We show that a dynamic general equilibrium model with efficiency wages and endogenous capital accumulation in both the formal and (non-agricultural) informal sectors can explain the full range of confounding stylized facts associated with minimum wage laws in less developed countries.

Abstract

We show that a dynamic general equilibrium model with efficiency wages and endogenous capital accumulation in both the formal and (non-agricultural) informal sectors can explain the full range of confounding stylized facts associated with minimum wage laws in less developed countries.

1 Introduction

Minimum wage (MW) laws are now an important policy for combatting poverty in many LDCs, but, as in developed countries, there is considerable controversy about whether they achieve their stated objective. First-generation analyses of the MW relied on the canonical Segmented Labor Markets Model (SLMM). According to SLMM, a higher MW reduces employment and output in the formal sector. Some of the workers who lose their jobs then seek employment in the informal sector (where MW laws cannot be enforced). The influx of labor to the informal sector increases employment and output but also depresses the real wage. Underemployment worsens, total output declines, and any improvement in the overall distribution of income comes at the expense of the poorest group in the country, low-paid workers in the informal sector. For standard production functions and plausible parameter values, job losses in the formal sector and the redistributive effects are large. In short, MW laws derive from good intentions but are hard to recommend.

The data have not been kind to this narrative. Empirical evidence accumulated over the past twenty years casts doubt on, or strongly contradicts, every claim advanced by the SLMM. Sometimes employment increases in the informal sector; typically, however, it decreases more than employment in the formal sector (Betcherman, 2014). The real wage in the informal sector does not decline; reflecting the ubiquitous “lighthouse effect,” it almost always increases: “No study has found that a higher minimum wage depresses wages for informal sector workers as a whole” (Gindling, 2014). Completing the rout, employment losses in the formal sector are often surprisingly small. The mean employment elasticities in the meta-analysis of Nataraj et al. (2014) and in surveys of the literature by Bhorat et al. (2017), the World Bank (2006), and this paper (Appendix C) are -.08, -.011, -.20, and -.23, respectively. In some countries, the evidence suggests a positive impact on formal sector employment.

These stylized facts represent a major challenge for theory. The lighthouse effect is consistent with employment decreasing in the informal sector. But what explains the effect in the first place? The usual explanation, that the MW serves as a norm for fairness in the informal sector, is incomplete and unconvincing.1 Most informal sector capitalists are quite poor (La Porte and Shleifer, 2013). The notion that they feel a social obligation to respond to an increase in the MW by paying much higher wages strains belief; evidently some unspecified change in the economic environment, causally linked to the MW, makes it profitable for firm owners to raise wages.

The finding that employment losses are often very small in the formal sector – nil is a common descriptor – is perhaps the most perplexing result uncovered by empirical studies. For a CES production function with two inputs, capital and labor, the elasticity of employment with respect to the wage equals —σ/θK, where σ is the elasticity of substitution and θK the cost share of capital.2 This yields an employment elasticity of 1.5 — 3 when σ = .5 — 1 and θK = .33. Yet .5 is at the high end of empirical estimates, and the literature surveys cited earlier place the mean elasticity between .08 and .20. The true employment elasticities may be higher (in absolute value) than those reported in the literature, and certainly the variation in outcomes among LDCs deserves more attention.3 We return to these points later. If anything, however, they add to the list of unresolved empirical puzzles. A satisfactory theory should account for both high and very low employment elasticities. As Bhorat et al. (2017) observe: “There is a range of potential impacts of minimum wages on employment. The heterogeneity of outcomes in LMI countries, in particular, suggests that a variety of context-specific factors interact with the minimum wage.” (Our emphasis.)

There are pros and cons to the approach taken by the existing literature. On the credit side of the ledger, the provocative stylized facts, amassed through decades of careful empirical research, are important in their own right and exceptionally informative about the right way to model the labor market in LDCs. This will be a recurrent theme in our paper.

But the literature’s strength is also its weakness. From a policy standpoint, the lopsided emphasis on empirical investigation is troubling. Absent any substantive input from theory, the stylized facts are something of a black box: a set of potentially important, policy-relevant results that we do not understand and therefore cannot fully trust. The black box problem was noted thirty years ago in the developed country literature by Brown (1989) and has persisted largely unchanged to the present day. In the development literature, Eyraud and Saget (2005), Lemos (2009), Betcherman (2014), and Fields (2011) have called for research to “look for the factors behind [the] weak effect” on employment (Eyraud and Saget); to develop a “coherent theoretical framework” that makes sense of the “puzzling results” in Brazil and othe countries (Lemos); to help understand the long-run effects of MWs (Betcherman); and, more generally, to meet the “the need for empirically-grounded theoretical labor market models that can be used in the formulation of policy” (Fields). The appeals have yet to elicit a response. Writing in 2017, Bhorat et al. assert that “While work on minimum wages is fairly mature in many OECD countries, our understanding of minimum wage policy in SSA is not.” To a lesser but still significant extent, the same assessment applies to Latin America and Asia.4

Our objective in this paper is to bridge the divide between theoretical and empirical research. Toward that end, we develop a dynamic general equilibrium model with efficiency wages (EW) and endogenous capital accumulation in both the formal and (non-agricultural) informal sectors. A large body of empirical work already attests that EW models can explain the most important characteristics of labor markets in developing countries. We show that they can also explain the full range of confounding stylized facts – those emphasized in the literature plus others that have flown below radar – associated with MWs in LDCs. This will not settle the debate on how to model the labor market in developing countries. It does, however, enhance the appeal of EW theory and strengthen the case for its general relevance.

The main body of the paper is organized into five sections. Section 2 takes two pages to review the empirical evidence bearing on EWs in LDCs. In Section 3 we derive analytical results in a stripped-down model that assumes constant employment and output in the informal sector. The analytical results elucidate many of the key mechanisms that limit employment losses in the formal sector. In a standard setup where firms operate a CES production function and worker effort depends only on the real wage, EW effects reduce the employment elasticity from 2 — 3 to 1. This is substantial but inadequate progress: 1 is a long way from .1 — .3, the range that brackets the majority of empirical estimates. The solution to the problem is to strengthen fidelity to the stylized facts by incorporating two other effects: (i) the impact of the unemployment rate on work effort, as measured by wage curves estimated for LDCs, and (ii) the link between monitoring costs, effort, and the firm-size wage premium (much larger in LDCs than in developed countries). When these effects are added to the mix, the MW decreases the effective cost of labor, inducing firms to increase output and investment.5 The increase in output lowers the employment elasticity to .2 — .6 in the short run. Moreover, as the capital stock grows, labor demand recovers and output continues to rise. In the limiting case where the goods produced by the formal and informal sectors are perfect substitutes, labor demand recovers fully – the employment elasticity equals zero across steady states.

In Section 4 we present the full model that features EWs in both the formal and informal sectors. Following this, we calibrate the model and explore the sensitivity of the lighthouse effect and sectoral employment to alternative empirically-relevant values of key parameters. The variation in the numerical results mirrors the variation in outcomes documented in empirical studies. Four “context-specific factors” condition the impact of an increase in the MW: (i) the relative size of the formal sector; (ii) the degree of substitutability between formal and informal sector output; (iii) the absolute and relative degree of wage flexibility embodied in the sectoral wage curves; and (iv) the tradability of formal sector output. For certain configurations of the context-specific factors, employment losses are large overall and in the formal sector. But these outcomes are a minority. Consistent with the majority of empirical estimates, small employment elasticities of .1 — .3 predominate in the relevant parameter space at all time horizons. While this is encouraging, it does not mean that increasing the MW is a good bet in all LDCs. Our results suggest a well-defined heirarchy of MW effectiveness. Moving up the development ladder from LICs to MICs to EMEs brings progressively larger increases in GDP and real wages in the informal sector and progressively smaller employment losses. Disturbingly, at the lowest rung of the ladder, there is a small but tangible risk of harm: in the case of LICs – and only LICs -the MW may reduce output and welfare.

Our paper is only a first pass at solving the MW puzzle. As such, it ignores a number of important issues. The final section discusses this and some of the topics that should be addressed in future research.

2 The Case for Efficiency Wages

Efficiency wages are rarely seen in development macromodels. This is perplexing, for evidence in support of EW theory is broad, deep, and compelling across the development spectrum. Over the past twenty years, empirical studies have amassed abundant, compelling evidence that efficiency wages operate throughout the non-agricultural sector in LDCs. Estimates of the impact of unemployment on real wages confirm the existence of wage curves in the formal and informal sectors in Argentina, Turkey, Colombia, Uruguay, Chile, S. Africa, Cote d’lvoire, Mexico, China, S. Korea, and a host of other developing countries (Blanchflower and Oswald, 2005). There is also powerful, if indirect evidence supportive of efficiency wages in the stylized facts documented in microeconomic studies of LDC labor markets. In LICs, EMEs, and everything in between, wage and employment data exhibit the same patterns: (i) firm-size wage premiums that start at very small establishment size and are much larger than in developed countries; (ii) persistent, remarkably stable inter-industry wage differentials; (iii) high correlation of industry wage premiums across occupations; (iv) large wage premia for formal vs. informal sector employment and for informal non-agricultural employment vs. agricultural employment; (v) large cyclical flows into and out of unemployment in both the formal sector and the informal sector; (vi) virtually identical lists for low- and high-paying industries; (vii) large, stable wage differentials between firms in the same industry; and (viii) lower quit rates and longer job tenure in the formal sector. At present, only efficiency wage models can explain all of these stylized facts. We do not have the space here to survey the literature in greater depth or to discuss myriad estimation issues. References and capsule summaries of the results for 50+ studies are available, however, at http://mypage.iu.edu/~ebuffie/.

2.1 Efficiency Wages in the Informal Sector?

Admittedly, EWs are a harder sell for the informal sector than for the formal sector. We need to elaborate on some of the empirical evidence cited above:

  • Appendix B collects estimates of wage curves that relate the level of the real wage to the unemployment rate in LDCs. Clearly, wage curves are not confined to the formal sector; they also operate in the informal sector. This does not mean that wages are equally rigid in the two sectors. The common perception that wages are more flexible in the informal sector is correct. Most studies find that wages in the informal sector are more responsive to the unemployment rate than wages in the formal sector. But a large gap separates more responsive from highly responsive. The informal sector does not approximate a frictionless buffer sector with flexible, market-clearing wages.

  • The firm size effect kicks in very quickly, starting at micro enterprises with 2–5 employees (Velenchik, 1997; Schaffner, 1998; Badaoui et al., 2010).

  • If wages are rigid in the informal sector, the data should show large movements into and out of unemployment during booms and recessions. This is precisely what Bosch and Maloney (2007) find in their study of labor market dynamics in Mexico, Argentina, and Brazil.6 Salaried jobs in the informal sector showed high rates of separation toward unemployment and inactivity (i.e., dropping out of the labor force). In fact, in all three countries transitions out of informal sector employment contributed much more to unemployment than transitions out of formal sector employment. In Mexico, for example, transitions into unemployment from salaried informal employment were three times greater than transitions from formal employment; equally striking, none of the workers laid off in the formal sector found jobs in the informal sector – entry from the formal into the informal sector declined during downturns.

  • For at least one important country, there is strong, direct evidence of job rationing in the informal sector. In labor force surveys in S. Africa, eighty percent of the unemployed reported that they could not find any work; only three percent cited an inability to find “suitable work” as the reason for being unemployed (Heinz and Posel, 2008). Several other studies corroborate the survey findings. Nattras and Walker (2005) and Burgess and Schotte (2017) estimate that the reservation wage of the unemployed is far below their predicted earnings and link their results to data showing a shortage of job offers is the principal cause of unemployment; job refusals are rare. Kingdon and Knight (2004) present data affirming that the unemployed are substantially worse off than the employed in the informal sector in income, consumption, and various indicators of non-economic well-being.

  • Labor force participation rates are implausibly low in much of SSA (Falco et al., 2009; Teal, 2014). The most plausible explanation is that discouraged workers, who cannot find a job even in the informal sector, are misclassified as “out of the labor force.”

3 Insights From a Simplified Model

The full model has a lot of moving parts. It is not a black box, however. To facilitate comprehension of the model and the numerical results presented in Section 3 and 4, we first analyze a simplified model that abstracts from most of the general equilibrium interactions between the formal and informal sectors.

Variable names are familiar or at least mnemonic. Ki, Li, Qi, Wi, Ci, and Pi refer to capital, labor, output, wages, consumption, and prices, with subscript 1 for the formal sector and 2 for the informal sector. The informal good serves as the numeraire (P2 = 1).

Technology

The simplified model fixes output and employment in the informal sector in order to focus on the response of the formal sector to a higher MW. The numerous complications associated with the lighthouse effect are on hold for the time being.

Firms in the formal sector operate a linearly homogeneous CES production function. The elasticity of substitution between capital and labor is σ1 and the supply of labor services depends on the amount of effort e1 that workers expend:

Q1=af[a11/σ1(e1L1)(σ11)/σ11+(1a1)1/σ1K1(σ11)/σ1]σ1/(σ11).(1)

Factories are built by combining one unit of the informal good with f units of the formal good. The supply price of capital is thus

Pk=1+fP1.(2)

Preferences, Saving and Investment

All economic activity is undertaken by a single representative agent. Preferences of the agent qua consumer are given by

C=[(1κ)1/εC1(ε1)/ε+κ1/εC2(ε1)/ε]ε/(ε1).(3)

C is a CES aggregate of C1 and C2, with substitution elasticity ε. The optimal choices for C1 and C2 minimize the cost of purchasing C. This yields the demand function

C1=(1κ)(P1P)εC(4)

and the exact consumer price index

P=[κ+(1κ)P11ε]1/(1ε).(5)

After choosing the best mix of C1 and C2, the agent solves the problem

Max{C}U=C11/τ11/τeρtdt,(6)

subject to

PkK˙=P1Q1+Q2PCPkδK,(7)

where δ, ρ, and τ denote, respectively, the depreciation rate, the pure time preference rate, and the intertemporal elasticity of substitution, and managers/supervisors. On an optimal path, consumption satisfies the Euler equation

C˙=τC(r1Pkρδ),(8)

where r1 = P1 ∂Q1/∂K1 is the capital rental and we have assumed that P1 enters Pk and P with the same weight.7

The Effort Function

Work effort depends on the real wage, the unemployment rate u, and the number of managers/supervisors S who monitor employee performance. The supplies of production labor and managers/supervisors are fixed at unity. So

e1=g0+g1ln(w1/P)+g3ug4lnL1,(9)

where

u=1L1L2.(10)

Naturally, workers exert more effort when they are paid a higher real wage and when high unemployment increases their gratitude for having a job. Effort also increases when L1/S is low [S = 1 in (9)] and firms monitor work performance more closely and/or provide more input to workers about how to do their job properly. As will become apparent shortly, this gives rise to a firm-size wage premium.

The effort function in (9) may be derived either (i) in a more general version of the micro-theoretic model in Shapiro and Stiglitz (1984) where effort is a continuous variable, the intensity of monitoring depends on L1/S, and the utility loss from being fired for shirking is increasing in the unemployment rate8 or (ii) by appending a separable term in the utility function a la Collard and de la Croix (2000) and Danthine and Kurmann (2004, 2010) that captures the nonpecuniary loss from effort at the job. Neither method affects the other first-order conditions associated with the solution to the private agent’s optimization problem here or in the full model developed in Section 4.

Labor Demand and the Wage Curve

Firms recognize the connection between labor productivity and the real wage. Hence they optimize over L1 and w1. The profit-maximizing choices satisfy

P1Q1/L1=w1L1=a1Q1(afe1)(σ11)(1g4/e1)σ1(w1P)σ1(11)

and

af(Q1af)1/σ1(e1L1a1)1/σ1w1/P1(e1g4)e1(w1/P)P1P=1,(e1(w1/P)w1/Pe1)StandardSolowConditione1e1g4=1.(12)

Equation (9) and the modified Solow condition in (12) imply9

g1e1g4=1.(13)

Without loss of generality, we set ei equal to unity at the initial equilibrium. The wage curve defined by (9) and (13) then reads

ln(w1/P)=1g0g3u+g4lnL11g4.(14)

There is no “natural rate of unemployment,” just a curve relating the equilibrium wage to the unemployment rate. Firm size shifts the wage curve in the manner shown in Figure 1. When employment rises, monitoring/managerial input per worker declines and effort decreases. The optimal response of the firm is to buy back the lost effort by paying a higher wage.

Figure 1:
Figure 1:

Impact of higher employment on the wage curve. (P1 = P = 1, so w1 equals the real wage.)

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Raising the MW

An increase in a MW that is already binding misses the effects on output and employment of previous increases in the MW. Accordingly, we assume the MW initially equals the EW firms pay in equation (14). When the government announces a new, higher MW, equations (13) and (14) are suspended and effort is determined by (9) with the real minimum wage wm replacing w1/P:

e1=g0+g1lnwm+g3ug4lnL1.(9')

The nominal MW is indexed to the CPI to maintain the real MW. This makes the product wage in (11) a function of the real price of the formal good:

L1=a1Q1(afe1)(σ11)(1g4/e1)σ1(wmPP1)σ1.(11')

Market-Clearing Conditions

Two market-clearing conditions close the model. Demand equals supply in the formal sector and in the rental market for capital goods when

Q1=(1κ)(P1P)εC+f(K˙1+δK1)(15)
K1=(1a1)Q1af(σ11).(16)

3.1 The Short Run

Getting down to business, differentiate (9’) and (11’). After slight manipulation,

θK1L^1=θK1K^1+(σ11g4θK1)e^1σ1[w^m(1γ)P^1],(17)
e^1=g1w^m(g3L1+g4)L^1,(18)

where θj is the cost share of factor j; a hat over a variable signifies a percentage change (i.e., x^=dx/x); and we made use of the adding-up condition θK1 + θL1/(1 — g4) = 1.10 Although the capital stock is fixed in the short run, we carry it around in anticipation of future needs.

Without EW effects, the partial equilibrium solution for the employment elasticity (i.e., the solution with P1 constant) is L^1/w^ For θK1 = .33, textbook neoclassical economics cannot explain very small employment elasticities unless 100+ econometric estimates are badly wrong and the true value of σ1 is less than .1.

EW effects reduce the employment elasticity, assuming σ1 > θK1(1-g4) Substituting for ê1 in (17) leads to

L^1=θK1moK^1+σ1(1γ)moP^1θK1(1g4)mow^m,(19)

where 7 is the share of the formal good in aggregate consumption and

moθK1(1g3L1g4)+σ1g3L1+g41g4>0.

In the expression for m0, the sign of 1 — g3L1 — g4 determines whether the supply of labor services (e1L1) rises or falls with L1. For empirically-plausible values of g3, g4, and the share of formal sector employment in total employment, 1 — g3L1 — g4 > 0 is likely, but not guaranteed, to hold.11 We assume the condition always holds; none of the results in the paper depend on perverse general equilibrium effects (e.g., a downward-sloping supply curve).

The solution in (19) is involved but easy to break down. Three distinct effects operate. All are needed to bring the employment elasticity into the general vicinity of the elasticity estimates in empirical studies. To see this, consider the outcome in an overly simple model where effort depends only on the real wage (g3 = g4 = 0). The partial equilibrium employment elasticity then reduces to L^1/w^m=1. The intuition for the result stems from the Solow condition and is quite general. For P1 = 1 and Q = F(e1L1, K1), the first-order condition for employment is F1(e1L1, K1) = w1/e1. Starting from an equilibrium where firms pay the EW, the elasticity of effort with respect to the MW equals unity, per the standard Solow condition. It follows that e1L1 is constant in partial equilibrium and hence that L^1/w^m=e^1/w^1=1.

Return now to the solution in (19) and incorporate the firm-size wage premium (g4 > 0) and the impact of higher unemployment on work effort (g3 > 0). The empirical evidence discussed later in Section 3.1 places g3 between .4 and 1.2, g4 between .14 and .33, and L1 between .30 and .75. For our base case calibration where θK1 = -40, σ1 = .75, g3 = .80, and g4 = .20, the partial equilibrium employment elasticity equals .332.12 This is not the complete solution, of course. (Pi is endogenous.) It is clear, however, that a fully-loaded EW model has the potential to explain why big increases in the MW seldom result in big employment losses.

3.1.1 The Impact on Real Output

The results for employment strengthen the case for raising the MW. Surprisingly, so also do the results for real output and investment. Equations (1), (18), and (19) give

Q^1=θK1[1+θL1mo(1g4)(1g3L1g4)]K^1+σ1(1γ)mo(1g4)(1g3L1g4)P^1+σ1θL1mo(1g4)(g3L1+g4)w^m.(20)

Real output increases in the short run. (P1 decreases, but only in response to output rising.) This strong result is inherent in the logic of the EW model. Figure 2 depicts the solution for labor services eiLi when there is no firm-size wage premium (g4 = 0) and P1 = 1 . As before, Q = F(e1L1, K1) and firms maximize profits by hiring labor up to the point where F1(e1L1, K1) = w1/e1. In partial equilibrium, nothing happens: ê1m = 1, so there is no change in the effective cost of labor (ECL) or the supply of labor services. In general equilibrium, however, a coordination externality comes into play: when each firm reduces employment, the increase in the unemployment rate induces workers to put out more effort. The combined effect of the higher wage and higher unemployment shifts the ECL schedule downward, increasing the supply of labor services and output.

Figure 2:
Figure 2:

Impact on the total supply of labor services when the minimum wage increases the real wage in the formal sector from w1,o to (P1 = P = 1).

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

The coordination externality is sufficient but not necessary for output to increase. The firm-size wage premium (g4 > 0) also figures in the positive output response. If a larger workforce is more difficult to manage/supervise, then effort decreases with employment at the level of the firm. Thus the marginal ECL increases with employment. Turning this around, when a higher MW increases effort, the average ECL rises but the marginal ECL declines. Since L^1=e^1 when g3 = g4 = 0, the firm-size wage premium implies L^1=e^1>0; again, the total supply of labor services increases. There are clear parallels with impact of a MW on labor demand at firms that exercise monopsony power.13 But while both output and employment increase under monopsony, employment declines in the EW case.14

3.1.2 The Full General Equilibrium Solution

Finally, we bring demand-side parameters into the solution. To minimize algebraic clutter, we assume the cost share of the formal good in production of investment goods is the same as its share in aggregate consumption. Solving (15) for P1 then yields

P^1=θK1V[1+θL1mo(1g4)(1g3L1g4)]K^1σ1θL1mo(1g4)V(g3L1+g4)w^m,(21)

where

Vσ1(1γ)θL1mo(1g4)(1g3L1g4)+εC1Q1.

Higher output in the formal sector depresses P1. Consequently, employment decreases more in the full general equilibrium solution than in the partial equilibrium solution that holds P1 constant. Exactly how much more depends on ε, the elasticity of substitution between the formal and informal goods. When the two goods are (not) close substitutes, ε is large (small) and the partial equilibrium solution is a good (poor) approximation to the general equilibrium solution. We will be more precise about what “close substitutes” means and about the value of ε compatible with small employment losses when we present numerical results for the full model in Section 5.

3.2 The Long Run

Across steady states,

r1=(ρ+δ)Pk.(22)

We rewrite (22) as

MPK=RCC,(23)

where MPK and RCK = (ρ + δ)Pk/P1 = (ρ + δ)(1/P1 + f) are the marginal product of capital and the real cost of capital in the formal sector.

When the government raises the MW, the supply of labor services increases and P1 falls. Both the MPK and RCC schedules shift upward therefore in Figure 3. The relative strength of the competing effects depends on the size of the informal sector and the elasticities of substitution in consumption and production. Equations (16) and (19) — (21) deliver

K^1w^m=σ1θL1(g3L1+g4)mo(1g4)S[εC1/Q1σ1(1γ)],(24)
L^1w^m=θK1moV[εC1/Q1σ1(1γ)]K^1w^m[θK1(1g4)mo+σ12(1γ)θL1mo2(1g4)V(g3L1+g4)],Short-runoutcome(25)
Q^1w^m=θK1(1+θL1Δ)VϵC1Q1K^1w^m+σ1θL1mo(1g4)(g3L1+g4)ϵC1Q1Short-runoutcome(26)
Figure 3:
Figure 3:

Impact on the capital stock in the formal sector when the real minimum wage increases and ε > ε*.

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

where

Δ1g3L1g4mo(1g4)>0,(27)
S=σ1[θL1(g3L1+g4)mo(1g4)V+θK1(1γ)(1+θL1Δ)2]>0.(28)

The equilibrium capital stock increases iff

ε>ε*=σ1(1γ)Q1C1.(29)

In our base case calibration, γ = .65, σ1 = .75, and Q1/C1 = 1.095.15 For these values, γ* is only .287. Sensible alternative calibrations produce higher (and lower) values for γ*, but there remains a general presumption that macroeconomic life is better in the long run than in the short run. Employment always decreases less in the long run. In addition, when ε > ε*, the capital stock and real output increase continuously on the path to the new steady state.

Could employment in the formal sector increase in the long run? This is asking too much of the current simplified model. It is possible, however, to get very close to a positive result. In the limiting case where the formal and informal goods are perfect substitutes (in consumption),

K^1w^m|ϵ==1g4,(30)
L^1w^m|ϵ==0.(31)

Eventually, employment fully recovers.

The full model includes additional general equilibrium effects that reduce employment losses relative to the losses in the simplified model. These effects can flip the sign of the employment elasticity in the formal sector from negative in the short run to positive in the long run for large but believable values of γ.

3.3 The Transition Path

The transition path is governed by the two differential equations for C and K in (7) and (8). Linearizing these two equations around the stationary equilibrium (C*,K1*) gives

C˙=τC(ρ+δ)(r^1P^k),(32)
PkK˙1=P1Q1Q^1PdCPkδdK1.(33)

Equations (2), (16), (20), and (23) link the paths of Pk, r1, Q1 and P1 to the path of K1. The solutions for Q1, r1, and Pk are

Q^1=θK1(1+θL1Δ)VεQ1¯K^1,(34)
r^=1V[(1γ)θL1Δ+θK1(1+θL1Δ)+εQ1¯θL1g3L1+g4mo(1g4)2],(35)
P^k=γP^1=γθK1V[1+θL1mo(1g4)(1g3L1g4)]K^1.(36)

Feeding the above solutions into (32) and (33) produces

[C˙K˙]=[0u11/Pku2][CC*KK*],(37)

where

u1τCK1ρ+δσ1V{εC1Q1σ1θL1(g3L1+g4)mo(1g4)2+σ1(1γ)[θK1+θL1Δ(1+θK1)]}<0,u21V{εC1Q1[ρ(1+θL1Δ)+δθL1Δ]δσ1(1γ)θL1Δ}.

The stationary equilibrium is saddle-point stable. On the convergent path,

CC*=(K1,0K1*)u1λeλt,(38)
K1K1*=(K1,0K1*)eλt(39)

where

λ=u2u224u1/Pk2<0.

Figures 4 and 5 depict the transition paths of K1, C, and L1. The saddle path is positively sloped and the capital stock increases or decreases monotonically depending on whether ε ≷ ε* = σ1(1 — γ)Q1/C1. In the fourth quadrant, the slope of the LL schedule takes the same sign as ε — ε*. Thus, after decreasing at t = 0, employment rises continuously. From (25) and (39),

L˙1L1=θK1moV[εC1/Q1σ1(1γ)]λSignofK1*K1,oK1*K1,oK1,oeλt>0.(40)
Figure 4:
Figure 4:

Transition path when K increases.

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Figure 5:
Figure 5:

Transition path when K decreases.

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Consumption increases in the short run when ε < ε* but not necessarily for ε > ε*. Two conflicting effects operate when ε > ε*. The increase in the equilibrium capital stock creates an incentive to temporarily reduce consumption, while the rise in output at t = 0 and the agent’s desire for a smooth consumption path pull in the opposite direction. In the case shown in Figure 4, the intertemporal elasticity of substitution (τ) is relatively low and the consumption-smoothing motive wins out. The private sector allocates some of the increase in real income at t = 0 to investment and some to consumption. The counterintuitive outcome where consumption decreases in the short run obtains only when the intertemporal elasticity of substitution is implausibly large. In our base case calibration, for example, ε must exceed 1.27.

3.3.1 Welfare

Although we are primarily interested in positive analysis, we take the opportunity in passing to comment on the welfare implications of the results. The punchline is easy to guess: the MW increases welfare, subject to the caveat that a model with a representative agent ignores distributional concerns or assumes, optimistically, that the newly unemployed are compensated enough for their lost wage income. This is obvious in Figure 4, where the path of consumption is continuously higher. Other paths are possible. Consumption may be lower either in the short/medium run or in the long run (Figure 5). In every case, however, welfare improves. In Appendix A we show that the percentage equivalent variation (EV) welfare gain is

EV=(1g3L1g4)θK1γmo(1g4)V(εε*)K1*K1,oK1,oSignofεε*λρλρ+εγσ1θL1(g3L1+g4)mo(1g4)VDirecteffectofwm.(41)

The welfare arithmetic in (41) is straightforward. Both employment and the real wage are suboptimal at the initial equilibrium. Raising the MW ameliorates the coordination externality. It also reduces employment. But since the total supply of labor services increases, the net welfare effect is positive. This gain is captured by the second term in (41). The first term measures the additional welfare gain generated by changes in the capital stock. Variations in K1 have no direct effect on welfare. Indirectly, however, changes in K1 increase welfare by increasing the supply of labor services. The sign of ε — ε* determines both the change in the equilibrium capital stock and the impact of increases in the capital stock on employment. Thus, regardless of whether the equilibrium capital stock rises or falls, the supply of labor services continues to increase as some of the workers laid off at t = 0 get rehired on the transition path to the new steady state. The MW always increases welfare because it always moves the supply of labor services closer to its social optimum.

4 The Full Model

The full model assumes an open economy where production in the export sector is constant at Qx and imports comprise machinery and equipment as well as consumer goods. The export good is not consumed domestically and all world prices equal unity (i.e., the country is small in world markets).

Many elements of the full model will be familiar from the exposition of the simplified model. To save space, we present the model with minimum commentary.

Technology

CES production functions convert inputs into output. Scarce entrepreneurial talent H is a fixed factor in the informal sector:

Q1=af[a11/σ1(e1L1)(σ11)/σ1+(1a1)1/σ1K1(σ11)/σ1]σ1/(σ11),(42)
Q2=ai[a21/σ2(e2L2)(σ21)/σ2+a31/σ3K2(σ21)/σ2+(1a2a3)1/σ2H(σ21)/σ2]σ2/(σ21)(43)

Factories are assembled by combining one imported machine with f1 and f2 units of formal and informal sector capital inputs. In both sectors,

Pk=1+f1P1+f2P2.(44)

Preferences, Saving, and Investment

Preferences are given by

C=[κ21/ϵ2Cj(ϵ21)/ϵ2+(1κ2)1/ϵ2C2(ϵ21)/ϵ2]ϵ2/(ϵ21),
Cj=[(1κ3)1/ε3Cm(ε31)/ε3+κ31/ε3C1(ε31)/ε3]ε3/(ε31).

The lower tier defines Cj as a CES aggregate of C1 and consumption Cm of an imported consumer good. At the upper tier, Cj combines with C2 in another CES function. The optimal choices for Cm, C1, and C1 yield

C1=κ3(P1Pj)ε3κ2(PjP)ε2C,(45)
C2=(1κ2)(P2P)ε2C,(46)

and the associated price indices

P=[κ2Pj1ε2+(1κ2)P21ε2]1/(1ε2),(47)
Pj=[κ3P11ε3+1κ3]1/(1ε3).(48)

The representative agent solves the more elaborate Ramsey problem

Max{C,I1,I2,g,h}U=011/τ¯eρtdt,(49)

subject to

PC=P1Q1+P2Q2+QxPk[I1+I2+v12(I1K1δ)2K1+v22(I2K2δ)2K2]w1L1w2L2P2v3g22P1v42h2+R(50)
K˙1=I1δK1,(51)
K˙2=I2δK2,(52)
L˙1=hL1,(53)
L˙2=hL2.(54)

where R ≡ w1L1 + w2L2; Ij is investment in sector j (j = 1, 2); and the terms v1(·)2K1/2} v2(·)2K2/2, v3g2/2, and v4h2/2 capture adjustment costs incurred in changing the capital stocks and employment.16

The first-order conditions for an optimum can be compressed into a set of four Euler equations for I1, I2, g, and h. On an optimal path, investment adjusts so that the return on capital, net of adjustment costs and depreciation, continuously equals the real interest rate. Similarly, adjustment costs to changing employment drive a wedge between the marginal product of labor {Qih) and the product wage:

v1K1I˙1=[1+v1(I1K1δ)][C˙Cτ+ρ+δ(α1γ1)P˙1P1(α2γ2)P˙2P2]+v12(I1K1δ)2r1Pk,(55)
v2K2I˙2=[1+v2(I2K2δ)][C˙Cτ+ρ+δ(α1γ1)P˙1P1(α2γ2)P˙2P2]+v22(I2K2δ)2r1Pk,(56)
h˙=(w1/P1Q1L)L1v4+ρh+h[C˙Cτ+(1γ1)P˙1P1+γ2P˙2P2],(57)
g˙=(w2/P2Q2L)L1v4+ρg+gt[C˙Cτ+(1γ1)P˙1P1+γ2P˙2P2],.(58)

where αi = Pifi/Pk is the cost share of the good i in the production of a factory and γiPiCi/PC is the consumption share of good i.

The Effort Functions

EW effects operate in both sectors:

e1=g0+g1lnwm+g3ug4lnL1,(59)
e2=bo+b1ln(w2/P)b2lnwm+b3u.(60)

The effort function in the informal sector differs from its counterpart in the formal sector in two ways. First, effort is independent of employment on the assumption that supervision of the small workforce at micro firms is not a problem. Second, and more importantly, the MW shifts the norm for fairness among workers. When wm increases, workers perceive their current real wage as less fair than before; disgruntled, they express their dissatisfaction with the status quo by reducing effort.

Labor Demand and the Wage Curve in the Informal Sector

The sectoral demands for labor are

L1=a1Q1(afe1)(σ11)(1g4/e1)σ1(wmPP1)σ1,(11')
L2=a2Q2(aie2)(σ21)w2σ2.(61)

Enforcement of the MW law is confined to the formal sector. In the informal sector, firms pay an EW well below wm. Equation (60) and the Solow condition

e2(w2/P)w2/Pe2=1(62)

yield

e2=b1.(63)

Conveniently, effort is constant in general equilibrium. We set e2 equal to unity, the initial level of effort in the formal sector. The resulting wage curve is

ln(w2/P)=1bo+b2lnwmb3u.(64)

At first glance, equation (64) delivers a lighthouse effect. This is not necessarily the case, however. Layoffs in the formal sector exert downward pressure on the real wage by increasing the unemployment rate. Moreover, estimates of wage curves find, as expected, that real wages are considerably more responsive to unemployment in the informal sector than in the formal sector. A significant lighthouse effect requires not only b2 sufficiently large, but also relatively small employment losses in the formal sector. The MW puzzle is multifaceted, but the three most important stylized facts – small employment losses in the formal sector, larger employment losses in the informal sector, and the lighthouse effect – are all of a piece.

Raising the MW

The policy experiment is the same as in the simplified model. Initially the MW is a penny below the EW firms pay in the formal sector. The announcement of a higher MW thus increases the wage in the formal sector dollar-for-dollar.

Market-Clearing Conditions

Four market-clearing conditions close the model. Demand equals supply in the formal sector, the informal sector, and the rental markets for the two capital stocks when17

Q1=C1+f1[I1+I2+v12(I1K1δ)2K1+v22(I2K2δ)2K2]+v4h22,(65)
Q2=C2+f2[I1+I2+v12(I1K1δ)2K1+v22(I2K2δ)2K2]+v3g22,(66)
K1=(1a1)Q1af(σ11)(r1P1)σ1,(67)
K2=a3Q2ai(σ21)(r2P2)σ2.(68)

4.1 Model Calibration

Table 1 shows the values assigned to various deep parameters, to the formal sector wage premium, and to factor shares and expenditure shares at the initial equilibrium. We chose ordinary values for the depreciation rate (δ), the intertemporal elasticity of substitution (τ), the urban unemployment rate (u), and the cost share of capital in the formal sector K1) With respect to the other choices (save one):

  • Pure time preference rate (ρ) and the real return on private capital. Across steady states, the real return on private capital (net of depreciation) equals ρ. We set ρ at 10%. This is line with estimates of the return to private investment in Isham and Kaufmann (1999), Dalgaard and Hanson (2005), and Marshall (2012), and with hard data on real loan rates in LDCs.18

  • Elasticity of substitution between capital and labor services1, σ2). Estimates of σ in LDCs range from .5 to 1.2.19 Overall, there is more support for σ < 1 than for σ ≥ 1. Since separate estimates do not exist for the informal sector, we fix both σ1 and σ2 at .75. The results do not change significantly when σ equals .5 or f.

  • Adjustment costs to changing the capital stock (v1, v2) and the q-elasticity of investment spending (Ω). The first-order condition for investment in the formal sector is [1+v(I1/K1 — δ)] = φ12Pk, where φ1 and φ2 are multipliers attached to the private agent’s budget constraint and to the law of motion for the capital stock [the constraints in (50) — (52)]. To link the adjustment cost parameter v1 to an observable elasticity, note that φ1/φ2) is the shadow price of capital measured in dollars. Thus φ1/φ2Pk is effectively Tobin’s q, the ratio of the demand price to the supply price of capital. Let Ω1I^1/q^ denote the q-elasticity of investment spending. Evaluated at a stationary equilbrium, the first-order condition for investment then gives v1 = 1/δΩ1. There are only a couple of reliable estimates of for LDCs. The estimates for Egypt in Shafik (1992) and for Korea in Hong (1998) and Kim et al. (2015) are 2.11 — 2.56, 3.1, and 2.08 — 2.36, respectively. The assigned value is consistent with these estimates and with high-end estimates for developed countries. A sensible case can be made for both higher and lower numbers. Fortunately, the results are highly insensitive to Ω. The impulse responses presented in Sections 4 and 5 change very little when equals .5 or 5.

  • Adjustment costs to changing employment (v3, v4). The empirical literature on adjustment costs for employment is frustrating to read. Some estimates find that adjustment costs are quite small, others suggest that they are much larger than adjustment costs for the capital stock.20 Taking a conservative position, we assume adjustment costs are 50% as large as adjustment costs for the capital stock in the formal sector. This implies v4 = .5v1PkK1/P1.21 Not much is known about adjustment costs in the informal sector, but they are probably a small fraction of adjustment costs in the formal sector.22 Our poorly educated guess is that v3 = .1v4.

  • Firm-size wage premium [g4/(1 — g4)]. Velenchik (1997), Soderbom and Teal (2004),Falco et al. (2011), Aigbokhan (2011), and Rand and Torm (2012) report elasticities of the real wage with respect to employment of .16 in Zimbabwe, .15 in Ghana, .38 — .50 in Tanzania, .26 in Nigeria, and .24 in Vietnam. This elasticity pins down 54 in the formal sector wage curve in (14). Our choice, .25, equals the average of the five estimates. The associated value of g4 is .20 [g4/(1— g4) = sizepremiumg4 = sizepremium/’(1 + sizepremium)].

  • Formal sector wage premium (ψ = w1/w2)- The formal sector wage premium is large in LDCs. Numerous empirical studies find, after controlling for observable human capital characteristics, unobservable heterogeneity, self-selection, and workplace conditions, that workers in the formal sector earn 20 — f 20% more than workers in the informal sector.23 A wage premium of 50% is representative, if slightly conservative. As explained later, the wage premium should be set jointly with the sectoral factor cost shares and the consumption share of the formal good to be consistent with the observed share of the formal sector in total employment.

  • Consumption shares1, γ2, γm). There is considerable variation in the size of the formal sector across LDCs. To accommodate this, we set γm at .14 and let γ1 take low, average, and high values of .39, .56, and .69. The average value, together with the values assigned to other parameters, generates an output share of the formal sector in non-agricultural GDP equal to the average share in the World Bank Enterprise Surveys (La Porte and Shleifer, 2014).

  • Elasticity of substitution in consumption between the composite formal good (Cj) and the informal good2). Estimates of demand systems do not distinguish between goods produced by formal and informal firms. The right value for ε2 is a judgment call therefore that depends on whether firms in the formal and informal sectors sell in similar or distinct product markets. Variation across countries in the sectoral overlap between formal and informal firms suggests that both high and low values of ε2 are defensible. Lacking a strong prior, we carry out runs for ε2 = -5 — 5.

  • Elasticity of substitution between imported consumer goods and the formal good3). The law of one price does not hold for manufactured goods or services like tourism, which, unlike primary products, are highly heterogeneous. The characterization of the formal sector as tradable or nontradable depends therefore on the value assigned to ε3. When ε3 = 1, formal sector output is either nontradable or a poor substitute for imports. In runs where ε3 = 10, the sector produces manufactured goods competitive with imported varieties. ε3 = 3 is an in between case (e.g., the formal sector produces a mix of nontradable services and highly tradable manufactured goods).

  • Cost share of the formal/informal good in production of investment goods (α1, α2). The base case in the full model maintains the assumption of the simplified model that αi = γi.

  • Lighthouse effect (b2)- There are no empirical estimates on which to base the value of 62-In these circumstances we set b2 = 1 in which case effort in the formal sector depends on the ratio of the wage to the MW. The simulation results discussed below suggest this represents a plausible calibration, although we also investigate the consequence of a weaker lighthouse effect.

  • Real wage flexibility in the formal and informal sectors [g3/(1 —g4), g3]. Most estimates of wage curves in LDCs find that g3 >> g3/(1—g4) (see Table 2). In other words, the common perception that real wages are much more flexible in the informal sector than in the formal sector is correct. But much more flexible does not always mean highly flexible. In both the formal and informal sector, the sensitivity of the real wage to the unemployment rate varies considerably across countries, time periods, and states of the economy. Aiming for generality with minimum taxonomy, we examine low, average, and high wage flexibility scenarios, but impose b3 = 2g3/(1 —g3) in all runs.

Table 1:

Calibration of the Model.

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The cost shares for capital and production labor satisfy the adding-up constraint θK1 + θL1/(1 – g4) = 1. This and the value of g4 backed out from the size premium imply θL1 = .48 and a cost share of . 12 for managerial/supervisory labor

Table 2
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Source: Cross sectional means from 19 World Bank Informal Firms Survey (see Note 23)Notes: [a] Total self-reported labour costs as a share of derived value added; [b] Average reported wage time total employment (including family members); [c] Labour share initially calculated excluding firms where measured labour share in excess of 1; trimmed calculation excludes firms with calculated labour share less than 0.15.

4.1.1 The Problem Child: Cost Shares in the Informal Sector

One important part of the model proved difficult to calibrate. Good, sensible data are not readily available for factor cost shares in the informal sector. National Income Accounts data are especially unreliable (Gollin, 2002).

We calibrate the labor share in informal sector value added directly from the 19 Informal Enterprise Surveys collected by the World Bank.24 We focus exclusively on manufactured firms and compute the labor share at the level of the firm as 9u = {wL/VA)i. The denominator, value added, is defined as VAi = PYi — PMMi — PEEi, where PYi denotes the total value of sales, PMMi is the cost of material inputs, and PEEi is the value of energy and transport costs. We consider two measures of the numerator, labor costs. The first is simply the firm’s self-reported “labor costs” and the second (“wage bill”) is computed as the product of the (reported) average wage times reported employment. As noted by Gollin (2002), in many low-income countries payments to informal labor, including family employees, are treated as residual payments to capital; to control for this, we impute the average wage for “unpaid” family members working in the firm.

Both labor measures (“labor costs” and “wage bill”) are computed on a country-by-country basis where the usable sample of manufacturing firms ranges from 50 to 250 informal firms. Missing and clearly mis-reported data are endemic in the informal surveys and we therefore censor the firm-level data, excluding firms with labor shares in value added that exceed 100% or fall below 15%. Table 2 and the associated kernel densities in Figure 6 summarize the information in the 19 surveys. Mean employment in informal firms is approximately four (of which 1.75 are unpaid family/other employees) and the labor share in informal sector value added is approximately .50. Since production is less capital intensive in the informal sector than in the formal sector, we set θK2 = .25. This and the value of .50 for θL2 imply a cost share for entrepreneurial skill of .25.

The initial distribution of non-agricultural employment between the formal and informal sectors is tied down by the formal sector’s share in consumption and investment expenditure, γ = α; the initial formal sector wage premium, ψ = w1/w2] and factor cost shares in the two sectors. If the values assigned to these variables are reasonable, the employment share of the formal sector should lie between .35 and .75, the range observed in the data (Terrell and Almeida, 2008; Gasparini and Tornarolli, 2009). The base case and alternative calibrations of the model satisfy this consistency check. In the baseline calibration where 71 = γ1 = .56, formal labour accounts for 54% of total (non-agricultural) employment. Increasing the expenditure share of the formal sector to .69 implies that formal sector labour accounts for 72% of the total, which aligns with non-agricultural employment shares in higher-income countries in Latin America, while for γ1 = α1 = .39, the share of formal employment in non-agricultural employment falls to 34%, consistent with that observed in low-income countries.

4.1.2 Solution Technique

There are a variety of ways to approximate the stable manifold. Given the substantial non-linearities present in the model, we judged the method in Novales et al.\thinspace (1999) to offer the best tradeoff between solution speed and minimization of approximation error. The method derives stability conditions from a linear approximation around the steady state, but incorporates the nonlinear structure of the model when tracking the transition path.

5 Numerical Results

Different calibrations of the model are appropriate for countries at different stages of development. To keep the taxonomy sparse, we limit the analysis in this section to a comparison between two archetypes: a middle-income developing country (MIC), corresponding roughly to the middle two quartiles of per capita income of the countries analysed by La Porta and Shleifer (2008, Table 1), in which the formal sector accounts for approximately 65 percent of non-agricultural output, and a high-income, Emerging Market (EM) economy where the formal sector share is around 80 percent (La Porta and Shleifer’s top quartile of countries). These archetypes reflect the broad structural characteristics of the countries that dominate the empirical evidence reviewed in Appendix B. In Section 6 we report the results of solving the model calibrated for a representative low-income country (LIC) where the formal sector accounts for only 35% of non-agricultural output. In each case we report the long-run consequences of an increase in the real minimum wage in the formal sector for key macroeconomic indicators: the percentage change across steady states in sectoral and total employment; sectoral capital stocks; sectoral and aggregate output; and the real consumption wage in the informal sector. Reading from top to bottom of each table, the panels summarize the solution results under alternative characterizations of the structure of consumption, defined by the elasticities of substitution between formal and informal goods (ε2) and between the domestic formal good and the imported good (ε3), while reading left to right within each panel shows variations in outcomes as the slope of the wage curves in both sectors increases. The central settings for the unemployment semi-elasticity of wages are g3/(1— g4) = 1 in the formal sector and b3 = 2 in the informal sector, against which we consider a relatively flat wage curve (g3/(1 — g4) = .5 and b3 = 1) and a relatively steep curve (g3/(1 — g4) = 1.5 and b3 = 3).25 In each case we consider a permanent 10% increase in the formal sector real minimum wage: to compare these results with the elasticities typically reported in the empirical literature, simply divide our results through by 10.

5.1 Middle Income and Emerging Market calibrations

5.1.1 The long-run

The first two panels of Table 3 show the effects of reducing the elasticity of substitution in consumption between the formal and informal good (from ε2 = 3 to ε2 = 1.5) holding the corresponding elasticity of substitution between the formal and imported good constant at ε3 = 3. In the remaining panels we assume the domestically produced formal good and the imported good are close substitutes in consumption (ε3 = 10) and then progressively reduce the substitutability between the formal good and the informal good.

Table 3:

Long-run outcome, MIC calibration.

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Focusing first on the central spine of Table 3, three main results stand out. First, in the long run the aggregate economy adds capital, expands output and sheds labor.26 The output and capital elasticities both lie between 0.31 and 0.38, and the employment elasticities are around —0.25. These long-run changes strongly favor the formal sector but informal sector wages also rise and aggregate welfare increases in all cases (see below). The mechanics of these outcomes are consistent with the intuition developed in Section 3, and can be traced through panel [a] in the first instance. A higher minimum wage leads to a modest contraction in long-run employment in the formal sector, but this is offset by increased capital accumulation and output in this sector. These changes are accompanied in the informal sector by a proportionately larger contraction in employment (so that aggregate employment falls) and by a mild contraction of the capital stock and a modest contraction in output. Specifically, total employment contracts by 2.8%, comprising a contraction of 1.9% in formal sector employment and a 3.9% reduction in employment in the informal sector. Total output expands by 3.9%, but also in an unbalanced fashion; formal sector output expands by 7.2% while informal sector output contracts by 2.1%.

The strong growth in formal output reflects large increases in both the capital stock and labor services. Because of EW effects, effective labor input in the formal sector (e1L1) rises by 7.9% as increased effort outweighs the contraction in formal sector employment. This growth, in turn, increases the marginal product of capital and stimulates investment; capital in the formal sector thus grows by 6.1% across steady states. By contrast, the decrease in employment in the informal sector leads to a modest net disinvestment so that output contracts. Because aggregate employment losses are small, however, the unemployment effect in the informal wage curve is relatively weak so that the lighthouse effect is observed with the informal real wage rising by just under 5%.

Second, higher substitutability (between formal and informal goods and between the formal good and the imported good) means higher aggregate gains to the economy, leveraged in favor of factors employed in the formal sector (compare column 2 of panels [a] and [c] in Table 3). Total output growth increases from 3.9% to 4.8%, while the contraction in overall employment is slightly lower (—2.5% as opposed to —2.8%). These aggregate effects, however, conceal highly asymmetric sectoral effects: in panel [c], formal sector employment marginally increases, while contraction in the informal sector increases sharply and likewise in the responses of sectoral capital accumulation and output.

The final three panels of Table 3 explore these changes further by considering cases where the formal and informal sectors are progressively less substitutable in demand (with the formal and import goods remaining highly substitutable). As this occurs, aggregate outcomes are attenuated and the net gains shift back in favor of the informal sector, although the principal driver of GDP growth remains the expansion of formal sector output, irrespective of the level of wage flexibility. Moreover, as substitutability falls, employment losses in the formal sector increase and eventually exceed those in the informal sector, to the point where, if formal and informal goods are very poor substitutes, employment in the informal sector may increase, especially when the wage curves are relatively steep (panel [f]). Whilst this movement in employment is consistent with the standard segmented labor market model, the associated increase in output and the informal sector wage is not.

Third, the steeper the wage curves, the stronger are the positive effects on output and employment in both sectors. Per the analysis in Section 3, the larger the unemployment semi-elasticity in the formal and informal sector wage curves, the more rising unemployment leverages effort, minimizing employment losses in both sectors. The extra boost to effective labor spurs greater capital accumulation, further reducing employment losses. Indeed, in combination with high general substitutability in consumption, formal sector employment may actually increase in the long run. This paradoxical result stems from general equilibrium interactions associated with the lighthouse effect. Indirectly, via its impact on the unemployment rate, the lighthouse effect increases work effort, labor productivity, and labor demand in the formal sector. We observe this in columns 2 and 3 of panel [c], but it follows that for any plausible slope to the wage curve there exists critical values of ε2 and ε3 for which formal sector employment increases across steady states. Naturally, the critical value of ε2 is smaller the steeper the wage curves. In the MIC calibration with ε3 = 10, for example, the borderline value of ε2 declines from 7.5 when g3/g1 = .5 and b3 = 1 to 3.4 for g3/g1 = 1.5 and b3 = 3.

Table 4 replicates panels [a], [d] and [f] from Table 3 for the Emerging Market (EM) calibration where the informal economy accounts for only 20% of non-agriculture output. The qualitative nature of the results is broadly similar to the MIC calibration with the key quantitative difference being that the larger formal sector leverages the aggregate gains to the economy, again with the employment and output gains accruing primarily to the formal sector. For example, in the case of ε2 = 3 and ε3 = 10, long run output is between 1.4 and 1.9 percentage points higher than in the MIC case, although in this case the effect on informal wages is significantly stronger.

Table 4:

Long-run outcome, HIC/EME calibration.

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5.1.2 Coherence With Empirical Estimates

Our simulation results are generated for a range of plausible model calibration choices that are themselves disciplined by the relevant research evidence. Nonetheless, the range of results displayed in Tables 3 and 4 displays a pleasingly high degree of fidelity with the empirical evidence discussed in the Introduction. Much the largest share of this evidence focuses on the short- to medium-run employment consequences of changes in minimum wages and, to a lesser extent, on the impact on wages in the uncovered sectors; there is much less empirical evidence on sectoral or aggregate output effects. Figure 7 presents a stylized summary of our simulated employment elasticities for the MIC calibration (the results from Table 3 shown in red) and the EM calibration (from Table 4, shown in green), against a range of estimates from the empirical literature (from Appendix B). The distribution of the simulated results is statistically indistinguishable from that of the empirical estimates: the mean of the former is -0.24 with a standard deviation of 0.18 against a mean of -.22 and standard deviation of 0.20.

Figure 7:
Figure 7:

Empirical and simulated employment elasticities

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

As noted, the evidence on other variables is less complete but nonetheless our simulations are consistent with the key results emerging from the literature. The bulk of the empirical evidence suggests that wages in informal/uncovered sectors rise – or at least do not fall – following increases in the formal-sector minimum wage. Gindling and Terrell (2005) estimate an elasticity of .15 for urban informal workers and .40 for rural informal workers (Costa Rica); Neumark et al. (2006) estimate an elasticity of .43 (Brazil); and Rani and Ranjbar’s (2015) estimated elasticities vary from .45 (for India) to around .80 – .90 (for Indonesia and South Africa). See also Bhorat et al (2016), Andalon and Pages (2009), Lemos (2009), Gindling and Terrell (2007). The results from Tables 3 and 4 return uniformly positive informal wage elasticities that range from .41 to .71. Finally, while only a few empirical papers attempt to measure the impact on macro variables other than employment, those that do strongly support the predictions of our model that big positive effects on GDP, labor productivity, and investment are the norm. Rama (2001), Azam (1997), Kertesi and Kollo (2003), Bhorate et al.(2014), and Mayneris et al. (2014) report very large increases in labor productivity in Indonesia, Morocco, Hungary, South Africa, and China (Table Cl, Appendix C).2728 Mayneris et al. (2014), for example, estimate the elasticity of labor productivity with respect to the MW in China to be .38 for the private sector and .19 for the state sector. By way of comparison, in simulations for our base case, the mean elasticity is approximately .41 across steady states and .20 to .40 in the short/medium run.

5.1.3 Transition Paths and Welfare

We conclude our analysis of these results by examining the transitional dynamics for employment, capital, output and consumption along with the welfare implications of raising the minimum wage. Figures 8 and 9 report the first 50 periods of the transition paths for the MIC and EM calibrations respectively. Consider first the MIC calibration in Figure 8, which displays the transition path for the case analysed in column 2 of Table 3, panel [d]. As per Figure 4, consumption and output jump on impact – reflecting the instantaneous adjustment in effort – before converging on their long-run values as capital stocks adjust. Given the calibrated adjustment costs in capital, the latter converge relatively slowly towards their long-run values (K1 achieves half its long-run value after approximately 25 periods). The path for employment is highly sensitive to adjustment costs. When these are absent, as shown in the final panel of Figure 8, formal employment substantially overshoots its long-run value (the short-run elasticity is -0.48 compared to the long-run elasticity -0.10) and informal employment undershoots its long-run value. Allowing for small adjustment costs in employment, as shown in the penultimate panel of Figure 8, recognizing these are likely to be substantially higher in the formal sector than the informal sector, generates a more modest degree of overshooting and smoother and more realistic paths for employment.29

Figure 8
Figure 8

Transition Path: Table 3, panel [d]

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Figure 9
Figure 9

Transition Path: Table 4, panel [c]

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Notes: see Figure 8.

These patterns are broadly replicated in Figure 9 for the EM calibration, corresponding to column 3 of Table 4, panel [c]. Recall that in this case the low substitutability in consumption between the formal and informal goods means that employment and capital accumulation both increase in the informal sector. In this case, for the same parameterisation of adjustment costs, the degree of overshooting in formal sector employment is substantially reduced and the short-run overshoot of consumption and output witnessed in Figure 8 is eliminated.

Figures 10 to 13 pick out panels from Tables 3 and 4 to explore how the transition dynamics for employment vary with changes in the calibration of the wage curves and economic structure. Two features emerge. First, except when the elasticity of substitution between formal and informal goods is low (for example Figure lie and Figure 12), the notion that the formal sector employment elasticity may be greater in the short- to medium-run than in the long-run is quite general: to the extent that much of the empirical literature is concerned with short-run evidence, these results suggest that this evidence may overstate the true long-run formal sector employment effects of MW increases. The second and related feature is that when the elasticity of substitution is low, employment losses in the informal sector may initially exceed those in the formal sector, even though the long run outcome for informal sector employment is more favorable.

Figure 10
Figure 10

Transition Paths: Table 3, column 2

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Figure 11
Figure 11

Transition Paths: Table 3, column 3

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Notes: see Figure 8.
Figure 12
Figure 12

Transition Paths: Table 3, panel [b]

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Figure 13
Figure 13

Transition Paths: Table 4, column 2

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Finally turning to welfare considerations, recall the striking result in the simplified model that the MW always increases welfare, at least in the simple case of a single representative agent. This result, which does not generalize to the full model (see Section 6), is highly robust in the relevant parameter space considered here.30 In all 27 runs reported in Tables 3 and 4, the path of consumption is qualitatively similar to the path shown in Figures 8 & 9: aggregate consumption jumps upward at t = 0 and then converges smoothly to its steady-state level, closely tracking the path of GDP.

5.1.4 Coherence with empirical estimates revisited

Although we noted the close fidelity of the of our simulated long run employment elasticities with the empirical estimates, we need to recognize that the latter tend to be measure short-to medium-term employment effects. A more relevant test of fidelity, therefore,is whether our simulated short-run elasticities are consistent with the empirical evidence. Comparing the transition paths with Figure 7 suggests they are: while the over-shooting of employment necessarily means the short-run simulated elasticities are substantially larger, the reported values along the transition paths shown in Figures 813, still remain within the range of empirical estimates reported in Figure 7.

Even so, there are a number of reasons why our simulated (long-run and short-run) estimates from our model may still be ‘too high’ relative to those derived from empirical studies. Three in particular are worth mentioning. First, we assume that coverage of and compliance with MW legislation is complete in the formal/covered sector. Second, our simulations are generated from a starting point where the initial (efficiency) wage in the formal sector is equal to the MW prior to its increase and that firms have optimized employment and output to this MW. Both assumptions will tend to leverage up our simulated elasticities relative to estimates from environments where coverage and compliance is incomplete and wages may initially be substantially below the prevailing MW. Third, the calibrated unemployment elasticities we use in our model wage curves are defined in terms of the aggregate, economy-wide unemployment rate rather than an arguably more salient skill- or sector-specific unemployment rate, with the consequence of weakening the employment effect of minimum wage effects.

6 The Low-Income Country Case

The results in Tables 3 and 4 sit comfortably with the rich evidence from those middle-income developing countries whose MW programs have been studied extensively in the empirical literature (e.g., Brazil, Costa Rica, Honduras, Mexico, Indonesia, and South Africa). By contrast, however, there is very little robust empirical evidence on low-income economies, such as those of Sub-Saharan Africa, and hence nothing with which to discipline the results of solving the full model for a LIC calibration. It is nonetheless of interest to consider the implications of our model for a stylized low-income country where the informal sector is much more dominant and where coverage and compliance of MW regulations is very significantly lower. Table 5 reports a set of runs for a calibration where the informal/non-compliant sector accounts for a large share (65%) of the non-agricultural economy and whose output, arguably, is less substitutable in consumption with output of the formal sector. To reflect the lower substitutability with formal sector output and with imports, we concentrate on runs where ε2 = 1,63 = 3 (panel [b]) and ε2 = ε3 = 1 (panel [c]), although for comparison with Tables 3 and 4 we retain the ε2 = ε3 = 3case. Compared to Table 3, the aggregate response and response in the formal sector are significantly attenuated. For ε2 = ε3 = 3 and the wage curve parameters at their central values (Panel [a], column 2), aggregate output growth collapses from 3.9% to 0.7%, while the contraction in aggregate employment increases from 2.8% to 3.6% between steady states. Outcomes for the formal sector are correspondingly less favorable, with employment elasticities much closer to the high end estimates reported in Figure 7. If we combine these low-income country structural characteristics with a relatively flat wage curve, as in Column 1, employment losses increase even further, to 5.9% for aggregate employment and 5% for the formal sector. And it is here where the kicker comes in: aggregate output and investment stagnates or contracts slightly, with the minimal output gains in the (now relatively small) formal sector failing to offset the contraction in informal sector output. This has an unfortunate corollary. While consumption is continuously higher in the six runs where g3/g1 = 1 — 1 .5 and b3 = 2 — 3, it is short-lived when wage curves are relatively flat. This is shown in Figure 14. After an upward jump at t = 0, consumption decreases monotonically, dropping below its initial level at year four. The end result is an equivalent variation welfare loss equal to .10 — .15% of consumption when the social discount rate is 10% (the private rate) and .43 — .50% when the discount rate is 5%.31 If our LIC calibration is broadly plausible, this suggests that the favorable aggregate effects from MW policies documented for Middle Income and Emerging Market countries are much less likely to emerge in LICs where the formal sector is small and produces goods that are relatively poor substitutes for imports and for informal sector goods and where wage curves are flat.

Table 5:

Long-run outcome, LIC calibration.

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Figure 14
Figure 14

Transition Paths: Table 5, column 1

Citation: IMF Working Papers 2020, 023; 10.5089/9781513527888.001.A001

Notes: see Figure 8.

7 Concluding Remarks

We have shown that a dynamic general equilibrium model with efficiency wages in both the formal and informal sectors can explain the salient features of the empirical evidence on how binding MW regulations affect employment, wages, and output in middle-income and emerging market developing countries. Calibrated to conventional values for structural parameters, to micro-level data for informal firms, and to consensus estimates of sectoral wage curves, the “fully-loaded” model has considerable leverage, generating results for the short- and long-term that are capable of replicating the full range of empirical estimates in the existing literature. Building on this platform, we extend the model to consider the implications for a stylized low-income country and identify the channels through which MW regulations may have distinctly inferior and possibly adverse aggregate output and welfare effects in LICs compared to MICs.

This is, however, only a first pass. There are a number of areas in design and application that require to be addressed in future research. On the modelling side, we have already hinted at modifications, including the explicit treatment of coverage and compliance,32 that may be required to further strengthen our ability to match the key characteristics of the empirical evidence, but there are some others. These include allowing for efficiency wage effects to operate in the public sector as well as the private sector, and to allow for habit formation or adjustment costs in effort so as to remove the rather unrealistic impact effects we observed on the transition paths. Our priority, however, is to engage more directly with welfare considerations since the results presented here are merely suggestive. They show only that welfare often increases when the MW is slightly above the equilibrium wage in the formal sector, but more importantly they are necessarily silent on distributional concerns. The latter qualification is obviously important. A proper analysis requires welfare comparisons in a more elaborate model with heterogeneous households.

The Minimum Wage Puzzle in Less Developed Countries: Reconciling Theory and Evidence
Author: Mr. Christopher S Adam and Mr. Edward F Buffie