I. Introduction

The nature and extent of labor market segmentation in developing countries has been the subject of much debate over the years, particularly in the context of discussions related to urbanization and migration between rural and urban areas. In a seminal paper, Harris and Todaro (1970) showed that the existence of a binding minimum wage in the urban sector leads, even if the rural labor market is competitive, to a persistent wage differential between the rural and urban sectors and to the emergence of unemployment in equilibrium. Moreover, expansion of labor demand or real wage restraint in the urban sector will not restore full employment.

More recent work has focused on the role of labor market segmentation in the context of trade and structural reforms.^1/ By contrast, the implications of various types of labor market dualism for the short-run determination of output and employment in an open economy have not received much attention in the existing literature.^2/ The importance of accounting for labor market segmentation and the degree of wage flexibility for a proper understanding of the effects of macroeconomic shocks on unemployment can be illustrated with a simple graphical analysis. Consider a small open economy producing traded and nontraded goods using only labor, the supply of which is given. The determination of wages and employment under four different assumptions regarding labor market adjustment are shown in Figure 1 to 4. In all four figures the horizontal axis measures total labor available to the economy, $O_T{O}_N$. The vertical axes measure the wage rate in the two sectors of the economy, which is either uniform across sectors or sector specific. The demand for labor in the traded (nontraded) goods sector is represented by the downward-sloping curve $L_T^d\left(L_N^d\right)$. Consider first Figure 1, which assumes that wages are perfectly flexible and labor perfectly mobile across sectors. The initial equilibrium position of the labor market obtains at point E, where the economy-wide wage rate is equal to $w^{*}$ labor employed in the traded goods sector is $O_T{L}_T^{*}$, and labor used in the production of nontraded goods $L_T^{*}{O}_N$.

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Labor Market Adjustment with Flexible Wages and Perfect Inter-Sectoral Mobility

Citation: IMF Working Papers 1993, 079; 10.5089/9781451850161.001.A001

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Labor Market Adjustment with Partial Wage Rigidity and Perfect Inter-Sectoral Mobility

Citation: IMF Working Papers 1993, 079; 10.5089/9781451850161.001.A001

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Labor Market Adjustment with Partial Wage Rigidity and No Inter-Sectoral Mobility

Citation: IMF Working Papers 1993, 079; 10.5089/9781451850161.001.A001

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Labor Market Adjustment in a Harris-Todaro Framework

Citation: IMF Working Papers 1993, 079; 10.5089/9781451850161.001.A001

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Figure 2, 3 and 4 assume that the wage rate in the traded goods sector is fixed at $w_T^c$ (above the economy-wide, market-clearing wage) while wages in the nontraded goods sector remain flexible.^3/ However, the figures differ in the underlying assumptions regarding the degree of inter-sectoral labor mobility. In Figure 2, labor can move freely across sectors, as in Figure 1. Perfect labor mobility, together with wage flexibility in the nontraded goods sector, prevents the emergence of unemployment. The initial equilibrium obtains at point A in the traded goods sector and corresponds to an employment level of $O_T{L}_T^c$, and at point $E_N$ in the nontraded goods sector, with wages equal to $w_N$ and employment to $L_T^c{O}_N$. In Figure 3, labor is completely immobile within the time frame of the analysis. The labor force in the traded goods sector is equal to $O_T{\overline{L}}_T$, while the supply of labor in the nontraded goods sector is measured by ${\overline{L}}_T{O}_N$. Since sectoral labor supply is completely inelastic and wages cannot adjust in the traded goods sector, unemployment will typically emerge in that sector. The situation depicted in Figure 3 indicates that employment in the traded goods sector is equal to $O_T{L}_T^c$ and unemployement to $L_T^c{\overline{L}}_T$. Finally, Figure 4 assumes that sectoral employment is determined through the labor allocation mechanism formalized by Harris and Todaro (1970), which postulates that equilibrium obtains when the wage rate in the nontraded goods sector is equal to the expected wage in the traded goods sector.^4/ The downward-sloping locus QQ is a rectangular hyperbola along which the above equality holds continuously, and is known as the Harris-Todaro curve (Corden and Findlay, 1975). The intersection of the $L_N^d$ curve with QQ determines the wage rate and the employment level in the nontraded goods sector, while the intersection of the $L_T^d$ curve with the locus QQ and the horizontal line drawn at $w_T^c$ determines employment in the traded goods sector. The initial equilibrium of the economy is therefore characterized by aggregate unemployment, measured by $L_T^c{L}_N$.

Suppose that the demand for labor in the traded goods sector falls, as a result of a macroeconomic shock—a reduction, say, in autonomous demand for tradables—shifting the labor demand curve to the left, from $L_T^d$ to $L_T^{d,}$.^5/ If wages are perfectly flexible and labor perfectly mobile across sectors, adjustment of the labor market leads to a fall in the overall wage rate in the economy and a re-allocation of labor across sectors, leading the economy to a new equilibrium (point E' in Figure 1) with full employment.

Consider now what happens in the presence of a sector-specific wage rigidity. If labor is perfectly mobile across sectors, the demand shock leads again to a reallocation of the labor force across sectors, together with a fall in wages in the nontraded goods sector (Figure 2). However, if workers cannot move across sectors—because, say, different skills are required for different activities—the reduction in demand leads to an increase in unemployment in the traded goods sector (from $L_T^c{\overline{L}}_T$ to $L_T^{c,}{\overline{L}}_T$) with no effect on wages and employment in the nontraded goods sector (Figure 3). ^6/ With a labor allocation mechanism of the Harris-Todaro type, the demand shock also reduces employment in the traded goods sector as in the preceding case. However, the effect on the unemployment rate is now ambiguous. This is because the QQ curve also shifts to the left following the shift in $L_T^d$, since the fall in employment reduces the likelihood of being hired and therefore the expected wage in the traded goods sector. As a result, more workers elect to seek employment in the nontraded goods sector, bidding wages down. Employment therefore increases in the nontraded goods sector while wages fall. Nevertheless, because the reallocation of labor across sectors is only partial, in equilibrium unemployment may well increase in the traded goods sector. The thrust of the analysis, therefore, is that it is critically important to assess correctly the functioning of the labor market in order to evaluate the implications of macroeconomic shocks on wages, employment and the unemployment rate in the economy.

While the foregoing analysis was presented in a partial equilibrium framework, the remainder of this paper analyzes the effects of macroeconomic policy in a dynamic, general equilibrium model of a small open economy with segmented labor markets. Section II presents the basic framework, under the assumption that labor is homogeneous and perfectly mobile across sectors. Section III examines the short- and long-run effects of a deflationary macroeconomic policy, which takes the form of a permanent reduction in the devaluation rate. Section IV extends the basic model to account for the existence of gradual labor mobility across sectors and contrasts the effects of macroeconomic policy on unemployment with the results obtained previously. Finally, Section V summarizes the main implications of the analysis.

II. A Basic Framework

Consider a small open economy in which there are four types of agents: producers, households, the central bank, and the government. All firms and households are identical. The official exchange rate is devalued at a predetermined rate by the central bank. The economy produces two goods, a nontraded good that is used only for final domestic consumption, and a traded good whose price is determined on world markets. The capital stock in each sector is fixed during the time frame of the analysis, while labor is assumed initially homogenous and perfectly mobile across sectors. The labor market consists of two sectors: a primary segment, where employment is determined by firms in the traded goods sector, and a secondary segment, which corresponds to the nontraded goods sector. An above-equilibrium real wage is set in the primary market as a way to elicit effort and maintain productivity, while in the secondary market wages are fully flexible and adjust to equilibrate supply and demand.^7/ Firms in the traded goods sector make their employment decisions first. The secondary sector absorbs all workers that are not hired in the primary segment of the market, so that unemployment cannot emerge. Households consume both traded and nontraded goods, supply labor inelastically and hold two categories of financial assets in their portfolios: domestic money (which bears no interest) and a traded bond issued abroad, which bears a real rate of return determined on world markets. Domestic households and firms can borrow and lend freely at that rate, which varies inversely with the economy's total stock of foreign assets. ^8/ The government consumes only nontraded goods, collects lump-sum taxes and receives transfers from the central bank. It finances its budget deficit either by borrowing from the central bank, or by varying taxes on households. Finally, while agents form rational expectations with regard to exchange rate and price movements, wage and employment expectations—which play a role only under imperfect sectoral mobility—are assumed to depend on prevailing conditions in the labor market.

1. Output and the labor market

Setting the world price of traded goods to unity, the domestic price of traded goods is given by $P_T\left(t\right)-E_t$, where $E_t$ denotes the exchange rate. The production technology in the traded goods sector is given by ^9/

$Q_T\left(t\right)=Q_T\left[e_t{L}_T\right(t\left)\right],Q_T^{\prime }>0,Q_T^{\prime \prime }<0,\left(1\right)$

where $Q_T$, denotes output, $L_T$ employment measured in “natural” units, and $e_t$ efficiency. Production takes place under decreasing returns to labor. Efficiency is positively related to the real wage in the traded goods sector and negatively to the real wage in the nontraded goods sector, which measures the opportunity cost of effort:

$e_t=e\left[{\omega }_T^{+}\right(t),{\omega }_N^{-}(t\left)\right],{\partial }^{2}e/\partial {\omega }_T^2<0,\left(2\right)$

where ${\omega }_T\left(t\right)=w_T\left(t\right)/E_t$ denotes the real product wage in the traded goods sector, ${\omega }_N\left(t\right)=w_{N\left(t\right)/E_t}$ the real wage in the nontraded goods sector measured in terms of traded goods, and W_T (respectively w_N denotes the nominal wage in the traded (respectively nontraded) goods sector. The conditions imposed on the efficiency function indicate that the marginal effect of an increase in wages in the traded goods sector on effort is positive but decreasing.

The representative firm in the traded goods sector maximizes its real profits, given by

${\mathrm{\Pi }}_T=Q_T\left(t\right)-{\omega }_T\left(t\right)L_T\left(t\right),$

with respect to ${\omega }_t$ and $L_T$, for ${\omega }_N\left(t\right)$ given. ^10/ The first-order conditions for this optimization problem are:

${\omega }_T/e\left[\mathrm{.}\right]=Q_T^{\prime },\left(3a\right)$

$1/e_{{\omega }_T}^{\prime }\left[\mathrm{.}\right]=Q_T^{\prime }\mathrm{.}\left(3b\right)$

These optimality conditions imply:

$e_{{\omega }_T}^{\prime }\left[\mathrm{.}\right]{\omega }_T\left(t\right)=e\left[\mathrm{.}\right],\left(4\right)$

which indicates that in equilibrium the elasticity of effort with respect to the product wage is unity. Equation (4) generalizes the “Solow Condition” (see Solow, 1979) to a two-sector economy and can be solved for the real efficiency wage in the traded goods sector for a given value of the secondary sector wage:^11/

${\omega }_T\left(t\right)=h\left[{\omega }_N\right(t\left)\right]\mathrm{.}{h}^{\prime }>0\left(5\right)$

Consider, for instance, the case where the effort function takes the form

$e_t={\omega }_T(t{)}^{\gamma }-{\omega }_N(t{)}^{\gamma },0<\gamma <1\left(2^{\prime }\right)$

which satisfies $e_{{\omega }_T}>0,{\partial }^{2}e/\partial {\omega }_T^2<0,{\partial }^{2}e/\partial {\omega }_N\partial {\omega }_T=0,$ and $e_t=0$ for ${\omega }_T\left(t\right)={\omega }_T\left(t\right)$.

Solving equation (4) yields

${\omega }_T\left(t\right)-{\mathrm{\delta \omega }}_N\left(t\right),\delta =(\frac{1}{1-\gamma }{)}^{1/\gamma }>1\left(5^{\prime }\right)$

which indicates that the efficiency wage is always higher than the opportunity cost of effort. A graphical determination of the efficiency wage is shown in Figure 5.

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Efficiency Wages and Effort

Citation: IMF Working Papers 1993, 079; 10.5089/9781451850161.001.A001

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Substituting the optimal value of ${\omega }_T\left(t\right)$ from equation (5) in equation (2) and the result in equation (3a) determines the equilibrium effort level and the demand for labor in the traded goods sector, $L_T^d:$

$L_t^d\left(t\right)=\frac{1}{e\left[\mathrm{.}\right]}{Q}_T^{{\prime }^{-1}}\{{\omega }_T\left(t\right)/e\left[\mathrm{.}\right]\}=L_T^d\left[{\omega }_N\left(t\right)\right]\mathrm{.}{L}_T^{d,}\frac{>}{<}0\left(6\right)$

The effect of an increase in the real wage in the nontraded goods sector on the demand for labor in the traded goods sector is, in general, ambiguous. Using the effort function defined by (2'), however, indicates that $L_T^{d,}<0.$ ^12/ A rise in the real wage in the nontraded goods sector increases more than proportionately the real efficiency wage in the traded goods sector, thus raising effort. However, the increased effort is not sufficient to dampen the negative effect of the increase in the real efficiency wage on labor demand. In addition, the increase in effort leads to a direct reduction in labor demand in order to keep constant the marginal product of labor, measured in efficiency units. As a result of both effects, labor demand falls with an increase in ${\omega }_N\left(t\right)$.

Substituting equations (2), (5) and (6) in (1) yields

$Q_T\left(t\right)=Q_T\left[{\omega }_N\left(t\right)\right]\mathrm{.}{Q}_T^{\prime }<0\left(7\right)$

An increase in the real wage in the nontraded goods sector has an unambiguously negative effect on output of traded goods (regardless of whether it increases or lowers labor demand) because of its positive effect on the efficiency wage.

Production in the nontraded goods sector is determined by

$Q_N\left(t\right)=Q_N\left[L_N\left(t\right)\right],Q_N^{\prime }>0,Q_N^{\prime \prime }<0,\left(8\right)$

and real profits (in terms of prices of traded goods) are given by

${\mathrm{\Pi }}_N=z_t^{-1}{Q}_N\left(t\right)-{\omega }_N\left(t\right)L_N\left(t\right),\left(9\right)$

where $z_t=E_t/P_N\left(t\right)$ denotes the real exchange rate, and $P_N\left(t\right)$ the domestic price of nontraded goods. Profit maximization yields the familiar equality between marginal revenue and marginal cost:

${\omega }_N\left(t\right)=z_t^{-1}{Q}_N^{\prime }\left[L_N\right(t\left)\right],\left(10\right)$

from which labor demand can be derived as $L_N^d\left(t\right)=Q_N^{{\prime }^{-1}}\left[z_t{\omega }_N\left(t\right)\right].$ Substituting this result in (8) implies

$Q_N\left(t\right)=Q_N\left[z_t{\omega }_N\left(t\right)\right],Q_N^{\prime }<0\left(11\right)$

where $z_t{\omega }_t\left(t\right)$ measures the real product wage in the nontraded goods sector. From equations (7) and (11), real factor income—measured in terms of traded goods—is given by

$q_t=z_t{}^{-1}{Q}_N\left[z_t{\omega }_N\left(t\right)\right]+Q_T\left[{\omega }_N\left(t\right)\right]\mathrm{.}\left(12\right)$

The mechanism through which equilibrium of the labor market obtains in this economy is as follows.^13/ Each period, available workers queue up to seek employment in the primary segment of the labor market. Firms in the primary market determine the real efficiency wage and hire randomly from the queue—since labor is homogenous, firms treat workers symmetrically—up to the point where their optimal demand for labor is satisfied. Workers who are unable to obtain employment in the primary sector become suppliers in the secondary market and, together with demand there, determine the wage that equilibrates the secondary market. Formally, let $\overline{L}$ be total labor supply in the economy. The equilibrium condition in the secondary market is given by

$\overline{L}-L_T^d\left[{\omega }_N\right(t\left)\right]=L_T^d\left[z_t{\omega }_N\left(t\right)\right],\left(13\right)$

which, for a given value of the real exchange rate, can be solved for the equilibrium value of ${\omega }_N\left(t\right)$ .

III. Devaluation, Real Wages and Employment

Before examining the long-run properties of the model, it is convenient to re-write it in a more compact form. The labor market clearing equation (13) yields a solution in which, fc>r the effort function (2'), ${\omega }_N\left(t\right)$ is inversely related to z_t and $\overline{L}$. Substituting this result in equation (7) yields

where, for simplicity, $\overline{L}=0$. A depreciation of the real exchange rate has a positive effect on the supply of traded goods.

Suppose also that $v\left(\right)=\mathrm{In}\left[c_N\right(t\left)c_T\right(t\left)\right]\mathrm{.}$. Equation (19a) yields

where $b_t=b_t^p+R_t$ denotes the economy's total stock of foreign assets. Equation (28) indicates that consumption of traded goods is inversely related to the marginal utility of wealth and positively related to the stock of foreign assets held by the central bank and the public. Using equations (19b) and (28), the equilibrium condition of the nontraded goods market (equation 26) can be written as

In general, the net effect of a real depreciation on output of nontraded goods is ambiguous $\left(q_N^{\prime }\frac{<}{>}0\right)$. On the one hand, a real depreciation raises directly the product wage, exerting a negative effect on output. On the other hand, it reduces indirectly the product wage because it leads to a fall in the real wage in the nontraded goods sector, which in turn lowers the real wage and effort in the traded goods sector. The resulting increase in the supply of labor in the nontraded goods sector exerts a downward pressure on the real wage there, which may be large enough to dominate the upward direct effect associated with a depreciation of the real exchange rate on the real product wage. We will, however, assume in what follows that the direct effect dominates, so that $q_N^{\prime }<0$.

Solving equation (26') yields the equilibrium solution for the real exchange rate:^18/

Substituting equations (12) and (25) to (29) in equation (17) together with ${\dot{d}}_t=0$ yields

which determines the rate of accumulation of foreign assets. Finally, equation (19d) can be re-written as

Equations (30) and (31) determine the behavior of foreign assets and the marginal utility of wealth over time, while equation (29) determines the equilibrium level of the real exchange rate, for given values of ${\lambda }_t$ and b_t.

A linear approximation around the steady state to equations (30) and (31) yields

where $\mathrm{\Omega }=\rho \left(b^{*}\right)+b^{*}{\rho }^{\prime }+q_T^{\prime }\left(\frac{\partial }{\partial }\frac{z}{b}\right)-\partial c_T/\partial b\frac{<}{>}0$. Assuming that the net effect of an increase in the economy's total stock of bonds is a reduction in interest income provides a sufficient (although not necessary) condition for $\mathrm{\Omega }<0$. ^19/ ${\lambda }^{*}$ and b_* denote the steady-state solutions of the system. Equation (31) shows that the steady-state level of bonds is determined independently from the rest of the system: $b^{*}={\rho }^{-1}\left(\alpha \right)$.

Given that the stock of foreign assets is predetermined, the system described by (32) is locally saddlepoint stable. ^20/ The steady-state equilibrium is depicted in Figure 6, under the assumption that $\mathrm{\Omega }<0$. The curve $[{\dot{\lambda }}_t=0]$ gives the combinations $({\lambda }_t,b_t)$ for which the marginal utility of wealth remains constant, while the curve $[{\dot{b}}_t=0]$ depicts the combinations of $\mathrm{\lambda t}$ and b_t for which the stock of foreign assets does not change over time. The saddlepath, denoted SS in the figure, has a negative slope. Given an initial level of foreign bonds b₀, the equilibrium level of the shadow price of wealth is the unique level ${\lambda }_0$ that places the economy on the convergent trajectory SS leading to the steady-state equilibrium at point E. ^21/

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Steady-State Equilibrium

Citation: IMF Working Papers 1993, 079; 10.5089/9781451850161.001.A001

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Consider now a permanent, unanticipated reduction at t = 0 in the devaluation rate, from a value of ${ϵ}^h$ to ${ϵ}^s<{ϵ}^h$. The dynamics of adjustment are illustrated inFigure 7. Suppose that the economy is initially located at point A, where the rate of accumulation of foreign assets is positive and the marginal utility of wealth is declining. The reduction in ${ϵ}_t$ shifts the $[{\dot{b}}_t=0]$ upwards. On impact, the shadow price of wealth jumps upwards, from point A to point B on the new saddlepath S'S'. From then on, the economy continues to accumulate foreign assets, reducing ${\lambda }_t$ until the new steady-state equilibrium is reached at point E', which is located above the pre-shock steady state (point E).