment: average from 2000 to 2007 and expressed as a percent of non-agricultural employment. Source: OECD (2009).

A.2

Value Functions and Nash Bargaining

Let Ws,t (We,t ) be the net value to the household of having an additional member in salaried employment (self-employment): Ws,t = ws,t −

h′t + Et Ξht+1|t {(1 − ρs ) Ws,t+1 } , ′ u (ch,t )

We,t = zt − re,t −

gt′ + Et Ξht+1|t {(1 − ρe ) We,t+1 } . u′ (ch,t )

In turn, let Js,t be the value to the salaried firm of having an additional worker: Js,t = zt Fns (ns,t , ks,t) − ws,t + Et Ξht+1|t {(1 − ρs ) Js,t+1 } Finally, the value to a capital producer from having an additional capital relationship is: Je,t = re,t + (ρe − δ) + Et Ξkt+1|t {(1 − ρe ) Je,t+1 } . 36

Assuming free entry implies that the value of a vacancy is zero in equilibrium. The Nash bargaining problems for the wage and the rental rate are formally given by   max (Ws,t )ν (Js,t)1−ν , max (We,t )ν (Je,t − (1 − δ))1−ν , ws,t

re,t

where ν denotes the (common) bargaining power of salaried workers and self-employed individuals. Finally, note that the threat point for capital producers is the value of a unit of idle capital (1 − δ) (Finkelstein Shapiro, 2014; Finkelstein Shapiro and Mandelman, 2016). The first-order conditions yield Ws,t =

ν Js,t , 1−ν

We,t =

ν (Je,t − (1 − δ)) . 1−ν

First, note that from the salaried firms’ and capital producers’ optimality conditions, we can write ψ = Et Ξht+1|t (1 − ρs ) Js,t+1 , qs,t 1 gt′ = Et Ξht+1|t (1 − ρe ) We,t+1 , ′ u (ch,t ) fe,t and rs,t + (1 − ρe ) qe,t = Et Ξkt+1|t (1 − ρe ) Je,t+1 , qe,t First, we derive the Nash wage. Using the value functions and the Nash first-order conditions above, we have   h′t ν h s ws,t − ′ + Et Ξt+1|t (1 − ρ ) Js,t+1 u (ch,t) 1−ν  ν  = zt Fns (ns,t , ks,t) − ws,t + Et Ξht+1|t {(1 − ρs ) Js,t+1 } , 1−ν which can be rewritten as h′t ν ψ + ′ u (ch,t ) 1 − ν qs,t   ν ψ = zt Fns (ns,t , ks,t) − ws,t + , 1−ν qs,t ws,t −

37

or ws,t

 h′t = νzt Fns (ns,t , ks,t) + (1 − ν) ′ . u (ch,t ) 

Now, we derive the Nash rental rate. Using the value functions and the Nash first-order conditions above, we have gt′ zt − re,t − ′ + Et Ξht+1|t (1 − ρe ) We,t+1 u (ch,t )  ν  = re,t + (ρe − δ) + Et Ξkt+1|t {(1 − ρe ) Je,t+1 } − (1 − δ) . 1−ν which can be rewritten as gt′ 1 gt′ + ′ zt − re,t − ′ u (ch,t ) u (ch,t ) fe,t   ν rs,t + (1 − ρe ) qe,t e = re,t + (ρ − δ) + − (1 − δ) . 1−ν qe,t Finally, rearranging, we have re,t

A.3

 = (1 − ν) zt +

gt′ u′ (ch,t )



1 −1 fe,t





 r s,t −ν . qe,t

Calibration Details: Alternative Models

I use the same parameters from related literature and the same calibration targets adopted in the benchmark model for all model alternatives unless otherwise noted. Benchmark Model Without Self-Employment

In the absence of self-employment, the

only parameters that require calibration targets are: λ, ψ, Ms , ν(= ξ), b∗ , φ, σz , σR∗ , where I continue to assume that the bargaining power and the matching elasticity are equal (ν = ξ). The calibration targets are: a labor force participation rate of 0.60, a cost per vacancy of 3.5 percent of wages, a job-finding probability of 0.75, a share of total consumption in GDP of 0.68, a foreign debt-GDP ratio equal to 0.30, a volatility of participation of 0.865, a volatility of output of 2.294, and a volatility of consumption of 2.729. The resulting calibrated parameters are: λ = 5.9971, ψ = 0.051, Ms = 0.0300, ν = ξ = 0.2566, b∗ = 1.790, φ = 0.447, σz = 0.014974, σR∗ = 0.016740. Note that this model requires more volatile aggregate productivity shocks to match the volatility of output compared to the benchmark 38

model, suggesting that the latter embeds a non-trivial amplification mechanism. Benchmark Model Without Self-Employment and Labor Force Participation In the absence of labor force participation, parameters ψ, Ms , ν(= ξ), b∗ , σz , σR∗ are chosen to match: a cost per vacancy of 3.5 percent of wages, a job-finding probability of 0.75, a share of total consumption in GDP of 0.68, a foreign debt-GDP ratio equal to 0.30, a volatility of output of 2.294, and a volatility of consumption of 2.729. The resulting values in the absence of self-employment and labor force participation are: ψ = 0.051, Ms = 0.0300, ν = ξ = 0.2566, b∗ = 2.9834, σz = 0.016479, σR∗ = 0.016195. A similar comment regarding the amplification mechanism embedded in the benchmark model applies.

39

A.4

Response to a Negative Aggregate Productivity Shock

Figure A1: Response to an Adverse Aggregate Productivity Shock: Benchmark, No LFP, No SE and No LFP

% Dev. from SS

Total Output

Agg. Consumption

0

0

−0.5

−1 −0.5

−1 −1.5

−2

0

10

20

30

−1

0

10

% Dev. from SS

Unemployment

30

−3

1

0

10

20

30

Labor Force Participation

5

0.5

0

0

0 −5

−1 0

10

20

30

−10

0

Wage % Dev. from SS

20

Vacancies

2

−2

10

20

30

−0.5

0

Salaried Employment

0

10

20

30

Salaried Searchers

0.5

5

0

0

−0.5 −1 −1.5

0

10

20

30

% Dev. from SS

Self−Employment

−0.5

0

10

20

30

−5

0

Self−Employment Searchers

0.4

3

0.3

10

20

30

Aggregate Productivity 0

2

0.2

−0.5 1

0.1 0

0

10

20

30

0

0

Quarters

10

20

30

−1

0

Quarters Benchmark

A.5

Investment

0

No SE

10

20

30

Quarters No SE, No LFP

Alternative Modeling Assumptions: Firm Ownership

Table A1 compares the benchmark model under alternative assumptions about ownership of capital producers and salaried firms (see columns numbered (1) through (3)). Specifically, column (1) presents the benchmark model from the main text, column (2) shows a version of the benchmark model where households own capital producers, and column (3) shows a

40

version where capital producers own salaried firms.37 For these alternatives, I introduce capital adjustment costs since the volatility of investment becomes excessively high otherwise (therefore, σinv,t becomes a targeted moment in columns (2) and (3)). The table also includes a version of the benchmark model without self-employment under the aforementioned alternative assumptions for completeness. Comparison of columns (1) and (2) reveals that having households and capital producers as separate agents, as in the benchmark model, is important to quantitatively match the data amid foreign interest rate shocks. In fact, the benchmark model outperforms an alternative model where households own salaried firms and capital producers on virtually all margins (the only exception being the variability of wages). Comparison of columns (1) and (3) show that assuming that salaried firms are owned by capital producers also produces a worse fit when we consider all variables of interest. Importantly, note that the volatility of unemployment is particularly low despite the fact that the model replicates the volatility of participation. This traces back to the fact that, in order to match the latter, the model requires an implausibly high steady-state unemployment rate. In turn, this dilutes the impact of shocks on unemployment volatility. Table A1 also shows that when we abstract from self-employment and consider the same modifications to the benchmark model, the results are similar to those under the baseline assumptions regarding firm ownership (the only exception being with regards to the volatility of wages when capital producers own salaried firms). Therefore, the distinction between ownership of capital producers and salaried firms matters only if the model includes selfemployment, where the latter framework plays an important role in generating the best fit with the data.38

37

The model in column (2) would be akin to the framework in Finkelstein Shapiro and Mandelman (2016), with the key differences being that I abstract from remittances, I include interest rate shocks, and I calibrate the model to match the volatility of participation. 38 As shown in Finkelstein Shapiro and Mandelman (2016), a model where households own all firms (and, importantly, there are no interest rate shocks) can be consistent with the data as long as cyclical (and volatile) remittance fluctuations are a feature of the economic environment. However, such a model, while successful in generating higher unemployment volatility as a result of endogenous participation, still falls short of quantitatively generating the volatility observed in the data under a conventional set of shocks.

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Table A1: Data, Benchmark Model, and Model Alternatives I

Targeted Moments

Data

σy,t σinv,t σc,t σlf p,t Non-Targeted Moments σinv,t σu,t σv,t corr(yt , ct ) corr(yt , invt ) corr(yt , ut ) corr(yt , tbt /yt )

2.294 6.470 2.729 0.865

σw,t σne ,t corr(yt , wt ) corr(yt , ne,t ) corr(yt , lf pt ) corr(yt , Rt )

Benchmark Model

Benchmark, Capital Prod. Own Salaried Firms (3) 2.294 6.470 2.729 0.865

No SE, HHs Own Capital Producers

No SE, Capital Producers Own Salaried Firms

(1) 2.294 − 2.729 0.865

Benchmark, HHs Own Capital Producers (2) 2.294 6.470 2.729 0.865

(4) 2.294 6.470 2.729 0.865

(5) 2.294 6.470 2.729 0.865

6.470 15.90 − 0.952 0.911 −0.802 −0.685

6.086 14.76 40.62 0.602 0.902 −0.630 −0.093

− 6.380 21.22 0.304 0.213 −0.403 0.363

− 3.530 9.516 0.191 0.656 0.218 0.283

− 14.00 18.11 0.421 0.332 −0.244 0.265

− 11.23 10.87 0.197 0.739 −0.160 0.275

5.200 2.901 0.560 −0.346 0.507 −0.300

7.155 0.783 0.601 −0.510 0.428 −0.491

5.391 0.172 0.396 −0.007 0.130 −0.037

2.458 0.128 0.859 −0.153 0.064 0.093

5.081 − 0.508 − 0.376 −0.130

2.138 − 0.951 − 0.171 0.108

Notes: σx denotes the standard deviation of variable x. All relevant series are logged (when appropriate) and HP-filtered using a smoothing parameter of 1600. SE refers to self-employment. All second moments pertaining to macro aggregates are based on data from 1993Q1 to 2014Q4 unless otherwise noted. The volatility and cyclical correlation of wages is from Boz, Durdu, and Li (2015). The stylized facts for selfemployment and labor force participation are based on data from Mexico’s labor force survey for period 2000Q2 to 2010Q4. The sample period is restricted to post-2000 data due to changes in the labor force survey methodology in the early 2000s. However, Bosch and Maloney’s (2008) empirical analysis suggests that the same quantitative patterns for self-employment and labor force participation hold using data going back to 1987Q1 and ending with the change in methodology in the early 2000s. The benchmark model where households own capital producers or where capital producers own salaried firms produce excessive investment volatility. As a result, I introduce capital adjustment costs to match the volatility of investment in the data.

A.6

Frictionless Self-Employment Capital and Alternative Parameterizations

Table A2 compares the benchmark model to a version of the model in the absence of capital search (see columns (1) and (2)). In particular, for comparability, I assume that households continue to choose the measure of self-employed searchers, but a capital match is no longer needed to produce. Instead, similar to salaried firms, capital in self-employment is rented in frictionless markets.39 First, as highlighted in Finkelstein Shapiro (2014) and Finkelstein 39

Assuming that the self-employed do not require capital and simply use a unit of their own labor to produce does not change the main conclusions with regards to the relevance of capital search for matching the facts about sectoral and aggregate labor market dynamics.

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Shapiro and Mandelman (2016), the absence of these frictions implies that the cyclicality of self-employment is close to zero and is no longer consistent with the data. Second, selfemployment becomes less volatile relative to both the data and the benchmark model, which percolates into the cyclical behavior of unemployment. This ultimately makes unemployment much less volatile. From a broader perspective, the presence of capital search makes the cyclicality of self-employment more consistent with the data, which in turn allows the model to capture a comprehensive set of facts in the presence of endogenous labor force participation. Next, note that advanced economies, which are well-known to exhibit lower aggregate volatility relative to EMEs, also tend to have much lower average self-employment shares (OECD, 2009). Column (3) in Table A2 shows the results from recalibrating the capital matching efficiency parameter in the benchmark model in order to generate a lower steadystate self-employment share (10 percent of the labor force instead of 23 percent in the baseline calibration). I do so while holding all other calibrated parameters at their original values. In addition, interest rate shocks continue to be operative. Of note, the fact that interest rate shocks are still operative implies that consumption will continue to be fairly volatile, as should be the case in the presence of these shocks. As shown in the table, the economy with lower average self-employment exhibits lower output, investment, unemployment, and wage volatility, as well as an acyclical trade balance-output ratio relative to the benchmark economy. All these facts are factually consistent with advanced economies—economies with lower average self-employment—being less volatile on average, as in the data. Finally, column (4) of Table A2 shows a version of the benchmark model where I shut down the interest rate shocks without recalibrating the model to match the original targets (then, the volatility of participation is no longer a target in this experiment). While the model continues to successfully capture particular features of the labor market (all cyclical correlations of labor market variables with output are consistent with the data), the volatility of sectoral employment, unemployment, and most notably participation are considerably lower.

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Table A2: Benchmark Model, No Capital Search, and Lower Self-Employment

Targeted Moments

Data

Benchmark Model

No Capital Search

Benchmark Lower SS SE

2.294 2.729 0.865 15.90

(1) 2.294 2.729 0.865 −

(2) 2.294 2.729 0.865 −

(3) − − − −

Benchmark Model, No IR Shocks, Not Recalibrated (4) − − − −

σy,t σc,t σlf p,t σu,t Non-Targeted Moments σy,t σc,t σlf p,t σinv,t σu,t σv,t corr(yt , ct ) corr(yt , invt ) corr(yt , ut ) corr(yt , tbt /yt )

2.294 2.729 0.865 6.470 15.90 − 0.952 0.911 −0.802 −0.685

− − − 6.086 14.76 40.62 0.602 0.902 −0.630 −0.093

− − − 3.767 4.460 32.41 0.455 0.997 −0.473 0.265

2.099 2.774 1.204 4.411 12.38 37.40 0.509 0.929 −0.603 0.029

1.455 0.429 0.108 2.681 2.100 4.727 0.974 0.999 −0.593 0.995

σw,t σne ,t corr(yt , wt ) corr(yt , ne,t ) corr(yt , lf pt ) corr(yt , Rt )

5.200 2.901 0.560 −0.346 0.507 −0.300

7.155 0.783 0.601 −0.510 0.428 −0.491

8.512 0.572 0.438 −0.061 0.277 −0.240

6.880 0.393 0.505 −0.434 0.374 −0.391

1.377 0.198 0.992 −0.426 0.633 0.185

Notes: σx denotes the standard deviation of variable x. All relevant series are logged (when appropriate) and HP-filtered using a smoothing parameter of 1600. SE denotes self-employment. All second moments pertaining to macro aggregates are based on data from 1993Q1 to 2014Q4 unless otherwise noted. The volatility and cyclical correlation of wages is from Boz, Durdu, and Li (2015). The stylized facts for selfemployment and labor force participation are based on data from Mexico’s labor force survey for period 2000Q2 to 2010Q4. The sample period is restricted to post-2000 data due to changes in the labor force survey methodology in the early 2000s. However, Bosch and Maloney’s (2008) empirical analysis suggests that the same quantitative patterns for self-employment and labor force participation hold using data going back to 1987Q1 and ending with the change in methodology in the early 2000s.

A.7

Correlated Productivity and Interest Rate Shocks

The benchmark model produces a lower countercyclicality of the trade balance-output ratio relative to the data. I follow related literature (Neumeyer and Perri, 2005; Lama and Urrutia, 2011; Boz, Durdu, and Li, 2015) and introduce a negative correlation between productivity and interest rates. In particular, I consider the same calibration targets as in the baseline calibration and choose the correlation between productivity and interest rate shocks to get the cyclicality of the trade balance-output ratio as close to the data as possible in order to test whether this affects the main results.40 Table A3 compares the benchmark model 40

The resulting correlation between shocks is -0.99 for the benchmark model. While this correlation may seem high, what ultimately matters is that interest rates increase during downturns, thereby making

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based on the calibration in the main text to a version of the same model with correlated shocks (column (2)), a version of the benchmark model with correlated shocks that abstracts from self-employment (column (3)), and a version of the benchmark model with correlated shocks that abstracts from both self-employment and endogenous labor force participation (column (4)). First, note that adding correlated shocks to the benchmark model improves the fit of the model across all margins and quantitatively matches virtually all non-targeted moments very well. Importantly, though, the amplification mechanisms that were present in the baseline calibration in the main text remain intact, implying that matching the cyclicality of the trade balance is not critical to a good fit with the data. Second, the models without self-employment or labor force participation (columns (3) and (4)) also improve relative to their counterparts without correlated shocks (the latter were presented in Table 3 in the main text). The most important message from Table A3 is that the limitations of the benchmark model in quantitatively capturing the countercyclicality of the trade balance in the absence of correlated shocks—a limitation that standard models also face—plays little role in the model’s success in quantitatively matching a comprehensive set of second moments in the data. Furthermore, allowing the model to capture the countercyclicality of the trade balance implies that the framework presented in this paper captures the patterns in the data even better without worsening the fit of particular variables.

consumption more procyclical and the trade balance-output ratio more countercyclical.

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Table A3: Benchmark Model, and Model Alternatives with Correlated Productivity and Interest Rate Shocks

Targeted Moments

Data

σy,t σc,t σlf p,t Non-Targeted Moments σinv,t σu,t σv,t corr(yt , ct ) corr(yt , invt ) corr(yt , ut ) corr(yt , tbt /yt )

2.294 2.729 0.865

σw,t σne ,t corr(yt , wt ) corr(yt , ne,t ) corr(yt , lf pt ) corr(yt , Rt )

Benchmark Model (1) 2.294 2.729 0.865

Benchmark, Correlated Shocks (2) 2.294 2.729 0.865

No SE, Correlated Shocks (3) 2.294 2.729 0.865

No SE, No LFP,Correlated Shocks (4) 2.294 2.729 −

6.470 15.90 − 0.952 0.911 −0.802 −0.685

6.086 14.76 40.62 0.602 0.902 −0.630 −0.093

6.437 14.69 39.99 0.785 0.946 −0.704 −0.382

3.591 14.33 18.57 0.862 0.999 −0.318 −0.299

3.543 5.183 6.903 0.925 0.999 −0.771 −0.491

5.200 2.901 0.560 −0.346 0.507 −0.300

7.155 0.783 0.601 −0.510 0.428 −0.491

7.260 0.825 0.756 −0.682 0.603 −0.751

6.227 − 0.851 − 0.758 −0.767

6.241 − 0.904 − − −0.793

Notes: σx denotes the standard deviation of variable x. All relevant series are logged (when appropriate) and HP-filtered using a smoothing parameter of 1600. SE (LFP) refers to self-employment (labor force participation). All second moments pertaining to macro aggregates are based on data from 1993Q1 to 2014Q4 unless otherwise noted. The volatility and cyclical correlation of wages is from Boz, Durdu, and Li (2015). The stylized facts for self-employment and labor force participation are based on data from Mexico’s labor force survey for period 2000Q2 to 2010Q4. The sample period is restricted to post-2000 data due to changes in the labor force survey methodology in the early 2000s. However, Bosch and Maloney’s (2008) empirical analysis suggests that the same quantitative patterns for self-employment and labor force participation hold using data going back to 1987Q1 and ending with the change in methodology.

A.8

Benchmark Model and Alternatives with Shocks from Benchmark Model

Table A4 compares the benchmark model (column (1)) to alternative versions of the model without self-employment (column (2)) and without self-employment and labor force participation (column (3)). For the latter two cases, I use the same values for the standard deviation of aggregate productivity and interest rate shocks obtained in the calibration of the benchmark model. As such, I present all volatilities relative to the volatility of output since the model versions in columns (2) and (3) generate different absolute output volatilities. As shown below, the benchmark model continues to outperform simpler versions of the model by quantitatively replicating a more comprehensive set of second moments in the data. Note that the version of the benchmark model without self-employment continues

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to generate a relatively low countercyclicality of unemployment and exhibits limitations in quantitatively capturing other important features of the business cycle that the benchmark model can, in fact, replicate more comprehensively. Table A4: Data vs. Benchmark Model and Model Alternatives with Calibrated Shocks from Benchmark Model

Targeted Moments

Data

No SE

2.294 2.729 0.865

Benchmark Model (1) 2.294 2.729 0.865

(2) − − −

No SE, No LFP (3) − − −

σy,t σc,t σlf p,t Non-Targeted Moments σc,t /σy,t σinv,t /σy,t σu,t /σy,t σv,t /σy,t corr(yt , ct ) corr(yt , invt ) corr(yt , ut ) corr(yt , tbt /yt )

1.190 2.820 6.931 − 0.952 0.911 −0.802 −0.685

1.190 2.653 6.563 17.71 0.602 0.902 −0.630 −0.093

1.806 1.566 9.884 12.95 0.397 0.999 −0.356 0.070

2.143 1.544 4.275 5.969 0.290 0.999 −0.289 0.106

σw,t /σy,t σne ,t /σy,t σlf p,t /σy,t corr(yt , wt ) corr(yt , ne,t ) corr(yt , lf pt ) corr(yt , Rt )

2.267 1.265 0.377 0.560 −0.346 0.507 −0.300

3.119 0.341 0.377 0.601 −0.510 0.428 −0.491

3.857 − 0.576 0.427 − 0.341 −0.248

4.747 − − 0.298 − − −0.084

Notes: σx denotes the standard deviation of variable x. All relevant series are logged (when appropriate) and HP-filtered using a smoothing parameter of 1600. SE (LFP) refers to self-employment (labor force participation) and IR refers to interest rate. All second moments pertaining to macro aggregates are based on data from 1993Q1 to 2014Q4 unless otherwise noted. The volatility and cyclical correlation of wages is from Boz, Durdu, and Li (2015). There is no available data for vacancies in Mexico. The stylized facts for self-employment and labor force participation are based on data from Mexico’s labor force survey for period 2000Q2 to 2010Q4. The sample period is restricted to post-2000 data due to changes in the labor force survey methodology in the early 2000s. However, Bosch and Maloney’s (2008) empirical analysis suggests that the same quantitative patterns for self-employment and labor force participation hold using data going back to 1987Q1 and ending with the change in methodology in the early 2000s.

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A.9

Empirical Evidence on Capital Constraints Among Small Firms

Table A5 shows that, on average, the majority of firms in EMEs are informal and have little access to formal (bank) credit relative to formal firms. Tables A6 and A7 present evidence on access to formal credit and external financing for formal firms only (due to data limitations on similar facts for informal firms). Table A5: Share of Formal and Informal Firms and Access to Formal (Bank) Credit

Country Argentina Brazil Chile Colombia Ecuador Malaysia Mexico Peru Philippines South Africa Turkey

Firm Category Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal Formal Informal

% of Total Firms 22 78 24 76 39 61 31 69 59 41 17 83 33 67 29 71 16 84 19 81 62 38

% With Access to Formal (Bank) Credit 74 6 86 13 73 13 88 13 92 13 76 11 25 13 77 25 44 11 62 8 78 11

Source: IFC Enterprise Finance Gap Database 2010. Notes: Formal firms encompass registered firms (regardless of size(micro, very small, small, or medium)). Firms are categorized as informal if they are unregistered with their municipality or tax authorities. They include owner-only firms regardless of registration status (see https://www.smefinanceforum.org/data-sites/ifc-enterprise-finance-gap). Similar evidence is presented in Epstein, Finkelstein Shapiro, and Gonz´ alez G´omez (2016). Table A6: Share of Formal Firms with Line of Credit or Loan from Financial Institution

Country Group High Income Upper Middle Income Lower Middle Income

Small Firms 45 38 25

Medium Firms 60 54 39

Large Firms 66 65 51

Source: Table 5 in Allen, Carletti, Qian, and Valenzuela (2013), based on World Bank Enterprise Surveys, 2002-2010. Notes: Small Firms have 5-19 workers, Medium Firms have 20-99 workers, and Large Firms have 100+ workers. All firms in the survey are categorized as being formal (i.e., registered with government authorities).

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Table A7: Financing of Formal Firms in Emerging Economies

Country

Argentina Brazil Chile Colombia Ecuador Malaysia Mexico Peru Philippines South Africa Thailand Turkey Average

Proportion of External Financing from Alternative Financing Sources (% of External Financing) 80.65 58.14 34.69 36.54 44.23 37.93 73.08 24.14 58.54 59.52 11.25 33.33 44.00

Trade Credit (% of Alternative Financing Sources) 19 35 34 40 54 21 62 59 33 3 40 17 32.15

Proportion of External Financing from Bank Financing (% of External Financing) 16.13 32.56 61.22 63.46 51.92 58.62 26.92 65.52 31.71 40.48 72.50 38.10 47.41

Source: Table 4 in Allen, Carletti, Qian, and Valenzuela (2013), based on World Bank Enterprise Surveys, 2002-2010. Notes: External financing includes Market Finance, Bank Finance, and Alternative Finance. Alternative Finance includes trade credit, leasing funds, resources from friends and family, development banks, and other informal sources. All firms in the survey are categorized as being formal (i.e., registered with government authorities).

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