Unemployment, wage indexation and commercial policies

CHICHUR CHAO Oregon State Unioersity

Corvallis, Oregon

JOHN R. CONLON The University of Mississippi

University, Mississippi

Unemployment, Wage lndexation and Commercial Policies *

This paper shows the effects of wage indexation schemes in the presence of relative price variations. In particular, it is shown that indexation schemes which seem reasonable can nevertheless leave the level of employment vulnerable to terms of trade shocks. The indexation scheme which isolates the employment level from the effects of price variations is derived, and the effects of commercial policies in the presence of indexation are examined.

1. Introduction A number of small open economies have pursued the policy

of indexing wages to the price level. Such indexation has frequently been used as a form of minimum wage policy, which maintains a wage rate above the market-clearing level at the expense of a cer- tain amount of unemployment. Indexation then keeps this real wage relatively constant in the face of a variable price level. More generally, indexation might help nominal wages to follow the price level, reducing fluctuations in real wages and employment in the face of a volatile price level caused, for example, by inconsistent monetary policy (see Fischer 1977).

Indexation is generally adapted, therefore, to isolate the economy from variations in the price level caused, say, by monetary shocks. As Fischer (1977) points out, however, an indexation formula which isolates real variables from monetary shocks will generally aggravate the consequences of real shocks operating through the aggregate supply curve. A different but related issue relevant for a small open economy would be the effect of indexation when domestic relative prices vary because of changing terms of trade or commercial policies.

*We thank two anonymous referees for valuable comments.

Journal of Macroeconomics. Winter 1993, Vol. 15, No. 1, pp. 165-174 165 Copyright Q 1993 by Louisiana State University Press 0164-0704/93/$1.50

Chi-Chur Chao and John R. Cordon

Section 2 develops the production structure of the economy, and Section 3 treats the effect of changes in domestic relative prices on output and unemployment in the presence of various indexation schemes. In particular, the indexation scheme which isolates the employment level from terms of trade shocks is derived. In Section 4 the welfare implications of commercial policies in the presence of wage indexation are examined. Section 5 concludes.

2. Production Structure of the Model Many people have modeled economy-wide unemployment

created by stickiness in the real wage when nominal wages are fully indexed to commodity prices. However, in the Heckscher-Ohlin setting, real wage stickiness, with constant returns to scale tech- nology, results in a linear transformation curve, and so, to inde- terminacy of employment and output (see Brecher 1974).’

Little effort, however, has been made to examine the transformation curve for the sector-specific factor production model under indexation. This omission is important because this model plays a significant role in our understanding of the short-run effects of price fluctuations and trade policies. We will show that the usual nonlinear transformation curve is obtained under full indexation of nominal wages to commodity prices with constant returns to scale. However, the effects of terms of trade shocks and government policies depend crucially on the choice of weights for commodity prices in the indexation formula.

Let a small economy use two factors, labor and capital, to pro- duce two goods, X1 and X,, with prices pl and p,, respectively. Capital is sector-specific, while labor can move freely. Full indexation of nominal wages to commodity prices is assumed:

w = mb P2) 3 0)

where F is assumed to be homogeneous of degree one in goods prices. This isolates the economy from monetary shocks (ignoring dynamic considerations such as the Tobin effect). Let the weight on the ith price in the function F be vi = (p,/w)(dF/ap,), which is assumed to be in the interval (0, 1). By the homogeneity property, we have v1 + v2 = 1.

‘See Batra and Seth (1977), Yu (1982), Yip (1988), and Batra and Beladi (1990) for related studies.

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Unemployment, Wage Indexation and Commercial Policies

With the zero profit condition for competitive firms, unit cost for each good will equal price. Thus,

Ci(w, ri) = pi, i=l,2, (2)

where ri denotes the rental rate of capital in sector i. Turning to the factor markets, the quantity of labor hired &)

by sector i equals XC; and capital used (ZQ equals XC: by Shep- hard’s lemma, where subscripts in the unit cost functions represent partial derivatives and Xi denotes the output of sector i. Denoting the total endowments of labor and sectoral capital by L and &, respectively, we can write

Ci(w, r,)X, = Ki ) (3)

cgw, ?-1)X, + C$(w, f-2)& = L1 + L, < L , (4)

where (4) assumes the existence of unemployment. Let 6Li = wCL/C’ and 0xi = riC b/C i be the distributive share

of labor and capital in sector i, and Ui = CiCL,./CiCL represent the elasticity of factor substitution in sector i. Totally differentiating (l)- (3) yields

rZi = -a,eLi(s - Pi) , (7)

where a (^) over a variable denotes a rate of change. By choosing good 2 as the numeraire, we can set p, = p and

p, = 1. Then w and ri are the wage rate and rental rate in terms of good 2. Solving (5)-(7) yields the change of sectoral output as:

Since ui lies in the interval (0, l), (8) and (9) show the normal price- output response.

Define the transformation curve to be the curve traced out by the point (X,(P), &(P)), as the price ratio p varies. Then the mar-

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ginal rate of transformation (MRT), dX,/dX,, can be obtained by dividing (9) by (8) as:

dX,ldx, = -PP > (10)

where B = ullz(oz/e,)/uzLl(al/exl) > 0 denotes a distortion pa- rameter induced by wage indexation.2

Equation (10) states that, as the domestic goods-price ratio p = p,/p, increases, fSp units less of X2 are produced for every ad- ditional unit of Xi produced. If, for example, B > 1, then this substitution will reduce measured GNP. This follows from GNP = pX1 + X2, so that as p rises, dGNP = X,dp + pdx, + dx, = X,dp + p(1 - p)dX,. The term p(1 - p)dX, represents the effect of substitution, and it is negative if ~3 > 1 and dX, > 0.

By rearranging terms of ~3, we obtain

(3 Z 1, when u1 31 sr , (11)

where s1 = Ll(ul/Ox,)/[L,(u,/e,,) + L2(u2/8&]. Note that, as shown by Jones (1971), oi/Oxi signifies the elasticity of demand for labor in sector i. Just as in Jones (Equation ll), s1 is the share of the weighted elasticities for sector 1.3 The reason for (11) can be ex- plained by the change in employment caused by the change of the domestic goods-price ratio, as shown in the next section.

3. Goods Prices and Employment The employment effect provides an explanation for the diver-

gence between the marginal rate of transformation and goods-price ratio, derived above. Totally differentiating (4), and then utilizing (8) and (9), yields

Equation (12) states that total employment will decrease (increase) when p = p,/p, rises and ur > (<) sl. Hence, it suggests that, to keep employment constant in the face of terms of trade variations, s, should be chosen as the weight for good 1 in the wage indexation

‘This is consistent with the literature on distortions. See Bhagwati (1971). 3Jones (1971) examines effects of commodity price changes on factor prices, as-

suming full employment.

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Unemployment, Wage lnderation and Commercial Policies

formula. If the actual weight o1 is greater than the suggested weight si (over indexation to pJ, an increase in p = pJp, will reduce.total employment, so the fall in XZ will be greater than p times the rise in X1. That is, the MRT will be larger than p, so that p > 1. The case of ui < s1 (under indexation to pJ can be analyzed similarly.

The indexation scheme which will isolate unemployment from changes in the domestic goods-price ratio, therefore, should set ui = si and u2 = 1 - si. Thus, the indexation weights ui and u2 should reflect not only the sizes of sectors 1 and 2, as measured by L1 and L2, but also their elasticities of demand for labor, cr,/tIk,. In other words, if the elasticity of demand for labor in sector I is large, then the wage should closely follow p, in order to keep the real wage relative to p,, w/p,, more nearly constant. This is because any variations in w/p1 will have relatively strong employment effects in sector 1 if the elasticity of demand for labor in sector 1 is large.

The indexation scheme with weights ui = si and u2 = 1 - si will therefore isolate employment from changes in the domestic price ratio caused, for example, by changes in the terms of trade.4 Other seemingly reasonable weights, however, such as consumer expenditure weights or the labor weights, will leave the level of employment vulnerable to terms of trade shocks.’ The indexation weights will also have implications for commercial policies, as will be shown next.

4. Commercial Policies and Welfare We are ready to use the above production structure to analyze

the welfare implications of commercial policies. Using duality, the demand side of the economy is represented by an expenditure function defined as

Up, 4 = min (PC1 + C,) ,

where the minimization is with respect to the demand for the two commodities, C, and Cz, subject to a strictly quasi-concave utility function u(Ci, CJ 2 u.

%e optimal wage indexation scheme in the sense of welfare maximization is, of course, essentially no indexation, that is, allowing wages to adjust freely to clear markets. If a higher than market-clearing wage is desired, however, then the indexation weights which will isolate employment from terms of trade variations is given by q = si.

‘Consumer expenditure weights might be larger or smaller than s,, depending on the country’s demand preference. The labor weight, q = L,/(L, + I& is larger or smaller than si, when a,/& is larger or smaller than uI/OKI.

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Chi-Chur Chao and John R. Conlon

For concreteness, let good 1 be the importable good and good 2 be the exportable good. We assume that, while there is no re- striction on the trade in the exportable, tariffs or quotas are im- posed to restrict imports. Thus,

Q = E&P> 4 - X,(P) > (14)

where E, = aE(p, u)/@ = C, and Q is the level of imports. The budget constraint under trade restrictions may be written

as

E(P, 4 = PXI + & + (P - p*)Q , (15)

where p* is the world price ratio which is smaller than the domestic goods-price ratio, p. The term (p - p*)Q is the revenue of tariffs or import quotas, which is assumed to be redistributed back to the private sectors in a lump-sum fashion so that the tariff or quota revenue is spent in the same manner as other incomes.

Before discussing trade restrictions, we first examine the op- timality of free trade. Free trade is defined as a situation involving equality of domestic and world prices of all traded goods. The necessary condition for free trade to be the optimal policy is du/dp = 0, holding p* constant. Therefore, we differentiate (15), then im- pose p = p* and utilize (10) and (14) to yield

E,du = p(1 - p)dX, , (16)

which shows du # 0 if R # 1. Thus, free trade is not the optimal policy if the wage rate is over- or under-indexed to p,, while free trade remains the optimal policy if the wage rate is just-indexed.

Hence, free trade in the presence of wage indexation may be inferior to trade restrictions such as import quotas or tariffs.

Zmport Quotas Let dW = E,du denote the welfare change. Differentiating

(15) and utilizing (10) and (14) yields

do = sQ(l - Wp + (p - p*)dQ , (17)

where s = b/QWd&) is the substitution in production in response to a change in p. From (8), we have s > 0. The first term on the RHS of (17) d enotes the employment effect caused by wage

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Unemployment, Wage Indexation and Commercial Policies

indexation and the second term is the first-order effect of changes in import quotas. Note that under the just-indexed case, the distortion effect will vanish. Thus, dW/dQ = (p - p*) > 0: a tightening of import quotas; that is, dQ c 0, causes a decline in social welfare while a loosening improves welfare. This standard result, however, must be revised if p # 1.

Under import quotas, the domestic goods-price ratio is en- dogenous; dp can be obtained by differentiating the equilibrium condition (14) as follows:

E&u - (e + s)(Q/ddp = dQ , (18)

where E, = aE,/au and e = -(p/Q)(aE,/ap) is the substitution in consumption for a given utility. Note that since the expenditure function is homogeneous of degree one in goods prices, the marginal propensity to consume good 1 can be defined as m = pE,,/ E,. Therefore, (18) can be rewritten as

blp)~ - (e + s)(Q/p)& = dQ . (1%

Substituting (19) into (17) and collecting terms, we obtain

&/dQ = -(p/Q){1 - Wp>(p - p*Me + 41 - 4 - ENI, (20)

where the stability condition requires that {e + s[l - m(l - p)]} > 0.6 Hence, it follows that dp/dQ -C 0: a tightening of import quotas (dQ < 0) always raises the domestic price ratio of the importable good. However, the rise of the goods-price ratio is higher if wage indexation under-emphasizes the imported goods price p,. The reason is as follows: When indexation under-emphasizes p,, a quota-induced rise in p, increases total employment, thereby rais- ing national income. This leads to a higher demand for the importable good and hence a higher price.

‘Following Dei (1985), the adjustment process for the goods market under quotas is @ = c&T(p), where the dot is the time derivative, a is a positive constant and Z = E,(p, u) - X,(p) - Q is the excess demand for good 1. From (15), we obtain that u is a function of p. By keeping Q constant, a linear approximation of the adjustment process around the equilibrium point p’ is 9 = a(dZ/dp)(p - p’). Hence, the necessary and sufficient condition for the stability of this system is dZ/dp < 0. From (17) and (lQ), we obtain dZ/dp = -(Q/p){e + s[l - m(1 - p)]}, which is always negative if and only if {e + s[l - m(1 - f3)]} > 0.

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By substituting (20) into (17), the welfare effect of a change in the import quota in the presence of wage indexation is obtained as

WldQ = {(e + S)(P - P*) - SPU - P)l/{e + 41 - 41 - P)ll . (21)

Consider the case of over-indexation to the import price p,, that is, p > 1. A tightening of quotas raises pr and thus reduces total employment. This production loss plus the first-order loss would def- initely lower the home country’s welfare. However, when the wage indexation under-emphasizes p, (fl < l), the total employment will be increased and hence leads to a production gain.

To summarize, a tightening (loosening) of quotas will reduce (increase) unemployment if the wage is under-indexed to the import price p,. lf the resulting employment/production effect is stronger than the usual first-order welfare effect, then a tightening (loosening) of quotas will also increase (reduce) welfare. Zf the wage is just- or over-indexed to the import price pl, then a tightening (loosening) of quotas always reduces (increases) employment and wel- f are.

Tariffs When the country levies a tariff at the rate of t on imports,

the domestic price ratio of the importable is p = p*(l + t). Dif- ferentiating (15) and (14) yields

Ldu - [pt/(l + t)ldQ = Qts(l - P) - l/(1 + t)ldp + [p*QlU + t)ldt, (259

E,& - dQ = (e + s)(Q/p)dp > (23)

where dp = p*dt since p* is constant. Prior to examining the welfare effect, we need first to obtain

the domestic price elasticity of import demand under tariffs. By solving (22) and (23), we obtain

(pIQ)(dQ/dp) = -b + 41 - 4 - @I + ml0 + t))M , (24)

where M = [l - mt/(l + t)]-’ is the tariff multiplier. By substituting (24) into (22), we obtain

dW/dt = p*Q{s(l - p) - (e + s)t/(l + t)}M . (25)

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Unemployment, Wage Indkation and Commercial Policies

Under just- or over-indexation to p,, an increase in the tarti rate always increases unemployment and lowers welfare. However, in the case of under-indexation to the import price p,, an increase in the tariff rate will increase total employment, which will bring a production gain. If the production gain dominates the tariff revenue loss, then welfare will improve. Similarly, a reduction of the tariff will reduce welfare under these circumstances.’

5. Conclusions This paper has examined the consequences of wage indexation

in a sector specific capital model. In general, a change in the domestic goods-price ratio in the presence of wage indexation affects the level of employment. A set of indexation weights which isolates employment from the price variations should take account of sectoral elasticities of demand for labor, as well as sectoral employment levels. Indexation also implies that commercial policy can affect the level of unemployment. Employment effects of commercial policy in the presence of an indexation scheme could either compound, mitigate, or reverse the usual effect through gains from trade.

To summarize, a small open economy implementing a wage indexation scheme should consider the interaction between the domestic goods price and employment in choosing an indexation formula, and a small open economy with indexation should consider the employment effects of indexation when choosing commercial policies.

Received: May 1991 Final version: March 1992

References Batra, Raveendra N., and Avinash C. Seth. “Unemployment, Tariffs

and the Theory of International Trade.” Journal of International Economics 7 (August 1977): 297-306.

Batra, Raveendra N., and Hamid Beladi. “Pattern of Trade between Underemployed Economies.” Economica 57 (November 1990): 485-93.

‘The optimal level of import quotas and tariffs under wage indexation can be obtained by solving dW/dQ = 0 in (21) and dW/dt = 0 in (W), respectively, as (p” - p*)/p* = ~(1 - P)/(e + sfl) for both cases, where p” denotes the optimal domestic goods-price. Hence, tariffs and quotas are equivalent in the present model under various indexation schemes represented by 1 - p.

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Bhagwati, Jagdish N. “The Generalized Theory of Distortions and Welfare.” In Trade, Balance of Payments, and Growth, edited by Jagdish N. Bhagwati et al., 69-90. Amsterdam: North-Hol- land, 1971.

Brecher, Richard A. “Minimum Wage Rates and the Pure Theory of International Trade.” Quarterly Journal of Economics 88 (Feb- ruary 1974): 98-116.

Dei, Fumio. “Voluntary Export Restraints and Foreign Invest- ment. ” Journal of international Economics 19 (November 1985): 305-12.

Fischer, Stanley. “Wage Indexation and Macroeconomic Stability.” Journal of Monetary Economics 3 (Supplement 1977): 107-47.

Jones, Ronald W. “A Three-Factor Model in Theory, Trade, and History.” In Trade, the Balance of Payments, and Growth, edited by Jagdish N. Bhagwati et al., 3-21. Amsterdam: North Holland, 1971.

Yip, Chong K. “The Employment Effects of Tariffs in an Efficient Bargain Model.” Journal of Macroeconomics 10 (Summer 1988): 477-85.

Yu, Eden S. H. “Unemployment and the Theory of Customs Unions. ” Economic Journal 92 (June 1982): 399-404.

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Unemployment, wage indexation and commercial policies