Employment and Firm Heterogeneity, Capital Allocation, and Countercyclical Labor Market Policies

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1115 August 2014 Employment and Firm Heterogeneity, Capital Allocation, and Countercyclical Labor Market Policies Brendan Epstein Alan Finkelstein Shapiro NOTE: International Finance and Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IDFPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from Social Science Research Network electronic library at www.ssrn.com.

Employment and Firm Heterogeneity, Capital Allocation, and Countercyclical Labor Market Policies (cid:3) Brendan Epstein Alan Finkelstein Shapiro y z Federal Reserve Board Universidad de Los Andes August 23, 2014 Abstract Many countries have large employment shares in micro and small (cid:133)rms that have limitedaccesstoformal(cid:133)nancingandthereforerelyoninputcredit. Suchcountriesare mainlyemerginganddevelopingeconomies, whosebusinesscycledynamicsareincreasingly important for the global economy in light of the dramatic rise in international linkages and spillovers that have occurred over the last several decades. Emerging and developingeconomiesimplementedahostofcountercyclicallabormarketpoliciesamid the global (cid:133)nancial crisis, but data limitations on high-frequency labor and job (cid:135)ows preventadetailedempiricalassessmentofthee⁄ectivenessofthesepolicies. Toaddress this problem, we develop a business cycle model with frictional labor markets that is novel in light of its consistency with the employment and (cid:133)rm structure of emerging and developing economies. We use the model to assess the aggregate impact of key countercyclical labor market policies. We (cid:133)nd that hiring subsidies and job intermediation services for large (cid:133)rms are particularly e⁄ective in aiding recoveries. Policies targeting smaller (cid:133)rms yield limited aggregate bene(cid:133)ts and may even be detrimental to the recovery process. The labor market structure shapes sectoral allocation and explains the economy(cid:146)s di⁄erential response to policy. JEL Classi(cid:133)cations: E24, E32, J64 Keywords: business cycles, search frictions, (cid:133)scal policy, self employment, small (cid:133)rms, input credit. Thispaperwaspreviouslycirculatedas(cid:147)FirmandJobCreationPoliciesDuringRecessionsinEmerging (cid:3) Economies.(cid:148)Theviewsinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpreted as representing the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. The authors thank, without implicating, William Maloney, MarianoBosch,JuliÆnMessina,AndrØsGonzÆlezG(cid:243)mez,andseminarparticipantsinthe2014LACEALabor Network for valuable comments and feedback. The authors are also grateful for useful discussions during visits to Brown University, the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of Philadelphia, and the Federal Reserve Bank of Richmond. Any errors are the authors(cid:146)own. E-mail: brendan.epstein@frb.gov. Phone: 202-721-4593. Correspondence: Board of Governors of the y Federal Reserve System; 20th St. and Constitution Ave. NW; Washington, D.C. 20551. E-mail: alanfshapiro@gmail.com. Phone: (571) 313-805-9115. Correspondence: Calle 19A No. 1-37 z Este, Bloque W; Department of Economics, Universidad de los Andes; BogotÆ, Colombia.

1 Introduction Manycountrieshavelargeemploymentsharesinmicro(cid:133)rms(alsoreferredtoasown-account or self-employment (cid:133)rms, that is, one-worker (cid:133)rms) and small (salaried) (cid:133)rms. These (cid:133)rms, compared to large (cid:133)rms, are less capital-intensive, often have limited access to formal (cid:133)nancing, and rely on inter(cid:133)rm input credit and other informal sources to meet their non-labor input needs (Global Financial Development Report, 2014). Countries with this employment and (cid:133)rm structure are mainly emerging and developing economies, which increasingly generateanontrivialfractionofworldoutput. Emerginganddevelopingeconomiesimplementeda host of countercyclical labor market policies amid the global (cid:133)nancial crisis (Table 1). Some of the most prominent policies included temporary wage and hiring subsidies, the temporary expansion of job intermediation services, and the expansion of public expenditures to support the creation of micro and small (cid:133)rms via credit facilities, among others (Table 2). Limitations on the frequency and availability of detailed data on labor and job (cid:135)ows for most emerging economies pose a serious challenge for in-depth empirical assessments of the bene(cid:133)ts, costs, and aggregate e⁄ects of these policies on employment and economic activity. As these economies continue to improve their ability to implement countercyclical policy, it is increasingly important to understand the impact of di⁄erent policy tools in response to adverse shocks, and especially so given the dramatic rise in international linkages and spillovers that have occurred over the last several decades. Yet, extrapolating conclusions from similar labor market policies implemented in advanced economies is ultimately inadequate given several distinctive characteristics of emerging economies(cid:146)labor market and (cid:133)rm structure. Table 1: Percent of Low- and Middle-Income Countries that Implemented Labor Demand and Job Matching Policies Type of Policy Percent of Countries Direct Job Creation and Employment Incentives 80 Credit Facilities, Access to Credit 65 Lower Non-Wage Labor Costs, Other Taxes 58 Public Employment Services 53 Special Measures for Small and Medium Enterprises 49 Subsidies for Job Creation 44 Source: Figures 10 and 14, ILO and World Bank (2012). Notes: The sample of low- and middle-income economies includes 55 countries. 58 percent of the country sample introduced training for the unemployed. 1

Table 2: Allocation of Expenditures, Labor Demand and Job Matching Policies: Low- and Middle-Income Countries Budget Allocation within Labor Demand Policies Policy Category (Percent ) Direct Job Creation and Employment Incentives 66.95 Subsidies to Employers Maintaining Existing Jobs 14.54 Credit Facilities, Access to Credit 12.97 Special Measures for Small and Medium Enterprises 3.04 Budget Allocation within Programs that Improve Job Matching Skills Policy Category (Percent) Public Employment Services 43 Training for Unemployed 31 Training for Employed 20 Source: Figures 11 and 15, ILO and World Bank (2012). Notes: The sample of low- and middle-income economies includes 55 countries. Subsidies to employers maintaining jobs include wage subsidies. To get around these limitations, we develop a tractable and novel business cycle model with frictional labor markets and (cid:133)rm heterogeneity. The model is consistent with the employment and (cid:133)rmstructure of emerging and developing economies. In particular, we exploit the increasingly rich evidence on the employment and (cid:133)rm structure of several Latin American economies to guide our modeling choices. Then, we use the model as a tractable laboratory to study the aggregate consequences and e⁄ectiveness of several cyclical labor-demand and (cid:133)rm-creation policies that were implemented by emerging and developing economies during the global (cid:133)nancial crisis. The structure of the model is based on the following facts. First, relative to advanced economies, the share of self-employment in Latin American economies is substantial, ranging anywhere from 20 to 40 percent of total employment and reaching even higher rates in many developing economies (Perry et al., 2007; Loayza and Rigolini, 2011). Second, a larger fraction of (cid:133)rms in these economies are micro or small, and they employ a larger share of salariedemploymentrelativetoadvancedeconomies(Table3; GlobalFinancialDevelopment Report, 2014). Third, while bank credit and other formal (cid:133)nancing sources are more often available for larger(cid:133)rmsinemerginganddevelopingeconomies, microandsmall(cid:133)rmstendtobeinformal and face severe di¢ culties in obtaining formal external (cid:133)nancing. In fact, micro and small (cid:133)rms often cite access to (cid:133)nance as their biggest obstacle (Kantis, Ishida, and Komori, 2002; IDB, 2005a, 2005b; Global Financial Development Report, 2014). As a consequence of the 2

lack of formal external (cid:133)nancing, many of these (cid:133)rms exhibit a smaller scale, must search for suppliers and customers to obtain input credit, and hence must rely on alternative, informal (cid:133)nancing sources generally based on relationship lending (Tables 4 and 5; Farazi, 2014). Table 3: Size Distribution of Salaried Employment and Establishment for Select Countries Firm U.S. Mexico Argentina Bolivia Size Empl. Estab. Empl. Estab. Empl. Estab. Empl. Estab. 1-9 4.2 54.5 22.7 90.5 22 84.0 43.6 91.7 10-19 4.8 14.5 5.5 4.2 25 12.9 10.0 4.2 20-49 11 14.7 8 2.7 19 2.5 13.6 2.6 50-99 12.3 7.4 7.5 1.1 35 0.8 9.8 0.8 100+ 67.7 8.9 56.3 1.6 18 0.2 23.0 0.6 Source: Taken directly from Busso, Madrigal, and PagØs (2012). Notes: Empl. and Estab. stand for Employment and Establishments, respectively. The sample year varies by country. The data in the table is for manufacturing (cid:133)rms only, although similar patters hold for other sectors. The evidence in the table provides a lower bound for the share of small (cid:133)rms, small-(cid:133)rm salaried employment, and self-employment since the Mexican census only considers (cid:133)rms with a (cid:133)xed location and hence excludes a non-negligible share of employment and (cid:133)rms in the economy. Table 4: Consequences of Lack of External Financing for Latin American Small Firms Consequence of Restricted Access to Financing Percent of Entrepreneurs Reduced Scale 56.0 Search for Partners 11.0 Search for Support from Suppliers or Customers 51.0 Delay in Launching Enterprise 32.0 Source: Taken directly from Table 6.5, IDB (2005b). Table 5: Percent of Small Entrepreneurs Using Alternative Financing Sources: Latin America Financing Sources Startup Early Years Suppliers 32.0 36.6 Purchase of Second-Hand Machinery and Equipment 27.5 20.6 Customers 18.0 19.1 Delaying Payment of Services 8 3.5 Source: Taken directly from Table 6.2, IDB (2005b). Importantly, Table 5 shows that as small (cid:133)rms grow older their reliance on alternative (cid:133)nancingsources,suchascreditfromsuppliers,customers,andthepurchaseofusedmachinery 3

and equipment(cid:151)all being relationship-based sources of input credit(cid:151)remains important.1 These are key di⁄erences relative to advanced economies where small (cid:133)rms, while also constrained relative to larger (cid:133)rms, usually have better access to formal (cid:133)nancing. Finally, as a simple example, Table 6 shows the allocation of resources by (cid:133)rm size in Mexico. This evidence(cid:151)which is similar for other economies in the region(cid:151)suggests that a very small share of total capital is allocated among micro and small salaried (cid:133)rms. Table 6: Allocation of Resources by Firm Size in Mexico Firm Size Capital Workers Value Added 0-5 13.2 37.8 10.3 6-10 4.5 8.8 4.6 11-50 10.2 14.9 12.5 50+ 72.1 38.5 72.5 Source: Busso, Fazio, and Levy (2012). Notes: The evidence in the table provides a lower bound for the share of small (cid:133)rms, small-(cid:133)rm salaried employment, and self-employment since the Mexican census only considers (cid:133)rms with a (cid:133)xed location and hence excludes a non-negligible share of employment and (cid:133)rms in the economy. Basedontheabovefacts, ourmodeldi⁄erentiatesbetweenself-employed(ormicro)(cid:133)rms, small salaried (cid:133)rms, and large (cid:133)rms based on capital intensity, productivity, and the reliance of input credit by micro and small (cid:133)rms in a tractable way. Following Finkelstein Shapiro (2014), large salaried (cid:133)rms act as input credit suppliers to self-employed (cid:133)rms through frictional capital markets. We expand this framework on two fronts. First, owner-only (selfemployed, or micro) (cid:133)rms can choose to expand to become small salaried (cid:133)rms. The notion of size in the model is related to a restriction on variable capital usage by small salaried (cid:133)rms and their continued reliance on external (cid:133)nancing from larger (cid:133)rms via capital relationships, asinthedata. Second, small(cid:133)rmscanhireadditionalworkers. Thus, themodelincorporates bothendogenoussmall(cid:133)rmcreationandexpansion. Overall, thisstructureisconsistentwith the small allocation of capital among small (cid:133)rms in developing economies (Busso, Fazio, and Levy, 2012), and establishes an important link between large (cid:133)rms, self-employed, and small (cid:133)rms through input credit markets.2 We show that the model successfully captures the 1While (cid:133)rms in East Asia tend to rely less on these (cid:133)nancing sources as they age, input credit remains a relevant source of (cid:133)nancing (IDB, 2005b). 2In order to clearly focus on labor-market issues, we assume the context of a closed economy. However, as discussed in the Appendix, assuming instead a small open-economy context does not change our main results. 4

cyclical dynamics of salaried employment, self-employment, and their respective (cid:135)ows from unemployment in the data. We consider the aggregate consequences of introducing cyclical hiring subsidies for large and small salaried (cid:133)rms, hiring subsidies for self-employed (cid:133)rms (which foster the creation of small salaried (cid:133)rms), subsidies for the creation of self-employed (cid:133)rms, and wage subsidies. We also consider policies that improve the matching process between salaried (cid:133)rms and the unemployed during downturns, where these policies are meant to capture the expansion of government-provided job intermediation services during recessions. All these policies were important policy tools during the global (cid:133)nancial crisis (Tables 1 and 2; ILO and World Bank, 2012). Ouranalysisfocusesonindividualcyclicalpoliciesthatgeneratethesame(cid:133)scalcostatthe onset of a downturn. Results show that the type of (cid:133)rm targeted by the policy (owner-only or micro, small, or large) matters for the e⁄ectiveness of cyclical labor market interventions in aiding employment and output recoveries. In particular, the reallocation of capital across (cid:133)rms (and hence the functioning of inter(cid:133)rm input credit markets and their interaction with the labor market) along with the e⁄ect that this reallocation has on relative employment by small and large (cid:133)rms plays an important role in the e⁄ectiveness of policy. Certain policies can generate tradeo⁄s between limiting the rise in unemployment as the recession hits and aiding the recovery in the medium term. Other policies not only yield gains along both of those margins but also provide better income protection. In particular, our results imply that, while policies that focus on small (cid:133)rms can successfully protect employment, these policies have limited e⁄ects on the output recovery path. In contrast, policies that improve intermediation between the unemployed and larger (cid:133)rms yield gains across the board. Moreover, policies that foster the creation of micro(cid:133)rms can be detrimental to the recovery process and yield negligible bene(cid:133)ts in terms of employment and income protection. Model-implied (cid:133)scal multipliers suggest that hiring subsidies and job intermediation for large (cid:133)rms are particularly e⁄ective in aiding recoveries. These results are important in light of the fact that, amid the global (cid:133)nancial crisis, many emerging economies introduced particular policies targeting micro and small and medium enterprises (SMEs). Our work is related to the growing literature on business cycles and search frictions, as 5

well as the literature on the impact of (cid:133)scal policy in the context of the recent crisis. Most related to our paper is the work by Nicoletti and Pierrard (2006) who develop a model where small salaried (cid:133)rms must (cid:133)rst match with a (cid:133)nancial intermediary to obtain capital and then search for a single worker to produce. Our model di⁄ers from that of Nicoletti and Pierrard in three key aspects. First, while small (cid:133)rms in our framework are also created endogenously, they can employ multiple workers and, once established, can also expand by hiring additional workers. Second, we introduce self-employed (cid:133)rms(cid:151)a key characteristic of emerging-economy labor markets(cid:151)which can endogenously expand and become small salaried (cid:133)rms. Finally, we use capital search in such a way that, in line with the data, selfemployment is countercyclical, small (cid:133)rm owners (and therefore small (cid:133)rms) are procyclical, and both self-employed and small (cid:133)rms rely on input credit relationships.3 Less directly related to our work, but among research exploring the e⁄ects of labor market policies during the global (cid:133)nancial crisis, are studies that focus on advanced economies. Kitao, S‚ahin, and Song (2010) study the impact of job creation policies introduced in the U.S. using a partial-equilibrium search and matching model. Campolmi, Faia, and Winkler (2011) analyze the impact of (cid:133)scal policy and hiring subsidies on employment in a general equilibrium setting with labor search frictions and show that hiring subsidies can yield large (cid:133)scal multipliers. Also, Totzek and Winkler (2010) explore the role of (cid:133)scal policy in an environment with endogenous (cid:133)rm entry, but abstract from studying labor market dynamics.4 Finally, Lee and Mukoyama (2013) build a model of industry dynamics that captures the cyclical properties of entry and exit in the U.S. manufacturing sector to analyze the role of entry subsidies during recessions, but they abstract from labor market frictions. We contribute on three main fronts to: the existing literature on (cid:133)rm and labor market dynamics over the business cycle in emerging economies; and to recent studies on the impact of cyclical labor market policies during recessions. First, our model accounts for the large shares of self-employment in developing countries in a way that is consistent with the cyclical dynamics of self-employment and salaried employment in the data, and does so in 3As shown in Finkelstein Shapiro (2014), the capital search structure we use is important to capture the cyclical dynamics of self-employment and entry into self-employment in developing countries. 4For related work on (cid:133)rm entry and business cycles, see Shao and Silos (2008). For studies that merge labor market and (cid:133)rm dynamics in a business cycle context, see SedlÆ(cid:181)cek (2011), SedlÆ(cid:181)cek and Sterk (2013) and Siemer (2013), among others. 6

a tractable environment with (cid:133)rm heterogeneity based on capital intensity and access to external (cid:133)nance among small (cid:133)rms. Existing models of (cid:133)rm entry over the business cycle generally abstract from the fact that many new (cid:133)rms, particularly in emerging economies, start o⁄as being one-person (cid:133)rms that either remain without workers or slowly expand via salariedemploymentcreation. Ourframeworktractablyaccommodatesthisfeature. Second, to the best of our knowledge, we are the (cid:133)rst to analyze the aggregate impact of cyclical labor market policies in developing countries within the context of a business cycle model consistent with the employment and (cid:133)rm structure of these economies. Third, with regards to the policies we consider, a key di⁄erence relative to the existing business cycle literature is that we analyze interventions that explicitly support the creation and expansion of self-employment ventures and small (cid:133)rms during downturns. These interventions have been common in several emerging economies and are particularly relevant in economies with both large self-employment shares and large employment shares among small (cid:133)rms. Importantly, we characterize the e⁄ectiveness of policies that speci(cid:133)cally target these (cid:133)rms. The remainder of this paper is organized as follows. Section 2 develops the model. Section 3 describes the model(cid:146)s calibration. Section 4 presents the main results from our policy experiments and discusses the (cid:133)scal implications of di⁄erent policies. Finally, Section 5 concludes. 2 The Model Theeconomyisinhabitedbyanin(cid:133)nitely-livedrepresentativehouseholdwithalargenumber of members whose population consists of a unit mass. All household members participate in the labor force. Following related literature, there is perfect risk-pooling across household members. Final output, whose price is normalized to 1, is produced using as intermediate inputs the production of large (cid:133)rms, small (cid:133)rms, and owner-only (cid:133)rms. The product market isperfectlycompetitive.5 However,labor-marketfrictionsaresuchthatthewagesforsalaried workers inbothlarge andsmall (cid:133)rms, as well as thecapital rental rates forself-employedand 5Also, whilethemodelaccountsfor(cid:133)rmandemploymentheterogeneity, forsimplicitywefocusonhomogeneous workers. See Epstein (2012) and Arseneau and Epstein (2014), among others, for research on the aggregate implications of both (cid:133)rm and worker heterogeneity. 7

small business owners, are negotiated via Nash bargaining. Taken together, our assumptions on large and small (cid:133)rms yield a larger concentration of capital in the large-(cid:133)rm sector, which is consistent with the evidence in Busso, Fazio, and Levy (2012) and others. Large (cid:133)rms are capital intensive (compared to small (cid:133)rms), undertake capital accumulation internally, and make capital allocation decisions(cid:151)that is, they choose the share of capital used in their own production and consequently the share of capital available as input credit for self-employed individuals and small (cid:133)rms. This capital is supplied through frictional capital markets. Large (cid:133)rms also hire salaried workers in frictional labor markets. Self-employed (or own-account) individuals operate owner-only (cid:133)rms. These (cid:133)rms produce using a single unit of capital and a (cid:133)xed (normalized) unit of self-employment labor. Importantly, these (cid:133)rms cannot accumulate capital internally. As in Finkelstein Shapiro (2014), obtaining capital to enter self-employment is subject to search frictions so that production capital is obtained by establishing an input credit relationship with large (cid:133)rms (capital suppliers). Owner-only(cid:133)rms also post vacancies andtherefore canbecome small salaried (cid:133)rms by hiring employees through frictional labor markets. If at least one of these vacancies is successfully (cid:133)lled, a self-employed individual becomes a small salaried (cid:133)rm owner. Small(cid:133)rmscannotaccumulatecapitalinternally, theyarelesscapitalintensivethanlarge (cid:133)rms, and they continue to rely on a capital relationship with large (cid:133)rms to be operational (after having made the transition from micro (cid:133)rm to small salaried (cid:133)rm). For aggregation purposes(discussedbelow)weassumethateachsmall(cid:133)rmalsoneedsone, andonlyone, unit of capital to be operational. Thus, each small salaried (cid:133)rm uses a unit of capital and salaried workers to produce. These salaried workers are hired through frictional labor markets. 2.1 Self-Employment, Small Firms, and Households 2.1.1 Self-Employment Total pro(cid:133)ts from self-employed individuals are: (cid:5) = (p z r (cid:28)vSE v )n , (1) SE;t SE;t SE;t SE;t t SE SE;t SE;t (cid:0) (cid:0) 8

where: p is the price of self-employment output; z is self-employment productivity; SE;t SE;t r is the endogenous Nash rental rate of capital paid by small businesses; (cid:28)vSE is a policy SE;t t that equals 1 in steady state and decreases (increases) when output is below (above) trend (thus, it acts as a hiring subsidy during downturns); is the (cid:133)xed, exogenous (cid:135)ow cost of SE posting vacancies; v is the number of vacancies posted by each self-employed individual SE;t in order to expand and become a small (cid:133)rm owner; and n is the mass of self-employed SE;t individuals. Total output from self-employment is given by y = z n . SE;t SE;t SE;t 2.1.2 Small Salaried Firms Total pro(cid:133)ts from small (cid:133)rms are given by n n (cid:5) = p z F SB;t ;1 (cid:28)wSBw SB;t o (2) SB;t SB;t SB;t o (cid:0) t SB;t o SB;t (cid:20) (cid:18) SB;t (cid:19) SB;t(cid:21) r o (cid:28)vSB v o , SB;t SB;t t SB SB;t SB;t (cid:0) (cid:0) where: p isthepriceofoutputinthesmall(cid:133)rmsector; z istheexogenousproductivity SB;t SB;t of small (cid:133)rms; the production function of an individual small (cid:133)rm, F ( ; ), is increasing and (cid:1) (cid:1) concave in each of its arguments (the (cid:133)rst argument is salaried labor used per small (cid:133)rm and the second argument is capital usage per small (cid:133)rm(cid:151)we assume that all operating small (cid:133)rms are identical, which, as shown below, leads to straightforward sectoral aggregation); n is the total mass of individuals employed by small (cid:133)rms; w is the wage paid to SB;t SB;t small-(cid:133)rm employees; o is the total mass of small (cid:133)rm owners; r is the endogenous SB;t SB;t rental rate of capital paid by small (cid:133)rms; is a (cid:133)xed and exogenous (cid:135)ow cost of posting SB vacancies; v is the number of vacancies posted by each small (cid:133)rm; and (cid:28)vSB and (cid:28)wSB are SB;t t t time-varying policies (hiring and wage subsidies, respectively) that equal 1 in steady state and decrease (increase) when total output is below (above) trend. Given our assumptions on the production function of individual small (cid:133)rms, equation (2) 9

can be restated as: (cid:5) = p z F(n ;o ) (cid:28)wSBw n (3) SB;t SB;t SB;t SB;t SB;t t SB;t SB;t (cid:0) r o (cid:28)vSB v o . SB;t SB;t t SB SB;t SB;t (cid:0) (cid:0) It follows that, from a sectoral perspective, total output from small businesses is increasing andconcaveinsmall(cid:133)rmemployeesandsmall(cid:133)rmcapital. Notethatbecauseeachindividual productionentityusesoneandonlyoneunitofcapital, o representsboththemassofsmall SB business owners and the total mass of capital rented by small (cid:133)rms. Total output from small (cid:133)rms is given by y = z F(n ;o ). SB;t SB;t SB;t SB;t 2.1.3 Employment-State Evolution All job (cid:133)nding and (cid:133)lling probabilities, discussed further below, depend on market tightness andarethereforeendogenous. Jobdestructionprobabilities, alsodiscussedfurtherbelow, are assumed to increase (decrease) when total output is below (above) trend. This assumption is broadly in line with the introduction of countercyclical job-destruction probabilities in Shimer (2005). We make these assumptions on job destruction in order to keep the model tractable while still being able to get at the issue of how labor market policies may a⁄ect the pace of recoveries and hence of job destruction itself. An unemployed job seeker (cid:133)nds a job in a large (cid:133)rm with probability f and these jobs L;t are destroyed with probability (cid:26)L. Therefore, from the household(cid:146)s labor supply perspective t the mass of individuals employed by large (cid:133)rms n evolves in the following way: L;t n = (1 (cid:26)L)(n +f u ), (4) L;t+1 (cid:0) t L;t L;t t where u is the mass of unemployed individuals. t For a self-employment opportunity to arise the household must form a match with a capital supplier. In order to form such matches, the household spends resources s on K;t capitalsearch. Matcheswithcapitalsuppliersareformedwithprobabilityf . Onceamatch K;t with a capital supplier is formed, an unemployed individual is assigned to self-employment 10

status. As noted earlier, self-employed individuals post vacancies v , which allows them SE;t to expand and become small (cid:133)rm owners by hiring workers. Transitioning from being a self-employed individual into a small (cid:133)rm owner occurs with endogenousprobabilityq . Bothexistingandnewlyformedmatcheswithcapitalsuppliers SE;t are destroyed with probability (cid:26)K. In addition, a small (cid:133)rm is destroyed with probability t (cid:26)O, but in that instance the former small (cid:133)rm owner retains the capital supplier relationship t and transitions back to self-employment. Finally, the probability that a salaried position is destroyed in a surviving small (cid:133)rm is (cid:26)S. t It follows that, from the household(cid:146)s perspective, the mass of self-employed individuals n satis(cid:133)es: SE;t n = (1 (cid:26)K) 1 (1 (cid:26)O)(1 (cid:26)S)v q n +(cid:26)Oo +s f , (5) SE;t+1 (cid:0) t (cid:0) (cid:0) t (cid:0) t SE;t SE;t SE;t t SB;t K;t K;t (cid:8)(cid:2) (cid:3) (cid:9) and the mass of small (cid:133)rm owners evolves as follows: o = (1 (cid:26)K)(1 (cid:26)O) o +(1 (cid:26)S)v q n . (6) SB;t+1 (cid:0) t (cid:0) t SB;t (cid:0) t SE;t SE;t SE;t (cid:2) (cid:3) From a labor demand perspective, at the start of a period nd individuals are employed SB;t by small (cid:133)rms. Self-employed individuals seeking to become small (cid:133)rms post a total of v n vacancies and existing small (cid:133)rms post a total of v o vacancies. Therefore, SE;t SE;t SB;t SB;t nd = (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S) nd +n v q +o v q (7) SB;t+1 (cid:0) t (cid:0) t (cid:0) t SB;t SE;t SE;t SE;t SB;t SB;t SB;t (cid:0) (cid:1) gives the evolutionof salariedemployment insmall (cid:133)rms fromthe labordemandperspective, where: q is the probability that a small (cid:133)rm (cid:133)lls a vacancy. From a labor supply per- SB;t spective, at the start of a period ns individuals are employed by small (cid:133)rms. Unemployed SB;t individuals (cid:133)nd a job with a newly-formed small (cid:133)rm with probability f and they (cid:133)nd a SE;t job with an existing small (cid:133)rm with probability f . Therefore, SB;t ns = (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S) ns +u (f +f ) . (8) SB;t+1 (cid:0) t (cid:0) t (cid:0) t SB;t t SE;t SB;t (cid:2) (cid:3) 11

In equilibrium, ns = nd = n . SB;t SB;t SB;t Finally, unemployment at time t is given by u = 1 n n n o . t L;t SE;t SB;t SB;t (cid:0) (cid:0) (cid:0) (cid:0) Because the labor force is normalized to unity, u is also the aggregate unemployment rate. t 2.1.4 Household Optimization In solving its optimization problem, the household takes all job-(cid:133)nding, -(cid:133)lling, and destruction probabilities as given. Also, we assume that from the perspective of small (cid:133)rms the household maximizes utility as a demander of labor. This assumption keeps the solution to the household(cid:146)s labor-supply and -demand problems explicitly decentralized. The household(cid:146)s problem is to choose sequences of consumption c , the desired measure t of self-employed individuals (achieved by spending resources on capital search) n , the SE;t+1 desired demand for salaried workers by small (cid:133)rms (achieved by vacancy posting) nd , SB;t+1 the desired measure of small (cid:133)rm owners (also achieved by vacancy posting) o , total SB;t+1 expenditures on capital search s , vacancies posted per small (cid:133)rm v , and vacancies K;t SB;t posted per self-employed individual v SE;t , in order to maximize E0 1 t=0 (cid:12)tu(c t ), where: E is the expectation operator; (cid:12) (0;1) is the constant subjective dPiscount factor; u is the 2 instantaneous utility function with u(c) > 0 and u (c) < 0; and c is consumption. Note 0 00 that because there is no labor force participation or sectoral search-intensity decision, the household has no explicit choice over ns and n . Instead, the household simply takes SB;t+1 L;t+1 as given the labor supply side equations (4) and (8). The household(cid:146)s maximization problem is subject to equations (1), (3), (5), (6), (7) and also to the household(cid:146)s budget constraint: c +(cid:28)(cid:20)(cid:20)(s )+T = (cid:5) +(cid:5) +(cid:5) +w ns +w n +bu , t t K;t t SB;t SE;t L;t SB;t SB;t L;t L;t t where: the price of consumption is normalized to unity and the household must pay lumpsum taxes T ; the large (cid:133)rm, whose problem is described below, is owned by the household t 12

and its pro(cid:133)ts (cid:5) are taken as given; individuals employed by the large (cid:133)rm earn the L;t real wage w ; individuals employed by small (cid:133)rms earn the real wage w ; unemployed L;t SB;t individuals obtain the constant and exogenous per-period unemployment (cid:135)ow bene(cid:133)t b; the household spends resources s at total cost (cid:20)(s ) to search for capital suppliers (large K;t K;t (cid:133)rms) that provide capital for self-employment ventures, with (cid:20) (s ) > 0 and (cid:20) (s ) 0; 0 K;t 00 K;t (cid:21) (cid:28)(cid:20) is a time-varying policy that equals 1 in steady state and decreases (increases) when total t output is below(above) trend (thus, when output is belowtrend, the policy acts as a subsidy that reduces the cost of (cid:133)nding external (cid:133)nancing to start a self-employment venture, i.e. this policy acts as a self-employment startup subsidy). 2.1.5 Household Optimality Conditions As shown in the Appendix, the household(cid:146)s decision on s to search for a capital supplier K;t is given by (cid:28)(cid:20)(cid:20)(s ) (cid:28)(cid:20) (cid:20)(s ) t f 0 K;t K;t = (1 (cid:0) (cid:26)K t )Et (cid:4) t+1 j t (cid:26) p SE;t+1 z SE;t+1 (cid:0) r SE;t+1 + t+1 f K 0 ;t+ K 1 ;t+1 (cid:27) , where (cid:4) = (cid:12)u(c )=u(c ) is the stochastic discount factor. This expression equates t+1t 0 t+1 0 t j the expected marginal cost of spending resources to (cid:133)nd capital to the expected marginal bene(cid:133)t. The latter is given by individual earnings in self-employment if the match takes place and becomes productive next period, p z r , plus the continuation value (see SE SE SE (cid:0) Finkelstein Shapiro, 2014). Note that the cost of posting vacancies during self-employment does not appear in this optimality condition because the household internalizes the fact that a self-employed individual may be able to become a small business owner in the future (the only relevant objects that a⁄ect the decision to enter self-employment is the revenue net of the cost of capital plus the continuation value of a capital relationship). The cost of posting vacancies will, in turn, a⁄ect the decision to transform a self-employment venture into a small salaried (cid:133)rm. The household(cid:146)s optimal choice of transforming a self-employed (cid:133)rm into a small salaried 13

(cid:133)rm is: 1 (cid:28)vSE (cid:28)vSB t SE t SB (1 (cid:26)S)(1 (cid:26)K)(1 (cid:26)O) q (cid:0) q (cid:0) t (cid:0) t (cid:0) t (cid:18) SE;t SB;t (cid:19) p z F (n ;o ) SB;t+1 SB;t+1 oSB SB;t+1 SB;t+1 = Et (cid:4) t+1 j t 8 > > (cid:0) r SB;t+1 (cid:0) (p SE;t+1 z SE;t+1 (cid:0) r SE;t+1 ) 9 > > . > < + 1 (cid:28) v t+ S 1 E SE (cid:28) v t+ S 1 B SB > = (1 (cid:0) (cid:26)S t+1 ) qSE;t+1 (cid:0) qSB;t+1 > > (cid:16) (cid:17) > > > > : ; The left-hand side of this expression captures the expected marginal cost, which in this case is given by the expected cost of posting a vacancy(cid:151)a necessary condition to transition from being a self-employed individual to a small business owner(cid:151)net of the cost of posting a vacancy faced by existing small (cid:133)rms (the latter is shown below and embodies the value of having an additional salaried worker as an existing small (cid:133)rm). The right-hand side of this expression gives the expected marginal bene(cid:133)t of becoming a small business owner and is comprised of two terms: the continuation value, and the net bene(cid:133)t of being a small business owner. In particular, the latter term is given by the di⁄erence between the marginal product ofhavingahouseholdmemberrunningasmallbusinessnetofthecostofthematchedunitof capital, p z F (n ;o ) r ;andself-employmentrevenuenetofthecostofmatched SB SB oSB SB SB (cid:0) SB capital, p z r . Note that a self-employed individual is not only taking into account SE SE SE (cid:0) the net value of being a small business owner, but also the value of having a salaried worker as a small salaried (cid:133)rm, which is implicitly given by the term (cid:28)vSB =q : t SB SB;t Finally, the optimal choice of vacancies posted per existing small (cid:133)rm yields a standard job creation condition (1 (cid:0) (cid:26)K t )(1 (cid:0) 1 (cid:26)O t )(1 (cid:0) (cid:26)S t ) (cid:28)v t q S S B B ;t SB = Et (cid:4) t+1 j t 8 < p SB;t+ (cid:0) 1 z (cid:28) S w t+ B S 1 ; B t+ w 1 S F B n ; S t+ B 1 (n + SB (cid:28) q ; v t t + S S + B 1 B 1 ; t ; + S o 1 B SB;t+1 ) 9 = . : ; Thisexpressionsimplyequatestheexpectedmarginal cost of postingavacancytohireworkersinasmall(cid:133)rmtotheexpectedmarginalbene(cid:133)t. Thelatterincludesthemarginalproduct of labor net of the wage and the continuation value from the employment relationship. 14

2.2 Large Firms A representative large (cid:133)rm chooses desired large-(cid:133)rm employment (achieved by vacancy posting) n , total vacancies devoted to hiring workers v , total capital k , a target L;t+1 L;t L;t+1 for the capital to be lent out to the self-employed n , a target for the capital to be lent SE;t+1 out to small businesses o , and the fraction of capital used within the (cid:133)rm ! , in order SB;t+1 t to maximize: 1 p L;t z L;tF(n L;t ;! t k L;t )+r SE;t n SE;t +r SB;t o SB;t E0 (cid:4) t0 2 , j 8 (cid:28)wLw n (cid:28)vL v i ’ k kL;t+1 1 k 9 X t=0 < (cid:0) t L;t L;t (cid:0) t L L;t (cid:0) t (cid:0) 2 kL;t (cid:0) L;t = (cid:16) (cid:17) : ; where: p is the price of large-(cid:133)rm output; z is an exogenous sectoral productivity pa- L;t L;t rameter; F( ; ) is the production function, which is increasing and concave in each of its (cid:1) (cid:1) arguments; i is investment; is the (cid:133)xed and exogenous (cid:135)ow cost of posting employment t L vacancies; and the last term re(cid:135)ects a standard capital adjustment cost. Also, similar to the caseofsmallbusinesses, weintroduceatime-varyingpolicythata⁄ectslarge-(cid:133)rmwages(cid:28)wL, t and another policy that a⁄ects the cost of hiring (cid:28)vL; where both policies equal 1 in steady t stateanddecrease(increase)whentotaloutputisbelow(above)trend. Notethat, foragiven stock of capital, a rise in ! implies a fall in the supply of capital to the self-employment t sector. The(cid:133)rm(cid:146)soptimizationproblemissubjecttotheperceivedlawofmotionfortheevolution of large-(cid:133)rm employment: n = (1 (cid:26)L)(n +v q ), L;t+1 (cid:0) t L;t L;t L;t where: q is a large (cid:133)rm(cid:146)s job (cid:133)lling probability; the perceived evolution of capital used in L;t the self-employment sector: n = (1 (cid:26)K) 1 (1 (cid:26)O)(1 (cid:26)S)v q n +(cid:26)Oo +(1 ! )k q , SE;t+1 (cid:0) t (cid:0) (cid:0) t (cid:0) t SE;t SE;t SE;t t SB;t (cid:0) t L;t K;t (cid:2)(cid:0) (cid:1) (cid:3) where: q is the large (cid:133)rm(cid:146)s probability of forming a new capital supplier match; the K;t 15

perceived evolution of capital used by small businesses: o = (1 (cid:26)K)(1 (cid:26)O) o +(1 (cid:26)S)v q n ; SB;t+1 (cid:0) t (cid:0) t SB;t (cid:0) t SE;t SE;t SE;t (cid:2) (cid:3) and the evolution of the (cid:133)rm(cid:146)s total capital stock (following Finkelstein Shapiro, 2014, and similar to Kurmann and Petrosky-Nadeau, 2007): k = (1 (cid:14))! k +((cid:26)K (cid:14))n + (1 (1 (cid:26)K)(1 (cid:26)O)) (cid:14) o +i L;t+1 (cid:0) t L;t t (cid:0) SE;t (cid:0) (cid:0) t (cid:0) t (cid:0) SB;t t + (1 (cid:14)) (1 (cid:26)K(cid:2))q (1 ! )k , (cid:3) (cid:0) (cid:0) (cid:0) t K;t (cid:0) t L;t (cid:2) (cid:3) where: (cid:14) is the exogenous depreciation rate of capital. 2.2.1 Large-Firm Optimality Conditions The (cid:133)rm(cid:146)s choice of total capital satis(cid:133)es a standard capital Euler equation: (cid:20) 1+’ k (cid:18) k k L L ;t+ ;t 1 (cid:0) 1 (cid:19)(cid:21) = Et (cid:4) t+1 j t 8 < +(1 (cid:0) (cid:14)) p (cid:0) L;t ’ + 2 k 1 z L k k ; L L t+ ; ; t t + + 1F 2 1 ! (cid:0) Lk 1 L (n 2 L + ;t+ ’ 1 k ;! k k t k L L ; ; L t t + + ;t 2 1 +1 (cid:0) ) 1 k k L L ; ; t t + + 2 1 9 = . (cid:16) (cid:17) (cid:16) (cid:17) : ; A standard job creation condition for large (cid:133)rm salaried employment also obtains: (cid:28)vL (cid:28)vL t q L;t L = (1 (cid:0) (cid:26)L t )Et (cid:4) t+1 j t (cid:26) p L;t+1 z L;t+1FnL (n L;t+1 ;! t k L;t+1 ) (cid:0) (cid:28)w t+ L 1 w L;t+1 + q t L + ; 1 t+1 L (cid:27) . Finally, the (cid:133)rm(cid:146)s optimal decision to devote capital to forming new capital matches satis(cid:133)es p L;t z L;tF!LkL (n L;t ; q ! K t k ;t L;t )+(1 (cid:0) (cid:26)K t )q K;t = (1 (cid:0) (cid:26)K t )Et (cid:4) t+1 j t J SE;t+1 , where: J is the large (cid:133)rm(cid:146)s capital gains from a new capital match (see the Appendix SE for further details). This last expression equates the expected marginal cost of devoting an additional unit of capital to matching to the expected marginal bene(cid:133)t. The former is comprised of two terms: the expected marginal cost of that unit of capital within the large (cid:133)rmsector, pL;tzL;tF!kL;t, andtheopportunitycost of keepingamatchedunit of capital within qK;t the (cid:133)rm until it becomes active in the self-employment sector next period, (1 (cid:26)K). The (cid:0) t 16

expected marginal bene(cid:133)t is given by the value of having a capital relationship next period. Note that J takes into account the value of becoming a small (cid:133)rm in future periods (see SE the Appendix for more details).6 2.3 Matching Processes Let m = m (v n ,u ), m = (cid:28)mSBm (v o ,u ), m = (cid:28)mLm (v ,u ) and SE;t SE SE;t SE;t t SB;t t SB SB;t SB;t t L;t t L L t m = m ((1 ! )k ,s ) bestandardmatchingfunctionsthatareincreasingandconcave K;t K t L;t K;t (cid:0) in each of their arguments. (cid:28)mL and (cid:28)mSB are cyclical policies that equal 1 in steady state, t t but improve (reduce) matching e¢ ciency for large and existing small (cid:133)rms, respectively, relativetotrendduringdownturns(upturns). Thispolicyspeci(cid:133)cationtractablycapturesthe expansion(contraction)ofgovernment-providedjobintermediationservicesduringrecessions (expansions). The matching functions imply the following job-(cid:133)nding probabilities: f = mSE;t; SE;t ut f = mSB;t; f = mL;t; and f = mK;t. The matching functions also imply the following SB;t ut L;t ut K;t sK;t job-(cid:133)lling probabilities: q = mSE;t ; q = mSB;t ; q = mL;t; and q = mK;t . SE;t vSE;tnSE;t SB;t vSB;toSB;t L;t vL;t K;t (1 !t)kL;t (cid:0) Labor market tightness for potential new small (cid:133)rms is (cid:18) vSE;tnSE;t, and labor mar- SE;t (cid:17) ut ket tightness for existing small (cid:133)rms is (cid:18) vSB;toSB;t. Large-(cid:133)rm labor market tightness SB;t (cid:17) ut is (cid:18) vL;t: In turn, capital market tightness is (cid:18) sK;t . All salaried job-(cid:133)nding L;t (cid:17) ut K;t (cid:17) (1 !t)kL;t (cid:0) probabilities are increasing in market tightness, while all salaried job-(cid:133)lling probabilities are decreasing in market tightness. Given our de(cid:133)nition of capital market tightness (cid:18) , f K;t K;t (q ) is decreasing (increasing) in capital market tightness. K;t 2.4 Wages For the sake of brevity, the value functions used in the determination of Nash prices as well as the statements of all Nash problems are relegated to the Appendix. From the perspective of a large (cid:133)rm: the value of having an additional salaried worker is J ; the value of having a L;t capital relationship with a self-employed individual is J ; and the value of having a capital SE;t 6Theconditionthatcharacterizesthelarge(cid:133)rm(cid:146)soptimalchoiceoverthedesiredmeasureofsmallbusiness ownersisgivenbythevaluefunctionofhavinganadditionalunitofmatchedcapitalinthesmall(cid:133)rmsector. For expositional brevity, this value function is included in the Appendix. 17

relationship with a small (cid:133)rm is J : From the perspective of the small (cid:133)rm sector: the SB;t value of having an additional salaried worker is J ; and the value of having an additional OSB;t capital relationship with large (cid:133)rms is W . From the perspective of the household, the OSB;t values of having a household member in salaried employment in a large (cid:133)rm, in salaried employment in a small (cid:133)rm, in self-employment, and in unemployment, are, respectively, W , W , W , andW . (cid:31) (0;1)and(cid:31) (0;1)are, respectively, thebargaining L;t SB;t SE;t U;t L SB 2 2 power of workers negotiating with large (cid:133)rms and of workers negotiating with small (cid:133)rms. (cid:31) (0;1) and (cid:31) (0;1) are, respectively, the bargaining power of self-employed and SE O 2 2 small business owners. The implicit expressions for the Nash wages are given by (cid:31) L J = (W W ), (1 (cid:31) )(cid:28)wL L;t L;t (cid:0) U;t L t (cid:0) for w and L;t (cid:31) SB J = (W W ) (1 (cid:31) )(cid:28)wSB OSB;t SB;t (cid:0) U;t SB t (cid:0) for w . The implicit expressions for the Nash rental rates are given by SB;t (cid:31) K (J (1 (cid:14))) = (W W ), SE;t SE;t U;t (1 (cid:31) ) (cid:0) (cid:0) (cid:0) K (cid:0) for r and SE;t (cid:31) O (J (1 (cid:14))) = (W W ) SB;t OSB;t U;t (1 (cid:31) ) (cid:0) (cid:0) (cid:0) O (cid:0) for r . Note that the outside option of large (cid:133)rms is the value of a unit of capital net of SB;t depreciation, (1 (cid:14)) (Finkelstein Shapiro, 2014). (cid:0) 2.5 Closing the Model Final output results as follows. We assume that composite output from the small (cid:133)rm and self-employment sectors is given by y = y (y ,y ). In turn, (cid:133)nal output aggre- S;t S SB;t SE;t gates large-(cid:133)rm output and the preceding composite output using the production function y = y(y ,y ). Turning toward pro(cid:133)t maximization, because the price of (cid:133)nal output is t L;t St 18

normalized to 1, the problem of the (cid:133)nal goods producer is: max y p y p y p y . t L;t L;t SB;t SB;t SE;t SE;t yL;t;ySB;t;ySE;t f (cid:0) (cid:0) (cid:0) g The government uses lump-sum taxes to (cid:133)nance expenditures, and its budget constraint is T = bu +(1 (cid:28)vL) v +(1 (cid:28)vSE) v n +(1 (cid:28)vSB) v o t t t L L;t t SE SE;t SE;t t SB SB;t SB;t (cid:0) (cid:0) (cid:0) +(1 (cid:28)(cid:20))(cid:20)(s )+g +(1 (cid:28)wL)w n +(1 (cid:28)wSB)w n (cid:0) t K;t t (cid:0) t L;t L;t (cid:0) t SB;t SB;t +((cid:28)mL 1)m (v ;u )+((cid:28)mSB 1)m (v o ;u ). t L L; t t SB SB;t SB;t t (cid:0) (cid:0) Above, g is exogenous government spending and the last two terms represent the (cid:133)scal cost t of job intermediation services. In what follows, we assume that g is constant.7 t The resource constraint of the economy is given by y = c +g +i +(cid:20)(s )+ v + v n + v o t t t t K;t L L;t SE SE;t SE;t SB SB;t SB;t ’ k 2 + k L;t+1 1 k +((cid:28)mL 1)m (v ;u )+((cid:28)mSB 1)m (v o ;u ), 2 k (cid:0) L;t t (cid:0) L L; t t (cid:0) SB SB;t SB;t t (cid:18) L;t (cid:19) where the cost of posting vacancies, searching for capital, and providing job intermediation services are resource costs. 2.6 De(cid:133)nition of Competitive Equilibrium Taking the stochastic processes z , z , z and the policies as given, the allocations L;t SE;t SB;t f g and prices n , n , o , n , u , (cid:18) , (cid:18) , (cid:18) , ! , k , (cid:18) , c , w , w , r , L;t SB;t SB;t SE;t t K;t SE;t SB;t t L;t L;t t L;t SB;t SE;t f r , T , y and p , p , p satisfy: the law of motion for salaried employment SB;t t t L;t SB;t SE;t g f g 7As part of our robustness checks, we analyze the case where cyclical policies are (cid:133)nanced through government debt. We also consider a case where the cyclical subsidies for small (cid:133)rms are (cid:133)nanced through an increase in large-(cid:133)rm payroll taxes. This last case is particularly relevant when the informal sector is large, as is the case in most developing countries. The main results and conclusions remain the same under these alternative scenarios. Also, the assumption of lump-sum taxation is not restrictive considering that some developing countries used commodity revenue to (cid:133)nance part of their stimulus packages. One example isMexico,whichusedoilrevenueasasourceof(cid:133)nancingforsomeofitsstimulusprogramsduringtheglobal (cid:133)nancial crisis. 19

in large (cid:133)rms; the law of motion for small (cid:133)rm salaried employment; the law of motion for small business owners; the law of motion for self-employed individuals; the de(cid:133)nition of unemployment; the household(cid:146)s optimal choice to search for capital suppliers; the optimal decision to transition from self-employment into small business owner status; the job creation decision by small business owners; the capital supply decision by large (cid:133)rms; the capital Euler equation of large (cid:133)rms; the job creation decision by large (cid:133)rms; the resource constraint; the Nash wage for salaried workers in large (cid:133)rms; the Nash wage for small (cid:133)rm salaried workers; the Nash rental rate for self-employed individuals; the Nash rental rate for small business owners; the three relative prices of sectoral output; the government budget constraint; and the de(cid:133)nition of total output. 3 Calibration We assume a time period of 1 quarter. In addition, we choose Mexico as our benchmark reference since this country has quality data on labor (cid:135)ows and existing studies provide well-documented stylized facts about cyclical employment dynamics. 3.1 Functional Forms and Shocks Final output is given by a constant elasticity of substitution (CES) aggregate of large (cid:133)rm output and composite output from the self-employment and small (cid:133)rm sectors: 1 y = (cid:13) y (cid:30) a +(1 (cid:13) )y (cid:30) a (cid:30)a , t a L;t (cid:0) a S;t h i where (cid:13) (0;1) and (cid:30) 1. In turn, composite output from the small (cid:133)rm and selfa a 2 (cid:20) employment sectors is given by the CES aggregate: 1 y = (cid:13) y (cid:30) s +(1 (cid:13) )y (cid:30) s (cid:30)s , S;t s SB;t (cid:0) s SE;t h i 20

where (cid:13) (0;1) and (cid:30) 1:8 The production function for large (cid:133)rms is Cobb-Douglas: s s 2 (cid:20) F(n L;t ;! t k L;t ) = (n L;t )1 (cid:0) (cid:11)L(! t k L;t )(cid:11)L, where (cid:11) L (0;1): The production function for the 2 aggregate small (cid:133)rm sector is also Cobb-Douglas: F(n ;o ) = (n )1 (cid:11)SB (o )(cid:11)SB, SB;t SB;t SB;t (cid:0) SB;t where (cid:11) (0;1). We assume that (cid:11) > (cid:11) so that, in line with existing evidence, L L SB 2 production in large (cid:133)rms is more capital intensive. In each intermediate production sector productivity follows an AR(1) process with a common aggregate shock: lnz = (1 (cid:26) )ln(z )+(cid:26) lnz +"z, i;t (cid:0) zi i zi L;t (cid:0) 1 t where for i L, SB,SE : z is a constant and we assume that i (cid:26) = (cid:26) ; and "z 2 f g i 8 zi z t (cid:24) N(0,(cid:27)2) denotes the aggregate productivity shock (i.e., common to all sectoral productivity z processes). Therefore, while all sectors are subject to a common productivity shock, each sector(cid:146)s steady state productivity can potentially di⁄er. We follow related literature and assume that all matching functions are Cobb-Douglas. In particular, m L;t = (cid:28)m t LM L (u t )(cid:24) L(v L;t )1 (cid:0) (cid:24) L, m SB;t = (cid:28)m t SBM SB (u t )(cid:24) SB (v SB;t o SB;t )1 (cid:0) (cid:24) SB, m SE;t = M SE (u t )(cid:24) SE (v SE;t n SE;t )1 (cid:0) (cid:24) SE, and m K;t = M K (s K;t )(cid:24) K ((1 ! t )k L;t )1 (cid:0) (cid:24) K where, for (cid:0) j L,SB,SE,K : M isthematchinge¢ ciencyparameter; and(cid:24) isthematchingelasticity j j 2 f g parameter. For tractability, we assume that all separation probabilities are countercyclical relative to (cid:135)uctuations in total output so that y (cid:26)j = (cid:26)j exp (cid:17) 1 t , t ss (cid:26)j (cid:0) y (cid:20) (cid:18) (cid:18) ss(cid:19)(cid:19)(cid:21) for j L,K,O,S , where: (cid:17) > 0 determines the sensitivity of the separation probabilities (cid:26)j 2 f g to output deviations from trend; (cid:26)j is the steady-state job destruction probability; and y ss ss is steady-state (cid:133)nal output. This speci(cid:133)cation implies that separation probabilities increase (decrease) above their steady state values when output is below (above) trend. Finally, with regards to the household, we assume that the cost of searching for capital is (cid:20)(s ) = K;t (s )(cid:17) K, with > 0 and (cid:17) 1: In addition, the household(cid:146)s utility function is K K;t K K (cid:21) characterized by constant relative risk aversion so that u(c ) = c1 t(cid:0) (cid:27) . t 1 (cid:27) (cid:0) 8The elasticities of substitution are 1 and 1 , respectively. 1 (cid:30) 1 (cid:30) (cid:0) a (cid:0) s 21

3.2 Parameters From Related Literature The elasticity of substitution parameters in the CES aggregator functions are set to 0.7 so thatproductioninputsaresomewhatimperfectlysubstitutable.9 Thepersistenceparameters for each of the sectoral productivity shocks are set to 0.92. The capital depreciation rate (cid:14) is in line with other studies on Mexico. Based on Busso, Fazio, and Levy (2012), we compute productivity di⁄erentials by type of (cid:133)rm so that the model is consistent with the large productivity di⁄erences that exist between self-employed (cid:133)rms, small (cid:133)rms, and large (cid:133)rms (see the Appendix for further details). Table 7: Parameterization for Benchmark Economy, Part I Parameter Value Parameter Description Parameter Source (cid:11) 0.32 Capital Share, Large Firms DSGE Literature L (cid:11) 0.27 Capital Share, Small Firms - SB b 0 Unempl. Insurance No Unempl. Bene(cid:133)ts (cid:12) 0.985 Discount Factor DSGE Literature (cid:14) 0.025 Capital Depreciation DSGE Literature (cid:17) 1 Curvature Search Cost Search Literature K (cid:31) 0.50 Bargaining Power Search Literature (cid:24) 0.50 Matching Elasticity Search Literature (cid:30) 0.7 Elasticity Param. Assumption a (cid:30) 0.7 Elasticity Param. Assumption s (cid:26)L 0.05 Sep. Prob., Large Firms Bosch, Maloney (2008) ss (cid:26)K 0.03 Sep. Prob., SE Bosch, Maloney (2008) ss (cid:26)S 0.03 Sep. Prob., Small Firms Assumption ss (cid:26) 0.92 Autocorrelation of z DSGE Literature zL L (cid:26) 0.92 Autocorrelation of z DSGE Literature zSB SB (cid:26) 0.92 Autocorrelation of z DSGE Literature zSE SE (cid:27) 2 CRRA Utility Parameter DSGE Literature z 5.17 Large Firm Productivity Busso et al. (2012) L z 3.57 Small Firm Productivity Busso et al. (2012) SB z 1 SE Productivity Normalization SE Most Latin American and other developing countries, including Mexico, do not have a national unemployment insurance scheme, so we set b to 0. The subjective discount factor (cid:12) is set to 0.985, in line with the literature (Boz, Durdu, and Li, 2012). The curvature of capital search is (cid:17) = 1 (assuming that the cost of searching for capital is convex does not K change our main conclusions). The coe¢ cient of relative risk aversion is set to 2. We set the bargaining power for salaried workers, self-employed individuals, and small business owners 9We explore di⁄erent parameterizations in the Appendix. 22

to0:5. Thematchingelasticitiesareset0:5sothattheHosiosconditionholds(Hosios, 1990). The steady-state separation probabilities are based on Bosch and Maloney (2008).10 3.3 Calibrated Parameters Calibrated parameters are summarized in Table 8. The matching e¢ ciency parameters are chosen so that the model is in line with the allocation of employment across (cid:133)rms in the data. Our mapping between the data and the model is based on evidence on (cid:133)rm size and formality/legality status for Mexico (Busso, Fazio, and Levy, 2012), and yields the following distribution of individuals across employment states: the self-employed (or micro (cid:133)rms) represent 16 percent of the labor force; small business owners represent 7 percent; salaried workers in small (cid:133)rms represent 30 percent; and salaried workers in large (cid:133)rms account for 42 percent of the labor force.11 Table 8: Parameterization for Benchmark Economy, Part II Parameter Value Parameter Description Target g 0.0967 Steady State Gov. Spending 10.2 percent of output M 0.111 Large Firm Match. E⁄. n =0:42 L L M 0.045 SE Match. E⁄. n =0:16 K SE M 0.213 Old Small Firm Match. E⁄. o =0:07 SB SB M 0.027 New Small Firm Match. E⁄. n =0:30 SE SB ’ k 0.496 Capital Adj. Cost Param. (cid:27) pu K;t =9:4 0.027 Large Firm Vacancy Cost 3.5 percent of w L L 0.735 Capital Search Cost 3 months of w K SB 0.026 Small Firm Vacancy Cost 3.5 percent of w SB SB 0.026 SE Vacancy Cost 3.5 percent of w SE SB (cid:26)O 0.022 Destruction Rate, Small Firms (1 (cid:26)SB)=0:92 (cid:17) s L s 1.27 Sensitivity, Sep. prob. (cid:26)L (cid:27)F (cid:0) U =1:22 ss t (cid:27)I ! U (cid:17)K 1.00 Sensitivity, Sep. prob. (cid:26)K As!sumption ss t (cid:17)O 1.00 Sensitivity, Sep. prob. (cid:26)O Assumption ss t (cid:17)S 1.00 Sensitivity, Sep. prob. (cid:26)S Assumption ss t (cid:27) 0.0173 SD Productivity Shock (cid:27) =2:39 z y (cid:13) 0.192 CES Parameter pLyL =0:55 a y (cid:13) 0.453 CES Parameter pSBySB =0:33 s y 10Forthesalariedseparationrateinlarge(cid:133)rmswetakeintoaccountthatasmallshareofworkersinthese (cid:133)rms is informal using existing evidence on the share of labor informality by (cid:133)rm size. 11Total self-employment in Mexico, which includes small business owners and own-account workers, is around 23 percent. Based on Perry et al. (2007) and others, between 65 and 70 percent of the self-employed areown-accountworkers(theremainingsharebeingmostlyindividualswhooperatesmall(cid:133)rms). Thisyields a self-employment (or own-account) share of 16 percent. 23

The cost of adjusting capital is set to replicate the volatility of the probability of entering self-employment from unemployment (Bosch and Maloney, 2008). We set the cost of posting vacancies in small and large (cid:133)rms to 3.5 percent of sectoral wages (Levy, 2007).12 The perunit cost of searching for capital is set to 3 months of (small (cid:133)rm) wages, in line with the evidence in McKenzie and Woodru⁄ (2006) (the results do not change if we assume much lower costs). We set the steady-state job destruction probability of small (cid:133)rms (cid:26)O so that the sepss aration probability for small (cid:133)rm workers (a combination of (cid:26)K;(cid:26)O; and (cid:26)S) is 8 percent, in line with the evidence on informal separation probabilities (Bosch and Maloney, 2008). To establish the sensitivity of separation probabilities to output deviations, we (cid:133)x (cid:17)K, (cid:17)O, ss ss and (cid:17)S to 1. In turn, we set (cid:17)L to capture the volatility of transitions from formal salaried ss ss employment to unemployment relative to the volatility of transitions from informal salaried employment to unemployment from Bosch and Maloney (2008).13 We calibrate the standard deviation of the aggregate productivity shock to match the standard deviation of Mexican real GDP for the years 1993 through 2007. In addition, we calibrate the steady-state government spending-output ratio to be 10.2 percent of output, which is representative of the Mexican economy. 4 Quantitative Analysis To compare the model to the data, we use Mexican time series from 1993:Q1 to 2007:Q4 for output, consumption, and unemployment to compute second moments, as well as the evidence in Bosch and Maloney (2008) and FernÆndez and Meza (2014) for the labor market. The output, consumption, and unemployment series are obtained from the Federal Reserve 12Neither of these costs include the cost of hiring regulations. The results remain the same if we assume that the cost of posting vacancies for large (cid:133)rms includes the cost of hiring regulations, or if we assume a di⁄erent calibration target for small (cid:133)rm vacancy postings. 13Since we do not have data on separation rates by (cid:133)rm size, this assumes that a majority of informal salaried workers are in small (cid:133)rms, which is consistent with the evidence (Perry et al., 2007). The model is unable to generate the volatility of separation rates in the data without running into convergence problems. Targeting the relative volatility of transitions from self-employment to unemployment yields qualitatively similar results and generates additional unemployment volatility, but signi(cid:133)cantly reduces the countercyclicality of self-employment. However, the main conclusions do not change. 24

Bank of Saint Louis(cid:146)FRED database.14 4.1 Aggregate Dynamics without Policy Table 9 shows that qualitatively and quantitatively the model can match several stylized facts about business cycles and labor-market dynamics that we do not explicitly target. The model captures the countercyclicality of unemployment and self-employment, and also generates a relative volatility of unemployment higher than 1, which is di¢ cult to generate in standard search models. The model also delivers a higher volatility in the job-(cid:133)nding probability in large (cid:133)rms relative to small (cid:133)rms that is broadly in line with the data. Table 9: Business Cycle Statistics: Data vs. Model Targeted Second Moments Data Benchmark Model (cid:27) 2:39 2:39 yt (cid:27) fu 9:40 9:40 K;t (cid:27) =(cid:27) 1:22 1:23 (cid:26)SB (cid:26)L t t No-Targeted Moments Data Benchmark Model (cid:27) =(cid:27) 1:13 0:56 ct yt (cid:27) =(cid:27) 2:78 7:54 it yt (cid:27) =(cid:27) 6:28 1:31 u;t yt (cid:27) =(cid:27) [1:00;1:05] 0:92 nL;t nSB;t (cid:27) =(cid:27) 2:18 2:29 fL;t (fSB;t+fSE;t) (cid:26)(n ;y ) [0:740;0:840] 0:778 L;t t (cid:26)(n ;y ) [ 0:470;0:740] 0:767 SB;t t (cid:0) (cid:26)(n ;y ) 0:450 0:886 SE;t t (cid:0) (cid:0) (cid:26)(u ;y ) 0:889 0:706 t t (cid:0) (cid:0) (cid:26)(f ;y ) 0:798 0:984 L;t t (cid:26)(f +f ;y ) 0:366 0:524 SB;t SE;t t (cid:26)(fu ;y ) 0:433 0:538 K;t t (cid:0) (cid:0) (cid:26)(y ;y ) 0:846 0:734 t t 1 (cid:26)(u ;u(cid:0) ) 0:878 0:748 t t 1 (cid:0) The cyclical correlation of large-(cid:133)rm employment and output and the probability of entering self-employment from unemployment are also consistent with the evidence. Finally, the cyclical correlation between the job-(cid:133)nding probability in large (cid:133)rms is higher than the one in small (cid:133)rms. The fact that the cyclical correlation of the job-(cid:133)nding probabilities 14We log-linearize the model around the non-stochastic steady-state and implement a (cid:133)rst-order approximation. Wesimulatethemodelfor2100periods,discardthe(cid:133)rst100periods,andapplytheHodrick-Prescott (cid:133)lter with smoothing parameter 1600 to the simulated series to obtain the data(cid:146)s cyclical component and compute second moments. We use Dynare for all dynamic simulations. 25

for salaried workers is particularly high is due to the presence of a single aggregate shock driving the model(cid:146)s dynamics. Introducing (correlated) sectoral shocks would allow us to quantitatively match the cyclical correlation of these (cid:133)nding probabilities in the data. 4.2 Policy Experiments We compare the response of the economy to a negative aggregate productivity shock when no labor market policies are in place(cid:151)the no-policy scenario(cid:151)to the response under the earlier noted set of cyclical labor market policies. We assume that these policies respond to (cid:135)uctuations in aggregate productivity as follows. For j v , v , v , (cid:20), m , m , w , L SB SE L SB L 2 f w SB g y (cid:28)j = exp (cid:28)j t 1 , (9) t ss y (cid:0) (cid:20) (cid:18) ss (cid:19)(cid:21) where: (cid:28)j 0 captures the intensity of the policy (for a related approach, see Canzoneri et ss (cid:21) al., 2011). The speci(cid:133)cation in equation (9) has several attractive features. First, given how we introduced the policies in the model, (cid:28)j is purely cyclical in nature and has no impact on t steady-state allocations. Second, for (cid:28)j 0, the policy acts as a subsidy when output is ss (cid:21) below trend and as a tax when output is above trend, so that the government budget is always balanced.15 Third, in the case of a negative aggregate shock, the policy becomes active on impact and exhibits endogenous persistence, where the latter is determined by the severity and length of the recession. We calibrate each of the individual policies (cid:28)j to obtain ss a stimulus of 0.2 percent of output in the period of the negative aggregate shock. This (cid:133)scal package is in line with the size of the labor market measures introduced in Mexico as part of the stimulus package during the (cid:133)nancial crisis (ILO, 2011).16 15While subsidies for micro and small (cid:133)rms may be easier to implement during downturns (via cash transfers, for example), recovering the revenue spent on these subsidies via the same instruments during expansionsmaybeharderifmostsmall(cid:133)rmsareinformal. Ifweassumethatmicroandsmall-(cid:133)rmsubsidies are (cid:133)nanced through a higher payroll tax on larger (cid:133)rms, the aggregate bene(cid:133)ts from these subsidies are more subdued. As an example, we discuss the case of small-(cid:133)rm wage subsidies (cid:133)nanced through payroll taxes on large (cid:133)rms in the Appendix. 16Recall that policy is endogenously determined once the shock takes place, which implies that the total (cid:133)scal cost in present value terms (once the economy returns back to steady state) is around 2.5 percent of GDP. Assuming a smaller (cid:133)scal package of 0.1 percent of output on impact, which naturally also delivers a lowertotal(cid:133)scalcostinpresentvaluetermsofaround1.45percentofGDP,yieldsverysimilarresultsacross 26

4.3 Main Results Figures 1 and 2 show the impulse responses of key variables to a one standard deviation negative aggregate productivity shock. All impulse responses (including the ones in the Appendix) are in percent deviations from steady state. Along the (cid:133)gures(cid:146)columns a particular policy is in place, and the (cid:133)gures(cid:146)rows show a particular variable(cid:146)s response. Hiring Subsidies Job Interm. Subsidies Firm Creation Subsidies Wage Subsidies 0 0 0 0 tu 0.5 0.5 0.5 0.5 p tu O 1 1 1 1 la to T 1.5 1.5 1.5 1.5 2 2 2 2 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0 0 0 0 n o itp 0.5 0.5 0.5 0.5 m u s n 1 1 1 1 o C 1.5 1.5 1.5 1.5 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 5 3 3 3 tn e 2 2 2 m y o 0 1 1 1 lp m e n 0 0 0 U 5 1 1 1 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t v t m t v t w L L SE L t v t m t k t w SB SB SB Figure 1 Response to a 1 percent negative productivity shock (quarters after shock): Total output, consumption, and unemployment. We focus on total output ((cid:133)rst row of Figure 1), consumption (second row of Figure 1), the unemployment rate (third row of Figure 1), the average wage (that is, the employmentweighted average of wages in large and small (cid:133)rms; (cid:133)rst row of Figure 2), subsidy rates policies. 27

(second row of Figure 2), and the (cid:133)scal cost as a percent of GDP (third row of Figure 2). For reference, the (cid:133)gures also show impulse responses of variables under the benchmark (nopolicy) scenario. Inspection of Figures 1 and 2 implies that, for a (cid:133)scal package of given size, thereis considerablevariationinthee⁄ectthat di⁄erent policies haveonaggregatevariables, with some policies being detrimental to the recovery process. Hiring Subsidies Job Interm. Subsidies Firm Creation Subsidies Wage Subsidies 0 0 0 0 e g 0.5 0.5 0.5 0.5 a W e 1 1 1 1 g a re v 1.5 1.5 1.5 1.5 A 2 2 2 2 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 40 10 15 1 e ta R 30 10 y d 20 5 0.5 is b 5 u 10 S 0 0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0.4 0.4 0.4 0.4 )P D G 0.3 0.3 0.3 0.3 % ( ts 0.2 0.2 0.2 0.2 o C la 0.1 0.1 0.1 0.1 c s iF 0 0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t v t m t v t w L L SE L t v t m t k t w SB SB SB Figure 2 Response to a 1 percent negative productivity shock (quarters after shock): Average wage, subsidy rate, and (cid:133)scal cost as percent of GDP. 4.3.1 Total Output Regarding total output, hiring subsidies and job intermediation services for large (cid:133)rms have the greatest impact in aiding the recovery, followed by subsidies for the creation of small (cid:133)rms (that is, hiring subsidies for micro (cid:133)rms). Interestingly, hiring subsidies and job in- 28

termediation subsidies for small businesses induce an improved near-term recovery in total output, but thereafter the recovery is dampened and the path of total output falls below that of the no-policy case. In the case of subsidies for the creation of micro (cid:133)rms, total output is always below the path of output in the no-policy case. In turn, for all purposes wage subsidies have no impact on the recovery of total output.17 While the magnitude of adjustment is di⁄erent, the impact of policies on total output re(cid:135)ects the fact that, intuitively, policies that are directed toward the relatively more productive and capital intensive (cid:133)rms, that is, large (cid:133)rms, will tend to have a greater impact in aiding economic recoveries. Hiring subsidies and job intermediation subsidies for large (cid:133)rms decrease hiring costs for these (cid:133)rms (the latter by increasing large (cid:133)rms(cid:146)job-(cid:133)lling probability, which drives down the expected cost of posting vacancies). As a result, employment is reallocated to large (cid:133)rms and, consequently, capital usage by large (cid:133)rms and investment will adjust accordingly (see the Appendix). All told, the recovery in total output is boosted as production is reallocated to the relatively more productive large-(cid:133)rm sector. Importantly, the capital allocation decision by large (cid:133)rms in response to the policy implies a smaller contraction in investment, which, coupled with the added incentive to hire workers from the policy, bolsters the recovery in large-(cid:133)rm output and total output.18 In turn, hiring subsidies and job intermediation for small (cid:133)rms aid the recovery in the near term, but as employment and capital is reallocated to the relatively less productive small-(cid:133)rm sector the recovery in total output eventually falls behind the no-policy case. 17The Appendix elaborates in greater detail on the underlying dynamics that drive the main results by showingimpulseresponsesforseveralothervariables,includinglarge-andsmall-(cid:133)rmwages,self-employment earnings, investment, and capital usage by large (cid:133)rms. The Appendix also includes a summary of the resultsfromaseriesofrobustnesschecks,includingdi⁄erent(cid:133)nancingalternativesforsubsidiesanddi⁄erent parameterizations of the model. The main results of the paper are robust to these and other alternative experiments, assumptions, and calibrations, all of which are discussed in more detail in the Appendix. 18Thequantitativeimpactontotaloutputofjobintermediationsubsidiesforlarge(cid:133)rmsisgreaterthanthat ofhiringsubsidiesforsimilar(cid:133)rmsbecause,althoughbothsubsidiesprovideanincentiveforvacancyposting, the job intermediation subsidy gives a boost to the large-(cid:133)rm job-(cid:133)lling probability by increasing matching e¢ ciency as well, which ampli(cid:133)es the results. The opposite is true when we consider the same policies for existingsmallsalaried(cid:133)rms. Thereareseveralreasonsforthis. First,duetothein(cid:135)uenceofsectoralmarket tightness on wages, the latter fall by less with an improvement in small-(cid:133)rm job intermediation services relative to the case with hiring subsidies. This e⁄ect, in turn, boosts small-(cid:133)rm vacancy posting by less. Second, better intermediation between the unemployed and small (cid:133)rms implies that the value of having a worker in an existing small (cid:133)rm falls by less (again, relative to the case with hiring subsidies). This limits the contraction in small (cid:133)rm owners, which in turn reduces the volatility of vacancy postings by existing small (cid:133)rms. 29

In the case of subsidies for the creation of small (cid:133)rms, that is, hiring subsidies for micro (cid:133)rms, this policy also induces employment and capital usage reallocation to micro and small (cid:133)rms. However, in this case the magnitude of this reallocation is greater because of two forces: 1) existing micro (cid:133)rms take advantage of the subsidy, which increases the (cid:135)ows from self-employment status to small (cid:133)rm owner; 2) all else equal the value of self-employment is higher, whichboostscapital-searchexpendituresandultimatelythein(cid:135)owofindividualsinto self-employment status. Jointly, the extent to which these two forces reallocate production to less productive sectors leaves the recovery of total output only a touch improved relative to the no-policy case. In the case of a subsidy for the creation of micro (self-employed) (cid:133)rms (that is, a capitalsearchexpendituresubsidy),onlyforce(2)fromaboveisatplay,which,allelseequal,reduces capital usage among large (cid:133)rms and increases the supply of capital to the relatively less productive sector but does not yield signi(cid:133)cant salaried employment gains. Consequently, in thiscasetherecoveryintotaloutputissubduedandliesbeneaththatoftheno-policycase.19 Importantly, these results take place within a context where the reallocation of capital to the self-employed and small (cid:133)rm sectors relative to the total amount of capital in the economy is not very large. Yet, the policies generate important di⁄erences in the recovery process despite the relatively low usage of capital among micro and small (cid:133)rms. Wage subsidies will, all else equal, increase (cid:133)rm pro(cid:133)ts. Or, in the case of a recession, prevent pro(cid:133)ts from falling as much as they would otherwise. However, as shown in Figure 1 the (cid:133)scal package under consideration is insu¢ cient to induce an impact on pro(cid:133)ts substantial enough to trigger mechanisms that a⁄ect the behavior of total output in any discernible way.20 19A caveat regarding hiring subsidies for self-employed individuals: the model assumes that self-employed individuals are homogeneous, and the only requirement to become a small (cid:133)rm is to successfully match with salaried workers via vacancy posting. However, in the data, the self-employed that expand tend to be those who are more successful and have higher ability and skills, which would translate into higher productivity. The model in its current form implicitly assumes that those who expand automatically inherit higher productivity. If we were to di⁄erentiate between high and low-ability entrepreneurs and use targeted subsidies for those with high ability (or the most potential), the quantitative impact of hiring subsidies for the self-employed would likely be smaller since only a very small fraction of the self-employed would bene(cid:133)t from the subsidy (those with higher ability). As such, our results represent an upper bound of the impact of these subsidies on aggregate dynamics. 20From a practical standpoint, wage subsidies for small (cid:133)rms may be hard to implement since these generally operate via temporary changes in payroll taxation, and as argued previously, obtaining revenue for these subsidies from these same (cid:133)rms during expansions is not trivial when a large proportion of small (cid:133)rms operates in the informal sector and hence does not face payroll taxes. Assuming that only a fraction 30

4.3.2 Consumption, Unemployment, and Wages Inspection of Figure 1 also shows that, intuitively, the behavior of consumption is largely in line with that of total output. One exception is the path of consumption in the case of subsidies for the creation of self-employed (micro) (cid:133)rms. Under this policy, on impact consumption contracts considerably below the no-policy case. Intuitively, this takes place becauseasubsidyforthe creationof micro(cid:133)rms induces households toincreasetheresources devoted to capital search at the expense of the resources for consumption.21 Turning to unemployment, Figure 1 highlights that to greater or lesser degree all policies mute the increase in unemployment, with hiring subsidies for small (cid:133)rms and job intermediation services for both small and large (cid:133)rms even inducing a decline in unemployment. This is due to the strong response of sectoral vacancies to each of the policies. The only exception is the case of wage subsidies for large (cid:133)rms, which actually exacerbate the rise in unemployment. This policy keeps wages in large (cid:133)rms from declining as much as they would otherwise, which puts upward pressure on small-(cid:133)rm wages as workers(cid:146)outside options remain higher than otherwise. Consequently, all else equal small-(cid:133)rm pro(cid:133)ts fall by more than otherwise, sharply reducing these (cid:133)rms(cid:146)vacancy posting incentives. Thus, a greater decline in small-(cid:133)rm employment takes place, which explains the fact that unemployment initially rises more than in the no-policy case. As shown in Figure 2, when looking at the average wage in the economy (that is, employment-weighted large-(cid:133)rm and small-(cid:133)rm wages), all subsidies tend to provide some degreeofincomeprotectionforsalariedworkers, withtheexceptionofjobintermediationservices for small businesses and subsidies for the creation of micro (cid:133)rms (see the Appendix for the behavior of wages by type of (cid:133)rm, as well as the behavior of self-employment earnings). Job intermediation for large (cid:133)rms has the greatest bene(cid:133)cial impact on income protection. Wage subsidies will naturally provide income protection. In other cases, the response of the average wage is heavily in(cid:135)uenced by the response of unemployment, or, equivalently, the response of employment. Intuitively, a greater damping in the rise of unemployment is of small (cid:133)rms bene(cid:133)t from the subsidy (those that are formal), or assuming that the subsidy is (cid:133)nanced via anincreaseinthepayrolltaxforlarge(cid:133)rms(seetheAppendix), yieldsqualitativelysimilarresults, withthe bene(cid:133)ts from small-(cid:133)rm wage subsidies under these two scenarios being more subdued. 21A similar comment applies to the behavior of investment, shown in the Appendix. 31

associated with higher measures of market tightness. In turn, higher measures of market tightness keep workers(cid:146)outside options higher than otherwise and put upward pressure on the average wage. Thus, the magnitude of labor income adjustments (and hence income protection) is ultimately driven by the quantitative impact of each policy on sectoral market tightness. 4.3.3 Fiscal Implications Inspection of Figure 2 also highlights that although the assumed size of the (cid:133)scal package in the period of the shock is 0.2 percent of output, the total (cid:133)scal cost can di⁄er across policies. These di⁄erences arise because policies a⁄ect the recovery speed of output di⁄erently and they remain in place as long as output is below trend. While the (cid:133)scal cost in the (cid:133)rst few periods after the shock is lower when hiring subsidies for small (cid:133)rms are in place, the (cid:133)scal cost of the policy falls back more rapidly with hiring subsidies for larger (cid:133)rms, job intermediation for large (cid:133)rms, and hiring subsidies for the self-employed (that is, small-(cid:133)rm creation subsidies). In addition, note that for the same size of the (cid:133)scal package, small and self-employed(cid:133)rmsrequirelargerhiringsubsidyratesrelativetothoseforlarge(cid:133)rms. Indeed, the subsidy rates for large (cid:133)rms do not have to be high to have an important quantitative impact on aggregate dynamics. Similarly, wage subsidy rates for both small and large (cid:133)rms end up being very small, below 1 percent on impact, which partly explains their limited impact on the recovery process. To provide a better metric of the e⁄ectiveness of each of the policies considered, we follow the literature and compute cumulative multipliers for employment and output after a negative aggregate shock in the following way (see, for example, Faia, Lechthaler, and Merkl (2013)): d (cid:12)i(x (p) x ) t+i t+i (cid:0) M (p) = i=0 ; d P d (cid:12)i(fc (p)) t+i i=0 P where d is the number of quarters after the shock and p is the policy for which the (cid:133)scal multiplier is computed. x(p) is either total output, y, or total employment, n, under policy p, whereas x represents either of these two variables under the no-policy scenario. fc(p) is 32

the (cid:133)scal cost of policy p, where the (cid:133)scal cost under the no-policy scenario is zero. As shown in Table 10, small (cid:133)rm creation and self-employed (cid:133)rm creation policies are not particularly e⁄ective in bolstering output or employment. Hiring subsidies for existing small (cid:133)rms yield output and employment multipliers higher than 1 in the (cid:133)rst year, which subsequently fall below 1 after three years. Focusing on employment, the (cid:133)scal multiplier is fairly stable in the medium run. Conversely, the output multiplier falls below 1 after three years. While hiring subsidies for large (cid:133)rms appear to be less e⁄ective in the (cid:133)rst year, the output multiplier rises above 1 in the medium run because the policy induces a faster recovery in total output, but the latter takes some time to materialize. However, the employment multiplier remains below 1. Table 10: Cumulative Multipliers During Recessions Output Multipliers Policy p Quarters d=4 Quarters d=12 Quarters d=30 (cid:28)vL 0:710 1:214 1:684 (cid:28)vSB 1:204 0:976 0:383 (cid:28)vSE 0:056 0:148 0:465 (cid:0) (cid:28)k 0:155 0:325 0:520 (cid:28)mL (cid:0) 1:494 (cid:0) 2:628 (cid:0) 3:727 (cid:28)mSB 0:594 0:455 0:096 (cid:28)wL 0:091 0:198 0:320 (cid:28)wSB 0:242 0:218 0:129 Employment Multipliers Policy p Quarters d=4 Quarters d=12 Quarters d=30 (cid:28)vL 0:310 0:521 0:681 (cid:28)vSB 1:284 1:403 1:308 (cid:28)vSE 0:256 0:291 0:288 (cid:28)k 0:062 0:058 0:032 (cid:28)mL 0:611 1:048 1:388 (cid:28)mSB 0:642 0:705 0:648 (cid:28)wL 0:093 0:080 0:051 (cid:28)wSB (cid:0) 0:126 (cid:0) 0:127 (cid:0) 0:103 Finally, the output multiplier generated by job intermediation services among large (cid:133)rms suggests that this policy is particularly e⁄ective in fostering a faster output recovery, even at shorthorizons. Ifweconsiderthemediumterm,thispolicydeliversanemploymentmultiplier above 1 as well. These last two results suggest that improvements in job intermediation for employment among large (cid:133)rms is the most e⁄ective policy tool, followed by hiring subsidies for large (cid:133)rms and existing small (cid:133)rms. Wage subsidies yield very small (or even negative) 33

output and employment multipliers and appear to be the least e⁄ective out of the set of policies considered. 5 Conclusions The global (cid:133)nancial crisis rekindled considerable interest in labor market policies that can lessen the employment and output costs of recessions. A number of recent studies have analyzed the impact of various employment subsidies for the United States. However, little work has focused on emerging and developing economies, where the breadth of self-employment and the large allocation of salaried employment in small (cid:133)rms implies non-trivial di⁄erences relative to advanced economies in the labor-market and (cid:133)rm structure. Understanding the aggregate implications of labor market structures and policies in emerging and developing economies is increasingly important given the dramatic rise in international linkages and cross-country spillovers that have occurred over the last several decades. Data limitations on high-frequency labor and job (cid:135)ows in emerging and developing economies makes it di¢ cult to assess empirically the e⁄ectiveness of any one countercylical policy. Furthermore, any empirical analysis will likely miss the general equilibrium e⁄ects of policy interventions. In order to get around these limitations, we use evidence on Latin America and build a business cycle model with frictional labor markets consistent with the salient features of the (cid:133)rmand employment structure of emerging and developing economies. In turn, we use the model to analyze the aggregate impact of di⁄erent cyclical labor market policies during downturns. We show that the model is consistent with the cyclical dynamics of the labor market in a representative emerging economy. With regards to policy, we obtain four main results. First, hiring subsidies for large (cid:133)rms and improved intermediation between large (cid:133)rms and the unemployed during downturns can yield gains across the board: a reduction in aggregate volatility, anaccelerationinthereboundof total output andconsumption, asmallercontractioninlaborearnings, alower rise inunemployment, lowerunemployment persistence aftera recession,andemploymentandoutput(cid:133)scalmultipliersabove1inthemediumterm. Second, hiring subsidies for small (cid:133)rms can yield non-negligible positive results for employment(cid:151)in 34

particular, employment among small salaried (cid:133)rms(cid:151)but these e⁄ects are short-lived and the policy slows down the recovery process in the medium term. Third, fostering the creation of self-employed (cid:133)rms during downturns can be detrimental for the recovery process and the economy as a whole, even as these (cid:133)rms may ultimately lead to future salaried employment creation. Thislastresultisparticularlyimportantinlightofthepoliciesthatmanyemerging countries implemented to support the creation of micro and small enterprises. Fourth, wage subsidies are relatively ine⁄ective in bolstering output when compared to other alternatives, but do provide some income protection. Model-implied (cid:133)scal multipliers suggest that hiring subsidies and job intermediation for large (cid:133)rms are particularly e⁄ective in aiding recoveries. The labor market structure determines the sectoral allocation of resources and explains the di⁄erential response of the economy to policy. Our model provides the basis for several interesting extensions. These include accounting for the implications of entry dynamics among larger (cid:133)rms, worker and consumption heterogeneity, as well as the di⁄erence between low and high-ability self-employed, and job-to-job transitions. Moreover, while the model is consistent with existing evidence on the continued use of informal input credit among small (cid:133)rms, studying the implications of (cid:133)nancial development is important as it may lead to a change in the availability of (cid:133)nancing sources and the productivity pro(cid:133)le of (cid:133)rms. Such changes could, in turn, modify the e⁄ectiveness of cyclical policies aimed at protecting employment and improving recoveries in emerging economies. We plan to explore these extensions in future work. References [1] Adjemian, StØphane, Houtan Bastani, Michel Juillard, Ferhat Mihoubi, George Perendia, Marco Ratto and SØbastien Villemot. 2011. (cid:147)Dynare: Reference Manual, Version 4,(cid:148)Dynare Working Papers, 1, CEPREMAP. [2] Arseneau, David M. and Brendan Epstein. 2014. (cid:147)The Welfare Costs of Skill-Mismatch Employment.(cid:148)Finance and Economics Discussion Series 2014-42, Board of Governors of the Federal Reserve System. 35

[3] Banerji, Arup, David Newhouse, Pierella Paci, and David Robalino. 2014. (cid:147)Working Through the Crisis: Jobs and Policies in Developing Countries during the Great Recession,(cid:148)The World Bank Group: Washington D.C. [4] Bosch, Mariano and Willam Maloney. 2008. (cid:147)Cyclical Movements in Unemployment and Informality in Developing Countries,(cid:148)mimeo. [5] Boz,Emine,CeyhunBoraDurdu,andNanLi.2012.(cid:147)EmergingMarketBusinessCycles: The Role of Labor Market Frictions,(cid:148)IMF Working Papers 12/237. [6] Busso, Mat(cid:237)as, Mar(cid:237)a Victoria Fazio, and Santiago Levy. 2012. (cid:147)(In)formal and (Un)productive: The Productivity Costs of Excessive Informality in Mexico,(cid:148) IDB Working Paper Series No. IDB-WP-341. [7] Busso, Mat(cid:237)as, Luc(cid:237)a Madrigal, and Carmen PagØs. 2012. (cid:147)Productivity and Resource Misallocation in Latin America,(cid:148)IDB Working Paper Series No. IDB-WP-306. [8] Campolmi, Alessia, Ester Faia, and Roland C. Winkler. 2011. (cid:147)Fiscal Calculus and the Labor Market,(cid:148)B.E. Journal of Macroeconomics, Vol. 11, Issue 1, Article 38, pp. 1-25. [9] Canzoneri, Matthew, Fabrice Collard, Harris Dellas, and Behzad Diba. 2011. (cid:147)Fiscal Multipliers in Recessions,(cid:148)mimeo. [10] Epstein, Brendan. 2012. (cid:147)Heterogeneous Workers, Optimal Job Seeking, and Aggregate Labor Market Dynamics.(cid:148) International Finance Discussion Papers 1053, Board of Governors of the Federal Reserve System. [11] Faia, Ester, Wolfgang Lechthaler, and Christian Merkl. (cid:147)Fiscal Stimulus and Labor Market Policies in Europe,(cid:148)Journal of Economic Dynamics and Control, Vol. 37, pp. 483-499. [12] Farazi, Subika. 2014. (cid:147)Informal Firms and Financial Inclusion: Status and Determinants,(cid:148)World Bank Policy Research Working Paper No. WPS 6778. [13] FernÆndez, AndrØs, and Felipe Meza. 2014. (cid:147)Labor Informality and Business Cycles in Emerging Economies," Review of Economic Dynamics, forthcoming. [14] Finkelstein Shapiro, Alan. 2014. (cid:147)Self-Employment and Business Cycle Persistence: Does the Composition of Employment Matter for Economic Recoveries?(cid:148)Journal of Economic Dynamics and Control, Vol. 46, September 2014, pp. 200-218. 36

[15] Global Financial Development Report. 2014. (cid:147)Financial Inclusion,(cid:148)The World Bank Group: Washington D.C. [16] Hosios, Arthur J. (1990). (cid:147)On the E¢ ciency of Matching and Related Models of Search and Unemployment.(cid:148)Review of Economic Studies, 57(2), 279-298. [17] IDB. 2005a. (cid:147)Unlocking Credit, The Quest for Deep and Stable Bank Lending,(cid:148) Research Department, Inter-American Development Bank: Washington D.C. http://www.iadb.org/res/ipes/2005/index.cfm. [18] IDB. 2005b. (cid:147)Developing Entrepreneurship: Experience in Latin America and Worldwide,(cid:148) Edited by Hugo Kantis, with collaboration of Pablo Angelelli and Virginia Moori Koenig, Inter-American Development Bank: Washington D.C. http://idbdocs.iadb.org/wsdocs/getdocument.aspx?docnum=834797. [19] ILO. 2011. (cid:147)A Review of Global Fiscal Stimulus,(cid:148)EC-IILS Joint Discussion Paper Series No. 5. [20] ILO and World Bank. 2012. (cid:147)Inventory of Policy Responses to the Financial and EconomicCrisis,(cid:148)ILO/WorldBankJointSynthesisReport.TheWorldBankGroup:Washington D.C. [21] Kantis, Hugo, Masahiko Ishida, and Masahiko Komori. 2002. (cid:147)Entrepreneurship in Emerging Economies: The Creation and Development of New Firms in Latin America and East Asia,(cid:148)Inter-American Development Bank: Washington D.C. [22] Kitao, Sagiri, Ay‚seg(cid:252)l S‚ahin, and Joseph Song. 2010. (cid:147)Subsidizing Job Creation in the Great Recession,(cid:148)Federal Reserve Bank of New York Sta⁄ Report No. 451. [23] Kurmann, Andre, and Nicolas Petrosky-Nadeau. 2007. (cid:147)Search Frictions in Physical Capital Markets as a Propagation Mechanism,(cid:148)Working Paper 07-12, Centre Interuniversitaire sur le Risque, les Politiques Economiques et l(cid:146)Emploi. [24] Lee, Yoonsoo, and Toshihiko Mukoyama. 2013. (cid:147)Entry, Exit, and Plant-Level Dynamics Over the Business Cycle,(cid:148)mimeo. [25] Levy, Santiago. 2007. (cid:147)Can Social Programs Reduce Productivity and Growth? A Hypothesis for Mexico,(cid:148)IPC Working Paper Series Number 37, Gerald R. Ford School of Public Policy, University of Michigan. 37

[26] Loayza, Norman, and Jamele Rigolini. 2011. (cid:147)Informal Employment: Safety Net or Growth Engine?(cid:148)World Development, Vol. 39, Issue 9, pp. 1503(cid:150)1515. [27] McKenzie, David J., and Christopher Woodru⁄. 2006. (cid:147)Do Entry Costs Provide an Empirical Basis for Poverty Traps? Evidence from Mexican Microenterprises,(cid:148)Economic Development and Cultural Change, Vol. 55,No. 1, pp. 3-42. [28] Nicoletti, Giulio, and Olivier Pierrard. 2006. (cid:147)Capital Market Frictions and the Business Cycle,(cid:148) Discussion Paper 2006-53, DØpartement des Sciences (cid:201)conomiques de l(cid:146)UniversitØ Catholique de Louvain. [29] Perry, Guillermo E., William F. Maloney, Omar S. Arias, Pablo Fajnzylber, Andrew D. Mason, and Jaime Saavedra-Chanduvi. 2007. (cid:147)Informality: Exit and Exclusion,(cid:148)The World Bank Group: Washington D.C. [30] SedlÆ(cid:181)cek, Petr. 2011. (cid:147)Firm Age, Business Cycles, and Aggregate Labor Market Dynamics,(cid:148)mimeo. [31] SedlÆ(cid:181)cek, Petr, and Vincent Sterk. 2013. (cid:147)Recession Scars and the Growth Potential of Newborn Firms in General Equilibrium,(cid:148)mimeo. [32] Shao, Enchuan, and Pedro Silos. 2008. (cid:147)Firm Entry and Labor Market Dynamics,(cid:148) Federal Reserve Bank of Atlanta Working Paper 2008-17. [33] Shimer, Robert. 2005. (cid:147)The Cyclical Behavior of Equilibrium Unemployment and Vacancies.(cid:148)American Economic Review, Vol. 95(1), pp. 25-49. [34] Siemer, Michael. 2013. (cid:147)Firm Entry and Employment Dynamics in the Great Recession,(cid:148)mimeo. [35] Totzek, Alexander, and Roland C. Winkler. 2010. (cid:147)Fiscal Stimulus in a Business Cycle Model with Firm Entry,(cid:148)mimeo. A Appendix A.1 Household Optimization Assigning the multipliers (cid:3) , (cid:3) , (cid:3) and (cid:3) to the household(cid:146)s budget constraint, t K;t OSB;t NSB;t the household(cid:146)s perceived law of motion for self-employment, its perceived law of motion for 38

small business owners, and its perceived (from the labor demand perspective) law of motion for employment in small (cid:133)rms, respectively, the corresponding (cid:133)rst order conditions are as follows. For consumption c , t u (c ) (cid:3) = 0. 0 t t (cid:0) For self-employed individuals, n , SE;t+1 (cid:12)Et (cid:3) t+1 (p SE;t+1 z SE;t+1 (cid:0) r SE;t+1 ) (cid:0) (cid:28)v t+ SE 1 SE v SE;t+1 +(cid:12)(1 (cid:0) (cid:26)K t+1 )E (cid:2) t [ 1 (cid:0) (1 (cid:0) (cid:26)O t+1 )(1 (cid:0) (cid:26)S t+1 )v SE;t+1 q((cid:18) SE;t+1 ) (cid:3)(cid:3) K;t+1 +(1 (cid:26)(cid:0)O )(1 (cid:26)S )v q((cid:18) )(cid:3) ] (cid:1) (cid:0) t+1 (cid:0) t+1 SE;t+1 SE;t+1 OSB;t+1 +(cid:12)(1 (cid:0) (cid:26)K t+1 )(1 (cid:0) (cid:26)O t+1 )(1 (cid:0) (cid:26)S t+1 )Et v SE;t+1 q((cid:18) SE;t+1 )(cid:3)d NSB;t+1 (cid:0) (cid:3) K;t = 0. For self-employment projects, s : K;t (cid:3) (cid:28)(cid:20)(cid:20)(s )+(1 (cid:26)K)p((cid:18) )(cid:3) = 0. (cid:0) t t 0 K;t (cid:0) t K;t K;t For small business owners, o : SB;t+1 (cid:12)Et (cid:3) t+1 [p SB;t+1 z SB;t+1 F oh SB;t+1 (n SB;t+1 ;o SB;t+1 ) (cid:0) r SB;t+1 (cid:0) (cid:28)v t+ SB 1 SB v SB;t+1 ] +(cid:12)(1 (cid:0) (cid:26)K t+1 )(cid:26)O t+1 Et (cid:3) K;t+1 +(cid:12)(1 (cid:0) (cid:26)K t+1 )(1 (cid:0) (cid:26)O t+1 )Et (cid:3) OSB;t+1 +(cid:12)(1 (cid:0) (cid:26)K t+1 )(1 (cid:0) (cid:26)O t+1 )(1 (cid:0) (cid:26)S t+1 )Et (cid:3) NSB;t+1 v SB;t+1 q((cid:18) SB;t+1 ) (cid:0) (cid:3) OSB;t = 0. The demand for individuals employed by small businesses, nd : SB;t+1 (cid:12)Et (cid:3) t+1 [p SB;t+1 z SB;t+1 F nd SB;t+1 (n SB;t+1 ;o SB;t+1 ) (cid:0) (cid:28)w t+ S 1 Bw SB;t+1 ] +(cid:12)(1 (cid:0) (cid:26)K t+1 ) 1 (cid:0) (cid:26)O t+1 1 (cid:0) (cid:26)S t+1 Et (cid:3) NSB;t+1 (cid:0) (cid:3) NSB;t = 0. (cid:0) (cid:1)(cid:0) (cid:1) 39

Vacancies posted per self-employed individual, v : SE;t (cid:3) (cid:28)vSE (cid:3) (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)q((cid:18) ) (cid:0) t t SE (cid:0) K;t (cid:0) t (cid:0) t (cid:0) t SE;t +(cid:3) (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)q((cid:18) ) OSB;t (cid:0) t (cid:0) t (cid:0) t SE;t +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)q((cid:18) )(cid:3) = 0. (cid:0) t (cid:0) t (cid:0) t SE;t NSB;t And vacancies posted per small business, v : SB;t (cid:3) (cid:28)vSB +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)q((cid:18) )(cid:3) = 0. (cid:0) t t SB (cid:0) t (cid:0) t (cid:0) t SB;t NSB;t From the (cid:133)rst-order condition for consumption, we know that (cid:3) = u(c ). t 0 t Then, we can write (cid:3) (cid:28)(cid:20)(cid:20)(s ) K;t = t 0 K;t , u(c ) (1 (cid:26)K)p((cid:18) ) 0 t t K;t (cid:0) and obtain (cid:3) (cid:28)vSB NSB;t = t SB . u(c ) (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)q((cid:18) ) 0 t t t t SB;t (cid:0) (cid:0) (cid:0) Also, we have (cid:3) (cid:28)vSE (cid:28)vSB (cid:28)(cid:20)(cid:20)(s ) (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S) OSB;t = t SE t SB + t 0 K;t . (cid:0) t (cid:0) t (cid:0) t u(c ) q((cid:18) ) (cid:0) q((cid:18) ) p((cid:18) ) 0 t SE;t SB;t K;t To determine the optimal decision to become a small (cid:133)rm, we write: (cid:3) (cid:3) OSB;t t+1 (cid:3) = Et (cid:12) (cid:3) f p SB;t+1 z SB;t+1 F oSB (n SB;t+1 ;o SB;t+1 ) t t (cid:3) r (cid:28)vSB v +(1 (cid:26)K)(cid:26)O K;t+1 (cid:0) SB;t+1 (cid:0) t SB SB;t+1 (cid:0) (cid:3) t+1 (cid:3) +(1 (cid:26)K )(1 (cid:26)O )(1 (cid:26)S ) NSB;t+1 v q((cid:18) ) (cid:0) t+1 (cid:0) t+1 (cid:0) t+1 (cid:3) SB;t+1 SB;t+1 t+1 (cid:3) + (1 (cid:26)K )(1 (cid:26)O ) OSB;t+1 . (cid:0) t+1 (cid:0) t+1 (cid:3) t+1 (cid:27) 40

Then, usetheexpressions aboveas well as theoptimal decisiontomove intoself-employment to yield (iterating forward when necessary): 1 (cid:28)vSE (cid:28)vSB t SE t SB (1 (cid:26)S)(1 (cid:26)K)(1 (cid:26)O) q (cid:0) q (cid:0) t (cid:0) t (cid:0) t (cid:18) SE;t SB;t (cid:19) p z F (n ;o ) SB;t+1 SB;t+1 oSB SB;t+1 SB;t+1 = Et (cid:4) t+1 j t 8 > > (cid:0) r SB;t+1 (cid:0) (p SE;t+1 z SE;t+1 (cid:0) r SE;t+1 ) 9 > > . > < + 1 (cid:28) v t+ S 1 E SE (cid:28) v t+ S 1 B SB > = (1 (cid:0) (cid:26)S t+1 ) qSE;t+1 (cid:0) qSB;t+1 > > (cid:16) (cid:17) > > > > : ; where: (cid:4) = (cid:12)u =u is the stochastic discount factor. This equation implicitly de(cid:133)nes t+1t 0t+1 0t j v . SE;t To derive the decision to enter self-employment, (cid:133)rst write: (cid:3) (cid:3) (cid:3) K;t = Et (cid:12) (cid:3) t+1 (p SE;t+1 z SE;t+1 (cid:0) r SE;t+1 ) (cid:0) (cid:28)v t+ SE 1 SE v SE;t+1 t t (cid:8) (cid:3) +(1 (cid:26)K ) 1 (1 (cid:26)O )(1 (cid:26)S )v q((cid:18) ) K;t+1 (cid:0) t+1 (cid:0) (cid:0) t+1 (cid:0) t+1 SE;t+1 SE;t+1 (cid:3) t+1 (cid:0) (cid:3) (cid:1) +(1 (cid:26)K )(1 (cid:26)O )(1 (cid:26)S )v q((cid:18) ) OSB;t+1 (cid:0) t+1 (cid:0) t+1 (cid:0) t+1 SE;t+1 SE;t+1 (cid:3) t+1 (cid:3) +(1 (cid:26)K )(1 (cid:26)O )(1 (cid:26)S )v q((cid:18) ) NSB;t+1 . (cid:0) t+1 (cid:0) t+1 (cid:0) t+1 SE;t+1 SE;t+1 (cid:3) t+1 (cid:27) Using the equations above, we can rewrite the above expression to have: (cid:28)(cid:20)(cid:20)(s ) (cid:28)(cid:20) (cid:20)(s ) t p((cid:18) 0 K; K t ) ;t = (1 (cid:0) (cid:26)K t )Et (cid:4) t+1 j t (cid:26) p SE;t+1 z SE;t+1 (cid:0) r SE;t+1 + t p + ( 1 (cid:18) K 0 ;t+ K 1 ) ;t (cid:27) : This equation implicitly de(cid:133)nes s . K;t A.2 Value Equations and Nash Price Determination A.2.1 Value Equations In what follows, we de(cid:133)ne the household and (cid:133)rm value functions to determine the Nash wage and rental rates. The value of having an additional salaried worker in a large (cid:133)rm, J , is given by the di⁄erence between the (cid:133)rm(cid:146)s marginal revenue product of labor and L;t the subsidy-adjusted wage, plus the continuation value in the event that the match survives 41

into the following period (in equilibrium the value of any vacancy is zero(cid:151)this re(cid:135)ects that vacancies are posted until the value of doing so is exhausted): J L;t = p L;t z L;tFnL (n L;t ;! t k L;t ) (cid:0) (cid:28)w t Lw L;t +(1 (cid:0) (cid:26)L t )Et (cid:4) t+1 j t J L;t+1 . Similar intuition lies behind the value of an additional salaried worker for a small business, J : SB;t J = p z F (n ;o ) (cid:28)wSBw OSB;t SB;t SB;t nSB SB;t SB;t (cid:0) t SB;t +Et (cid:4) t+1 j t (1 (cid:0) (cid:26)K t )(1 (cid:0) (cid:26)O t )(1 (cid:0) (cid:26)S t )J OSB;t+1 . (cid:8) (cid:9) The household(cid:146)s value of having an additional individual in salaried employment in a large (cid:133)rm, W , is given by corresponding wage payment plus the expected continuation L;t value: W L;t = w L;t +Et (cid:4) t+1 j t (1 (cid:0) (cid:26)L t )W L;t+1 +(cid:26)L t W U;t+1 , (cid:8) (cid:9) where: W isthehousehold(cid:146)svalueofunemployment. Similarintuitionliesbehindthevalue U of having an additional household member employed by a small business W : SB;t (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)W W = w +E (cid:4) (cid:0) t (cid:0) t (cid:0) t SB;t+1 . SB;t SB;t t t+1t j 8 + 1 (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S) W 9 < (cid:0) (cid:0) t (cid:0) t (cid:0) t U;t+1 = In turn, the household(cid:146)s value of unemp(cid:2)loyment is: (cid:3) : ; (1 (cid:26)L)p((cid:18) )W +(1 (cid:26)K)su f W (cid:0) t L;t L;t+1 (cid:0) t K;t K;t SE;t+1 8 +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)[f +f ]W 9 W U;t = b+Et (cid:4) t+1t > > > (cid:0) t (cid:0) t (cid:0) t SB;t SE;t SB;t+1 > > > , j > > 1 (1 (cid:26)L)f (1 (cid:26)K)su f > > > < + (cid:0) (cid:0) t L;t (cid:0) (cid:0) t K;t K;t W > = U;t+1 2 (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)[f +f ] 3 > > (cid:0) (cid:0) t (cid:0) t (cid:0) t SB;t SE;t > > > > > > 4 5 > > > > : ; where: W isthevaluetothehouseholdofanadditionalself-employedindividual(de(cid:133)ned SE;t below) and su is the amount of resources spent on searching for a capital supplier per K;t unemployed individual (su s =u ). K;t (cid:17) K;t t The value to a large (cid:133)rm of having a capital relationship with a self-employed individual, 42

J , is given by the corresponding rental rate adjusted for the probability that the capital SE;t relationship is destroyed net of the capital depreciation rate plus the expected continuation value: (1 (cid:26)K)(1 (1 (cid:26)O)(1 (cid:26)S)v q )J J = r +((cid:26)K (cid:14))+E (cid:4) (cid:0) t (cid:0) (cid:0) t (cid:0) t SE;t SE;t SE;t+1 . SE;t SE;t t (cid:0) t t+1 j t 8 +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)v q J 9 < (cid:0) t (cid:0) t (cid:0) t SE;t SE;t SB;t+1 = : ; Similar intuition lies behind the value to a large (cid:133)rm of having a capital relationship with a small business, J : SB;t (1 (cid:26)K)(1 (cid:26)O)J J = r + (1 (1 (cid:26)O)(1 (cid:26)S) (cid:14) +E (cid:4) (cid:0) t (cid:0) t SB;t+1 . SB;t SB;t (cid:0) (cid:0) t (cid:0) t (cid:0) t t+1 j t 8 +(1 (cid:26)K)(cid:26)OJ 9 (cid:2) (cid:3) < (cid:0) t t SE;t+1 = : ; In turn, the value to a self-employed individual of having a capital relationship with a large (cid:133)rm, W , is given by the di⁄erence between the marginal revenue product of capital and SE;t the rental rate, plus the expected continuation value: W = p z r SE;t SE;t SE;t SE;t (cid:0) (1 (cid:26)K) 1 (1 (cid:26)O)(1 (cid:26)S)v q W +Et (cid:4) t+1t (cid:0) t (cid:0) (cid:0) t (cid:0) t SE;t SE;t SE;t+1 . j 8 +(1 (cid:26)K)(1(cid:2) (cid:26)O)(1 (cid:26)S)v q J (cid:3)+(cid:26)KW 9 < (cid:0) t (cid:0) t (cid:0) t SE;t SE;t OSB;t+1 t U;t+1 = : ; Finally, similar intuition as before applies to the value to a household of having an additional capital relationship between a small (cid:133)rm and a large (cid:133)rm, W , which is given by: OSB;t W = p z F nd ;o r OSB;t SB;t SB;t oSB SB;t SB;t (cid:0) SB;t (1 (cid:26)K)(1 (cid:0) (cid:26)O)W (cid:1) +Et (cid:4) t+1t (cid:0) t (cid:0) t OSB;t+1 : j 8 +(1 (cid:26)K)(cid:26)OW +(cid:26)KW 9 < (cid:0) t t SE;t+1 t U;t+1 = : ; A.2.2 Nash Wage Rate Determination Large (cid:133)rms and salaried workers choose a wage w to L;t max (W L;t W U;t )(cid:31) L(J L;t )1 (cid:0) (cid:31) L . wL;t (cid:0) (cid:8) (cid:9) 43

Small business owners and small (cid:133)rm salaried workers choose a wage w to SB;t max (W SB;t W U;t )(cid:31) SB (J OSB;t )1 (cid:0) (cid:31) SB . wSB;t (cid:0) (cid:8) (cid:9) Above (cid:31) (0;1) and (cid:31) (0;1) are, respectively, the bargaining power of workers L SB 2 2 negotiating with large (cid:133)rms and the bargaining power of workers negotiating with small businesses. W W and J are the household(cid:146)s and large (cid:133)rm(cid:146)s respective capital L;t U;t L;t (cid:0) gains from large (cid:133)rm salaried employment. Similarly, W W and J are the SB;t U;t OSB;t (cid:0) household(cid:146)s and small business owner(cid:146)s capital gains from salaried employment in small (cid:133)rms. The implicit expressions for the Nash wages are given by (cid:31) L J = (W W ) (1 (cid:31) )(cid:28)wL L;t L;t (cid:0) U;t L t (cid:0) for w and L;t (cid:31) SB J = (W W ) (1 (cid:31) )(cid:28)wSB OSB;t SB;t (cid:0) U;t SB t (cid:0) for w . SB;t A.2.3 Nash Rental Rate Determination Large (cid:133)rms and the self-employed choose a rental rate r to SE;t max (W SE;t W U;t )(cid:31) K (J SE;t (1 (cid:14)))1 (cid:0) (cid:31) K . rSE;t (cid:0) (cid:0) (cid:0) (cid:8) (cid:9) Large (cid:133)rms and small business owners choose a rental rate r to SB;t max (W OSB;t W U;t )(cid:31) O (J SB;t (1 (cid:14)))1 (cid:0) (cid:31) O : rSB;t (cid:0) (cid:0) (cid:0) (cid:8) (cid:9) Above, the outside option of large (cid:133)rms is the value of a unit of capital net of depreciation, (1 (cid:14)). Also, (cid:31) (0;1) and (cid:31) (0;1) are, respectively, the bargaining power of self- SE O (cid:0) 2 2 employedandsmallbusinessowners. W W andJ (1 (cid:14))arethehousehold(cid:146)sand SE;t U;t SE;t (cid:0) (cid:0) (cid:0) large (cid:133)rm(cid:146)s respective capital gains from self-employment capital relationships. Similarly, W W and J (1 (cid:14)) are the household(cid:146)s and the large (cid:133)rm(cid:146)s respective capital OSB;t U;t SB;t (cid:0) (cid:0) (cid:0) 44

gainsfromsmall (cid:133)rmcapital relationships. TheimplicitexpressionsfortheNashrental rates are given by (cid:31) K (J (1 (cid:14))) = (W W ) SE;t SE;t U;t (1 (cid:31) ) (cid:0) (cid:0) (cid:0) K (cid:0) for r and SE;t (cid:31) O (J (1 (cid:14))) = (W W ) SB;t OSB;t U;t (1 (cid:31) ) (cid:0) (cid:0) (cid:0) O (cid:0) for r . SB;t A.2.4 Explicit Wage Expressions Without Policy To obtain explicit expressions for wages without the policies in place, (cid:133)rst note that q L L ;t = (1 (cid:0) (cid:26)L t )Et (cid:4) t+1 j t J L;t+1 , p L;t z L;tF!kL (n L;t ;! q t K k ; L t ;t )+(1 (cid:0) (cid:26)K t )q K;t = (1 (cid:0) (cid:26)K t )Et (cid:4) t+1 j t J SE;t+1 , and q S S B B ;t = (1 (cid:0) (cid:26)O t )(1 (cid:0) (cid:26)S t )(1 (cid:0) (cid:26)K t )Et (cid:4) t+1 j t J OSB;t+1 . Then, write W L;t (cid:0) W U;t = w L;t +Et (cid:4) t+1 j t (1 (cid:0) (cid:26)L t )W L;t+1 +(cid:26)L t W U;t+1 (cid:0) b (1 (cid:26)L)f W (cid:8) +(1 (cid:26)K)su f W (cid:9) (cid:0) t L;t L;t+1 (cid:0) t K;t K;t SE;t+1 8 +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)(f +f )W 9 +Et (cid:4) t+1t > > > (cid:0) t (cid:0) t (cid:0) t SB;t SE;t SB;t+1 > > > , j > > 1 (1 (cid:26)L)p (1 (cid:26)K)su f > > > < + (cid:0) (cid:0) t Lt (cid:0) (cid:0) t K;t K;t W > = U;t+1 2 (1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)(f +f ) 3 > > (cid:0) (cid:0) t (cid:0) t (cid:0) t SB;t SE;t > > > > > > 4 5 > > > > : ; where su s =u . After some algebra, we have K;t (cid:17) K;t t W L;t (cid:0) W U;t = w L;t (cid:0) b+Et (cid:4) t+1 j t (1 (cid:0) (cid:26)L t )(1 (cid:0) f L;t )(W L;t+1 (cid:0) W U;t+1 ) (1 (cid:26)K)su (cid:8)f (W W ) (cid:9) +Et (cid:4) t+1t (cid:0) t K;t K;t SE;t+1 (cid:0) U;t+1 : j 8 +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)(f +f )(W W ) 9 < (cid:0) t (cid:0) t (cid:0) t SB;t SE;t SB;t+1 (cid:0) U;t+1 = : ; 45

Using the (cid:133)rst-order conditions that determine the implicit functions for w ;w ; and L;t SB;t r , we can write SE;t (cid:31) (cid:31) (1 L (cid:31) ) J L;t = w L;t (cid:0) b+Et (cid:4) t+1 j t (1 (cid:0) (cid:26)L t )(1 (cid:0) f L;t ) (1 L (cid:31) ) J L;t+1 (cid:0) L (cid:26) (cid:0) L (cid:27) (1 (cid:26)K)su f (cid:31) K (J (1 (cid:14))) +Et (cid:4) t+1t (cid:0) t K;t K;t(1 (cid:0) (cid:31) K ) SE;t+1 (cid:0) (cid:0) : j 8 +(1 (cid:26)K)(1 (cid:26)O)(1 (cid:26)S)(f +f ) (cid:31) SB J 9 < (cid:0) t (cid:0) t (cid:0) t SB;t SE;t (1 (cid:0) (cid:31) SB ) OSB;t+1 = : ; Now, based on as the job creation and capital supply conditions above when the policies are suppressed, we have (cid:31) (1 f )(cid:31) (1 L (cid:31) ) p L;tFnL;t (n L;t ;! t k L;t ) (cid:0) w L;t + q L = w L;t (cid:0) b+ ( (cid:0) 1 L (cid:31) ;t ) L q L (cid:0) L (cid:18) L;t(cid:19) (cid:0) L L;t (cid:31) K su K;t f K;t p L;t z L;tF!kL (n L;t ;! t k L;t )+(1 (cid:0) (cid:26)K t )q K;t (cid:0) (1 (cid:31) ) q (cid:0) K (cid:18) K;t (cid:19) (cid:31) su f (cid:31) (f +f ) + ( K 1 K; (cid:31) t K K ) ;t Et (cid:4) t+1 j t (1 (cid:0) (cid:26)K t )(1 (cid:0) (cid:14)) (cid:0) SB (1 SB;t (cid:31) SB ) SE;t q S S B B ;t : (cid:0) (cid:0) Rearranging terms, we have w = (1 (cid:31) )b+(cid:31) (cid:18) + (1 (cid:0) (cid:31) L )su K;t f K;t (cid:23) K p L;t z L;tF!kL (n L;t ;! t k L;t ) L;t (cid:0) L L L;t L (1 (cid:31) ) q (cid:0) K (cid:18) K;t (cid:19) (1 (cid:31) )(cid:31) su f (cid:0) (cid:0) (1 L (cid:31) K K ) ;t K;t (1 (cid:0) (cid:26)K t ) 1 (cid:0) Et (cid:4) t+1 j t (1 (cid:0) (cid:14)) K (cid:0) (1 (cid:31) )(cid:31) (f +(cid:2)f ) (cid:3) + (cid:0) L SB SB;t SE;t SB ; (1 (cid:31) ) q SB SB;t (cid:0) where we make use of fact that f =q = (cid:18) . Finally, we can write L;t L;t L;t w = (1 (cid:31) )b+(cid:31) (cid:18) (cid:28)vL (A1) L;t L L L;t t L (cid:0) + (1 (cid:0) (cid:31) L )s K;t f K;t (cid:31) K p L;t z L;tF!kL (n L;t ;! t k L;t ) (1 (cid:31) ) q (cid:0) K (cid:18) K;t (cid:19) (1 (cid:31) )(cid:31) s f (cid:0) (cid:0) (1 L (cid:31) K K ) ;t K;t (1 (cid:0) (cid:26)K t ) 1 (cid:0) Et (cid:4) t+1 j t (1 (cid:0) (cid:14)) K (cid:0) (1 (cid:31) )(cid:31) (1 (cid:2)(cid:31) )(cid:31) f (cid:3) + (cid:0) L SB(cid:18) + (cid:0) L SB SE;t SB ; (1 (cid:31) ) SB;t SB (1 (cid:31) ) q SB SB SB;t (cid:0) (cid:0) 46

wherewemakeuseofthefactthatf =q = (cid:18) :Followingsimilarstepsbyconstructing SB;t SB;t SB;t (W W ), the wage for small-(cid:133)rm workers is SB;t U;t (cid:0) f w = (1 (cid:31) )b+(cid:31) (cid:18) +(cid:23) SE;t SB (A2) SB;t (cid:0) SB SB SB;t SB SB q SB;t + (1 (cid:0) (cid:31) SB )(cid:31) K su K;t f K;t p L;t z L;tF!kL (n L;t ;! t k L;t ) (1 (cid:31) ) q (cid:0) K (cid:18) K;t (cid:19) (1 (cid:31) )(cid:31) su f (1 (cid:31) )(cid:31) (cid:0) (cid:0) ( S 1 B (cid:31) K ) K;t K;t (1 (cid:0) (cid:26)K t ) 1 (cid:0) Et (cid:4) t+1 j t (1 (cid:0) (cid:14)) + ( (cid:0) 1 S (cid:31) B ) L(cid:18) L;t L : K L (cid:0) (cid:0) (cid:2) (cid:3) Note that both large-(cid:133)rm and small-(cid:133)rm wages depend on labor market tightness for large, small, and self-employed (cid:133)rms, as well as capital market tightness (recall that f , K;t q , f ; and q are functions of their respective market tightness). Intuitively, higher K;t SE;t SB;t labor market tightness (irrespective of the (cid:133)rm type) will put upward pressure on wages. This will also put downward pressure on capital rental rates as the outside options for both small (cid:133)rm owners and the self-employed are more attractive. Conversely, and similar to Finkelstein Shapiro (2014), higher capital market tightness will put downward pressure wages and upward pressure on capital rental rates. This is the case since higher capital market tightness(cid:151)a lower probability of becoming self-employed(cid:151)implies a less attractive self-employment outside option for salaried workers. By a⁄ecting market tightness, each of the cyclical subsidies will have an impact on wage dynamics and hence on labor demand. A.3 Calibration of Productivity Di⁄erentials Across Firm Types Busso, Fazio, and Levy (2012) use Mexican Census data to characterize the distribution of employment (as well as capital) based on (cid:133)rm size and the formality and legality status of the (cid:133)rm. FernÆndez and Meza (2014) use their evidence to determine the productivity gap between formal and informal (cid:133)rms focusing on legal (cid:133)rms alone since they consider that informal (cid:133)rms in their model are household (cid:133)rms that do not hire workers, i.e. household (cid:133)rms are self-employed (cid:133)rms (as de(cid:133)ned in Busso, Fazio, and Levy (2012), legal (cid:133)rms are those that comply with mandated social security contributions for the all their salaried workers. Semi-legal (cid:133)rms have salaried workers but pay social security for only a fraction of them). We follow their approach (and notation) in calibrating the productivity parameters 47

across (cid:133)rm types. In what follows, LSF denotes legal semi-formal (cid:133)rms, LF legal formal (cid:133)rms,LI legalinformal(cid:133)rms,SLSF semi-legalsemi-formal(cid:133)rms,andII illegalandinformal (cid:133)rms (see Busso et al., 2012, for more details). A.3.1 Distribution of Employment by Employment Status and De(cid:133)nition of Firm Size in the Model Giventhedi⁄erenttypesof(cid:133)rmsinourmodel,ourmappingbetweentotalfactorproductivity (TFP) in the data and productivity in the model is more detailed as it considers both (cid:133)rm size and legal/formality status. We assume that the self-employed are those workers in (cid:133)rms ofsize[0-5]thatarelegalandinformal. Theserepresentself-employed(own-account)(cid:133)rmsin the model. Workers in small (cid:133)rms are those working in (cid:133)rms of size [0-5] excluding informal and legal (cid:133)rms, as well as (cid:133)rms of sizes [6-10] and [11-50] excluding legal and formal (cid:133)rms. Large (cid:133)rms include workers that are formal and legal (regardless of (cid:133)rm size), as well as all workers in (cid:133)rms of size [+50]. We include all legal and formal (cid:133)rms within the same category (cid:150)regardless of (cid:133)rmsize (cid:150)since their legality implies that policy makers can readily introduce cyclical wage subsidies by using (cid:133)rms(cid:146)tax statements and social security records. This is not the case for (cid:133)rms that hire informal salaried workers since these workers are often not reported to the government. Combining evidence on the share of self-employment for Mexico and the share of workers that are informal but legal (Busso, Fazio, and Levy, 2012), we assume that the self-employed account for 16 percent of the labor force, and small business owners 7 percent of the labor force. In turn, salaried workers in small and large (cid:133)rms account for 30 and 42 percent of the labor force, respectively. A.3.2 Productivity Di⁄erentials Based on Firm Size and Formality/Legality Status Based on the mapping between (cid:133)rms in the data and (cid:133)rm types in the model, we can use evidence on productivity di⁄erences by (cid:133)rm size to compute the steady-state sectoral productivity di⁄erentials in the model. Using Table 10 in Busso, Fazio, and Levy (2012) and 48

following FernÆndez and Meza (2014), we have TFP TFP TFP LSF LF LSF log log = 0:959 = 0:3833; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP LI LF LI log log = 1:759 = 0:1722; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP SLSF LF SLSF log log = 0:214 = 0:8073; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP II LF II log log = 0:881 = 0:4144; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF for (cid:133)rms of size [0-5], TFP TFP TFP LSF LF LSF log log = 0:910 = 0:4025; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP LI LF LI log log = 0:688 = 0:5026; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP SLSF LF SLSF log log = 0:085 = 0:9185; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP II LF II log log = 0:632 = 0:5315; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF for (cid:133)rms of size [6-10], and TFP TFP TFP LSF LF LSF log log = 0:746 = 0:4743; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP LI LF LI log log = 0:395 = 0:6737; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP SLSF LF SLSF log log = 0:092 = 0:9121; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP II LF II log log = 0:701 = 0:4961; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF 49

for (cid:133)rms of size [11-50]. Finally, for (cid:133)rms of size [+50], we have TFP TFP TFP LSF LF LSF log log = 0:574 = 0:5633; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP LI LF LI log log = 0:491 = 0:6120; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP SLSF LF SLSF log log = 0:159 = 0:8530; TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF TFP TFP TFP II LF II log log = 1:039 = 0:3538: TFP (cid:0) TFP (cid:0) ) TFP (cid:18) (cid:19) (cid:18) (cid:19) LF Using Tables 6 and 10 in Busso, Fazio, and Levy (2012), we can construct employmentweighted measures of TFP for each type of (cid:133)rm (self-employed, TFP , small, TFP ; and SE SB large, TFP ). Then, TFP in self-employment is L TFP = TFP ; SE [0 5];LI (cid:0) TFP in small (cid:133)rms is computed as: 0:79 1:69 10:94 TFP = TFP + TFP + TFP SB [0 5];LSF [0 5];SLSF [0 5];II 32:17 (cid:0) 32:17 (cid:0) 32:17 (cid:0) (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 1:63 0:50 1:92 + TFP + TFP + TFP [6 10];LI [6 10];LSF [6 10];SLSF 32:17 (cid:0) 32:17 (cid:0) 32:17 (cid:0) (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 3:66 2:39 0:57 + TFP + TFP + TFP [6 10];II [11 50];LI [11 50];LSF 32:17 (cid:0) 32:17 (cid:0) 32:17 (cid:0) (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 4:72 3:36 + TFP + TFP ; [11 50];SLSF [11 50];II 32:17 (cid:0) 32:17 (cid:0) (cid:18) (cid:19) (cid:18) (cid:19) and TFP in large (cid:133)rms is computed as: 50

0:77 1:09 3:84 TFP = TFP + TFP + TFP L [0 5];LF [6 10];LF [11 50];LF 44:02 (cid:0) 44:02 (cid:0) 44:02 (cid:0) (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 14:67 7:74 1:19 + TFP + TFP + TFP [+50];LF [+50];LI [+50];LSF 44:02 44:02 44:02 (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 13:75 1:18 + TFP + TFP : [+50];SLSF [+50];II 44:02 44:02 (cid:18) (cid:19) (cid:18) (cid:19) UsingthevaluesforTFP relative to TFP by(cid:133)rmsizeandlegality/formalitystatusabove, LF we have TFP = 0:1722; SE 0:79 1:69 10:94 TFP = (0:3833)+ (0:8073)+ (0:4144) SB 30:54 30:54 30:54 (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 1:63 0:50 1:92 + (0:5026)+ (0:4025)+ (0:9185) 32:17 30:54 30:54 (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 3:66 2:39 0:57 + (0:5315)+ (0:6737)+ (0:4743) 30:54 30:54 30:54 (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 4:72 3:36 + (0:9121)+ (0:4961); 30:54 30:54 (cid:18) (cid:19) (cid:18) (cid:19) 0:77 1:09 3:84 TFP = (1)+ (1)+ (1) L 44:02 44:02 44:02 (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 14:67 7:74 1:19 + (1)+ (0:6737)+ (0:4743) 44:02 44:02 44:02 (cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19) 13:75 1:18 + (0:9121)+ (0:4161): 44:02 44:02 (cid:18) (cid:19) (cid:18) (cid:19) This yields TFP = 0:1722;TFP = 0:6150; and TFP = 0:8901: Then, normalizing SE SB L TFP to 1, and using the mapping TFP = z ;TFP = z ; and TFP = z between SE L L SB SB SE SE the data and the model, we have z = 5:1690; z = 3:5714; z = 1: L SB SE 51

A.4 Robustness and Additional Experiments A.4.1 Asymmetry in Elasticities of Substitution between Types of Output Assuming that (cid:30) = 0:8 and (cid:30) = 0:6 makes the main conclusions under the benchmark calia s bration starker. The main di⁄erences are as follows. With hiring subsidies for self-employed (cid:133)rms (i.e., small (cid:133)rm creation subsidies), consumption decreases by more (as capital search expenditures are more responsive) and there is no di⁄erence in the recovery speed of total output relative to the benchmark economy. A similar result obtains regarding the expansion of intermediation services for small (cid:133)rms, where consumption falls by more and the output recovery is more sluggish relative to the results in the main text. Similarly, with hiring subsidies for existing small (cid:133)rms, the gains in terms of a faster initial recovery in consumption, and output are more short-lived relative to the benchmark results. Finally, the gains from hiring subsidies for large (cid:133)rms and the improvement in matching for employment in large (cid:133)rms are larger. Thus, the main conclusions do not change. Conversely, assuming that (cid:30) = 0:6 and (cid:30) = 0:8 entails the following changes. Introducing hiring subsidies for a s self-employed (cid:133)rms make consumption less volatile and makes output recover faster. Thus, under this alternative calibration, the gains from these subsidies are somewhat larger relative to the benchmark calibration under the same policy. With hiring subsidies for small (cid:133)rms, the initial faster recovery in total output is longer (even though it still fades away in the medium term). Despite these changes, the main message of the paper does not change. Similarly, the recovery of output under better matching for employment in small (cid:133)rms is less sluggish, but the same policy for large (cid:133)rms still dominates. Importantly, regardless of the calibration of (cid:30) and (cid:30) , the adverse aggregate impact of introducing self-employment a s search (startup) subsidies does not change. A.4.2 Higher Volatility of Self-Employment Separation Probabilities Calibrating the model to capture the relative volatility of self-employment separation probabilities (as opposed to the relative volatility of salaried separation probabilities as in the benchmark model) in the data does not change the main conclusions. 52

A.4.3 Financing Cyclical Subsidies Through Government Debt WefollowCampolmi, Faia, andWinkler(2011)andallowforsubsidiesto(cid:133)rmstobe(cid:133)nanced partly through government debt. If the government uses lump-sum taxes and government debt to (cid:133)nance expenditures, the government budget constraint is T +b = bu +(1 (cid:28)vL) v +(1 (cid:28)vSE) v n +(1 (cid:28)vSB) v o t (cid:3)t t (cid:0) t L L;t (cid:0) t SE SE;t SE;t (cid:0) t SB SB;t SB;t +(1 (cid:28)(cid:20))(cid:20)(s )+R b +g +(1 (cid:28)wL)w n +(1 (cid:28)wSB)w n (cid:0) t K;t t (cid:0) 1 (cid:3)t (cid:0) 1 t (cid:0) t L;t L;t (cid:0) t SB;t SB;t +((cid:28)mL 1)m (v ;u )+((cid:28)mSB 1)m (v o ;u ). t L L; t t SB SB;t SB;t t (cid:0) (cid:0) where g is government spending. Following Totzek and Winkler (2010) and Campolmi, Faia t and Winkler (2011), we assume that a fraction (cid:13) of government expenditures is (cid:133)nanced b through debt, so that bu +(1 (cid:28)vL) v +(1 (cid:28)(cid:20))(cid:20)(s )+R b +g T t (cid:0) t L L;t (cid:0) t K;t t (cid:0) 1 (cid:3)t (cid:0) 1 t (cid:0) t 0 +(1 (cid:28)vSE) v n +(1 (cid:28)vSB) v o 1 t SE SE;t SE;t t SB SB;t SB;t b = (cid:13) (cid:0) (cid:0) : (cid:3)t bB B +(1 (cid:28)w t L)w L;t n L;t +(1 (cid:28)w t SB)w SB;t n SB;t C C B (cid:0) (cid:0) C B B +((cid:28)m t L 1)m L (v L; ;u t )+((cid:28)m t SB 1)m SB (v SB;t o SB;t ;u t ) C C B (cid:0) (cid:0) C @ A The impact of the policies is qualitatively similar to the one where the cyclical subsidies are fully (cid:133)nanced using lump-sum taxation. A.4.4 Financing Hiring Subsidies for Small Firms with Payroll Taxes on Large Firms While it may be feasible to introduce a hiring subsidy to small (cid:133)rms during a downturn, raising the revenue for that subsidy through distortionary taxes on small (cid:133)rms may be more di¢ cult given the high rates of informality among these (cid:133)rms. Assuming that the hiring subsidy for small (cid:133)rms is (cid:133)nanced through an increase in payroll taxes for large (cid:133)rms naturally reduces the bene(cid:133)cial impact from the subsidy relative to the case with lumpsum taxation or government debt. In particular, relative to the no-policy case, the recovery of consumption, investment, and output become more sluggish in the medium term, but 53

unemployment still falls due to a surge in small-(cid:133)rm employment. A.4.5 Policies with Identical Subsidy Rates The benchmark model assumed the same (cid:133)scal cost when analyzing each of the policies and allowed the cyclical subsidies to adjust endogenously. This generated di⁄erent subsidy rates depending on the type of policy. If we assume the same (impact) subsidy rate for all policies and let the (cid:133)scal cost adjust endogenously, the results can change in important ways for some of the policies. If we assume a subsidy rate of 5 percent on impact for all policies (see Banerji et al., 2014), hiring subsidies for small and self-employed (cid:133)rms have a negligible impact on consumption and output dynamics, though they still limit the initial rise in unemployment after the shock (in contrast to the benchmark results, a hiring subsidy for existing small (cid:133)rms only limits the rise in unemployment and does not lead to a drastic reduction in unemployment after the shock). This result occurs because the hiring subsidies need to be substantially higher to have a quantitative impact. In contrast, the e⁄ect of hiring subsidies for large (cid:133)rms is quantitatively similar to the main results, largely because the subsidy rate in the latter is not much higher than 5 percent. For similar reasons the results for improved matching for employment in either large or small (cid:133)rms do not change much either. Conversely, a subsidy of 5 percent implies that wage subsidies do have a larger quantitative impact (even though the (cid:133)scal cost also increases substantially), but the qualitative results do not change. A.4.6 Combining Individual Policies As should be the case, combining hiring subsidies with self-employment startup subsidies o⁄sets the bene(cid:133)ts from the hiring subsidies, so that the policy mix is much less e⁄ective in aiding the recovery of total output and reducing aggregate volatility, even though it does limit the rise in unemployment. Similarly, combining the self-employment startup subsidies with improvements in job intermediation (i.e., matching) implies that the gains obtained when intermediation is focused on large (cid:133)rms are smaller. 54

A.4.7 Exogenous Separation Probabilities The same policy experiments in a model with exogenous separation probabilities yield qualitatively similar results for the (cid:133)scal output and employment multipliers. Also, without the endogenous response in separations, all policies either limit the rise in unemployment or reduce unemployment by more relative to the benchmark model. The results for all other variablesunderexogenousseparationsremainqualitativelysimilartothoseinthebenchmark impulse response functions. A.5 Additional Details on Main Results Figures A1 through A5 present complementary impulse responses to those shown in the main text. Along the (cid:133)gures(cid:146)columns a particular policy is in place, and the (cid:133)gures(cid:146)rows show a particular variable(cid:146)s response. Using these (cid:133)gures, in what follows we present greater details on the dynamic adjustments driving the results shown in the (cid:133)gures in the main text. The impact of di⁄erent policies is always compared to the no-policy case. Moreover, the discussion makes use of the explicit wage statements in equations (A1) and (A2). In what follows, and given the input credit relationship between large (cid:133)rms and the self-employed in the model, when we refer to an increase (decrease) in the supply of capital to the selfemployment sector, we are implicitly referring to a fall (rise) in capital usage among large (cid:133)rms (even though the capital stock is also adjusting). Hiring Subsidy for Large Firms. (First column of Figures A1 through A5). This policy generates a rise in large-(cid:133)rm vacancy postings, which puts upward pressure on large- (cid:133)rm labor market tightness and limits the contraction in capital usage, which results in a smaller contraction in investment and also puts upward pressure on large- and small-(cid:133)rm wages, with the latter recovering earlier and the former initially falling by less. The fall in consumption is now limited by upward pressure on wages, the fall in expenditures on capital search, and the expansion in large-(cid:133)rm salaried employment (the contraction in selfemploymentearningsisalsosubdued). Thebehaviorofsalariedemploymentandthedecision to allocate relatively more capital within large (cid:133)rms aids the recovery in large-(cid:133)rm output, and in turn, total output. The expansion in large-(cid:133)rm employment counteracts the larger 55

contraction in small-(cid:133)rm employment and self-employment, which explains unemployment rising by less and returning back to steady state faster. These results are consistent with the positive e⁄ects of hiring subsidies documented in Campolmi, Faia, and Winkler (2011) and Faia, Lechthaler, and Merkl (2013) in a di⁄erent context, mainly in models with a single (cid:133)rm and employment type. Hiring Subsidy for Existing Small Firms. (First column of Figures A1 through A5). Higher vacancy postings by existing small (cid:133)rms puts upward pressure on small-(cid:133)rm salaried labor market tightness and leads to a reduction in both large-(cid:133)rm market tightness (which induces a larger initial fall in wages) and capital market tightness. The reduction in expenditures on capital search and the sharp expansion in small-(cid:133)rm salaried employment initially reduce the size of the contraction in consumption. The fall in large-(cid:133)rm vacancies reduces large-(cid:133)rm capital usage and increases capital supply to the self-employed in the period of the shock, ultimately resulting in a smaller initial fall in investment. Higher small (cid:133)rm vacancy posting puts upward pressure on large-(cid:133)rm wages, leading to a more sluggish recovery in large-(cid:133)rm vacancies and to a medium term slower recovery in investment. The sharp rise in small-(cid:133)rm employment aids the rebound in small-(cid:133)rm output, in turn aiding the recovery in total output (although only initially), and is large enough to o⁄set the fall in both large-(cid:133)rm employment and self-employment (so unemployment in fact decreases). Note that the large response of small-(cid:133)rm salaried employment is mainly due to the fact that the subsidy rate is much larger compared to the hiring subsidy rate for larger (cid:133)rms. This is partly explained by the fact that we are assuming a (cid:133)scal package of the same size (0.2 percent of output), but the cost of posting vacancies for small (cid:133)rms is slightly lower than the cost for large (cid:133)rms. Furthermore, the subsidy rate adjusts to the size of the (cid:133)scal package. If we were to assume the same subsidy rate for all policies (and let the cost of the (cid:133)scal package adjust endogenously), unemployment would rise by less, but remain fairly persistent as the recovery takes hold. Cyclical Improvements in Job Intermediation (Matching E¢ ciency) for Employment in Large Firms. (Second column of Figures A1 through A5). Results are analogous to hiring subsidies for large (cid:133)rms. The expected cost of posting vacancies for large (cid:133)rms decreases (mainly due to an increase in the job-(cid:133)lling rate instead of a fall in 56

the cost per vacancy as was the case with the hiring subsidy), bolstering vacancies in the period of the shock and increasing capital usage among large (cid:133)rms. This leads to a smaller fall in investment and in turn aids the recovery in total output. The reduction in capital search expenditures by households implies that consumption contracts by less. The behavior of large-(cid:133)rm vacancies a⁄ects labor market tightness and implies that the policy provides partial income protection by preventing wages across all (cid:133)rm types from falling as much. Finally, the policy induces an expansion in employment among large (cid:133)rms that more than o⁄sets the fall in employment among small (cid:133)rms and ultimately generates a reduction in unemployment. While the qualitative impact of the policy is similar to the hiring subsidy, the quantitative e⁄ects are larger. Cyclical Improvements in Job Intermediation (Matching E¢ ciency) for Employment in Small Firms. (Second column of Figures A1 through A5). There is a subdued e⁄ect on aggregate dynamics, and a similar e⁄ect to hiring subsidies for existing small (cid:133)rms. Interestingly, this job intermediation policy is less e⁄ective in reducing unemployment in the aftermath of the shock for this group of (cid:133)rms relative to a similar policy for large (cid:133)rms (despite the importance of small (cid:133)rms for aggregate employment). One key difference relative to hiring subsidies is that capital supply to the self-employed (capital usage in large (cid:133)rms) rises (falls) my more, which explains the behavior of investment. Moreover, since the downward adjustment in small (cid:133)rm wages is less stark, the recovery in small (cid:133)rm output is weaker, which in turn explains the short-term positive e⁄ects on unemployment. Hiring Subsidy for Self Employed Individuals. (Third column of Figures A1 through A5). Small (cid:133)rm owners expand, generating a larger reallocation of capital from the large-(cid:133)rm sector into the self-employment sector (the increase in vacancy postings by the self-employed puts upward pressure on large-(cid:133)rm wages via labor market tightness, reducing the incentive of large (cid:133)rms to hire workers and hence in-house capital usage). Capital supply to the self-employed surges, and the Nash rental rate for self-employed workers (not shown) falls by more so that self-employment earnings contract by less. Wages for both small and large-(cid:133)rm workers are less volatile, but consumption initially falls by slightly more given higher capital-search expenditures. Vacancy postings by existing small (cid:133)rms and the selfemployed bounce back after the shock putting upward pressure on wages via higher market 57

tightness. The rise in capital search expenditures is short-lived, and expenditures begin their return back to steady state faster, which explains why consumption does not fall by more after the shock. As capital usage among large (cid:133)rms initially contracts by more, investment exhibits a sharper contraction as well. The rise in both small-(cid:133)rm salaried employment and the measure of small business owners leads to a sharp recovery in small-(cid:133)rm output, aiding therecoveryintotaloutputdespitethemorepersistentcontractioninlarge-(cid:133)rmoutput. The behavior of employment outside the large (cid:133)rm sector is responsible for limiting the rise in unemployment. However, unemployment remains persistently above steady-state due partly to the persistent fall in both large-(cid:133)rm employment and self-employment, where the latter is explained by the out(cid:135)ow from of self-employment and into small business owner status. Subsidy for the Creation of Self-Employed Firms. (Third column of Figures A1 through A5). The demand for capital supplied by large (cid:133)rms rises and a reallocation of capital towards the self-employment sector takes place. The surge in capital demand from potential self-employed individuals reduces capital usage among large (cid:133)rms by more, leading to a larger contraction in large-(cid:133)rm vacancies and employment, large-(cid:133)rm output, and investment. A similar but milder e⁄ect is observed for small-(cid:133)rm salaried employment (small (cid:133)rms are not directly impacted by capital reallocation, but they are a⁄ected by the change in the self-employment outside option); if each small (cid:133)rm were using more than one unitofmatchedcapital, thereallocationprocesswouldlikelyhavealargerimpactonsalaried employment among large and small (cid:133)rms. Thus, our results can be seen as a lower bound for the response of small-(cid:133)rm salaried employment. Salaried labor market tightness across (cid:133)rm types contracts and puts downward pressure on wages, but it becomes easier to move into self-employment, which puts upward pressure on wages. Ultimately wages do not adjust muchrelative tothe benchmarkeconomy, but salariedemployment contracts bymore, which along with the sharp rise in expenditures on capital search explains the larger contraction in consumption. The rise in self-employment is large enough to generate a smaller increase in unemployment (this merely slows down the rise in unemployment, and the policy has no discernible impact on unemployment dynamics in the medium term). Finally, note that, while the contraction in small-(cid:133)rm output worsens only slightly, the more sluggish recovery in large-(cid:133)rm output explains the slower recovery in total output. Since it may be di¢ cult 58

to raise revenue for this policy by increasing the cost of hiring during an expansion, we can alternatively assume that this subsidy is (cid:133)nanced via a temporary increase in payroll taxes for large (cid:133)rms. This enhances the adverse quantitative e⁄ects of the policy by generating an even larger contraction in large-(cid:133)rm employment and output. Wage Subsidy for Large Firms. (Fourth column of Figures A1 through A5). The reductioninlarge-(cid:133)rmcapital usage is subdued, whichimplies that salariedvacancies among large(cid:133)rmsfallbyless,generatingasmallercontractionininvestmentandemploymentamong large (cid:133)rms and a faster recovery ininvestment. Inturn, large-(cid:133)rmoutput recovers at a faster rate. The supply of capital to the self-employed is smaller, so self-employment initially expands by less. The smaller decrease in large-(cid:133)rm vacancies implies that large-(cid:133)rm labor market tightness falls by less, putting upward pressure on wages among all (cid:133)rm types. Since the adjustment in wages is smaller, both small (cid:133)rms and the self-employed cut vacancies by more, generating a larger contraction in small-(cid:133)rm salaried employment in subsequent periods and small-(cid:133)rm output exhibits a more sluggish recovery. The smaller fall in large- (cid:133)rm employment and wages, combined with the fall in household resources spent on capital search, leads to a smaller fall in aggregate consumption. Importantly, the contraction in small-(cid:133)rm salaried employment more than o⁄sets the smaller fall in large-(cid:133)rm employment, which leads to a sharper increase in unemployment. Wage Subsidy for Small Firms. (Fourth column of Figures A1 through A5). The value of having salaried workers in small (cid:133)rms rises and limits the fall in vacancy postings among small and self-employed (cid:133)rms, putting upward pressure on labor market tightness and wages in both salaried (cid:133)rm types and pushing larger (cid:133)rms to reduce vacancy postings by more. Surprisingly, capital usage exhibits a similar fall to the one observed under the wage subsidies for large (cid:133)rms (despite having a larger fall in large-(cid:133)rm vacancies), which also implies a smaller fall in investment (existing small (cid:133)rms already have a capital relationship and the behavior of labor market tightness puts downward pressure on the Nash rental rates, which decreases the incentive to supply capital to the self-employed). Despite the larger contraction in salaried employment among large (cid:133)rms in the aftermath of the shock, the rise in small-(cid:133)rm salaried employment and wages for both (cid:133)rm types, along with the initial reduction in the resources devoted to capital search (not shown), leads to a marginally 59

smaller fall in consumption. Even though small-(cid:133)rm output recovers faster, the fall in large- (cid:133)rm output implies that the policy has a negligible e⁄ect on the recovery path of total output. Finally, given the large expansion in small-(cid:133)rm salaried employment, the rise of unemployment after the shock is smaller. Hiring Subsidies Job Interm. Subsidies Firm Creation Subsidies Wage Subsidies 0 0 0 0 tn e 5 5 10 5 m ts e v 10 10 20 10 n I 15 15 30 15 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0 0.2 0 0 e g 0.2 0 0.2 0.2 a s U la 0.4 0.2 0.4 0.4 tip a 0.6 0.4 0.6 0.6 C 0.8 0.6 0.8 0.8 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0 1 0 0 tu p tu 1 0 1 1 O m 1 riF e 2 2 2 2 g ra L 3 3 3 3 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t v t m t v t w L L SE L t v t m t k t w SB SB SB Figure A1 Response to a 1 percent negative productivity shock (quarters after shock): Investment, capital usage by large (cid:133)rms, and large (cid:133)rm output. 60

Hiring Subsidies Job. Interm. Subsidies Firm Creation Subsidies Wage Subsidies 1 1 2 1 tu p tu O 0 0 1 0 m 1 0 riF lla 1 2 1 1 m S 2 3 2 2 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0 0 0 0 e g 0.5 0.5 0.5 0.5 a W m 1 1 1 1 riF e g 1.5 1.5 1.5 1.5 ra L 2 2 2 2 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0 0 0 0 e g a 0.5 0.5 W 0.5 0.5 m 1 1 riF lla 1.5 1.5 1 1 m S 2 2 1.5 1.5 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t v t m t v t w L L SE L t v t m t k t w SB SB SB Figure A2 Response to a 1 percent negative productivity shock (quarters after shock): Small (cid:133)rm output, large (cid:133)rm wage, and small (cid:133)rm wage. 61

Hiring Subsidies Job Interm. Subsidies Firm Creation Subsidies Wage Subsidies 0 0 0 0 s 0.5 0.5 0.5 0.5 g n in ra 1 1 1 1 E E S 1.5 1.5 1.5 1.5 2 2 2 2 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 1 2 0 0 .lp m 1 0.2 E 0 m 0 0.5 0.4 riF e g 1 1 0.6 ra L 2 2 1 0.8 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 3 2 1.5 1 .lp m 2 1 1 E 0.5 m riF 1 0 0.5 lla 0 1 0 0 m S 1 2 0.5 0.5 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t v t m t v t w L L SE L t v t m t k t w SB SB SB Figure A3 Response to a 1 percent negative productivity shock (quarters after shock): Self employed earnings, large (cid:133)rm employment, and small (cid:133)rm employment. 62

Hiring Subsidies Job Interm. Subsidies Firm Creation Subsidies Wage Subsidies 1 1 2 1 tn e 0.5 1 0.5 m 0 y o lp 0 0 0 m E 1 fle 0.5 1 0.5 S 1 2 2 1 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 0 0 3 0.1 s re n 2 0 w 0.5 0.5 O m 1 0.1 riF 1 1 lla 0 0.2 m S 1.5 1.5 1 0.3 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 .d 10 10 15 10 n e p x 5 10 E 5 5 h c ra 0 5 e S 0 0 la 5 0 tip a 5 10 5 5 C 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t L v t L m t S v E t L w t S v B t S m B t k t S w B Figure A4 Response to a 1 percent negative productivity shock (quarters after shock): Self employment, small (cid:133)rm owners, and capital search expenditures. 63

Hiring Subsidies Job Interm. Subsidies Firm Creation Subsidies Wage Subsidies 4 15 0 0 .b o rP 2 10 1 1 F J m 5 riF e 0 0 2 2 g ra L 2 5 3 3 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 15 10 2 2 .b o rP F 10 5 1 1 J m 5 0 0 riF 0 lla 0 1 1 m S 5 5 2 2 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 10 10 15 10 .b o 5 5 10 5 rP F 0 5 J E 0 0 S 5 0 5 10 5 5 0 10 20 30 0 10 20 30 0 10 20 30 0 10 20 30 Quarters Quarters Quarters Quarters No Policy No Policy No Policy No Policy t v t m t v t w L L SE L t v t m t k t w SB SB SB Figure A5 Response to a 1 percent negative productivity shock (quarters after shock): Job-(cid:133)lling probabilities of large (cid:133)rms, small (cid:133)rms, and self-employed (micro) (cid:133)rms. 64