Self-Employment and Business Cycle Persistence: Does the Composition of Employment Matter for Economic Recoveries? Alan Finkelstein Shapiro∗ Universidad de los Andes
June 27, 2014
Abstract Self-employment comprises an important share of employment in many countries, and tends to expand during downturns through higher inflows from unemployment. Furthermore, countries with higher self-employment shares exhibit lower cyclical output persistence. I build a business cycle model with frictional labor markets where individuals can be self-employed or salaried employed. I show that economies with larger self-employment shares exhibit faster economic recoveries. Differences in the ease of entry into self-employment as the economy recovers explain the contrasting cyclical dynamics. The model successfully captures the cyclical patterns of self-employment and the relationship between self-employment and output persistence in the data. JEL Classification: E02, E24, E32 Keywords: Business cycles, search and matching frictions
∗ Contact information: Calle 19A No. 1-37 Este, Bloque W, Department of Economics, Universidad de los Andes, Bogot´ a, Colombia. Email:
[email protected]. Telephone: (+571) 313-805-9115.
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1
Introduction
Countries are well-known to exhibit differences in employment arrangements. While developed economies have high salaried employment and low self-employment shares, developing economies exhibit the opposite pattern (see Table 1 and Gollin, 2008). Several studies document that a majority of the self-employed are independent workers with no salaried employees, who nonetheless account for an important share of employment, firms, and economic activity (ILO, 2002; Perry et al., 2007; Kucera and Roncolato, 2008). Despite their small scale and limited capital usage, these individuals are often capital-constrained and must rely on external financing from input suppliers and other informal sources (Beck et al., 2008; Global Financial Development Report, 2014). Recent evidence highlights two more facts about self-employment. First, self-employment expands during downturns. Second, this expansion arises mainly from an increase in transitions from unemployment into self-employment in recessions (Table 2; Bosch and Maloney, 2008; Koellinger and Thurik, 2009; Loayza and Rigolini, 2011). Moreover, Figure 1 shows a negative relationship between the cyclical persistence of output and the share of self-employment in non-agricultural employment for a sample of developed and developing countries.1 Combined with the cyclical behavior of self-employment, this fact suggests that self-employment may play an important role for business cycle dynamics. I build a business cycle model with frictional labor markets and endogenous entry into self-employment where unemployed individuals can transition into salaried work or into self-employment. I use the model to shed light on the channels through which the composition of employment influences the pace of economic recoveries, and show that economies with higher self-employment shares exhibit faster recoveries from adverse aggregate shocks. This result hinges critically on whether self-employment is a feasible alternative to salaried work during downturns, and on the way the cyclical composition of employment affects this outside option to salaried employment as the economy recovers. The average share of self-employment in the economy plays a key role as it affects the strength of the self-employment outside option and the cyclical adjustment of wages in the salaried sector. This influences the hiring and investment decisions of salaried firms in response to shocks, which in turn shape short-run economic activity. This channel has not been previously explored. In the model, self-employment consists of own-account or independent workers who operate owner-only firms.2 Given my focus on cross-country differences in business cycles, I abstract from the determinants of 1
This link remains significant even after controlling for other factors that may affect output persistence. See the Appendix for details. This finding is in line with Calder´on and Fuentes (2010) regarding the recovery speed in emerging market economies. 2 Self-employment exhibits substantial heterogeneity, with a small share of individuals running businesses that
2
Table 1: Cyclical Correlations of Employment and Job-Finding Rates with Output Cyclical Correlation with Output: Self-Employment Formal Salaried Employment
Brazil -0.219 0.616
Mexico -0.415 0.780
Transition Rate from Unemployment to: Self-Employment Formal Salaried Employment
-0.600 0.652
-0.433 0.798
Notes: Taken directly from Bosch and Maloney (2008). Self-employment corresponds to informal self-employment (ownaccount workers and business owners with less than 5 employees) as a share of the working-age population. All series are quarterly, logged and HP-filtered with smoothing parameter 1600. Entry into informal (unprotected) salaried employment from unemployment is procyclical and therefore similar to formal salaried employment.
Figure 1: Self-Employment and Cyclical Output Persistence Across Countries 0.8
Linear Trend Developed Countries Developing Countries
Autocorrelation of Output
0.7
0.6
0.5
0.4
0.3
0.2 0
20
40 60 80 Self−Employment (% of Non−Agricultural Employment)
Notes: Author’s calculations. The self-employment share corresponds to the average of annual self-employment as a percent of non-agricultural employment from 2000 to 2007. The autocorrelation of output corresponds to the first-order autocorrelation of the cyclical component of log annual PPP-adjusted real GDP from 1985 to 2007, using an HP filter with smoothing parameter 100. Sources: OECD (2009) (self-employment) and World Development Indicators (2010) from Panizza and Saade (2010) (real PPP-adjusted GDP). A stronger relationship holds if we consider non-agricultural real PPP-adjusted GDP. Similar results hold if we exclude potential outliers (i.e., countries with self-employment shares higher than 80 percent, or countries with very low persistence.
start small but grow rapidly (often labeled opportunity self-employment). I explicitly abstract from opportunity self-employment and instead focus on those with businesses without salaried workers (which represent the majority of the self-employed) to explore whether the presence of an alternative to salaried employment matters for business cycle dynamics. See Epstein and Finkelstein Shapiro (2014) for an expansion of the model in this paper where
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entry into self-employment over the life-cycle (age, experience, wealth) as these tend to be similar across the development spectrum and do not necessarily apply to the analysis of cross-country cyclical dynamics. Frictions in obtaining capital are an important obstacle for small-firm creation (Blanchflower, 2004). Micro and small firms – a majority of which are owner-only – tend to be more credit constrained and consider access to credit as a major obstacle (Kantis et al., 2002; IDB, 2005a). Moreover, poor institutional quality – more prevalent in developing countries – worsens access to formal credit and pushes young, small firms to tap into informal financing sources (McMillan and Woodruff, 1999).3 Regardless of the economy’s level of development, small firms tend to rely more on credit from input suppliers (relationshipbased trade credit), friends and family, and informal lenders (Chavis, Klapper, and Love, 2011).4 In fact, input suppliers are one of the most important sources of external financing and working capital among small nascent firms in Latin America and Asia (Demirg¨ u¸c-Kunt and Maksimovic, 2001; IDB, 2005b; Beck, Demirg¨ u¸c-Kunt, and Maksimovic, 2008).5 Motivated by these facts, as well as the relationship nature of supplier credit, I use capital matching frictions to model the obstacles that afflict the creation of self-employment ventures. In particular, I assume that households spend resources to search for input credit relationships, where the latter are necessary to successfully send household members to self-employment. Importantly, the expenditures to start self-employment ventures are financed with internal resources, consistent with the data. Salaried firms act as capital suppliers by devoting part of their capital as input credit to self-employed firms through frictional capital markets. This setup has several desirable features: self-employment entry is frictional and depends on the availability of capital (embodied in capital market tightness) and, more indirectly, on labor market conditions; the model establishes a natural link between capital and labor markets; it generates higher idle capital during downturns and countercyclical capital renting (Gal and Pinter, 2013); and it replicates the countercyclicality of both transitions from unemployment into self-employment and the stock of self-employment in the data. Additionally, the model generates a relationship between the self-employment level and output consistent with the stylized facts. Finally, countercyclical entry into self-employed firms can endogenously become small salaried firms. 3 Furthermore, a deficient institutional environment makes credit based on goods – in-kind or input credit – more prevalent than cash-based credit (see Burkart and Ellingsen, 2004). Even in the U.S., many small firms lease a substantial amount of their capital from other firms (Eisfeldt and Rampini, 2009). As Chavis, Klapper, and Love (2011) point out, leasing is different from trade credit since the former is typically backed by assets, and hence more prevalent in developed economies. However, both leasing and input credit involve establishing a (long-term) relationship with input suppliers. 4 I use the terms trade, input, interfirm and supplier credit interchangeably. For more on the extent of interfirm credit in developed and developing countries, see Brown, Chavis, and Klapper (2011) and Kuntchev et al. (2012). 5 See Figure 2.7 in IDB (2005b), where suppliers and the purchase of used equipment (which is often provided by other firms) dominate as external sources of initial external financing.
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self-employment is difficult to rationalize in existing business cycle models that use collateral constraints or a financial accelerator to account for capital constraints.6 I offer a way to reconcile the countercyclical transitions from unemployment into self-employment in the data while accounting for the importance of capital constraints among small nascent firms. In the model, differences in the cyclical behavior of the self-employment option – which trace back to the average level of self-employment and hence the composition of employment in the economy – affect wage adjustments and the incentives to hire and invest in the salaried sector, which in turn drive the recovery process of aggregate output. In particular, in response to a negative aggregate productivity shock, salaried vacancies and the job-finding rate among salaried firms fall. This reduces salaried-firm capital usage, which increases the availability of capital for self-employment ventures (input credit).7 This raises the likelihood of entering self-employment, even as households increase expenditures on capital search during the downturn. In economies with higher average self-employment, the self-employment outside option exerts more influence on labor market conditions, such that the improvement of this outside option at the onset of the recession slows down the initial downward adjustment in salaried wages, thereby causing a larger initial reduction in the contemporaneous value of having salaried workers. Salaried firms respond by reducing vacancies and the share of capital used in the sector by more, causing a larger initial contraction in investment and salaried output. The fall in salaried vacancies and increase in capital availability for the self-employed leads to an expansion in self-employment and a contraction in salaried employment, or more generally, a change in the cyclical composition of total employment. As aggregate productivity slowly returns to trend, salaried firms adjust their capital usage upwards more drastically relative to economies with less self-employment to take advantage of the recovery in aggregate productivity, which curtails the initial increase in the availability of capital to the self-employed more rapidly. This makes the initial increase in the likelihood of entry into self-employment less persistent in economies with higher average self-employment, and continues to modify the cyclical composition 6
For example, collateral constraints become tighter during recessions, thereby preventing individuals from obtaining the necessary resources to successfully launch their self-employment ventures. This might be even more relevant when individuals are in unemployment since adequate collateral is likely to be scarcer. Similarly, in a financial accelerator model (Bernanke, Gertler, and Gilchrist, 1999), net worth decreases during downturns and leads to a higher cost for borrowed funds. If these funds are needed to become self-employed, then transitions into self-employment would be procyclical. For a model that incorporates a financial accelerator and also generates countercyclical self-employment entry, see Finkelstein Shapiro and Gonz´alez (2014). 7 Ramey (1992) suggests that trade credit is countercyclical in the U.S. Love, Preve, and Sarria-Allende (2007) find that trade credit provision to firms increases after financial crises. Klapper and Randall (2011) document that a non-negligible fraction of firms in Eastern European countries extended supplier credit to other firms during the 2008-2009 financial crisis. Finally, input credit is often used to manage inventories (Mateut, Mizen, and Ziane, 2011). Thus, during periods of low sales, firms may have an incentive use input credit to manage the cost of holding inventories. For other reasons behind the use of trade credit, see Cu˜ nat and Garcia-Appendini (2012).
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of total employment as the shock subsides. Since the initial increase in the probability of moving into self-employment in these economies is more short-lived, and self-employment has a larger presence in these economies, the upward adjustment in salaried wages that would otherwise occur after the shock is slower. This occurs because the deterioration in the self-employment outside option in the period after the shock puts downward pressure on salaried sector wages, much more so in economies with higher average self-employment. This initial rigidity in wage adjustments, coupled with the recovery in the marginal product of labor as aggregate productivity returns to trend, makes the contemporaneous value of having a salaried worker larger in subsequent periods. In turn, this leads to faster hiring and investment in the salaried sector. The faster recovery in salaried employment and investment boosts salaried sector output and ultimately translates into a faster recovery in total output. The general mechanism in the model, whereby changes in the composition of employment affect the cyclical adjustment of wages (and hence the recovery in employment and output), is in line with existing (albeit limited) evidence on the determinants of wage dynamics across economies. Furthermore, the model can broadly capture the empirical relationship between output persistence and self-employment in the data, which gives additional validity to the framework in this paper. Finally, while these results suggest that economies with larger self-employment shares recover faster, they also exhibit higher labor market and aggregate volatility. This points to an important tradeoff from having an economy with more self-employment. Coupled with the fact that these economies also exhibit lower consumption, employment, earnings, and output levels, the benefits from having faster recoveries in this context are not clear-cut. Previous studies have introduced self-employment into labor search models. Some of these include Rissman (2003, 2007), Hobijn and S ¸ ahin (2007), Kumar and Schuetze (2007). However, all of these abstract from capital constraints in self-employment, general equilibrium effects, and business cycles. Den Haan, Ramey and Watson (2003), Wasmer and Weil (2004), Nicoletti and Pierrard (2006), and Kurmann and Petrosky-Nadeau (2007) explore the role of capital search in the propagation of aggregate shocks.8 In contrast to their work, I focus on the behavior of own-account work and its influence on labor market and aggregate dynamics. Also, my framework yields a countercyclical probability of finding capital to enter self-employment, which is important to match the labor market facts about self-employment, as well as the cyclical differences in macro aggregates that arise from differences in the share of self-employment in the economy. More importantly, the business cycle labor search literature has placed little attention on the 8
See Arseneau et al. (2008) for an optimal policy application with capital search. Wasmer and Weil (2004) combine capital and labor search and matching to explore the link between capital and labor markets and its impact on aggregate fluctuations. My paper combines these frictions as well, but my focus is different since I introduce different employment states and study the business cycle implications of differences in the composition of employment across economies.
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role of self-employment in business cycle dynamics. Similarly, the theoretical literature on cyclical labor flows in developing countries has generally abstracted from incorporating self-employment. This paper makes a contribution by offering a tractable way to reconcile the cyclical dynamics of self-employment flows with the presence of capital constraints, and by showing that cyclical fluctuations in self-employment entry can have important implications for labor market and business cycle dynamics depending on the economy’s employment structure. More generally, the model in this paper is more in line with the labor market structure in developing countries, and can be easily incorporated into existing models for emerging economies to study a range of short-term and long-term issues relevant to these countries. The rest of the paper is organized as follows. Section 2 presents the model. Section 3 describes the calibration of the model, Section 4 discusses the simulation results, and Section 6 concludes.
2
The Model
The economy is comprised of households, which self-employed firms belong to, and salaried firms. A representative household of measure one with a large number of members spends resources to find available capital for self-employment ventures. There are three employment states – salaried employment, selfemployment, and unemployment – and no job-to-job transitions.9 There is perfect-risk pooling across household members. Salaried firms hire workers in frictional labor markets and accumulate capital to produce. They also choose the fraction of accumulated capital that is used in production within the firm. The remaining fraction is devoted to matching with the self-employed. I label this capital as input or supplier credit.10 A matching function brings together the supply of capital from salaried firms and the resources spent on capital search by households, and determines the creation of active self-employment ventures. Given the presence of matching frictions, a portion of the capital remains idle and becomes part of the salaried firms’ capital stock next period.11 Once a capital match materializes, salaried firms rent the matched capital – determined via Nash bargaining – to the self-employed while retaining full ownership 9
Direct transitions between salaried employment and self-employment are non-negligible (Bosch and Maloney, 2008). However, the countercyclicality of self-employment arises mainly from transitions from unemployment into self-employment, and not from job-to-job transitions. 10 One way to rationalize this is to consider that, given aggregate economic conditions, firms decide to use only a fraction of their accumulated capital in production. In my framework, firms can allocate that unused capital to potential self-employment ventures instead of simply keeping that unused capital idle, which will get carried into next period’s capital stock. If we take a broad definition of inventories that encompasses unused inputs which can readily be transformed into output (and hence consider unused, unmatched capital as part of firms’ inventories), the model is consistent with Mateut et al.’s (2011) evidence on the use of input credit to manage inventories. 11 As argued in Cooley, Hansen, and Prescott (1995) and Hansen and Prescott (2005), the presence of idle capital (and other resources) at any given point in time is commonly observed in many actual economies. Here, idle capital arises due to matching frictions (similar to Kurmann and Petrosky-Nadeau, 2007).
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during the length of the match. Each self-employed individual requires a single unit of matched capital to produce. Importantly, this implies that the measure of capital in self-employment is also the measure of self-employment. The matched unit of capital is combined with a normalized unit of the individual’s inelastically-supplied labor and a stochastic production technology to yield output of a self-employed firm. Salaried and self-employed firms produce identical goods. The timing of events is as follows. At the beginning of the period, stochastic productivity is realized. Exogenous separations in all employment states take place and unemployment is determined. Salaried firms recover the capital separated at the beginning of the period and cover the depreciation of capital in surviving capital relationships. Firms post salaried vacancies, choose the fraction of the capital stock used inside the firm, and choose investment. They also choose next period’s desired salaried employment and self-employment capital. At the same time, households spend resources to search for capital and decide on next period’s desired self-employment. Matching in labor and capital markets takes place, and Nash bargaining determines wages and rental rates. Production takes place, workers receive wage payments, and the self-employed pay the rental rate to firms.
2.1
Households and the Self-Employed
Household utility only depends on an aggregate consumption good whose price is normalized to one. The household’s problem is to choose sequences of consumption ct , self-employment capital nhSE,t+1 , and resources spent on capital search vSE,t to maximize ∞ X E0 β t [u(ct )] ,
(1)
ct + κ (vSE,t ) + Tt = (zt aSE,t − rSE,t)nhSE,t + wS,t nS,t + ΠS,t + but ,
(2)
t=0
subject to
and the perceived law of motion for self-employment capital nhSE,t+1 = (1 − δSE )(nhSE,t + vSE,tp(θSE,t)),
(3) ′
where κ (vSE,t ) is the total cost of searching for capital for new self-employed firms, κ (vSE,t ) > 0 and ′′
κ (vSE,t ) ≥ 0. b represents unemployment benefits and Tt are lump-sum taxes. As in standard models without a participation margin, the household has no choice over the desired measure of salaried workers, but there is a perceived law of motion in the background. Total production by self-employed firms is
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ySE,t = zt aSE,tnhSE,t, where nhSE,t is the measure of self-employment (or self-employment capital), zt is an aggregate productivity shock, and aSE,t is a sectoral productivity shock. The shock aSE,t captures the additional volatility inherent to the self-employment sector (Maloney, Cunningham, and Bosch, 2004), and generates higher volatility in self-employment earnings relative to wage earnings, as in the data (Hamilton, 2000, and others). Both zt and aSE,t follow independent stochastic processes. Individual self-employment earnings are given by (zt aSE,t − rSE,t), where rSE,t is the Nash capital rental rate. wS,t , nS,t , and ΠS,t are the salaried sector wage, salaried employment, and salaried firm profits, respectively. I define p(θSE,t) = mSE (vSE,t ,(1−ωt )kS,t ) . vSE,t
An unemployed individual’s probability of finding a capital supplier is defined as v u u vSE,t p(θSE,t), where vSE,t = SE,t . The matching function m(vSE,t, (1 − ωt )kS,t ) is constant-returnsut to-scale and takes the household’s total amount of resources devoted to capital search, vSE,t, and capital supply from salaried firms, (1 − ωt )kS,t , as inputs. Capital market tightness is defined as θSE,t ≡
vSE,t (1−ωt )kS,t .
A higher θSE,t implies a tighter capital market and corresponds to households finding it more difficult to match with a capital supplier, so p(θSE,t) is a decreasing function of capital market tightness. The total employed labor force is nt = nS,t + nSE,t. Normalizing the labor force to one, unemployment is ut = 1− nt . Combining first-order conditions yields an optimal decision to enter self-employment: u (c ) z a t+1 SE,t+1 c t+1 SE = (1 − δ )Et β . κ′ (vSE,t+1 ) uc (ct ) p(θSE,t) −rSE,t+1 + p(θSE,t+1 )
κ′ (vSE,t )
(4)
where uc (ct ) is the marginal utility of consumption. The left-hand side represents the expected marginal cost of searching for available capital. The right-hand side is the household’s expected marginal benefit of a capital match. The latter includes individual self-employment profits zaSE − rSE and the continuation value of the capital relationship next period. For future reference, the stochastic discount factor is defined (ct ) as Ξt|0 = β t uucc(c . 0)
2.2
Salaried Production
The representative salaried firm produces yS,t = zt aS f (nS,t, ωt kS,t ) where f (nS,t, ωt kS,t ) is a constantreturns-to-scale production function. nS is salaried labor, kS is physical capital, ω is the share of capital used in production, and aS is a parameter meant to capture the quality of the institutional environment in the economy. Varying this parameter will affect the steady-state composition of employment in the economy.12 The remaining capital (1 − ωt )kS,t is available for matching with the self-employed. Since 12
This is a natural parameter to vary since the institutional setting of a country affects mainly the salaried sector (Akyol and Athreya, 2009; Fiess et al., 2010).
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I assume a representative firm, a higher ωt can be interpreted in two ways: firms keep more capital inhouse, or the salaried sector keeps more capital within the sector (which can be interpreted as salaried firms selling capital to other salaried firms in frictionless markets). Firms choose sequences of salaried vacancies vS,t , desired salaried employment nS,t+1 , capital kS,t+1 , the fraction of capital used in production ωt , and desired capital in self-employment nfSE,t+1 to maximize
E0
∞ X t=0
zt aS f (nS,t, ωt kS,t ) − wS,t nS,t Ξt|0 , −ψ v − i + r nf S S,t
t
(5)
SE,t SE,t
subject to the firm’s perceived law of motion for salaried employment
nS,t+1 = (1 − δS )(nS,t + vS,t q(θS,t )),
(6)
the firm’s perceived law of motion for self-employment capital nfSE,t+1 = (1 − δSE )(nfSE,t + (1 − ωt )kS,t q(θSE,t)),
(7)
and the evolution of the firm’s capital13 kS,t+1 = it + (1 − δ)ωt kS,t + (δSE − δ)nfSE,t + (1 − δ)(1 − ωt )kS,t − (1 − δSE )(1 − ωt )kS,t q(θSE,t) .
(8)
The term ψS vS,t is the total cost of posting salaried vacancies.14 The salaried job-filling probability is q(θS,t) =
mS (ut ,vS,t ) , vS,t
where mS (vS,t , ut ) is a constant-returns-to-scale matching function for salaried
employment, and δS is the separation rate for salaried workers. The probability of finding a potential m
(v
,(1−ω )k
)
t S,t SE,t self-employed individual is q(θSE,t) = SE (1−ω , where q(θSE,t) is increasing in θSE,t. Idle, t )kS,t unmatched capital (1 − δ) − (1 − δSE )q(θSE,t ) (1 − ωt )kS,t stays within the firm after matching takes
place, where δ is the capital depreciation rate. Similar to Kurmann and Petrosky-Nadeau (2007), the firm considers unmatched capital as part of capital accumulation. The term δnfSE,t is an expense for the firm
since capital in self-employment depreciates each period and for simplicity firms cover that depreciation. Also, δSE nfSE,t is returned to the firm after separations take place. Combining first-order conditions yields 13
Combining the law of motion for capital held by the firm and the law of motion for capital in self-employment yields a standard law of motion for total capital in the economy. 14 Introducing an explicit cost of supplying capital to the self-employed does not change the main results of the paper.
10
a standard salaried job creation condition: a f (n , ω k ) z ψS t+1 S nS S,t+1 t+1 S,t+1 = (1 − δS )Et Ξt+1|t , q(θS,t ) −w + ψS S,t+1
(9)
q(θS,t+1 )
a standard Euler equation capital kS :
1 = Et Ξt+1|t {zt+1 aS fωkS (nS,t+1 , ωt+1 kS,t+1 ) + (1 − δ)} ,
(10)
and a condition that determines capital supply (input credit) to the self-employed:
(1 − δSE )Et Ξt+1|t
zt aS fωkS (nS,t, ωt kS,t ) + (1 − δSE )q(θSE,t) = q(θSE,t) rSE,t+1 + (δSE − δ) . + [zt+1 aS fωkS (nS,t+1 ,ωt+1kS,t+1 )+(1−δSE )q(θSE,t+1)] q(θSE,t+1 )
(11)
The job creation condition and its interpretation are standard. The capital Euler equation does not change relative to standard models despite the presence of the capital allocation margin in the firm’s problem. The capital supply condition is new. Its left-hand side captures the expected marginal cost of supplying an additional unit of capital to self-employed firms. This cost includes the opportunity cost of devoting a unit of capital to matching, zt aS fωkS (n S,t , ωt kS,t ), which is the marginal product of capital within salaried firms. Importantly, given the standard properties of the production function, salaried firms will never devote all of their capital to matching, despite the behavior of the Nash rental rate paid to the firms by the self-employed. The second term captures the fact that if capital is matched today with probability q(θSE,t) and survives with probability (1 − δSE ), the firm must set aside that capital and cannot count it as part of idle capital (after matching) within the firm. The right-hand side is the expected marginal benefit of a matched unit of capital, given by the Nash rental rate net of the depreciation of capital δ, which the firm covers for surviving relationships. Also, the firm takes into account that each period a match ends with probability δSE , in which case the firm gets back the unit of capital. The last term on the right-hand side reflects the continuation value of the capital relationship. As previously described, the expected cost of supplying capital to the self-employed depends on the marginal product of capital within the firm since the firm faces a tradeoff between trying to match capital and using it in-house. This tradeoff ultimately affects labor market conditions in self-employment. These are two key distinctions relative to other models with capital search.
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2.3
Value Functions and Nash Bargaining
Household Value Functions
The value functions of a salaried worker currently employed at a firm,
WS,t , a self-employed individual currently matched with a capital supplier, WSE,t, and an unemployed individual, WU,t , are given by WS,t = wS,t + Et Ξt+1|t (1 − δS )WS,t+1 + δS WU,t+1 ,
and
(12)
WSE,t = (zt aSE,t − rSE,t ) + Et Ξt+1|t (1 − δSE )WSE,t+1 + δSE WU,t+1 ,
WU,t
(1 − δS )p(θS,t )WS,t+1 +(1 − δSE )v u p(θSE,t)WSE,t+1 SE,t = b + Et Ξt+1|t +[1 − (1 − δS )p(θS,t ) u −(1 − δSE )vSE,t p(θSE,t)]WU,t+1
,
(13)
(14)
Firm Value Functions The value to a salaried firm from having an additional salaried worker, JS,t , and the value from renting a unit of capital to a self-employed individual, JSE,t, are JS,t = zt aS fnS (nS,t, ωt kS,t ) − wS,t + Et Ξt+1|t (1 − δS )JS,t+1 , JSE,t = rSE,t + (δSE − δ) + Et Ξt+1|t (1 − δSE )JSE,t+1 ,
(15) (16)
Firms must cover the depreciation of the matched unit of capital, δ, but gain a unit of previously matched capital if it separates with probability δSE , which yields the term (δSE − δ) in JSE,t. I define the value of having unused, idle capital as Juk ,t = (1 − δ). Wage and Rental Rate Determination
Real wages for salaried workers and the self-employment
capital rental rate are determined via Nash bargaining. The net surplus from having a member in salaried employment is (WS,t − WU,t ) . The net surplus from having a member in self-employment is (WSE,t − WU,t ) . Then, the Nash bargaining problems for wS,t and rSE,t are max (WS,t − WU,t )νS (JS,t )1−νS , wS,t
n o max (WSE,t − WU,t )νSE (JSE,t − Juk ,t )1−νSE , rSE,t
12
(17)
(18)
where νS and νSE are the worker and the self-employed’s respective bargaining powers, and the threat point for salaried firms is the value of unmatched, idle capital Juk ,t . The Nash bargaining solutions for the wage and the rental rate can be shown to be15 wS,t = νS [zt aS fnS (nS,t , ωt kS,t ) + ψS θS,t ] + (1 − νS )b
+
+
(19)
zt aS fωkS (nS,t , ωt kS,t ) (1 − νS )νSE u vSE,t p(θSE,t) 1 − νSE q(θSE,t) (1 − νS )νSE u vSE,t p(θSE,t)(1 − δSE ) 1 − Et Ξt+1|t (1 − δ) , 1 − νSE
and rSE,t
νS = (1 − νSE ) zt aSE,t − ψS θS,t − b 1 − νS
u p(θSE,t) − νSE vSE,t
zt aS fωkS (nS,t , ωt kS,t ) q(θSE,t)
(20)
u + νSE (1 − vSE,t p(θSE,t))(1 − δSE ) 1 − Et Ξt+1|t (1 − δ) . Note that the wage and rental rate depend on both capital and labor market tightness. Intuitively, in a model with search frictions and two types of employment, the prices of factors of production will depend on the marginal product of each of the factors and on the potential opportunities in other employment states (i.e. the outside options), which are embodied in market tightness in each of the employment states. Intuition Behind the Wage and Rental Rate Equations The wage equation in a standard onesector search model without self-employment is a function of the marginal product of labor, labor market tightness, and the value of unemployment. In this model, market tightness in the capital market (i.e., the self-employment outside option) is an additional component of the wage. Consider the second line of the wage equation. The first term inside the brackets is the foregone marginal product of capital inside the firm. The second element captures the fact that firms participating in the capital matching process must set aside (1 − δSE ) units of capital in the current period for those new matches that become productive next period, and must cover depreciation costs for matched capital. This second term is also 15
The Appendix describes the derivation of the wage and rental rate equations.
13
part of the opportunity cost of successfully matching capital. This cost is (1 − δSE ) 1 − Et Ξt+1|t (1 − δ)
since firms net out the depreciation of capital from the total opportunity cost of storing the capital today until it becomes productive next period. Using the fact that
p(θSE,t ) q(θSE,t )
=
1 θSE,t ,
note that an increase in
capital market tightness θSE,t ceteris paribus decreases the expected cost to the firm of devoting capital to matching but also reduces an unemployed individual’s probability of entering self-employment.16 This implies that an increase in θSE,t reduces the salaried sector wage since the worker’s outside option of going into self-employment is now weaker. We can do a similar analysis with the capital rental rate and summarize the results as follows: wS,t = ΘS,t(mplS , θS , θSE , mpkS ), (+)
(+) (−)
rSE,t = ΘSE,t( z , θS , θSE , mpkS ) (+) (−) (+)
(+)
(21)
(−)
where mplS and mpkS denote the marginal product of labor and capital, respectively. Lower capital market tightness θSE,t puts upward pressure on wS,t since the self-employment option becomes a more accessible employment alternative. Also, as shown below, wS,t and rSE,t are more sensitive to fluctuations in θSE,t in economies with higher steady-state self-employment.
2.4
Government, Total Output, and Resource Constraint
The government levies lump-sum taxes to finance unemployment benefits, so its budget constraint is Tt = but . Total output yt is given by the sum of salaried output and self-employment output, yt = yS,t + ySE,t. In the model, yt represents observed output in the data.17 The economy’s resource constraint is given by yt = ct + it + ψS vS,t + κ(vSE,t )
(22)
4.5 Competitive Equilibrium Definition (Competitive Equilibrium) Taking the exogenous processes {zt , aSE,t} as given, the statecontingent endogenous processes {ct , kS,t , nSE,t , nS,t , ωt , θS,t , θSE,t } and {ut , yt , wS,t , rSE,t } satisfy: the law of motion for capital used in self-employment (or simply self-employment), the definition of unemployment, 16
An increase in capital market tightness also has implications for the marginal product of capital used inside the salaried firm if tightness changes due to the supply of capital. Thus, the impact of a change in capital tightness is more complex than what the above description suggests. For the purposes of developing intuition, it proves useful to see how changes in capital tightness due to capital search expenditures, holding everything else constant, would affect each of the prices. 17 Most countries follow United Nations guidelines and incorporate estimates of output from the informal sector, which most of the self-employed belong to, into their national income accounts (United Nations, 2008). The main results of the paper hold even if we consider that observed output is output from salaried firms only.
14
the self-employed’s demand for capital (i.e., the decision to enter self-employment), the law of motion for salaried employment, the salaried firms’ salaried job creation condition, the Euler equation for capital, the salaried firms’ capital supply condition, the Nash wage and the Nash rental rate equations, the definition of total output, and the economy’s resource constraint.
3
Calibration and Solution Method
I choose Mexico as a benchmark because of its sizeable self-employment share and its household and firm surveys, which give a detailed overview of self-employment. In addition, Bosch and Maloney (2008) have documented the cyclical dynamics of employment in Mexico and their work offers readily available parameter values and calibration targets. I log-linearize the model around the non-stochastic steady state and compute a first-order approximation of the equilibrium conditions.
3.1
18
Functional Forms and Stochastic Processes
The salaried production function is Cobb-Douglas, f (nS,t , ωt kS,t ) = (nS,t )1−αS (ωt kS,t )αS , with 0 < αS < 1. Aggregate productivity zt and self-employment productivity aSE,t follow independent AR(1) processes: ln zt = ρz ln zt−1 + εzt ,
ln aSE,t = ρSE ln aSE,t−1 + εSE t ,
(23)
iid
where εjt ∼ N (0, σj ), ρj < 1, j = z, SE. The total cost of searching for capital is κ (vSE,t) = ψSE (vSE,t )ηSE with ψSE > 0 and ηSE ≥ 1. The matching functions for salaried employment and self-employment 1−ξ capital are Cobb-Douglas, so mS (ut , vS,t ) = MS uξt vS,t , 0 < ξ < 1, and mSE ((1 − ωt )kS,t , vSE,t ) =
MSE ((1 − ωt )kS,t )ξSE (vSE,t )1−ξSE , 0 < ξSE < 1, where Mj is the matching efficiency parameter for j = S, SE.
3.2
Parametrization and Calibration Targets
Parameters Taken from Existing Literature The time period is a quarter. The capital share in the firm’s production function is αS = 0.32, the discount factor β is 0.985, and the capital depreciation rate is 0.025, all standard values in the literature. I set the salaried separation rate as a combination of the formal and informal salaried separation rates documented for Mexico in Bosch and Maloney (2008), where 18
I simulate the economy for 2100 periods, drop the first 100 periods, and use the Hodrick-Prescott (HP) filter with smoothing parameter 1600 to filter the simulated data, extract the cyclical component and compute second moments. I use Dynare for all dynamic simulations.
15
the weights are given by each salaried type’s contribution to total salaried employment.19 The curvature of the capital search cost follows from Krause and Lubik (2010).20 Since Mexico does not have a national unemployment insurance scheme, I set b = 0. Table 2: Parametrization: Benchmark Economy Parameter αS β δ δS δSE ηSE b νS νSE ξ ξSE ρz aS
Value 0.32 0.985 0.025 0.06 0.02 1.10 0 0.50 0.50 0.50 0.50 0.92 0.60
Parameter Description Salaried Capital Share Discount Factor Capital Depreciation Rate Salaried Separation Rate SE Separation Rate Curvature, Search Cost Unemployment Insurance Salaried Bargaining Power SE Bargaining Power Matching Elasticity, Labor Matching Elasticity, Capital Autocorrelation of TFP Institutional Quality
Parameter Source DSGE Lit. DSGE Lit. DSGE Lit. Bosch, Maloney (2008) Bosch, Maloney (2008) Search Lit. No Unempl. Benefits Search Lit. Search Lit. Search Lit. Search Lit. DSGE Lit. Benchmark Assumption
The bargaining power parameters and elasticities of the matching functions are νS = νSE = 0.50 and ξ = ξSE = 0.50, respectively, consistent with the labor search literature.
21
I set the persistence
parameter for zt to 0.92. Finally, variations in aS allow me to generate sizeable changes in steady-state self-employment, ranging from 6 percent to 79 percent of the labor force. I treat this parameter as a proxy for institutional quality, and fix its value to 0.60 in the benchmark economy. This allows me to obtain the range of self-employment in the data while keeping the share of capital used in salaried production, ω, bounded below one for low levels of self-employment. Importantly, even with the benchmark value for aS , labor productivity is higher in the salaried sector relative to the self-employment sector, consistent with the evidence. Calibrated Parameters The remaining parameters are jointly calibrated by solving for the nonstochastic steady state and simulating the model. I choose the matching efficiency parameters Mj , for j = S, SE to match the average shares of salaried employment and self-employment in the labor force for 19 The conclusions remain intact if I make a distinction between formal and informal salaried employment in the model. 20 The results are robust to changes in the convexity of the search cost. 21 The main conclusions of the paper do not change with alternative values that introduce an asymmetry between salaried and self-employment, or that allow for a deviation from the Hosios condition.
16
Mexico, obtained from Mexico’s National Survey on Urban Employment.22 The vacancy posting cost for salaried positions ψS is set to 3.5 percent of wages (Levy, 2007). The capital search cost parameter ψSE is equivalent to three months of wages (McKenzie and Woodruff, 2006).23 I calibrate the persistence of self-employment productivity, the volatility of the self-employment productivity shock, and the volatility of the aggregate productivity shock to match the cyclical correlation between output and investment, the cyclical correlation between output and consumption, and the volatility of output in the data.24 Table 3: Calibrated Parameters and Targets: Benchmark Economy Parameter MS MSE ψS ψSE ρSE σSE σz
4
Value 0.217 0.021 0.028 0.807 0.68 0.022 0.0155
Parameter Description Salaried Matching Efficiency SE Matching Efficiency Formal Vacancy Cost Project Posting Cost Autocorr. SE Prod. SD SE Productivity Shock SD Aggregate TFP Shock
Target nS = 0.72 nSE = 0.23 3.5 percent of wages 3 months of wages ρ(inv, y) = 0.939 ρ(c, y) = 0.943 σy = 2.39
Simulation Results
First, the third column of Table 4 shows the moments generated by the benchmark model.25 The fourth column shows the same moments generated by a version of the model with endogenous self-employment entry but no capital search frictions calibrated using the same first and second-moment targets as the benchmark model.26 The fifth column shows the results from this last model instead using the same parameter values for the self-employment productivity process as the benchmark model. The benchmark model is able to qualitatively capture the negative cyclical correlations between output 22
The employment survey, ENEU, covers periods 1987Q1 through 2004Q4, when it was replaced by the ENOE. Using higher vacancy posting costs that incorporate the cost of hiring regulations or a much lower target for ψSE does not change the results. 24 To obtain these moments, I use Mexican data on real consumption, investment and output from 1993Q1 to 2007Q4, obtained from the Federal Reserve Bank of Saint Louis’ FRED database. 25 The non-targeted moments for the labor market in the second column are documented in Fern´andez and Meza (2013) (cyclicality of self-employment), Boz, Durdu, and Li (2013) (relative volatility of wages), and Bosch and Maloney (2008) (remaining second moments). 26 In this model, households spend resources to send unemployed individuals to self-employment, but a capital supplier is not needed to enter self-employment. To have a comparable framework, resources spent today allow unemployed individuals to become self-employed tomorrow. Also, in order to produce, each individual in selfemployment rents a unit of capital from salaried firms through frictionless capital markets. Similar results are obtained if I abstract from capital renting and simply assume that the self-employed access a stochastic production technology without having to use additional inputs. 23
17
and self-employment, output and unemployment, as well as the countercyclicality of transitions from unemployment into self-employment in the data (see Table 1).27 In contrast, a model without capital search frictions that is calibrated to match the same targets as the benchmark model fails along all these margins and generates counterfactual labor market dynamics.28 Using the same parameter values for the self-employment productivity process as the benchmark model does improve the behavior of unemployment and salaried employment, but still yields a very low negative cyclical correlation for self-employment relative to the data (and a higher cyclical correlation of investment with output). Table 4: Benchmark Economy vs. Model with Endogenous Transitions Into Self-Employment and No Capital Frictions Targeted Moments ρinvt ,yt ρct ,yt σy Non-Targeted Moments ρnSE,t,yt ρnS,t ,yt ρut ,yt ρp(θS,t ),yt ρp(θSE,t),yt ρvSE,t p(θSE,t ),yt σc /σy σinv /σy σu /σy σwS /σy
Data 0.939 0.943 2.39
Benchmark Model 0.939 0.934 2.39
No Capital Frictions 0.938 0.939 2.39
No Capital Frictions ρSE = 0.68, σSE = 0.022 0.987 0.929 2.39
−0.45 − −0.887 − − −0.433 1.13 2.78 6.28 2.22
−0.633 0.807 −0.717 0.819 −0.903 −0.600 0.231 6.955 0.818 0.737
0.045 −0.116 0.049 −0.156 − − 0.339 4.159 2.518 1.066
−0.060 0.787 −0.667 0.862 − − 0.323 4.382 0.510 0.903
For the main experiments, changes in the steady-state share of self-employment across simulations are engineered by varying the salaried sector productivity parameter aS . I interpret changes in this parameter very broadly as differences in institutional quality, which have been shown to be important for cross-country differences in self-employment rates (Loayza and Rigolini, 2011).29 27
Also, investment is more volatile than output. While the relative volatility of consumption is smaller than one, the model abstracts from interest rate shocks, which can help generate higher consumption volatility common in developing countries (Boz, Durdu, and Li, 2013, and others). Finally, similar to most of the labor search literature, the model cannot generate a relative unemployment volatility higher than one. 28 This alternative model does deliver higher unemployment volatility and lower investment volatility relative to the benchmark model, but the cyclical correlations between labor market variables and output are very different from those in the data and in the benchmark model. 29 The correlation between aS in the model and the index of Law and Order from Political Risk Services (Rule of Law from the World Bank’s Worldwide Governance Indicators) is 0.55 (0.63) and significant at the 1 percent level.
18
4.1
Steady State
Figure 2 shows the steady-state relationship between self-employment and other model variables traced out by variations in aS , holding other parameters fixed.30 The parameter aS varies between 0.545 and 0.623 to generate self-employment shares from 5 to 94 percent of total employment. Figure 2: Model Steady State and Self-Employment (Share of Labor Force)
0.2
Investment
Output
1.1 1
Consumption
0.9
1.2
0.15 0.1
0.8 0.7 0.6 0.5
0
0.2 0.4 0.6 0.8 SE
0
0.2 0.4 0.6 0.8 SE
0
0.2 0.4 0.6 0.8 SE
0
0.2 0.4 0.6 0.8 SE
0
0.2 0.4 0.6 0.8 SE
0.6 θSE
15
θ
S
20
0.06
10 5 0
0.2 0.4 0.6 0.8 SE
0.2 0.4 0.6 0.8 SE
0.84
1.2 1 0.8 0.6 0.4 0.2
0.82 0.8 0.78 0.76 0.74
0
0.2 0.4 0.6 0.8 SE
0.5 0.4
0
Nash Rental Rate
SE Capital Supply
0.05
Nash Wage
Unemployment
25 0.07
0
0.2 0.4 0.6 0.8 SE
0.15 0.14 0.13
First, an increase in aS causes a fall in steady-state self-employment by raising the marginal product of salaried labor and the marginal product of capital used in the salaried sector. These, in turn, increase salaried vacancies, capital usage by firms, and investment. The reduction in self-employment is more than offset by the rise in salaried employment, leading to a fall in unemployment. Both capital and labor market tightness increase with lower self-employment. The supply of capital to self-employment ultimately drives the response of capital market tightness even though the change in household capital search expenditures goes in the opposite direction as capital supply.31 Consistent with the evidence, the model delivers a 30
The general conclusions of the paper do not depend on the use of aS to change the share of self-employment. The results are similar when the share of self-employment changes due to differences in capital matching efficiency. Importantly, this shows that it is indeed changes in the share of self-employment that drive the results, and not particular parameters of the model. I use changes in aS because I can cover the whole range of self-employment shares in the data. 31 Note that the fact that the supply of capital to the self-employment sector is larger in economies with higher self-employment shares simply means that more capital is allocated to the self-employment sector in these economies. Importantly, these economies also have lower capital stocks relative to those with smaller self-employment shares.
19
negative link between output and self-employment (Loayza and Rigolini, 2011). The model also suggests that the impact on wages from lower labor market tightness outweighs the impact from lower capital market tightness. For the Nash capital rental rate, the effect of labor market tightness is stronger in steady state, which implies that the cost of capital is lower in economies with lower self-employment. In very broad terms, this is consistent with the higher cost of financing in developing countries (Global Financial Development Report, 2014).
4.2
Response to a Negative Aggregate Shock
Figures 3 and 4 illustrate how cyclical dynamics differ across three economies with different steady-state self-employment levels. The shocks are the same across economies. I examine economies with steadystate self-employment of 7.5 percent of total employment (similar to the United States), 23 percent selfemployment (the benchmark economy), and 50 percent self-employment (similar to Colombia). These three choices are only meant to be illustrative.32 The response of total output at the bottom of Figure 4 shows one of the main results: economies with higher average self-employment recover faster from adverse aggregate shocks. To understand this result, first consider the impact response across economies. Differences Across Economies on Impact
Salaried firms in economies with more self-employment
have a lower steady-state value of having a worker, which reflects the lower labor productivity in the salaried sector that arises from both a lower capital stock and lower capital usage.33 Thus, when the economy receives a negative aggregate shock, the proportional contraction in salaried vacancies (and labor market tightness) is larger in these economies. This causes investment to fall by more as well since lower vacancies today imply lower salaried employment tomorrow. These economies also exhibit larger contractions in capital usage in the salaried sector, ω, for a similar reason. Even though ω falls by more in economies with more self-employment, the lower steady-state capital stock in these economies implies that capital supply to the self-employed, (1 − ω)kS , expands by less on impact. Hence, the increase in u p(θ the probability of entering self-employment, given by vSE SE ), is smaller in economies with more self-
employment.34 Lastly, the larger drop in ω generates a larger initial contraction in salaried output and 32
I do not claim that the model economies with 7.5 and 50 percent self-employment quantitatively capture the U.S. or the Colombian economy in other respects. However, the general qualitative stylized facts on the differences between developed and developing countries (higher real consumption, investment, output, and earnings in the former group) do hold. 33 The lower aS also decreases labor productivity, but the bulk of the change is due to a lower ω and a smaller capital stock. 34 Since this implies a smaller expansion in self-employment after the shock, the model is consistent with the fact that the countercyclicality of self-employment is decreasing in the share of self-employment (Loayza and Rigolini, 2011).
20
Figure 3: Impulse Response Functions to a Negative Aggregate Productivity Shock
Capital Supply to SE % Dev. from SS
20
Capital Search Expenditures 20
Probability of Entering SE 20
10
10
10
0
0
0
−10
0
10 20 Quarters
−10
30
0
10 20 Quarters
−10
10
0
0
0
−0.5
−5
−10
−1
0
−20
10 20 30 Quarters Wage − MPL Ratio
0
% Dev. from SS
1 0.5 0 −0.5
0
10
20
30
20
30
−1.5
5
0
0
−5
−5
0
10
7.5% SE
20 23% SE
30
0
10
20
30 S
5
−10
20
Nash Rental Rate − MPK ratio
Nash Rental Rate
S
1.5
10
10
Nash Wage
5
−10
0
Investment
Salaried Vacancies % Dev. from SS
30
30
−10
0
10
20
30
50% SE
total output. The larger initial contraction in salaried labor market tightness in economies with higher self-employment would initially suggest that wages should fall by more. However, relative to economies with less selfemployment, the self-employment outside option plays a larger role in shaping labor market conditions and wage dynamics since there is a higher steady-state likelihood of entering self-employment. This prevents larger downward wage adjustments on impact and is due to the fact that the probability of becoming self-employed (capital market tightness), is endogenous and increases during recessions, which ultimately affects the response of wages. To see this more clearly, consider the coefficient in front of the
21
Figure 4: Impulse Response Functions to a Negative Aggregate Productivity Shock (Continued)
% Dev. from SS
Salaried Employment
Self−Employment
1.5
2
1
1
0.5
0
0
−1
−0.5
0
10 20 Quarters Unemployment
30
% Dev. from SS
2 1 0 −1
0
10
20
30
−2
Salaried Capital Usage 0.5 0 −0.5
0
10 20 Quarters Salaried Output
30
−1
1
0
0
−0.5
−1
−1
−2
−1.5
−3
0
10
7.5% SE
20
30
23% SE
−2
0
10 20 Quarters Total Output
0
10
20
30
30
50% SE
self-employment outside option from a log-linearized version of the wage equation: # vSE zaS fωkS (1 − δSE ) [1 − β(1 − δ)] MSE vSE ξSE b − + θSE,t, wS θSE wS θ ξSE "
(24)
SE
where θbSE,t refers to capital market tightness in log-deviations from steady state and variables without time subscripts are in steady state. Both terms inside the brackets are larger in economies with more
steady-state self-employment, mainly due to the lower steady-state values of wages wS and capital market tightness θSE . Intuitively, given that the self-employment sector is larger in these economies, any movements in capital market tightness will have a larger impact on wages through variations in the selfemployment outside option. Based on the expression above, a fall in capital market tightness will put upward pressure on wages, but wages will still fall due to the contraction in labor market tightness and the marginal product of salaried labor.35 In contrast, the rental rate is more sensitive to changes in capital market conditions in economies with more self-employment. While the fall in salaried labor market tightness puts upward pressure on the rental rate, this effect is weaker in economies with more self-employment. The opposite occurs when capital market tightness falls. This effect dominates, so the rental rate falls by Analyzing numerically each of the components of the coefficient in front of θbSE,t shows that the larger steadystate supply of capital for matching is responsible for bolstering the self-employment outside option in the period of the shock, which in turn reduces the impact response of wages in economies with more self-employment. 35
22
more in economies with more self-employment. Differences Across Economies After the Shock
The mechanism that generates differences in eco-
nomic recoveries across economies can be summarized as follows. Differences in average self-employment – or more generally in the composition of employment – imply contrasting cyclical dynamics for the probability of entering self-employment – and hence for the self-employment outside option and the cyclical composition of employment – in response to shocks. These differences in the cyclical evolution of entry into self-employment feed into salaried wage dynamics, which end up affecting salaried firms’ hiring and investment decisions over the business cycle. As Figure 4 suggests, it is the behavior of salaried output that is behind the faster recovery in output in economies with more self-employment. To see this more clearly, first note that steady-state capital market tightness is lower in economies with higher self-employment shares, which implies a smaller rise in the probability of self-employment entry on impact. Second, since all economies are subject to the same aggregate shock and the pace of recovery in the marginal product of capital is mostly driven by the aggregate shock, the share of capital used in salaried production recovers at a faster pace in economies with more self-employment since the former experienced a larger initial fall. This curtails the availability of capital for self-employment by more, which boosts the recovery in the Nash capital rental rate subsequent to the shock (since the rental rate is more sensitive to changes in capital supply in these economies). The faster recovery in the rental rate in the aftermath of the shock sharply reduces the benefit from searching for capital suppliers, Moreover, the larger initial collapse in salaried vacancies translates into a larger initial increase in unemployment. Combining these two facts, capital search expenditures per unemployed fall back to steady state earlier in economies with more self-employment as the shock subsides. More importantly, the larger contraction in capital supply in the aftermath the shock generates a less persistent rise in the probability of entry into self-employment in these economies. Put another way, the self-employment outside option deteriorates faster in the aftermath of the shock in economies with higher self-employment shares. As the likelihood of entering self-employed starts to fall back to steady state – which takes place earlier in economies with more self-employment since the initial increase in the availability of capital after the shock is less persistent – the drop in the self-employment outside option prevents salaried wages from immediately resuming their upward path back to steady-state. This effect is stronger in economies where with higher average self-employment. More importantly, as aggregate productivity starts to return back to steady state, the marginal product of labor recovers along with it but wages are slower in adjusting back to trend in these economies. This can be seen more clearly by looking at the dynamics of the ratio of
23
salaried wages to the marginal product of labor in Figure 3. In particular, this ratio shows a larger change in the contemporaneous value from hiring workers relative to economies with less self-employment in the aftermath of the shock. This fosters a faster recovery in salaried vacancies (and ultimately employment) in subsequent periods, which also leads to a faster recovery in investment. Finally, a faster recovery in salaried employment and investment bolster the recovery in salaried output, which in turn leads to a faster recovery in total output. More generally, behind this result is the fact that differences in the cyclical composition of employment, which are ultimately driven by the average composition of employment in the economy, generate differences in the adjustment of wages in response to shocks. The latter affect firms’ responses to shocks and determine the recovery path of the economy. Cross-Country Determinants and Differences in Real Wage Dynamics: Empirical Evidence There is limited evidence and knowledge on the underlying reasons behind cross-country differences in cyclical wage dynamics (Messina, Strozzi, and Turunen, 2009). Even within countries, wage dynamics vary based on a number of factors, including the extent of sectoral reallocation, changes in the composition of employment, inflation dynamics, and the type of recession or expansion (see, for example, Fang and Silos, 2012, or Calvo, Coricelli, and Ottonello, 2013). Thus, finding consistent patterns for cyclical wage dynamics across countries is particularly challenging. Using a small sample of developed and developing countries, Boz, Durdu, and Li (2013) document that real wages are more volatile in emerging economies.36 The best comparable cross-country data comes from the Wage Dynamics Network (supported by the European Central Bank and other national central banks in the European Union) and hence focuses on European countries. Existing studies to date find that inflation, the presence of inflation thresholds are important for characterizing real wage dynamics (Messina, Strozzi, and Turunen, 2009; Heinz and Rusinova, 2011). Importantly, Messina, Strozzi, and Turunen (2009) and ECB (2012) also find that changes in the composition of employment are important in explaining the cyclical behavior of real wages (including the apparent lack of adjustment in wages in certain countries during the recent crisis), which in turn affects employment and aggregate dynamics. This holds even after bargaining institutions are accounted for. The mechanism in my model depends 36
These results should be interpreted with caution. Comprehensive comparable wage data for a large set of developing countries is very limited, particularly at high frequencies. Furthermore, the way wages are defined, and the comprehensiveness of wage data may vary considerably by country (ILO, 2013). Also, Calvo, Coricelli, and Ottonello (2013) find that inflation plays a key role in characterizing wage, employment, and output dynamics in particular recession episodes in emerging economies. This points to two relevant issues. First, the recent trend in inflation stability in several developing countries may imply higher real wage rigidity. Second, differentiating between high-inflation and low-inflation episodes may yield deeper insights into cross-country differences in wage dynamics.
24
on both the average and cyclical composition of employment across economies (where the compositional differences are between salaried and non-salaried work). As argued above, the cyclical evolution of selfemployment (and hence the composition of employment) modifies the incentives to hire and invest in the salaried sector, and this can reconcile the contrasting recovery speeds across economies. While the model cannot generate higher wage volatility in economies with higher self-employment, the mechanism in the model appears consistent with existing evidence on the relevance of changes in employment composition as an important determinant of cyclical wage adjustments across economies.37 The Response to a Positive Self-Employment Productivity Shock
While self-employment tends
to be countercyclical on average, Fiess et al. (2010) document particular episodes where self-employment is procyclical in four Latin American countries, and argue that the source of shocks may be important in determining the response of self-employment to shocks. The inclusion of a sectoral productivity shock in self-employment in the model allows me test this. I find that in response to a positive self-employment productivity shock, both total output and self-employment expand. Intuitively, the shock increases the value of devoting resources to self-employment, thereby causing a reallocation of capital towards selfemployment and generating increased entry into the sector. The contraction in capital used by salaried firms reduces salaried vacancy postings, but the increase in the supply of self-employment capital causes wages in the salaried sector to increase. Despite the higher value of supplying capital to the sector, investment falls. The expansion in self-employment output due to higher entry into the sector more than offsets the contraction in salaried output, leading to an expansion in total output. Thus, the model generates higher real wages, self-employment, and output in response to a positive shock to the selfemployment sector (i.e., procyclical self-employment), in line with the evidence in Fiess et al. (2010).
4.3
Model and Data Comparison
As an additional validity test for the model, Figure 5 compares the prediction of the model against the empirical relationship between self-employment and output persistence in Figure 1.38 Figure 5 shows that 37
Given that the evidence on wage dynamics puts emphasis on the role of inflation volatility – particularly for developing countries – it is not surprising that the model cannot replicate some of the facts in Boz, Durdu, and Li (2013). However, even if wages were to fall by more on impact in economies with more self-employment, the evolution of the self-employment outside option in the aftermath of the shock would have a similar impact on the decisions to hire and invest in the salaried sector, so that the main conclusions in the paper are unlikely to change. This is the case because the mechanism of the model does not depend on the response of wages on impact, but rather on the evolution of wages after the shock. 38 Since the model was calibrated to a quarterly frequency, I construct an annual output series using the original simulated quarterly series and apply the appropriate transformations (logs and the HP-filter) to compare the annual simulated series to the data in Figure 1. More specifically, I compute the first-order autocorrelation of the cyclical
25
the model can capture the change in the autocorrelation of output for countries reasonably well, which gives additional validity to the model.39 Figure 5: Output Persistence and Self-Employment Rates: Data and Model Comparison Model Data: Linear Trend Data: Developed Countries Data: Developing Countries
0.8
Autocorrelation of Output
0.7
0.6
0.5
0.4
0.3
0.2 0
4.4
20
40 60 80 Self−Employment (% of Non−Agricultural Employment)
Alternative Modeling Assumptions
Small Open Economy Model
Economies with higher average self-employment tend to be open and
small relative to the rest of the world. Assuming a small open economy implies that households can obtain additional resources by borrowing from abroad, and these funds can be used to finance part of the capital search costs. This reduces the volatility of both capital search expenditures by households and hence the volatility of the probability of entering self-employment relative to an economy that is less open (and annual output series for different economies by varying the parameter aS to change the steady-state level of selfemployment. 39 Clearly, the model fit will vary somewhat if the countries with the highest shares of self-employment (70 percent or more) or with very low output autocorrelations are excluded. What is important is that the negative link between self-employment and cyclical output persistence will still hold despite changes in the country sample. The key message to take from this exercise is that the model – despite abstracting from various important aspects of self-employment – can qualitatively capture the relationship in the data. Also, the presence of the self-employment productivity shock plays an important role in capturing the quantitative relationship between self-employment and output persistence as it prevents the fall in the volatility of self-employment output from fully offsetting the rise in salaried output volatility as self-employment increases. More importantly, the inclusion of this shock allows me to determine whether my model encompasses the results in Fiess et al. (2010) as well as those documenting the average countercyclical behavior of self-employment. The shock also yields other desirable features in the data, such as higher earnings volatility in self-employment relative to salaried employment.
26
to the extreme, a closed economy). Importantly, a small-open-economy version of the benchmark model delivers very similar dynamics to those documented above. Furthermore, the model does an equally good job at capturing the link between output persistence and self-employment in the data. Thus, the results in this paper are not sensitive to having a small open economy. Alternative Setup with Financial Intermediaries Assume a competitive financial intermediary accumulates funds in the form of capital and makes an allocation decision between salaried and selfemployed firms, where the supply to the self-employed is subject to search frictions. This setup would yield exactly the same allocations as in the benchmark model: in equilibrium, the return from supplying capital to salaried firms – equal to the marginal product of capital in the salaried sector – must be equal to the opportunity cost of supplying capital to the self-employed. In turn, the latter must be equal to the expected marginal benefit of supplying capital to the self-employed. This is analogous to the salaried firms’ capital supply condition in the benchmark model. On-the-Job Search for the Self-Employed
We can introduce job-to-job flows by allowing for the
self-employed to search for salaried employment. Similar to Krause and Lubik (2010), this modification increases the potential pool of salaried workers and makes salaried vacancies, investment, unemployment, and output more responsive to aggregate shocks relative to the benchmark model. Moreover, the effect of on-the-job search on aggregate volatility is amplified in economies with higher average self-employment so that, consistent with the results presented above, these economies exhibit higher aggregate volatility relative to those with lower self-employment. Furthermore, the presence of job-to-job flows in principle strengthens the main mechanism in the benchmark model by creating additional frictions in the wage adjustment process in the aftermath of a downturn, where the slowdown in the upward adjustment of wages as aggregate productivity recovers is stronger in economies with higher average self-employment. Briefly, in an economy with on-the-job search and higher self-employment, salaried vacancies fall by more, and generate a larger increase in the availability of resources for self-employment relative to economies with lower self-employment. Since the initial rise in self-employment after a negative shock has more influence on salaried labor market conditions, the initial adjustment in wages is smaller not only because of the initial improvement in the self-employment outside option, but also because the larger pool of potential salaried workers puts additional downward pressure on wages as aggregate productivity slowly recovers. Importantly, this latter effect is stronger in economies with higher average self-employment. Since the initial rise in self-employment after the shock is persistent (due to the search frictions), as aggregate productivity returns to trend, the expansion in self-employment is putting downward pressure 27
on salaried market tightness and the rise in salaried vacancies is reducing the availability of capital for the self-employed. Both of these effects continue to put downward pressure on wages, which in turn further slows down the upward adjustment in wages that would otherwise take place in the aftermath of the shock. This generates an even faster recovery in economies with higher self-employment relative to the benchmark model with no on-the-job search. Thus, the results in the benchmark model would not be affected by the inclusion of on-the-job search.
5
Conclusion
I explore the role of self-employment in the recovery process from recessions. Four key facts motivate my focus on self-employment and business cycles: self-employment is a pervasive feature of labor markets around the world; most self-employed run owner-only businesses with no salaried workers, but still face difficulty in accessing capital and the resources to produce; and self-employment generally expands in recessions through higher transitions from unemployment to self-employment. I also document a negative relationship between the share of self-employment in the economy and the persistence of output over the business cycle. This link suggests that self-employment may be important for understanding differences in economic recoveries and business cycle dynamics. I build a business cycle model with frictional labor markets where unemployed individuals can move into salaried work or can become self-employed, and explore the channels through which self-employment influences the pace of recoveries. I find that economies with higher average self-employment shares recover faster from negative aggregate productivity shocks. In the model, unemployed individuals who want to enter self-employment must match with capital suppliers in order to finance their business ventures. This friction is in line with the presence of capital constraints and the prevalence of interfirm input credit among small firms. Salaried firms decide to supply internally-accumulated resources to the self-employed via frictional capital markets. The capital search structure generates both countercyclical transitions from unemployment into self-employment as well as countercyclical self-employment, as in the data. Additionally, the model is consistent with the relationship between self-employment and GDP in the data. I show that differences in the average composition of employment across economies affect the cyclical evolution in the ease of entry into self-employment, or more broadly, the cyclical composition of employment, which in turn has important consequences for aggregate dynamics. This relevant cyclical feature of self-employment had not been previously studied in detail. In the model, economies with higher self-employment shares exhibit sharper initial contractions in
28
vacancies, investment, and output. However, the self-employment outside option plays a more prominent role in affecting aggregate labor market conditions, and its cyclical response after a negative shock slows down the adjustment in salaried wages during the recovery phase. In turn, this generates a faster recovery in salaried employment and investment, which ultimately translate into a faster recovery in output. The mechanism in the model is in line with existing evidence on the relevance of changes in the composition of employment for cyclical wage adjustments. Moreover, the dynamic behavior of unemployment, investment, and output in response to shocks is consistent with the empirical evidence on business cycles in developed and developing economies. Finally, the model can generate a relationship between the persistence of output and the share of self-employment broadly in line with the data. The model abstracted from other relevant features of self-employment, such as the higher riskiness of self-employment, the heterogeneity inherent to the sector, and the fact that some owner-only firms do expand. These are issues worth exploring to gain deeper insights into the aggregate consequences of having differences in the labor market structure. I also plan to explore more deeply the interconnection between labor markets and the financial market structure in developing countries in future work.
Acknowledgements
This is a modified version of my Ph.D. dissertation at the University of Maryland.
I thank Bora˘ gan Aruoba, John Haltiwanger, John Shea, Pablo D’Erasmo, William Maloney, Sushant ´ Acharya, Alvaro La Parra P´erez, Julie Mullen, two anonymous referees, and seminar participants at the University of Maryland, Syracuse University, the Federal Reserve Board, Universidad de los Andes, the World Bank, Banco de la Rep´ ublica de Colombia, NEUDC 2013, Midwest Macro Fall 2013, the Federal Reserve Bank of Atlanta, the Eastern Economic Association 2014 conference, and the Inter-American Development Bank for valuable feedback. Any errors are my own.
29
6
Appendix
Derivation of Nash Prices
The Nash bargaining first-order condition for the wage and rental rate are
given by (WS,t − WU,t ) =
νS (JS,t ), 1 − νS
(WSE,t − WU,t ) =
νSE (JSE,t − Juk ,t ) 1 − νSE
(25)
First, using the value functions in the text, write (WSE,t − WU,t ) = (zt aSE,t − rSE,t) − b u (1 − vSE,t p(θSE,t))(1 − δSE ) +Et Ξt+1|t × (WSE,t+1 − WU,t+1 ) −p(θ )(1 − δS )(W S,t S,t+1 − WU,t+1 ) (WS,t − WU,t ) = wS,t − b +Et Ξt+1|t
(26)
(1 − p(θS,t ))(1 − δS ) (WS,t+1 − WU,t+1 )
(27)
−v u p(θ SE )(W SE,t )(1 − δ SE,t+1 − WU,t+1 ) SE,t
Using the first-order conditions from Nash bargaining, we have
νSE (JSE,t − Juk ,t ) = (zt aSE,t − rSE,t) − b + 1 − νSE u νSE (1−vSE,t p(θSE,t )) (1 − δSE ) 1−ν SE Et Ξt+1|t × (JSE,t+1 − Juk ,t+1 ) − p(θS,t )νS (1 − δS )J S,t+1 1−νS
νS (JS,t ) = wS,t − b + Et Ξt+1|t 1 − νS
(1−p(θS,t ))νS (1 − δS )JS,t+1 1−νS u νSE vSE,t p(θSE,t ) − (1 − δSE ) 1−νSE
× (JSE,t+1 − Juk ,t+1 )
(28)
(29)
Using the optimality conditions from the firm’s and household’s problems, we can write: ψS = Et Ξt+1|t (1 − δS )JS,t+1 q(θS,t )
zt aS fωkS (nS,t , ωt kS,t ) + (1 − δSE )q(θSE,t) = Et Ξt+1|t (1 − δSE )JSE,t+1 q(θSE,t)
30
(30)
(31)
Table 5: Self-Employment and Cyclical Persistence: Cross-Country Evidence Dep. Variable: Specification Self-Employment
(1) -0.002**
Autocorrel. (2) -0.003**
of (3) -0.003**
Output (4) -0.003**
(5) -0.003**
Log RGDPPC 1985
0.015
0.015
0.015
-
0.015
Openness
-
-0.001**
-0.001**
-0.000
-0.000
Gov. Spending
-
-
0.001
0.002
0.002
Law and Order
-
-
-
0.005
-0.000
Manuf.-GDP Ratio Adj. R2 Obs.
0.000 0.18 75
0.22 75
0.21 75
0.22 71
0.27 69
Sources: OECD (2009) (self-employment), World Development Indicators from Panizza and Saade (2010) (real PPP-adjusted GDP, government spending, openness (the sum of imports and exports over GDP), manufacturing-to-GDP ratio), and Political Risk Services (Law and Order). Notes: I omit the constant term for all specifications for expositional purposes. All variables except log real GDP per capita in 1985 (Log RGDPPC 1985) and Law and Order are averages from 1985 to 2007. Law and Order is an average from 1999 to 2007. A stronger (and significant) relationship holds if we consider the cyclical persistence of non-agricultural real PPP-adjusted GDP. Similar results hold if I include countries with self-employment rates higher than 85 percent and countries with very low cyclical output persistence, or if I restrict the sample to developing countries only. Controlling for employment in agriculture or the share of agricultural production in GDP (while excluding law and order and real GDP per capita given their very high correlation with these measures) has little impact on the results. Even though the quality of institutions is considered a relevant determinant of self-employment in the literature, the latter may influence the persistence of cyclical output through other channels other than the labor market. ** denote significance at the 5 percent level.
Recall that
p(θS,t ) q(θS,t )
= θS,t ,
p(θSE,t ) q(θSE,t )
=
1 θSE,t ,
and Juk ,t = (1 − δ). After some algebra and using the two facts
above, we obtain the expressions for wS,t and rSE,t in the text. Output Persistence and Self-Employment
31
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