Wage Indexation and the Real Exchange Rate in Small Open Economies: A Study of the Effects of Fluctuations in Export Earnings

Daniel Gros

doi:10.5089/9781451956726.024.A005

Author: Mr. Daniel Gros¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1986

eISBN:: 9781451956726

Language:: English

Keywords:: SP; indexing wage; indexation scheme; product wage; labor supply; wage contract; Real wages; Wage indexation; Labor supply

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This paper examines the consequences of indexation rules that link changes in wages or the exchange rate to changes in the price level in small countries with fluctuating export earnings. In countries with high and variable inflation rates, wage indexation rules often are implemented to protect workers from inflationary surprises, and the economy-wide use of this indexing minimizes the costs associated with the frequent renegotiations of wage contracts that would otherwise be necessary. The disadvantage of these rules is that they fix real wages and thereby impede adjustment to real shocks, such as fluctuations in export earnings, that can lead to high and variable unemployment rates.1 An exception to this experience has been provided by Iceland, where real wages have always reacted strongly to sharp changes in export earnings—even falling by over 15 percent in a single year—and where the unemployment rate has always been below 2 percent. This experience suggests that the adverse effects associated with wage indexation can be minimized by indexing wages not only on the basis of consumer prices but also of export earnings.2 By indexing wages to prices and to export earnings, workers are still protected from inflationary surprises, and, at the same time, the necessary adjustment to fluctuations in export earnings can take place without the need to renegotiate wages whenever export earnings change.

Abstract

This paper examines the consequences of indexation rules that link changes in wages or the exchange rate to changes in the price level in small countries with fluctuating export earnings. In countries with high and variable inflation rates, wage indexation rules often are implemented to protect workers from inflationary surprises, and the economy-wide use of this indexing minimizes the costs associated with the frequent renegotiations of wage contracts that would otherwise be necessary. The disadvantage of these rules is that they fix real wages and thereby impede adjustment to real shocks, such as fluctuations in export earnings, that can lead to high and variable unemployment rates.¹ An exception to this experience has been provided by Iceland, where real wages have always reacted strongly to sharp changes in export earnings—even falling by over 15 percent in a single year—and where the unemployment rate has always been below 2 percent. This experience suggests that the adverse effects associated with wage indexation can be minimized by indexing wages not only on the basis of consumer prices but also of export earnings.² By indexing wages to prices and to export earnings, workers are still protected from inflationary surprises, and, at the same time, the necessary adjustment to fluctuations in export earnings can take place without the need to renegotiate wages whenever export earnings change.

The analysis shows that the exact nature of the link between wages and export earnings that minimizes unemployment and maintains protection from inflationary surprises depends on various factors such as the elasticity of labor supply with respect to real wages, the share of nontradables in consumption, and the nature of the shocks that affect export earnings. When labor supply is inelastic relative to the real wage, however, it is argued that wages should be adjusted by a fraction (equal to 1 minus the share of nontradables in consumption) of any change in permanent export earnings. But no additional adjustment would be necessary if wages were indexed only to the domestic component of the consumer price index (CPI).

Another indexation rule used in some countries is to fix the real exchange rate (that is, the level of purchasing power parity, PPP) by depreciating the nominal exchange rate in line with the difference between world and domestic inflation. The rationale for this policy is that the high and variable inflation rates prevailing in these countries require periodic adjustment of the nominal exchange rate. PPP rules have been proposed as an alternative to discretionary adjustments.³ Because the equilibrium real exchange rate is affected by export earnings, these PPP rules also impede the necessary adjustment to changes in export earnings and thus create unemployment if export earnings fall.

To examine the implications of indexation rules on small open economies with fluctuating export earnings, three policies are considered:⁴ adjusting the exchange rate according to a PPP rule, and indexing wages on the basis of either the CPI or the domestic component of the CPI. The paper shows that, when there is a decline in export earnings, a PPP rule for the exchange rate causes more problems with unemployment than does full indexation of wages. In this situation, indexation of wages on the full CPI basket creates more unemployment problems than does partial indexation of wages on the domestic component of the CPI.

The remainder of the paper is organized as follows. Section I contains a description of the model and the equilibrium that would result with clearing labor markets (that is, in the absence of fixed nominal contracts and inflationary surprises). Section II analyzes the degree of indexation of wages that would replicate this equilibrium. Section III shows that the authorities could achieve the same outcome by indexing the real exchange rate. Section IV presents a calculation and comparison of the welfare losses that arise from fixed real exchange rates or real wages. If variable export earnings are the main source of uncertainty in the economy, then fixing the real exchange rate would lead to more unemployment than would fixing real wages. Section V contains some concluding remarks.

I. The Model

Consider a small open economy with two sectors, an export sector with export earnings subject to stochastic fluctuations and a nontradable sector. The export sector produces a primary commodity with an exogenous international price that is variable. The production process of that commodity is taken to be highly capital-intensive, with fixed proportions of capital to labor. With a fixed capital stock, the demand of labor by the export sector, or at least its variability, is taken to be very small.⁵

Movements in the overall demand for labor therefore reflect changes in the level of employment in the nontradable goods sector.⁶ The production process for nontradables, $n_{t}^{s}$ in logarithmic form, is specified as

\begin{matrix} n_{t}^{s} = β l_{t}^{d} + v_{t}, 0 < β < 1, & (1) \end{matrix}

where $l_{t}^{d}$ represents the logarithm of labor employed in the production of nontradables, β is the elasticity of the supply of nontradables with respect to labor input, and v_t, represents a stochastic shock that is distributed independently over time with zero mean and a constant variance $σ_{v}^{2}$ . Lowercase letters refer to deviations (in natural logarithms) from mean or to expected values of the corresponding variables or shocks.

Equation (1) two equations. In levels, the Cobb-Douglas production function corresponding to equation (1) would be

\ln (N_{t}^{s}) = \ln (A) + β \ln (L_{t}^{d}) + \ln (e^{v t}),

where capital letters indicate the levels of the respective variables, and A represents a productivity term. The nonstochastic supply of tradables is defined as the supply that would result if the stochastic shock, v, is equal to zero. The nonstochastic supply of nontradables is thus

\ln (N^{s}) = \ln (A) + β \ln (L^{d}) .

Subtracting this equation from the previous one yields

\ln (N_{t}^{s}) - \ln (N^{s}) = β [\ln (L_{t}^{d}) - \ln (L^{d})] + \ln (e_{t}^{v}) .

Defining $\ln (N_{t}^{s}) - \ln (N^{s}) \equiv n_{t}^{s} a n d \ln (L_{t}^{d}) - \ln (L^{d}) \equiv l_{t}^{d}$ , one finds that this expression is identical to equation (1). A similar procedure can be used to derive the other equations in the paper.

Profit-maximizing producers will hire labor until the marginal product equals the wage rate. Because producers are assumed to know the value of v_t, profits are maximized if

\begin{matrix} w_{t} - p_{n, t} = (β - 1) l_{t}^{d} + v_{t}, & (2) \end{matrix}

where w_t represents the wage rate, $l_{t}^{d}$ the labor demanded, and p_{n, t} the price of nontradables; w_t - p_{n, t} thus represents the logarithm of the product wage.

The supply of labor is assumed to be a function of the real wage rate:

\begin{matrix} l_{t}^{s} = δ (w_{t} - p_{t}), δ \geq 0, & (3) \end{matrix}

where p_t represents the CPI, which is given by

\begin{matrix} p_{t} \equiv α p_{n, t} + (1 - α) s_{t}, 0 < α < 1, & (4) \end{matrix}

where s_t is the nominal exchange rate, expressed as the domestic currency price of one unit of foreign currency. Because the international price of imports is normalized to unity, s_t also represents the domestic price of importables:⁷

\begin{matrix} n_{t}^{s} = [β δ (1 - α) (s_{t} - p_{n, t}) - (1 + δ) v_{t}] / [(β - 1) δ - 1] . & (5) \end{matrix}

These labor market relationships can be combined to give the supply of nontradables as a function of the real exchange rate. The real exchange rate is defined as the price of importables in terms of home goods (s_t -p_{n, t}). The supply of nontradables is thus a decreasing function of the real exchange rate.

In analyzing the consequences of fluctuating export earnings, it is important to note that these fluctuations would not represent a problem if they were purely temporary and if the country had access to an efficient international capital market or large reserves. With access to an efficient international capital market, the country could borrow to finance current account deficits in years with lower export earnings and could add to its reserves or repay its debt in years with higher export earnings. In this case consumption would not react at all to temporary fluctuations in export earnings. A country that is integrated into world capital markets thus faces only an intertemporal budget constraint, in that the expected present value of present and future export earnings has to be equal to the present value of present and future imports. With the discount factor denoted by B and the foreign currency value of export earnings and imports denoted by Y_t and I_t, respectively,⁸ this budget constraint can be written as

\begin{matrix} E_{t} (Σ_{j = 0}^{\infty} B^{j} I_{t + j}) = E_{t} (Σ_{j = 0}^{\infty} B^{j} Y_{t + j}) = Y_{p t} . & (6) \end{matrix}

Equation (6) defines the expected present value of export earnings, Y_pt, which also constrains the present value of imports.

In reality, however, export receipts are subject to fluctuations that are sometimes temporary and sometimes permanent. Because the nature of each shock is uncertain, the expected present value of future export receipts is often difficult to determine. One way to make this uncertainty tractable is to assume that export earnings have a permanent and a transitory component, but that only the sum can be observed:⁹

\begin{matrix} Y_{t} = Y_{T t} + Y_{s t} . & (7) \end{matrix}

Y_Tt represents the transitory component, which is assumed to be independently distributed over time with zero mean and a constant variance $σ_{T}^{2}$ . Y_st is the permanent component, which is assumed to be distributed as follows:

\begin{matrix} Y_{s t} = Y_{s t - 1} + W_{t} . & (8) \end{matrix}

W_t represents innovations in the permanent component and is distributed independently over time with a constant variance $σ_{w}^{2}$ . As indicated by Sargent (1979), the rational forecast of the present value of future export receipts when only Y_t, and not its components, are observable is based on a distributed lag of past export earnings, according to

\begin{matrix} E Σ_{j = 0}^{\infty} (B^{j} Y_{t + j}) = (1 - λ) / (1 - B) Σ_{i = 0}^{\infty} λ^{i} Y_{t + i} . & (9) \end{matrix}

In this formulation, the weight of each observed value of actual past export earnings is a declining function of time. How rapidly the weights decline depends on the coefficient λ, which is a function of the relative variances of the transitory and permanent components.¹⁰ If all shocks are permanent, λ is equal to zero, and only current observed export earnings should be used to forecast future export earnings. If all shocks are transitory, however, λ is equal to unity, and the average of all current and past observed export earnings should be used to forecast future export earnings. To simplify the analysis, y_pt is defined to equal the percentage change in the expected present value of future export earnings. From equation (9), changes in the present value of export earnings can be shown to be related to shocks in actual export earnings:

\begin{matrix} y_{p t} = \ln {λ + (1 - λ) [Y_{t} / E_{t - 1} (Y_{t})]}, & (10) \end{matrix}

where E_t-1 refers to an expectation formed at time t - 1. In this analysis it is assumed that no specific information is available about the nature of the shock in each period.

The demand for imports, which consist only of consumables, comes from consumers who maximize intertemporal utility, U_t, which is given by

\begin{matrix} U_{t} = E_{t} [Σ_{j = 0}^{\infty} (\frac{1}{1 - ξ} C_{t + j}^{1 - ξ}) R^{j}], ξ > 0, & (11) \end{matrix}

where R is the subjective intertemporal discount factor, which is assumed to be equal to B, the market discount factor. This utility function has constant relative risk aversion and a constant intertemporal elasticity of substitution equal to 1/ζ. The index C_t depends on consumption of two goods, nontradables (N_t) and importables (I_t), according to

\begin{matrix} C_{t} = N_{t}^{α} I_{t}^{1 - α}, 0 < α < 1. & (12) \end{matrix}

The demand function for nontradables depends on permanent income and the relative price of nontradables (that is, the real exchange rate):

\begin{matrix} n_{t}^{d} = y_{p t} + ρ (S_{t} - p_{n, t}) + u_{t}, \infty > ρ > α . & (13) \end{matrix}

All variables are again specified in terms of logarithmic deviations from nonstochastic values; ρ is the elasticity of demand for nontradables with respect to the real exchange rate—a composite parameter whose value depends on the discount factor and on the parameters of the utility function, $α < ρ < \infty$ .¹¹ The unitary elasticity of the demand for nontradables with respect to the permanent income from export earnings, y_pt, is a consequence of the intertemporal budget constraint, which implies that imports can rise by 1 percent if the present value of export earnings rises by 1 percent. It is assumed that the demand for nontradables is subject to shocks, u_t, that are distributed independently over time with zero mean and variance $σ_{u}^{2}$ .

When the supply of nontradables (equation (5)) is equal to the demand for nontradables (equation (13)), the percentage change in the real exchange rate can be expressed in terms of the change in export earnings, y_pt, and of the shocks v^t, and u_t:¹²

\begin{matrix} s - p_{n} = {(1 + δ) v - [δ (1 - β) + 1] (y_{p} + u)} / ω, & (14) \end{matrix}

where

\begin{matrix} ω \equiv ρ [1 + δ (1 - β)] + β δ (1 - α) . & (14 a) \end{matrix}

Positive shocks to permanent export earnings lead to a real appreciation (that is, a fall in s - p_n). In this formulation, shocks to export earnings and shocks to the demand for nontradables have similar effects on the real exchange rate. Inspection of equations (14) and (14a) also reveals that, if labor supply is completely inelastic (that is, if δ = 0), the elasticity of the real exchange rate with respect to export earnings is equal to 1/ρ. Moreover, if consumers have a unitary intertemporal elasticity of substitution, ρ is equal to unity, which implies that a 1 percent increase in permanent export earnings would lead to a 1 percent real appreciation.¹³

Finally, a shock that raises the supply of nontradables would lead to a real depreciation. In the analysis the real exchange rate is therefore determined by the supply of and demand for nontradables. Any change in a factor that has an effect on either the supply of or demand for nontradables would thus lead to a change in the equilibrium real exchange rate. This relationship suggests immediately that, in general, it is not advisable to fix the real exchange rate with a PPP rule.

The supply of and demand for home goods (equations (5) and (13)) can also be used to show that the change(s) in consumption of home goods is an increasing function of the change(s) in export earnings and the supply shock, v:

\begin{matrix} n^{d} = n^{s} = [β δ (1 - α) (y_{p} + u) + ρ (1 + δ) v] / ω . & (15) \end{matrix}

Because the equilibrium supply of nontradables depends on labor inputs (equation (1)), changes in employment also depend on changes in export earnings and shocks, u and v:

\begin{matrix} l^{s} = l^{d} = [(1 - α) (y_{p} + u) + α v] δ / ω . & (16) \end{matrix}

Not surprisingly, increases in export earnings raise the demand for home goods and employment, and positive shocks to the productivity of labor, v, also raise employment. If labor supply is rigid (that is, δ = 0), employment does not react to changes in export earnings. But, because labor supply is a function only of the real wage rate, w -p (equation (3)), the real wage rate is also a function of export earnings, which is identical to equation (16) except for the factor δ:

\begin{matrix} w - p = [(1 - α) (y_{p} + u) + α v] / ω . & (17) \end{matrix}

In equilibrium, then, positive shocks to export earnings, the demand for nontradables, and labor productivity would all lead to higher real wages.

It is important to recall that the shocks to permanent export earnings, y_p, that determine the real exchange rate, employment, and real wages in equations (14)—(17) represent shocks to the present value of future export earnings, which are not directly observable. The relationship between the present value of future export earnings and observed changes in earnings as described in equation (10) implies that the link between actual changes in export earnings and changes in the real exchange rate (or employment or real wages) depend on the parameter λ, which determines whether actual changes in export earnings are regarded as mostly temporary or mostly permanent.

Future export earnings can influence current consumption only if the country has access to a world capital market. The discussion so far has been based on the assumption of a perfect international capital market, but the model can be applied equally well to the other extreme case of no access to an international capital market. The only difference would be in the demand for nontradables (equation (13)). Given Cobb-Douglas preferences, the demand for nontradables would then be proportional to actual export earnings; that is, actual export earnings instead of the permanent income from exports would determine current demand for nontradables. Cobb-Douglas preferences also imply unitary price elasticity; that is, p should be set to equal unity. In this case, the link between actual export earnings and the real exchange rate would therefore be given directly by the parameters shown in equation (14), where ρ = 1 and ω = 1 + δ(1 - αβ). Although the domestic interest rate does not appear in any of the equations in this paper, it would have to vary if the country does not have access to international capital markets. The real interest rate that would clear the domestic capital market under these conditions can be calculated from the ratio of expected marginal utilities of consumption between two periods.

II. Optimal Wage Indexation Rules

The preceding section has shown that, in general, real wages should vary with export earnings and other shocks. This result suggests that it may be impossible to maintain full employment in economies that are subject to fluctuating export earnings and that have wage indexation schemes that fix real wages. In some countries with high and variable inflation rates, however, wage indexation schemes have been used to protect workers against inflationary surprises. This practice raises the question of whether it is possible to obtain the protection against inflationary surprises that is offered by wage indexation without incurring unemployment as a result of shocks to export earnings. The purpose of this section is to show, first, that simple wage indexation schemes purchase inflation protection at the cost of unemployment and, second, that these indexation schemes can be improved by adjusting nominal wages not only for changes in the price level but also for changes in export earnings.

A simple wage indexation rule by which wages rise equiproportionally with the CPI can be written as

\begin{matrix} w = p . & (18) \end{matrix}

With such a rule, employment is determined by the demand for labor. Given the demand for labor (equation (2)) and the demand for nontradables (equation (13)),¹⁴ the level of employment equals

\begin{matrix} l = {(1 - α) (y_{p} + u) + [ρ - (1 - α)] v} δ / (ω - ρ) . & (19) \end{matrix}

A comparison of equations (16) and (19) shows that, with fixed real wages, employment reacts more to variations in export earnings. This implies that whenever export earnings fall there will be unemployment because the demand for labor falls with the demand for nontradables and the supply of labor is constant because the wage indexation scheme keeps the real wage constant.¹⁵ A 1 percent fall in export earnings under these circumstances would lead to an unemployment rate of ρ(1 - α)/ω[(1- β)ρ+β(1- α)] percent.

Whereas a simple wage indexation rule such as equation (18) leads to unemployment problems, it is possible to construct a wage indexation scheme that does not lead to unemployment by taking proper account of fluctuations in export earnings. An indexation scheme that duplicates the path of the equilibrium real wage as described in equation (17) would clearly solve the unemployment problems that arise from the simple indexation rule (equation (18)) because equation (17) gives the real wage that would preserve full employment whatever the shocks to export earnings. But an indexation scheme that duplicates the path of the full employment real wage would also continue to offer workers protection against inflationary surprises. Real wages would follow the path of the full employment real wage described in equation (17) if the wage indexation takes the form

\begin{matrix} w = p + γ_{1} (y_{p} + u) + γ_{2} v, & (20) \end{matrix}

with

\begin{matrix} \begin{matrix} γ_{1}^{*} = (1 - α) / ω \\ γ_{2}^{*} = α / ω . \end{matrix} & (20 a) \end{matrix}

For the special case of an inelastic labor supply and a unitary intertemporal elasticity of substitution (that is, δ = 0 and ρ = 1; thus ω = 1), real wages should always be adjusted by a fraction, 1 - α, of any change in the permanent income from export earnings. Because changes in permanent export earnings are a function of only a fraction, λ, of actual changes in export earnings (equation (10)), it follows that the link between real wages and actual export earnings is given by the product of two fractions, 1 - α and λ, where 1 - α is equal to the share of imports in consumption and λ is related to the variances of the permanent and transitory shocks that affect export earnings.¹⁶

It has also often been suggested that the import component of the CPI should not be included in the basket used to index wages.

This implies that real wages would be indexed only on prices of home goods. The indexation rule could then be written as

\begin{matrix} w = p_{n} . & (21) \end{matrix}

However, w -p_n is the product wage that determines labor demand (equation (2)). Indexing wages only on the basis of nontradables prices would thus lead to a constant level of labor demand and employment if there were no productivity shocks. But this constant level of labor demand does not guarantee full employment if labor supply varies with the real CPI wage. Labor supply is given by equation (16), whereas the labor demand resulting from this indexation scheme can be calculated from equations (21) and (2). The potential unemployment caused by indexing wages only on prices of home goods can then be calculated as the difference between labor supply and labor demand:

\begin{matrix} \begin{matrix} l^{s} - l_{d} |_{w = p_{n}} = δ [(1 - α) / ω] (y_{p} + u) \\ + [α δ / ω - 1 / (β - 1)] v . \end{matrix} & (22) \end{matrix}

Equation (22) shows that fluctuations in export earnings would cause unemployment unless the labor supply were rigid (δ = 0). Equation (22) also shows that negative shocks to productivity would lead to unemployment because this wage indexation rule makes the appropriate fall in the product wage impossible. Indexing wages only on prices of home goods can therefore still lead to unemployment problems. The general form of the indexation rule that would avoid unemployment problems would be

\begin{matrix} w = p_{n} + γ_{1}^{'} (y_{p} + u) + γ_{2}^{'} v . & (23) \end{matrix}

Employment would then be given by

\begin{matrix} l^{d} = γ_{1}^{'} / (β - 1) (y_{p} + u) + (γ_{2}^{'} - 1) / (β - 1) v . & (24) \end{matrix}

Actual employment as described in equation (24) would be identical to full employment, as described in equation (16), only if the coefficients in equations (24) and (16) were the same; that is, if

* γ_{1}^{'} = (β - 1) δ (1 - α) / ω \begin{matrix} * γ_{2}^{'} = 1 + (β - 1) δ α / ω . & (25) \end{matrix}

Inspection of equation (25) reveals that wages should be negatively related to export earnings if they are fully adjusted for changes in home goods prices (0 < β < 1). This seemingly counterintuitive result is explained by noting that an increase in export earnings that increases the demand for home goods should lead to more employment. But a higher level of employment implies a lower marginal productivity of labor as capacity becomes a constraint; employers will then hire more labor only if wages rise by less than output prices (that is, if the product wage falls).

This section thus argues not only that it is inappropriate to fix real wages by letting wages rise in line with prices (in the sense that this would lead to unemployment problems), but also that the appropriate adjustment to wages in response to changes in export earnings depends on the price index to which wages are linked. If wages are indexed on the full CPI basket, they should be positively related to export earnings; but if wages are indexed only on the domestic component of the CPI, they should be negatively related to export earnings.¹⁷

III. Exchange Rate Policy and Export Earnings

As an alternative to indexing wages, some countries have adopted real exchange rate rules that involve adjusting the nominal rate according to the difference between world and domestic inflation.¹⁸ Such rules are often referred to as PPP (purchasing-power-parity) rules because they fix the real exchange rate. Because it has been shown that the real exchange rate should vary in response to fluctuations in export earnings and other shocks, these PPP rules can lead to unemployment problems. Indeed, a policy that fixes the real exchange rate by setting s = p would lead to a labor supply (taking into account only y_p) of l^s = y_p(β − 1)/β and a labor demand of l^d = y_p/β.¹⁹ This result implies that under such a policy a 1 percent fall in export earnings would lead to an unemployment rate of [(β − 1)δ]/β percent. The question therefore arises whether it is possible to formulate a rule that would adjust the nominal exchange rate automatically for domestic price developments and, at the same time, avoid the unemployment problems associated with simple PPP rules. The discussion in Section I suggests a rule of the form

\begin{matrix} s = p + μ (y_{p} + u) + μ_{2} v . & (26) \end{matrix}

The values for the coefficients μ₁ and μ₂ that would always preserve full employment can be calculated from equation (14). The rule in equation (26), however, is specified in terms of the CPI, whereas the full-employment solution for the real exchange rate in equation (14) is defined in terms of the relative price of nontradables. This discrepancy can be bridged by noting that α(s − p_n) = s − p; the full-employment solution for the real exchange rate in equation (14) can then be rewritten in terms of the CPI as

\begin{matrix} s = p - {[δ (1 - β) + 1] α / ω} (y_{p} + u) + [α (1 + δ) / ω] v . & (27) \end{matrix}

The indexation coefficients that would prevent unemployment in response to export earnings and productivity are equal to

\begin{matrix} \begin{matrix} μ_{1}^{*} = - [δ (1 - β) + 1] α / ω \\ μ_{2}^{*} = (1 + δ) α / ω . \end{matrix} & (28) \end{matrix}

For the special case of rigid labor supply and unitary inter-temporal elasticity of substitution, this result implies that a 1 percent change in (permanent) export earnings should lead to an a percent change in the real (CPI) exchange rate.

IV. Welfare and Employment Effects of Suboptimal Indexation Rules

A number of countries have indexation schemes that fix real wages or the real exchange rate without taking into account shocks that affect the economy. Which of these policies leads to more serious unemployment problems? This section investigates the question by using a social loss function that provides a criterion according to which these suboptimal policies can be ranked.²⁰ The theoretical justification for the specific form chosen is explained in detail in Aizenman and Frenkel (1984, 1985), who also present the economic rationale for the loss function in terms of the familiar “triangle” analysis of welfare loss. The loss function is given by

\begin{matrix} L = [l^{*} - l] [(w - p) - (w - p)^{*}], & (29) \end{matrix}

where l^* and (w − p)^* represent the market-clearing levels of employment and the real wage, respectively. The value of the loss function is equal to twice the area of the triangle under the labor demand function (Figure 1). The area of the triangle ABC measures the sum of the lost producers’ and consumers’ surplus; its area is proportional to [l* − l][(w − p) − (w − p)^*]. The welfare loss caused by a wage rule that fixes real wages can be determined by calculating first the equilibrium values of employment and the real wage, l^* and (w − p)^*, which are determined by equations (16) and (17). The actual real wage is determined by the policy rule (equation (18)), which implies that w − p = 0, and the employment level caused by this rule is determined by equation (19). These relationships can be substituted into the formula for the loss function (equation (29)). Concentrating only on the loss caused by fluctuations in export earnings, one finds that this substitution yields the following expression for the expected loss, E(L):

\begin{matrix} \underset{(w = p)}{E (L)} = (\frac{1 - α}{ω})^{2} [\frac{ρ}{ρ (1 - β) + β (1 - α)}] σ_{y}^{2} . & (30) \end{matrix}

Because the welfare loss is due to the stochastic shocks to export earnings, it is proportional to the variance of (the permanent income from) export earnings.

The expected loss that would be caused by a PPP exchange rate rule—that is, a rule that sets s = p—can be calculated in a similar fashion. The actual employment levels and real wage rates that would result from such a policy can be calculated by using the fact that s = p implies s = p_n and p = p_n (see footnote 19); changing the exchange rate in line with domestic inflation (international inflation is assumed here to be zero) thus fixes all relative prices. The value of the loss function under this policy is proportional to the area of the triangle BDE in Figure 1. The expected loss (more precisely, the component of the loss that derives from variations in export earnings) under such an exchange rate policy is therefore²¹

\begin{matrix} \underset{(s = p)}{E (L)} = (β ω)^{- 2} ρ [1 + δ (1 - β)]^{2} [(1 - α) β + (1 - β) ρ] σ_{y}^{2} . & (31) \end{matrix}

The exact welfare consequences of the two alternative, sub-optimal, policies having been derived, it is now possible to compare them by considering

\begin{matrix} \underset{(s = p)}{E (L)} - \underset{(w = p)}{E (L)} = {\frac{ρ σ_{y}^{2}}{ω^{2} β^{2} [ρ (1 - β) + β (1 - α)]}} . {[1 + δ (1 - β)]^{2} [(1 - α) β + (1 - β) ρ]^{2} - β^{2} (1 - α)^{2}} . & (32) \end{matrix}

Inspection of equation (32) reveals that the expression in the large braces is always positive; thus,

\begin{matrix} \underset{(s = p)}{E (L)} - \underset{(w = p)}{E (L)} \geq 0. & (33) \end{matrix}

That is, fixing the real exchange rate will lead to a larger welfare loss (for a given change in export earnings) than that from fixing real wages.²² This result is a consequence of the fact that the direct impact of changes in export earnings should have a direct effect on the real exchange rate and only an indirect effect on real wages. An exchange rate rule that fixes the real exchange rate by adjusting the nominal rate according to inflation differentials fixes the real exchange rate and thus does not allow the direct adjustment mechanism to work. In this context, fixing the real exchange rate will thus be worse than fixing real wages by indexing nominal wages on the full CPI basket.

Another indexation policy that has often been proposed is to index wages only on prices of home goods—that is, to set w =p_n (equation (21)). This policy would keep employment stable except for shocks to the production function, which affect the marginal productivity of labor. As mentioned above, such a policy would be optimal if the supply of labor were completely inelastic so that, at least in this limiting case, indexing wages on the domestic component of the CPI would be superior to indexing wages on the entire CPI. It is not clear, however, whether this superiority would still hold if labor supply is not completely inelastic. To resolve this uncertainty, it is necessary to compute the welfare loss that is caused by indexing wages on the domestic component of the CPI and to compare it with the loss that is caused by indexing wages on the entire CPI (equation (30)).

To calculate the welfare loss from indexing wages on prices of home goods only, it is necessary first to calculate the actual employment and real wages resulting from this policy. The loss function²³ would then appear as

\begin{matrix} \underset{(w = p_{n})}{E (L)} = (\frac{1 - α}{ω}) \frac{δ^{2}}{ρ} [ρ (1 - β) + β (1 - α)] σ_{y}^{2} . & (34) \end{matrix}

Equation (34) can now be compared with the expression that determines the welfare loss resulting from indexing wages on the entire CPI (that is, from setting w = p) in equation (30). The difference between the two equations is equal to

\begin{matrix} \underset{(w = p)}{E (L)} - \underset{(w = p_{n})}{E (L)} = (\frac{1 - α}{ω})^{2} \frac{1}{ρ} [ρ (1 - β) + β (1 - α)]^{- 1} . {ρ^{2} - δ^{2} [ρ (1 - β) + β (1 - α)]^{2}} σ_{y}^{2} . & (35) \end{matrix}

Inspection of equation (35) reveals that the entire expression is positive if δ < ρ/[ρ(1 − β) + β(1 − α)]. That is, if the elasticity of labor supply (with respect to the real wage rate) is below a critical value, it is better to eliminate prices of imported goods from the basket on which wages are indexed because such exclusion yields a lower welfare loss. For ρ ≥ 1, this critical value would be greater than unity, which implies that if the elasticity of labor supply is lower than unity it would be preferable to index wages only on home goods. Because it is usually assumed that labor supply is inelastic, it follows that it is preferable, although not optimal, to index wages only on the domestic component of the CPI. The optimal policy would be to take into account fluctuations in export earnings directly in the indexation formula as shown above.

This section has considered three policies: fixing the real exchange rate (s = p), fixing real wages (w = p), and fixing the product wage (w = p_n). In general, the worst policy would be to fix the real exchange rate because this rule would always lead to a higher social cost than that from fixing real wages.²⁴ There is also a presumption that it would be better to take imported goods out of the index to which wages are linked. Such exclusion would at least stabilize employment, although unemployment would not be avoided when labor supply responds to real wages.

V. Concluding Remarks

Small open economies have to sustain profound adjustments in response to fluctuations in export earnings. The required adjustment to these fluctuations usually includes changes in real wages and the real exchange rate. But countries with highly variable export receipts exist where real wage rates are fixed because nominal wages are indexed on the general price level, or where the real exchange rate is fixed because the nominal exchange rate is depreciated in line with the difference between domestic and foreign inflation rates.

It has been argued here that such indexation schemes, which might be useful in the face of high and variable inflation rates, should be “augmented” by rules that index either the real exchange rate or real wages on the basis of export earnings. By choosing the appropriate indexation coefficients, the authorities could replicate the equilibrium that would obtain under clearing labor markets; in the absence of inflationary surprises, this optimal indexation would mean that fluctuations in export earnings would no longer necessarily cause large unemployment problems. Linking wages to prices without taking into account fluctuations in export earnings would be appropriate only if labor supply were completely inelastic and if the index used to adjust nominal wages were to exclude prices of imported goods.

The optimal indexation coefficients obtained with the model presented here might seem complicated at first. If it is assumed that labor supply is inelastic, however, the coefficients all depend on only two parameters: the share of nontradables in consumption and the intertemporal elasticity of substitution.

Thus, the principal policy implication of the paper is that, in small open economies with fluctuating export earnings, it is important not to fix either the real exchange rate or real wages. Given an inflationary environment that requires some form of wage indexation, the best policy would be to link wages not only to changes in the general price level but also to changes in export earnings. Such a policy would protect workers from inflationary surprises and would simultaneously foster the necessary real adjustment to changes in export earnings.

APPENDIX: Deviation of the Elasticity of Demand of Nontradables with Respect to the Real Exchange Rate

The intertemporal utility function (equation (5) of the text), the consumption index (equation (6)), and the equality of the market rate of interest and the rate of time preference imply

\begin{matrix} \frac{\partial C_{t} / \partial N_{t}}{\partial C_{t + 1} / \partial N_{t + 1}} = \frac{C_{t}^{- ζ} I_{t}^{α} N_{t}^{- α}}{C_{t + 1}^{- ζ} I_{t + 1}^{α} N_{t + 1}^{- α}} = \frac{P_{N t}}{P_{N t + 1}} . & (36) \end{matrix}

The Cobb-Douglas specification of the consumption index also implies constant expenditure shares:

\begin{matrix} (1 - α) I_{t} P_{I t} = α N_{t} P_{N t,} f o r a l l t . & (37) \end{matrix}

Setting P_It = 1 and substituting equation (37) into equation (36) yields

\begin{matrix} (\frac{N_{t}}{N_{t + 1}}) - ζ = (\frac{P_{N t}}{P_{N t + 1}}) [1 - α (1 - ζ)]; & (38) \end{matrix}

or, solving for I_t, yields

\begin{matrix} (\frac{I_{t}}{I_{t + 1}}) - ζ = (\frac{P_{t}}{P_{t + 1}}) (1 - ζ) (1 - α) . & (39) \end{matrix}

For the special case of a logarithmic intertemporal utility function (that is, ζ = 1), it is apparent from equation (39) that

\begin{matrix} I_{t} = I_{t + 1} . & (40) \end{matrix}

Given the budget constraint (equation (7)) and the constancy of interest rates, equation (40) then implies that

\begin{matrix} I_{t} = r Y_{p t} & (41) \end{matrix}

and therefore, from equation (37), that

\begin{matrix} N_{t} = \frac{r Y_{p t} (1 - α)}{P_{N t}^{α}} . & (42) \end{matrix}

Equation (42) clearly implies a unitary price and income elasticity of the demand for nontradables.

In the general case, ζ ≠ 1, the demand for nontradables is somewhat more complicated. A solution can still be obtained if it is taken into account that for time t + 1 and thereafter all shocks are expected to be zero. Hence, all relative prices should be expected not to change, and the consumption profile should be expected to be flat. This expectation implies that for time t + 1 and thereafter the consumption of importables should be equal to permanent income available at time t + 1, which is linked to current permanent income by

\begin{matrix} r [(1 + r) (Y_{p t} - I_{t})] = I_{t + 1} = P_{N t + 1} N_{t + 1} α / (1 - α) . & (43) \end{matrix}

Equation (38) can be written as

\begin{matrix} N_{t} = N_{t + 1} (\frac{P_{N t}}{P_{N t + 1}})^{- [1 - α (1 - ζ)] / ζ} . & (44) \end{matrix}

Substituting equation (43) into equation (44) yields

\begin{matrix} N_{t} = \frac{r (1 + r) (Y_{p t} - I_{t}) (1 - α)}{P_{N t + 1}^{α}} (\frac{P_{N t}}{P_{N t + 1}})^{- [1 - α (1 - ζ)] / ζ} . & (45) \end{matrix}

In equation (45), I_t can be substituted by again using equation (37); simplifying yields finally

\begin{matrix} N_{t} = \frac{r (1 + r) Y_{p t} {(\frac{P_{N t}}{P_{N t}})}^{- [(1 - ζ) (1 - α)] / ζ} (1 - α)}{P_{N t} [1 + (1 + r) r (\frac{P_{N t}}{P_{N t + 1}})^{- [(1 - ζ) (1 - α)] / ζ}] α} . & (46) \end{matrix}

If it is assumed that a change in P_Nt does not affect expectations about P_Nt+1, the elasticity of N_t with respect to P_Nt is equal to

\begin{matrix} \frac{\partial \ln N_{t}}{\partial \ln P_{N t}} |_{P_{N t + 1}} \equiv ρ \\ = - {1 + \frac{(1 - ζ) (1 - α)}{ζ} [\frac{(P_{N t} / P_{N t + 1})^{[(1 - ζ) (1 - α)] / ζ}}{(P_{N t} / P_{N t + 1})^{[(1 - ζ) (1 - α)] / ζ} + (1 + r) r}]} . (47) \end{matrix}

For small shocks, P_Nt/P_Nt+1 would be close to unity, and hence ρ could be approximated by

ρ \equiv \frac{[(1 + r) r + 1] ζ + (1 - ζ) (1 - α)}{[(1 + r) r + 1] ζ};

ρ is a monotonic, increasing function of the intertemporal elasticity of substitution,1/ζ. It tends to infinity as the elasticity of substitution goes to infinity, and it goes to 1 − (1 − α)/[(1 + r)r + 1] > α as the elasticity of substitution goes to zero.

REFERENCES

Adams, Charles, and Daniel Gros, “Some Illustrative Examples of the Consequences of Real Exchange Rate Rules for Inflation” (unpublished; Washington: International Monetary Fund, 1985).
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Aizenman, Joshua, and Jacob A. Frenkel, “Supply Shocks and Optimal Wage Indexation in the Open Economy,” paper presented at the NBER-World Bank Conference on Structural Adjustment and the Real Exchange Rate in Developing Countries, Washington, November 29-December 1, 1984 (Cambridge, Massachusetts: National Bureau of Economic Research, 1984). Forthcoming in Economic Adjustment and Exchange Rates in Developing Countries, ed. by Sebastian Edwards and Shamed Liaguat (Chicago: University of Chicago Press, 1986).
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Aizenman, Joshua, and Jacob A. Frenkel, “Optimal Wage Indexation, Foreign-Exchange Intervention and Monetary Policy,” American Economic Review (Nashville, Tennessee), Vol. 75 (June 1985), pp. 402–23.
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Corden, W.M., “The Exchange Rate, Monetary Policy and North Sea Oil: The Economic Theory of the Squeeze on Tradables,” Oxford Economic Papers (London), Vol. 33 (July 1981), pp. 23–46.
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Corden, W.M., “Booming Sector and Dutch Disease Economics: A Survey,” Working Papers in Economics and Econometrics 79 (Canberrra: Australian National University, Faculty of Economics November 1982).
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Neary, J. Peter, and Douglas D. Purvis, “Sectoral Shocks in a Dependent Economy: Long-Run Adjustment and Short-Run Accommodation,” Scandinavian Journal of Economics (Stockholm), Vol. 84 (No. 2, 1982), pp. 229–53.
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Sargent, Thomas J., Macroeconomic Theory (New York: Academic, 1979).
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Strotz, R.H., “Myopia and Inconsistency in Dynamic Utility Maximization,” Review of Economic Studies (Edinburgh, Scotland) Vol. 23 (1956), pp. 165–80.
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Mr. Gros, an economist in the Research Department, is a graduate of the University of Chicago.

Export earnings can fluctuate because supply is unstable, because the international price of the export commodity is unstable, or because both are unstable. For example, in Iceland the fish catch (80 percent of exports) has at times fallen by 20 percent in a single year. In contrast, Chile has experienced a 30 percent fall in the price of its main export (copper) in a single year.

In Iceland real wages fall when the fish catch is bad and rise when the fish catch is good; this amounts to an informal indexation system that takes into account not only prices but also export earnings.

By fixing the real exchange rate, exporters are presumably protected from inflationary surprises; it is difficult to see the need for this, however, because exporters can change their prices (in domestic foreign currency) easily, whereas it is always more difficult to renegotiate wages. Floating exchange rates often are not considered because they are thought to lead to instability in the exchange rate market.

Markets would no longer be able to clear if both the real exchange rate and real wages were to be fixed by indexation rules; eventually only one of the indexation rules could be implemented.

This assumption has been adopted by several authors (see Corden (1981, 1982), and Neary and Purvis (1982)); it is justified by the observation that unemployment usually does not arise in the export sector but in the rest of the economy. In Chile, for example, the copper sector, which accounts for over half of total exports, employs only 6 percent of the labor force.

This assumption excludes any effects that might come from another export sector such as manufacturing. The exclusion seems to be justified because there are a number of primary commodity exporters so small that almost the entire work force that is not used in the primary export sector is used in the nontradables sector. In other cases, the country might be large enough to have a significant manufacturing sector, but a restrictive commercial policy has effectively turned the output of this sector into nontradables.

This definition of the CPI is justified by the constant-expenditure-shares utility function used below (see equation (12)).

The international price of imports is normalized to unity for all time periods; B is thus a real discount rate.

Export earnings in foreign currency are equal to the quantity of export production multiplied by export prices. A 1 percent change in either production or export prices would thus have the same effect in this framework.

That is,

λ = 1 + (σ_{w}^{2} / σ_{T}^{2}) / 2 - [σ_{w}^{2} / σ_{T}^{2} + (σ_{w}^{2} / σ_{T}^{2})^{2} / 4]^{1 / 2} .

See the Appendix; this consumption plan is time consistent, given the constant rate of discount R. For discussion of the time consistency of consumption plans with a constant rate of time preference, see Strotz (1956).

Because all variables are measured at the same point in time, the subscript t will henceforth be suppressed.

The real exchange rate in practice is often defined in terms of the CPI as s -p (instead of s -p_n, as here). The two are closely related, however, because manipulation of the definition of the CPI yields s -p = α(s -p). Under the CPI definition of the real exchange rate, the elasticity of the real exchange rate with respect to export earnings (in this special case) would be equal to a, the share of nontradables in consumption.

Equation (18) can be rewritten as w-p_n=(1 -α)(s -p_n) that is, in terms of the product wage and the real exchange rate. These two variables determine the demand for labor and the demand for nontradables.

Of course, whenever export earnings rise the opposite would happen, but in this case wage drift might alleviate the problem. Section IV contains a more rigorous analysis of the exact economic loss caused by this wage indexation scheme.

The optimal wage indexation rule (equation (20)) also implies that export earnings influence real wages through their effect on the demand for nontradables. Any change in the demand for nontradables should have the same effect on real wages, whether the change is caused by a change in export earnings, y_p, or by a temporary shock, u.

Recall that the optimal coefficients that link wages to export earnings implicitly represent a link between wages and the permanent income from exports. The link between the permanent income from exports and actual export earnings (more specifically, the fraction of any actual change in export earnings that can be regarded as temporary or permanent) is described by equation (10). Only the permanent income from exports is relevant if the country has access to an international capital market. The model, however, can also accommodate the opposite extreme of no access to an international capital market. In this case, the optimal coefficient would link wages directly to actual changes in export earnings, and φ) would be equal to 1 + δ(1 − αβ). The optimal indexation coefficient that links wages to actual export earnings thus depends not only on the parameters describing the structure of the economy, but also on whether the country has access to an international capital market.

In an economy with both wage indexation and a real exchange rate rule, two relative prices would be fixed. Shocks to the economy would therefore lead to disequilibrium not only in the labor market but also in other markets. It is difficult to see how markets could continue to function in this situation. This paper is concerned only with the real aspects of indexation rules. Real exchange rate rules, however, also have monetary implications in that the monetary authorities can no longer control inflation if they follow a real exchange rate rule. This aspect is discussed in Adams and Gros (1985).

The definition of the CPI (see equation (4)) implies that p − s = (1 − α)(p_n − s); thus, if the exchange rate rule sets s = p, it follows that p_n = s and that p_n = p. Using this in the equations for the supply and demand for nontradables (equations (5) and (13), respectively) yields an expression for employment:

l^d = [(y_p + u) − v]/β.

Substituting this into the labor demand equation (2) yields

w − p = [(β − 1)(y_p + u) + v]/β.

The rationales for simple wage indexation schemes and PPP exchange rate rules have been discussed in the previous section. This section implicitly assumes that market-clearing, full-employment equilibrium is the optimal or benchmark case. The analytical framework used in this section draws on Aizenman and Frenkel (1985).

The optimal values, l* and (w − p)^*, are still given by equations (16) and (17); the actual values are given in footnote 19. Substituting the actual values into the formula for the loss function, equation (29), yields

\underset{(s = p)}{E (L)} = [\frac{δ (1 - α)}{ω} - \frac{1}{b}] [\frac{β - 1}{b} - \frac{1 - α}{ω}] σ_{y}^{2},

which can be transformed into equation (31) in the text.

If there are constant returns to scale in the production of nontradables (that is, if β = 1), then equation (40) holds with equality (that is, the two policies lead to the same welfare loss). This result follows from the fact that if β = 1, then ω =p_n. Setting δ =p =p_n via the exchange rate rule, or ω =p via full wage indexation, is thus completely equivalent.

The labor demand function (equation (2)) and the policy w = p_n imply immediately that l = v/(l − β). Writing w − p_n ≡ w − p + p − p_n shows that with this policy w − p = − (1 − α)(s − p_n), which can be substituted into the demand for nontradables equation to yield w − p = [(1 - α)/ρ][(y_p+u) + v/(β - 1)]. The expected loss is thus equal to

\underset{(w = p_{n})}{E (L)} = [\frac{δ (1 - α)}{ω}] (\frac{1 - α}{ρ} - \frac{1 - α}{ω}) σ_{y}^{2} .

Given the definition of φ, this is equivalent to equation (34).

These statements are based only on the effects of the variability in export earnings. Because shocks to the demand for nontradables, u, have the same effect, the results continue to hold if these shocks are taken into account. Shocks to the production of nontradables, v, however, have different effects. But it can be shown that, as long as α < 0.5, it is still better (in terms of a smaller loss) to fix real wages than to fix the real exchange rate, even if productivity shocks are important. The presence of productivity shocks would, however, affect any welfare comparison between wage indexation based on the CPI and wage indexation based only on prices of nontraded goods.

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IMF Staff papers: Volume 33 No. 1

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1986: Issue 001

Publisher:: International Monetary Fund

ISBN:: 9781451956726

ISSN:: 1020-7635

Pages:: 218

DOI:: https://doi.org/10.5089/9781451956726.024

Keywords
I. The Model
II. Optimal Wage Indexation Rules
III. Exchange Rate Policy and Export Earnings
IV. Welfare and Employment Effects of Suboptimal Indexation Rules
V. Concluding Remarks
- APPENDIX: Deviation of the Elasticity of Demand of Nontradables with Respect to the Real Exchange Rate
REFERENCES

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Abstract

I. The Model

II. Optimal Wage Indexation Rules

III. Exchange Rate Policy and Export Earnings

IV. Welfare and Employment Effects of Suboptimal Indexation Rules

V. Concluding Remarks

APPENDIX: Deviation of the Elasticity of Demand of Nontradables with Respect to the Real Exchange Rate

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