Efficiency Wages and Labor Mobility in an Open Economy
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

The paper analyzes the role of labor market segmentation and relative wage rigidity in the transmission process of macroeconomic shocks in a two-sector optimizing model of a small open economy. The analysis is first conducted in the context of perfect intersectoral labor mobility. The discussion is then extended to consider the existence of short-run constraints on labor movements. The results highlight the role of efficiency considerations in the behavior of sectoral wages. A deflationary policy induces a reallocation of labor across sectors, but has no long-run effect on the unemployment rate.

Abstract

The paper analyzes the role of labor market segmentation and relative wage rigidity in the transmission process of macroeconomic shocks in a two-sector optimizing model of a small open economy. The analysis is first conducted in the context of perfect intersectoral labor mobility. The discussion is then extended to consider the existence of short-run constraints on labor movements. The results highlight the role of efficiency considerations in the behavior of sectoral wages. A deflationary policy induces a reallocation of labor across sectors, but has no long-run effect on the unemployment rate.

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, OTON. 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 LTd(LNd). 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 OTLT*, and labor used in the production of nontraded goods LT*ON.

Figure 1
Figure 1

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

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

Figure 2
Figure 2

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

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

Figure 3
Figure 3

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

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

Figure 4
Figure 4

Labor Market Adjustment in a Harris-Todaro Framework

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

Figure 2, 3 and 4 assume that the wage rate in the traded goods sector is fixed at wTc (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 OTLTc, and at point EN in the nontraded goods sector, with wages equal to wN and employment to LTcON. 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 OTL¯T, while the supply of labor in the nontraded goods sector is measured by L¯TON. 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 OTLTc and unemployement to LTcL¯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 LNd curve with QQ determines the wage rate and the employment level in the nontraded goods sector, while the intersection of the LTd curve with the locus QQ and the horizontal line drawn at wTc determines employment in the traded goods sector. The initial equilibrium of the economy is therefore characterized by aggregate unemployment, measured by LTcLN.

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 LTd to LTd,.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 LTcL¯T to LTc,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 LTd, 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 PT(t)-Et, where Et denotes the exchange rate. The production technology in the traded goods sector is given by 9/

QT(t)=QT[etLT(t)],QT>0,QT<0,(1)

where QT, denotes output, LT employment measured in “natural” units, and et 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:

et=e[ωT+(t),ωN-(t)],2e/ωT2<0,(2)

where ωT(t)=wT(t)/Et denotes the real product wage in the traded goods sector, ωN(t)=wN(t)/Et the real wage in the nontraded goods sector measured in terms of traded goods, and WT (respectively wN 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

ΠT=QT(t)-ωT(t)LT(t),

with respect to ωt and LT, for ωN(t) given. 10/ The first-order conditions for this optimization problem are:

ωT/e[.]=QT,(3a)
1/eωT[.]=QT.(3b)

These optimality conditions imply:

eωT[.]ωT(t)=e[.],(4)

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/

ωT(t)=h[ωN(t)].h>0(5)

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

et=ωT(t)γ-ωN(t)γ,0<γ<1(2)

which satisfies eωT>0,2e/ωT2<0,2e/ωNωT=0, and et=0 for ωT(t)=ωT(t).

Solving equation (4) yields

ωT(t)-δωN(t),δ=(11-γ)1/γ>1(5)

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.

Figure 5
Figure 5

Efficiency Wages and Effort

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

Substituting the optimal value of ωT(t) 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, LTd:

Ltd(t)=1e[.]QT-1{ωT(t)/e[.]}=LTd[ωN(t)].LTd,><0(6)

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 LTd,<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 ωN(t).

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

QT(t)=QT[ωN(t)].QT<0(7)

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

QN(t)=QN[LN(t)],QN>0,QN<0,(8)

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

ΠN=zt-1QN(t)-ωN(t)LN(t),(9)

where zt=Et/PN(t) denotes the real exchange rate, and PN(t) the domestic price of nontraded goods. Profit maximization yields the familiar equality between marginal revenue and marginal cost:

ωN(t)=zt-1QN[LN(t)],(10)

from which labor demand can be derived as LNd(t)=QN-1[ztωN(t)]. Substituting this result in (8) implies

QN(t)=QN[ztωN(t)],QN<0(11)

where ztωt(t) 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

qt=zt-1QN[ztωN(t)]+QT[ωN(t)].(12)

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 L¯ be total labor supply in the economy. The equilibrium condition in the secondary market is given by

L¯-LTd[ωN(t)]=LTd[ztωN(t)],(13)

which, for a given value of the real exchange rate, can be solved for the equilibrium value of ωN(t) .

2. Consumption and the dynamics of wealth

Households supply a quantity of labor L¯ in elastically and consume traded and nontraded goods. The representative household's lifetime discounted utility is given by

0v[cN(t),cT(t)]e-αtdt,α>0(14)

where α denotes the rate of time preference (assumed constant), cN(t) consumption of nontraded goods, and cT(t) consumption of traded goods. The instantaneous utility function v() is assumed to satisfy the usual properties. 14/

Nominal wealth of the representative household At is defined as

At=Mt+Etbtp,(15)

where Mt denotes the nominal money stock and btp the foreign-currency value of the stock of traded bonds. The flow budget constraint of the household is given by

At˙=Et[qt+ρtbtp-cT(t)-τt]-PN(t)cN(t)+E˙tbtp,(16)

where τt denotes real lump-sum taxes, ρt=ρ(bt) the world interest rate, which is assumed to vary inversely with the economy's total stock of foreign assets bt(ρ<0), and the last term represents valuation effects. Measuring real wealth in terms of traded goods as at=At/Et implies that, from (15) and (16):

a˙t=ρtat+qt-zt-1cN(t)-cT(t)-τt-itmt,(17)

where mt=Mt/Et denotes real money balances (measured in terms of traded goods) and it=ρt+ϵt the domestic nominal interest rate, with ϵt=E˙/Et denoting the rate of depreciation of the exchange rate.

Households are subject to a cash-in-advance constraint on total purchases of home and foreign goods: 15/

vMtPN(t)cN(t)+PT(t)cT(t),(18)

where v denotes the velocity of circulation, assumed constant. Equation (18) can be written equivalently as

vmtzt-1cN(t)+cT(t).(18)

Households treat ϵt,qt,zt,ρt and τt as given and maximize (14) subject to (17) and (18')—holding with equality—by choosing a sequence {cN(t),cT(t),mt,btp}t=0. Straightforward calculations show that the solution to this program is characterized by the following conditions:

ccT=λt(1+v-1it),(19a)
vcT/vcN=zt,(19b)
mt=v-1[zt-1cN(t)+cT(t)],(19c)
λ˙t=(α-ρt)λt,(19d)

in addition to (17) and the transversality condition limt(ate-αt)=0.

Equation (19a) shows the familiar result according to which in equilibrium the marginal utility of consumption of traded goods is equal to the marginal utility of wealth λt times the “effective” price of traded goods, which depends on the domestic interest rate. Equation (19b) indicates that the ratio of the marginal utility of consumption of traded and nontraded goods is equal in equilibrium to the real exchange rate. Equation (19c) is the cash-in-advance constraint (holding with equality), which determines the demand for money. Finally, equation (19d) describes the dynamics of the marginal value of wealth as a function of the difference between the discount rate and the world interest rate.

3. Money, deficits, and the balance of payments

There are no commercial banks in the economy considered here, and credit only flows from the central bank to the government. The nominal money stock is therefore equal to

Mt=Dt+EtRt,(20)

where Dt denotes the stock of domestic credit allocated by the central bank to the government, and Rt the stock of net foreign assets, measured in foreign currency terms. The change in the foreign currency value of the central bank's reserves is determined by

R˙t=QT(t)-cT(t)+ρt(btp+Rt)-b˙pt.(21)

The government's revenue sources consist of lump-sum taxes on households and transfers from the central bank resulting from interest receipts on net foreign assets and revaluation of foreign exchange reserves. 16/ It consumes nontraded goods and finances its budget deficit by borrowing from the central bank or varying taxes. In nominal terms, the government's budget constraint can be written as:

Dt˙=PN(t)gN(t)-Etγt-(ρtEt+Et˙)Rt,(22)

or, in real terms,

dt˙=zt-1gN(t)-τt-ρtRt-ϵtmt,(23)

where dt=Dt/Et..

Suppose that the central bank fixes the rate of growth of the nominal credit stock at μt0,, so that

dt˙=(>μt-ϵt)dt.(24)

Suppose also that the central bank sets the rate of growth of domestic credit so as to compensate the government for the loss in value in the outstanding stock of credit resulting from exchange rate depreciation (μt=ϵt). Given this credit rule—which implies that d.t=0 and thus m˙t=R˙t—the government maintains spending on nontraded goods at a constant level in real terms and adjusts lump-sum taxes to balance the budget: 17/

τt=zt-1g¯N-ρtRt-ϵtmt.(25)

To close the model requires specifying the equilibrium condition for the nontraded goods market. Using equation (11) yields

QN[ztωN(t)]-g¯N+cN(t).(26)

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'), ωN(t) is inversely related to zt and L¯. Substituting this result in equation (7) yields

QT(t)-qT(zt),qT>0(27)

where, for simplicity, L¯=0. A depreciation of the real exchange rate has a positive effect on the supply of traded goods.

Suppose also that v()=In[cN(t)cT(t)].. Equation (19a) yields

cT(t)=cT(λ-t,b+t;ϵ-t),(28)

where bt=btp+Rt 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

QN[ztωN(z¯t)]=qN(zt)-ztcT(λt,bt;ϵt)+gN.(26)

In general, the net effect of a real depreciation on output of nontraded goods is ambiguous (qN<>0). 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 qN<0.

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

zt=z(λ+t,b-t;ϵ+t,g-N).(29)

Substituting equations (12) and (25) to (29) in equation (17) together with d˙t=0 yields

b˙t=ρt(bt)bt+qt[z(λt,bt;ϵt,gN)]-cT(λt,bt;ϵt),(30)

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

λt˙/λt=α-ρ(bt).(31)

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 λt and bt.

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

[λt˙bt˙]=[0-λ*ρqT(zλ)-cT/λΩ][λt-λ*bt-b*],(32)

where Ω=ρ(b*)+b*ρ+qT(zb)-cT/b<>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 Ω<0. 19/ λ* 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*=ρ-1(α).

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 Ω<0. The curve [λ˙t=0] gives the combinations (λt,bt) for which the marginal utility of wealth remains constant, while the curve [b˙t=0] depicts the combinations of λt and bt 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 λ0 that places the economy on the convergent trajectory SS leading to the steady-state equilibrium at point E. 21/

Figure 6
Figure 6

Steady-State Equilibrium

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

Consider now a permanent, unanticipated reduction at t = 0 in the devaluation rate, from a value of ϵh to ϵs<ϵh. 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 ϵt shifts the [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 λt until the new steady-state equilibrium is reached at point E', which is located above the pre-shock steady state (point E).

Figure 7
Figure 7

Reduction in the Devaluation Rate

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

The transmission mechanism of this policy shock can be described as follows. On impact, the reduction in the devaluation rate leads to a one-to-one reduction in the nominal interest rate (since the stock of foreign assets, and therefore the world interest rate, remains constant) and reduces the opportunity cost of money holdings, which tends to increase consumption of traded goods. However, the marginal value of wealth must jump upwards on impact since the stock of bonds is given in the short run. This upward jump reduces consumption of traded goods. The net effect—given the assumption of a logarithmic instantaneous utility function—is a reduction in consumption of traded goods on impact. For a given level of the real exchange rate, consumption of nontraded goods also falls. This reduction requires a depreciation of the real exchange rate to dampen output of nontraded goods, mitigate the initial fall in demand, and therefore maintain equilibrium in the home goods market. The resulting reduction in the demand for labor compounds the initial downward movement in the real wage in that sector, and leads to a fall in the real efficiency wage in the traded goods sector. 22/ This reduction in wages has a positive net effect on output of traded goods (despite the negative impact on effort), increasing the demand for labor in that sector. The ensuing outflow of workers seeking employment into the traded goods sector dampens the downward pressure on the product wage in the nontraded goods sector.

During the transition to the new steady-state equilibrium, the marginal value of wealth falls while the economy continues to accumulate foreign assets. Consumption of traded and nontraded goods therefore rises over time, leading to a gradual appreciation of the real exchange rate. The increase in the relative price of nontraded goods reduces output and lowers the demand for labor in the traded goods sector. The flow of labor away from the traded goods sector exerts an upward pressure on the real wage (measured in terms of traded goods) in the nontraded goods sector. Under the assumptions made above, the net effect of the real appreciation and the movement in the real wage is a fall in the product wage in the nontraded goods sector, which has a positive effect on output and increases the demand for labor in that sector—therefore mitigating the reduction in the product wage. Because consumption of traded goods rises and output falls over time, the rate of accumulation of foreign assets is gradually reduced (thus dampening the rise in consumption over time). A permanent, unanticipated reduction in the devaluation rate is associated with a steady-state depreciation of the real exchange rate.

IV. Labor Mobility and Adjustment

The foregoing analysis was based on the assumption that workers who cannot find a job in the traded goods sector can apply for work in the nontraded goods sector, implying that there was no involuntary unemployment in the economy. However, the assumption of perfect mobility across sectors is not very appealing, particularly in a short-run context.23/ In migrating across sectors, workers typically incur a variety of costs (training, relocation expenses, etc.) that may prevent instant reallocation of the labor force. We now assume that, although labor is perfectly mobile across sectors in the long run, adjustment takes place gradually so that the allocation of labor to each sector is predetermined at any moment in time.

Let LTs(t) denote the available pool of workers in the traded goods sector at any given period t, and let LTs(t)=L¯-LTs(t).. Real wages and employment in the traded goods sector are determined, as assumed previously, by efficiency considerations. However, workers who are unable to obtain a job offer in the traded goods sector cannot shift instantaneously to the secondary sector, as assumed before. Short-run constraints on labor mobility thus introduces the possibility of unemployment in the traded goods sector. Wages in the secondary sector remain perfectly flexible and maintain full employment of the secondary sector labor force.24/ The equilibrium condition of the secondary labor market is now given by

L¯-LTs(t)=LNd[ztωN(t)],(33)

which can again be solved for the real wage:

ωN(t)=ωN[-zt,LTs+(t)].(34)

Substituting equation (34) in (11) and solving equation (26) yields the equilibrium real exchange rate:

zt=z(+λt,-bt,-LTs(t);+ϵt,-gN).(29)

Substituting this equation, together with (34), in equation (7) yields the supply function of traded goods:

qT(t)=qT[-λt,+bt,-LTs(t);-ϵt,+gN].(35)

Workers migrate across sectors in response to the perceived degree of labor market tightness in the two segments of the market. Wage expectations and the probability of finding a job are assumed to depend on current labor market conditions.25/ The expected payoff from queueing in, say, the primary market is equal to the primary sector wage weighted by the probability of being hired in the traded goods sector. Assuming that hiring is random, this probability is simply equal to the number of primary sector jobs over the number of workers seeking employment. Accordingly, the expected payoffs (θT,θN) associated with moving to each sector may be written as a function of the current wage in that sector and the prevailing employment ratio:

θT(t)=θT[ωT(t)LTd(t)LTs(t)],θT>0
θN(t)=θN[ωN(t)LNd(t)L¯-LTs(t)].θN>0

Over time, labor moves across sectors in response to the discrepancy between the payoffs available in the two sectors:26/

L˙sT(t)=k{θT[ωT(t)LTd(t)LTs(t)]-θN[ωN(t)LNd(t)L¯-LTs(t)]},k>0(36)

where K denotes the speed of adjustment. Using the equilibrium solutions for wages as a function of the real exchange rate, and substituting out the equilibrium condition (29') in (36) yields

LTs˙(t)=kL[λt,bt,LTs(t);ϵt,gN].(37)

In general, the signs of the partial derivatives appearing in equation (37) are ambiguous since they all depend on L/Z, which is itself ambiguous. In what follows we will assume that L/Z>0. This condition requires that a reduction in the payoff associated with working in the nontraded goods sector is large enough to dominate the ambiguous effect of a depreciation in the real exchange rate on the payoff associated with working in the traded goods sector. As a result, the gap between the two expected payoffs widens and workers migrate to the traded goods sector. Assuming thus that L/Z>0 implies that the sign of the partial derivatives appearing in equation (37) are identical to those appearing in equation (29'). This assumption implies, in particular, that L/LTs0.

The dynamic system driving the economy consists now of equations (30)—after substitution of equation (35) for qy—(31), and (37). A linear approximation around the steady state to this system can be written as

[λ˙tb˙tL˙Ts(t)]=[0*-λρ0qT(zλ)-cT/λΩqT/LTsk(L/λ)k(L/b)k(L/LTs)][λt-λ*bt-b*LTs(t)-Lts*],(38)

where we assume that 0<LTs*<L¯.

The system now has two predetermined variables and one jump variable, and therefore requires two negative roots and one positive root to ensure saddlepath stability. Sufficient conditions are therefore that the determinant of the coefficient matrix in (38) be positive and that the trace of the coefficient matrix be negative.27/ We assume in what follows that these two conditions hold.

The steady-state solution of the model implies an important property for the unemployment rate in the traded goods sector. Using the specific effort function defined earlier and assuming that T()θ=N()θ yields

uT*1-LTd*LTs*=δ-1(δ-1),δ>1(39)

which indicates that the "natural" rate of unemployment in the traded goods sector is always positive in equilibrium (0<uT*<1). Moreover, it can be established that an increase in the efficiency coefficient r reduces the steady-state rate of unemployment.

Consider, as before, a permanent, unanticipated reduction in the devaluation rate. The initial position of the economy is assumed to be such that the marginal utility of wealth is falling, and the rate of accumulation of foreign assets as well as the flow of workers migrating towards the traded goods sector are both positive. The behavior over time of the marginal utility of wealth, the efficiency wage and labor supply in the traded goods sector, consumption of traded goods, the real exchange rate, and the stock of foreign assets is shown in Figure 8. In general, whether or not the adjustment path of the economy differs from what obtains in the case of perfect labor mobility depends on whether the speed of adjustment of labor to changes in expected payoffs (the coefficient k) is small or large. When ic is large, the behavior of all variables is qualitatively similar to what obtains in the case of perfect labor mobility examined previously—except that now labor supply in the traded goods sector rises continuously over time (see Figure 8). The reason, of course, is the mono tonic increase in the efficiency wage in that sector before mnd after the policy shock, which maintains a positive payoff differential during the transition to the new steady state. In addition, at the moment the rate of devaluation is reduced, there is an increase in the flow of workers entering the traded goods sector. It can also be shown that, using the effort function described earlier, a permanent reduction in the devaluation rate reduces temporarily the unemployment rate in the traded goods sector—an unconventional result. In the long run, endogenous adjustment in labor supply and labor demand is such that, as shown in equation (39), the unemployment rate depends only on the efficiency coefficient.

Figure 8
Figure 8

Dynamics with Imperfect Labor Mobility

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

When the speed of adjustment of labor to changes in expected payoffs is small, changes in the flow of labor supplied in the two segments of the labor market will have a more limited effect on movements in wages in both sectors, and will dampen fluctuations in employment and output. At the same time, however, the transitory fall in the unemployment rate in the traded goods sector resulting from a reduction in the devaluation rate will also be dampened. The net welfare effect is thus ambiguous. But to the extent that workers’ productivity may also depend on the perceived risk of being unemployed—a relation that features in several efficiency-wage models—the effect of a low degree of mobility on the unemployment rate may be compounded by a reduction in output and labor demand.

V. Summary and Conclusions

The purpose of this paper has been to examine the implications of efficiency considerations and imperfect labor mobility for the short-run dynamics associated with macroeconomic policy shocks. The analysis was based on a two-sector optimizing model of a small open economy with segmented labor markets. While firms in the traded goods sector determine both wages and employment, wages in the nontraded goods sector are determined by the equilibrium condition between supply and demand. In addition, labor productivity in the traded goods sector depends on the attractiveness of opportunities—measured by real wages—that workers face inside and outside the sector. The equilibrium solution of the model indicates that firms in the traded goods sector always set the real wage above the level that prevails in the nontraded goods sector. In contrast to many existing models, sectoral real wage rigidity is thus not postulated but explicitly derived from optimizing conditions. Moreover, the formulation adopted here leads to an explicit specification of the interactions between wages in the different sectors of the economy.

We first considered the case where labor is homogeneous and perfectly mobile across sectors. The analysis showed that a permanent, unanticipated reduction in the devaluation rate leads to a drop in real wages in the traded goods sector, and an instantaneous reallocation of labor away from the nontraded goods sector. In the latter part of the paper, we considered the case where workers' movements across sectors occur gradually. The behavior of the economy with imperfect labor mobility was shown to be qualitatively similar to what obtains in the previous case when the speed of adjustment of labor to changes in expected payoffs is large, except that unemployment will typically emerge in equilibrium. However, a deflationary policy may not necessarily lead to an increase in unemployment in the short run. In the model developed here—as in standard efficiency wage models—firms in the traded goods sector do not reduce wages in the face of persistent sectoral unemployment because to do so would reduce productivity. When the speed of adjustment of labor is small, fluctuations in wages, employment and output are dampened but the transitory fall in the unemployment rate associated with a reduction in the devaluation rate will also be attenuated.

Beyond the specific results obtained here, two general lessons can be derived from the analysis. First, the issues of labor market segmentation and sectoral labor mobility deserve more attention than they have so far received in analytical and policy-oriented discussions on short-run macroeconomic adjustment. Shocks that lead to labor reallocation across sectors may have important aggregate effects that should be accounted for in the design of macroeconomic programs. Second, efficiency wage considerations provide a coherent explanation of sectoral real wage rigidity in an open economy as well as a logical framework for examining “spillover” effects that take place across markets. Accounting for alternative opportunities available to workers is crucial to understanding the interactions between different segments of the labor market and the ultimate effects of macroeconomic policy shocks on the level of unemployment.

Efficiency Wages and Labor Mobility in an Open Economy
Author: Julio A. Santaella and Pierre-Richard Agénor