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Appendix A

For small changes,

UU0C01/τ=0(CC0)eρtdt.(A1)

Linearizing the private agent’s budget constraint gives

CCo=ρPk(K1K1,0)PkK˙1+Q1θL1[1g3L1g41g4(m1K^1+m2P^1+m5θL1w^m],(A2)

where

m1=θK1/mo,m2=σ1(1γ)/mo,m5=σ1θL1(g3L1+g4)mo(1g4),

and we have chosen units to that P1 = P = 1 at the initial steady state.

The envelope theorem tells us that there is no first-order impact on welfare of changes in the capital stock, holding the supply of labor services constant. Hence the sum of the first two terms in (A2) equals zero. Formally, substitute

K1K1,0=(K1*K1,0)(1eλt)(A3)
K˙=λ(K1*K1,0)eλt(A4)

into (A2) and then substitute the resulting expression for C — Co into (Al):

UUoCo1/τ=Pk(K1*K1,0)[0ρeρtdt+0(λρ)e(λρ)tdt]+0Q1θL1[1g3L1g41g4(m1K^1+m2P^1+m5θL1w^m]eρtdt.(A5)

The two integrals enclosed by [•] sum to zero. Thus the welfare gain/loss depends only on how the MW affects the present value of the total supply of labor services (e1L1):

UUoCo1/τ=Q1θL10[1g3L1g41g4(m1K^1+m2P^1+m5θL1w^m]eρtdt.(A6)

Write the solution for P^1 in equation (21) as

P^1=m3VK^1m5Vw^m,(21')

where

m3θK1[1+θL1(1g3L1g4)m0(1g4)]

Substituting for P1 in (A6) and collecting terms yields

UUoCo1/τw^m=Q1θL10[1g3L1g41g4(m1+m2m3/V)K^1w^m(A7)+m5(1θL1m2V1g3L1g41g4)]eρtdt.

Now

m1m2m3V=m1V[εC1/Q1σ1(1γ)],m5(1θL1m2V1g3L1g41g4)=m5θL1VεC1Q1.

So the solution in (A7) may be rewritten as

UUoCo1/τw^m=Q1θL1(1g3L1g4)(1g4)Vm1K1[εC1/Q1σ1(1γ)]0(K1*K1,0)(1eλt)eρtdt+Q1m5VεC1Q10eρtdt.(A8)

(UUo)/Co1/τ is the welfare gain measured in units of consumption. To express the equivalent variation (EV) gain as a percentage of consumption, multiply by ρ/C. Doing this and substituting for m1 and reproduces the solution stated in equation (41) in the text:

EV=(1g3L1g4)θK1γm0(1g4)V(εε*)K1*K1,oK1,0Signofεε*λρλρ+εγσ1θL1(g3L1+g4)mo(1g4)VDirecteffectofwm.(69)

Appendix B

Wage Curves and Unemployment

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Appendix C

Minimum Wage Studies and Episodes

Notation: F = formal sector; I = informal sector; EE = employment elasticity; Overall = combined effect in formal and informal sectors; LE = lighthouse effect. Unless otherwise noted, employment elasticities are negative in the formal sector.

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The authors caution that, due to the limitations of the data and a weak identification strategy, the positive EE is not strong evidence of an indirect of the MW on employment in the informal sector.

The 13–18% figure is our estimate based on data in the paper.

1

This research was supported by funding from the United Kingdom’s Department For International Development under the IMF-DFID Macro Research for Development Program and from the Macroeconomic Research Division of the African Development Bank. We thank Sterre Kuipers for excellent research assistance. All errors and omissions are solely ours.

1

Kristensen and Cunningham emphasize this point: “. . enforcement mechanisms are weak, but for some reason employers, and particularly those in the informal sector who are not legally bound by the minimum, choose to adjuste wages when the legally mandated wage is changed.”

2

This is the solution for the short run, where the capital stock is fixed.

3

It is often asserted that failure to account for noncompliance biases estimates of the employment elasticity downward. This assertion is valid in the SLMM but dubious in our model. The informal sector in our model includes firms that do not comply with the MW law. But employment losses in the noncompliant sector are typically larger than in the compliant sector. Failure to account for noncompliance could therefore bias the estimated elasticity in the formal sector upward.

4

Bhorat et al. attribute the problem to lack of data. We partly disagree. In the case of SSA, we favor a combination of Bhorat et al. and Fields’ views: better policy analysis requires new, better theoretical models informed by better data.

5

Investment increases provided the elasticity of substitution in consumption between the formal and informal good is not implausibly low.

6

Berg and Contreras (2004) supply evidence for Chile. Neri (2002) and Ulyssea (2010) provide additional evidence for Brazil.

7

The general form of the Euler equation is C˙=τC[r1/Pkρδ(γα)P˙/P1], where α ≡ fP1/Pk is the cost share of the formal good in production of the investment good and γ ≡ P1C1/PC is the share of the formal good in aggregate consumption. Equation (8) assumes α = γ.

8

In the Shapiro-Stiglitz model where effort is either zero or one, L1/S and the unemployment rate will enter the no-shirking condition.

9

The Solow condition states that the wage maximizes profits when the elasticity of effort with respect to the real wage equals unity. The condition emerges whenever the first-order condition calls for w to minimize w/e(w).

10

Write the production function as Q = F[e(w1/P, L1/S1)L1, K1]. With constant returns to scale,

λQ = F[e(w1/P, L1/S1)L1, K1].,

Differentiating with respect to A gives

Q=F1eL1+FKK1Q=w1L1/P1(1g4)+r1K1/P11=θL1/(1g4)+θK1.
11

L1 and the unemployment rate determine the employment share of the formal sector: L1/(L1 + L2) = L1/(1-u).

12

L1 is backed out from the values of other parameters and variables. It equals .49 in the base case calibration.

13

When MW increases, e1 inreases and the marginal product of e1 decreases. This reduces the marginal ECL.

14

Rebitzer and Taylor (1995) develop a similar idea. They demonstrate in a variant of the Shapiro and Stiglitz model (1984) that a higher MW increases employment. The result depends, however, on the strong assumption that effort is constant once the no-shirking condition is satisfied.

15

Q1/C1 is backed out from other values.

16

Adjustment costs are required to support the assumption that capital is sector specific. The representative agent qua firm owner treats R as exogenous when optimizing over g and h.

17

We omit the market-clearing condition for H, which tracks the quasi-rent earned by entrepreneurial talent in the informal sector (a variable irrelevant to the issues under examination).

18

To give a few examples, the real loan rate in 2014 was 8.9% in Colombia,9.7% in Costa Rica, 10.3% in Guatemala, 8.4% in Kenya, and 11.1% in Tanzania (World Development Indicators, 2014). The estimates of the return on private capital cited in the text range from 12% to 16% and presumably incorporate a risk premium. Karabarbounis and Neiman (2013) assume a time preference rate of 10% in estimating a global (59-country) model of labor shares.

20

See, for example, Shapiro (1986), Merz and Yashiv (2007), Mumtaz and Zanetti (2015), and Mizobata (2015). Eslava et al. (2005) and Gonzaga (2009) estimate that adjustment costs for labor are comparable to or larger than adjustment costs for capital in Colombia and Brazil.

21

The ratio of both total and marginal adjustment costs for labor relative to capital is v4P1/v1PkK1 when K˙1/K1=L˙.

22

See the estimates in Gonzaga (2009) for large vs. small firms in Brazil.

23

Summary results for 36 case studies may be found at http://mypage.iu.edu/~ebuffie/.

24

Afghanistan (2008, 2009), Burkina Faso (2009), Cape Verde (2009), Cameron (2009), Cote d’lvoire (2009), Madagascar (2009), Mauritius (2009), Angola (2010), Botswana (2010), DRC (2010, 2013), Mali (2010), Argentina (2010), Ghana (2013), Guatamala (2010), Kenya (2013), Myanmar (2014), Peru (2010) and Rwanda (2011).

25

The wage curve has the real wage on the vertical axis. A steeper wage curve therefore exhibits a more elastic response of the wage to the unemployment rate.

26

The initial capital stock in the formal sector is approximately three times as large as that in the informal sector so that in all cases the expansion in formal sector capital substantially outweighs any contraction in capital in the informal sector.

27

Bhorat et al. (2014) also present evidence that an investment boom accompanied the sharp increase in the MW for agricultural workers in South Africa. Mayneris et al. (2014) do not discuss the impact on investment in China; they emphasize, however, that unit labor costs fell and firm profits held up nicely.

28

Kertesi and Kollo (2003) find the large increase in labor productivity “puzzling.” After noting the 57% increase in the real MW was associated with a sudden increase in labor productivity, they remark: “The question of how labor productivity was raised in many hard-hit low-wage enterprises seems a hard nut to crack.”

28

Note that the transition paths displayed for the other variables in Figure 8 are based on the adjustment costs and paths for employment shown in the penultimate panel.

30

To repeat an earlier disclaimer, a representative agent model of the form used here necessarily ignores distributional concerns. Positive results are therefore only suggestive of potential welfare gains.

31

See Sen (1967) and Feldstein (1964) for cogent arguments why the social time preference rate should be less than the private discount rate.

32

Analysis of the macroeconomic effects of greater enforcement of the MW is another promising area for future work. See Gindling et al. (2015) for empirical evidence on the impact of stronger enforcement in Costa Rica and Basu et al. (2010) for a detailed micro-theoretic model of how enforcement and the mandated MW interact with credibility and the structure of the labor market.

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