APPENDIX I: Derivation of the Results for the CES Production Function
The first tier of the production function outlined in equation (2) of the text can be written,
where λ = (1 - σ)/σ, ρL and ρK are constants, εA, εL, and εK are respectively factor-neutral, capital-augmenting and labor-augmenting technical change, and K and L are the physical (as opposed to effective) quantities of capital and labor. The real marginal products of labor and capital can be derived as follows,
Setting A.3 and A.4 equal to the real wage (w/PV) and the real cost of capital (r/PV) respectively leads to demand functions for labor and capital,
using the substitutions: (1 + λ) = (1/σ) and (-λ/1+λ) = (σ-1).
From A.1, the short run supply function can be written:
where φL and φK are the shares of capital and labor in value added. Using A.4, this can be rewritten:
with ψL being defines as φL /(1-φL).
It is also possible to express A.7 in terms of ULC. First it is necessary to rewrite A.4. Multiplying through by (L/V)-σ, A.4 becomes:
where α = σ/(1-σ).
Substituting A.4b in A.6,
The return per unit of capital services can also be written as a function of the labor share in value added (ULC/PV). Equating (r/PV) with the right hand side of A.3 produces:
Holding K constant (for the short run) and substituting from A.7a for
where β = 1/(1-σ). With value added and the return to capital expressed in terms of the labor share, it is interesting to see what determines the distribution of income among factors.
Multiplying A.4 by (W/PV),
Thus, (ULC/PV) is related to the real product wage. A decline in the real product wage reduces (ULC/PV), as long as the elasticity of substitution (σ) is less than one. The extent to which (ULC/PV) is reduced depends on σ. If σ is close to zero (i.e very low substitution between labor and capital), the percentage change in (ULC/PV) is close to the percentage change in the real product wage. With σ significantly greater than zero the effect on (ULC/PV) is smaller and, in the case of the Cobb-Douglas production function (σ=1), (ULC/PV) is completely unaffected by changes in the real product wage. Thus, for a given change in the real product wage, the larger is the effect on output (i.e., the higher is σ) the smaller will be the effect of ULC/PV. That is, countries which benefit most from an improvement in competitiveness will, other things being constant, have this reflected to the least extent either in the conventional ULC measure of competitiveness (for a given value of PV) or in the profit margin based measure (ULC/PV).
APPENDIX II: Data Sources
The data for charts 2-9 were drawn principally from the national accounts tapes of the OECD, supplemented (as noted below in items 6 to 9) with information from other OECD sources, national accounts publications of individual countries, and the IMF Data Fund.
Labor productivity was measured as the ratio of real value added to dependent employment. Adjustment for changes in the length of the working week was not possible, owing to lack of data.
Unit labor costs in manufacturing were derived by dividing compensation of dependent employees by real value added.
The business sector was defined as all sectors excluding government.
For Belgium, sectoral employment data for 1987 and 1988 were no available on the OECD tapes and the Belgian national accounts publication do not contain employment data by sector. Accordingly, information from the tapes was extrapolated for 1987-88 using data from the annual OECD Economic Survey of Belgium. Neither the OECD tapes nor the Belgian national accounts publications contain information on compensation of employees by sector. The data used here were taken from the IMF Data Fund.
For France, data on “manufacturing” were taken from the French national accounts publications, and were calculated by excluding the energy sector (code u3) from manufacturing and mining (codes u2-u6). Sectoral data on compensation of employees were not available for the years 1987-88, either from the OECD tapes or from the national accounts publications. Compensation of employees in the manufacturing sector in 1987 and 1988 was estimated by combining data on hours worked in manufacturing from the national accounts publications with information on hourly earnings in manufacturing from the IMF’s World Economic Outlook.
For Italy, data on “manufacturing” also include the mining sector.
For the Netherlands, data on real value added in manufacturing were not available on the OECD tapes. The data used here were derived from national accounts publications of the Netherlands. Charts for the Netherlands (available from the authors) were produced with the mining sector both included in and excluded from the “nontraded group” to examine the influence of the wide swings in energy prices on the internal terms of trade. The ERM charts in this paper do not exclude mining from the Netherlands data as this adjustment is of little consequence for the group of ERM countries.
Balassa, B., “The Purchasing-Power Parity Doctrine: A Reappraisal,” Journal of Political Economy, Vol. 72 (December 1964), pp. 584–96.
Feltenstein, A. and others, “A Multilateral Exchange Rate Model for Primary Producing Countries”, IMF Staff Papers, September 1979.
Lipschitz, L., “Exchange Rate Policy for a Small Developing Country and the Selection of an Appropriate Standard”, IMF Staff Papers, September 1979.
Lipschitz, L. and S. Schadler, “Relative Prices, Real Wages, and Macroeconomic Policies: Some Evidence from Manufacturing in Japan and the United Kingdom”, IMF Staff Papers, June 1984.
This paper has benefited from discussions with Bob Traa, from comments by Lars Svensson and by many colleagues in the European Department, and from the analysis in Marston (1986).
Much has been written on the calculation of appropriate weights for an effective exchange rate--see Artus and Rhomberg (1973), Thakur (1975), Bélanger (1976), Rhomberg (1976), Feltenstein and others (1979), Lipschitz (1979), and Lipschitz and Sundararajan (1980). This question is not addressed in the present paper.
Technology is interpreted as including institutional as well as technical factors that impinge upon production possibilities. Both static and dynamic differences in technology may be important. A static difference might, for example, relate to the degree of factor substitutability across countries. A producer with a more responsive productive structure will boost output more for any given favorable development in the cost-price environment and, thus, enjoy a larger increase in capital productivity. Such a producer might be able to absorb a larger increase in unit labor costs without reducing his rate of return on capital. Dynamic differences might relate to unequal rates of technological progress.
Consider a firm which experiences increased profitability of production owing, for example, to an exogenous currency depreciation. In response to an initial decline in the ratio of unit labor costs to the price of value added (an improvement in the profit margin), it will begin to expand production by adjusting its use of variable factors; in this process, the ratio of unit labor costs to the price of value added will rise. Ironically, the more flexible the production technology and thus the more responsive it is to the improved competitive position, the larger will be the erosion of the initial “improvement” in the profit margin; however, while profit margins decline as firms move up their short-run supply curves, total profits and the rate of return on capital increase. The erosion of the initial improvement in the profit margin will continue in the medium-term as the capital stock is adjusted to the improved profitability; indeed in this time frame the rate of return to capital will begin to fall back.
Empirical work has tended to find an elasticity of substitution between labor and capital of significantly less than 1. See, for example, Artus (1984), Lipschitz and Schadler (1984), and McDonald (1988a).
The degree of substitutability between value added and intermediate inputs is not crucial to the analysis.
Homogenous goods are subject to the law of one price, when prices are expressed in a common currency.
The percentage increase in PVT, is in line with the exchange rate change, but the increase in is rT larger. It is the relative return to a physical unit of capital in foreign currency terms that is relevant for comparing short-run output developments across countries. To see this, consider a devaluation accompanied by equal proportionate increases in the nominal return to a unit of capital and in wages. There would be no incentive to increase production although the return to a unit of capital in domestic currency terms has risen. Note that if capital goods are to some extent nontraded, the return to a unit of capital in foreign currency terms is not necessarily the most relevant variable for considering international investment decisions.
With σ < 1, as a firm moves up its short-run supply function, ULC increases at a slower rate than MC; this reflects the fact that marginal product is falling at a faster pace than average product.
This ignores the influence of taxes and restrictions on trade. As intermediate goods have not yet been introduced into the analysis, prices of traded goods are the same as value added prices.
Indeed, RERULC may even fall, reflecting the relative contraction of output as producers move down their short-run supply curves (see discussion on p. 5). Furthermore, if wages in the home country were reduced so as to maintain the country’s competitive position, RERULC would also incorrectly show an improvement in the competitive position.
In the case of a Cobb-Douglas production function (which reflects a rather strong supply response), there will in fact be no measured gain in competitiveness despite a large increase in output. Conversely, a fixed coefficients production function will exhibit a depreciation of RERULC, and RERPRF of a magnitude similar to the devaluation with no supply response, as the initial impact or the devaluation is not “eroded” by a movement up the supply curve. These cases are excluded from the present analysis, which assumes an elasticity of substitution between 0 and 1.
A rise in effective capital services increases the marginal product of labor (MPL) creating a wedge between MPL and the wage rate. Higher demand for labor bids up the wage rate. The degree to which the labor share rises depends on the responsiveness of labor supply to the real wage rate--the more responsive the labor supply the smaller the increase in the labor share and the larger the increase in output.
Labor-augmenting technical change boosts the effective supply of labor services per man-hour. If wage rates per man-hour grow by the same percentage, the wage cost per effective unit of labor services is unchanged and employers have no incentive to increase their employment of labor services. As a result, man-hours of labor are reduced in proportion to the rise in wages and the labor share in value added remains unchanged. To realize greater utilization of labor services (and, therefore, output gains), it is necessary that wage costs per man-hour grow by less than labor efficiency, producing a fall in the wage cost per unit of labor services. (To the extent that the output price needs to be reduced to sell the higher output, a larger fall in wages is required to achieve a given rise in output.) With an elasticity of substitution of less than 1, the increase in the utilization of labor services is less proportionately than the decline in wages costs per unit of labor services, so that the share of labor in value added declines.
If wage rates per man hour and the return per unit of capital increase by similar percentage amounts the share of labor would remain unchanged. However, higher wage rates may elicit a greater supply of labor man hours putting downward pressure on the labor share. On the other hand, reduced prices necessary to sell traded goods output will increase the real product wage tending to raise the share of labor.
A labor-augmenting productivity improvement does not shift the supply curve in labor-share: output space. For a given level of output and capital services, the firm uses the same amount of labor services before and after the productivity change (but a smaller number of man hours). For the firm to be on its supply curve, the real product wage per unit of labor services must be the same as before the productivity improvement and hence the labor share must be the same. In the case of a capital-augmenting productivity improvement, however, there is a shift in the supply curve. With the physical capital stock unchanged, the same output requires a lower input of labor services than before the productivity change. Given the elasticity of substitution of less than 1, the percentage increase in the real marginal product of labor (and the real wage) must be greater than the percentage decline in the utilization of labor services and thus, for a given output level, the labor share must have increased if the firm is on its supply curve.
If labor supply is completely inelastic, the rate of return increases only if the elasticity of substitution is greater than the labor share in value added. If labor supply is infinitely elastic with respect to the real wage the rate of return to capital unambiguously rises.
As an extreme scenario, consider a small country with a constant required return on capital (due for example to a fixed real world rate of interest) and a given price for its output on world markets. Assume this country experiences a positive productivity shock of a labor-augmenting kind. The long-term result will be that the capital stock will increase in proportion to the increase in effective labor services, which, assuming that the supply of man-hours is completely inelastic with respect to the real wage, will be the same as that resulting from the productivity shock. There will be no change in the labor share in value added, comparing the pre-shock level with the level after full adjustment of the capital stock. Although there will be no measured improvement in competitive position comparing the pre-shock situation with the final equilibrium, output will have increased relative to trading partners.
See p. 11 for conditions under which this might occur.
Lipschitz (1979) contains a discussion of the theoretical basis for using an aggregate price index as a measure of competitiveness.
In principle, a CPI based measure should give similar results in the absence of major changes in the external terms of trade. Here, the GDP deflator is used, as it is more closely linked to the allocation of resources.
Strictly speaking this requires that the shares of traded and nontraded goods [t and (1-t)] are similar at home and abroad.
The magnitude of resource flows will however depend on parameters of the production functions in the two sectors at home and in trading partners. The fact that relative prices indicate a stronger resource pull in the home country does not mean that actual resource flows will be larger in the home country; if production functions in the home country exhibit relatively low elasticities of substitution, then actual resource flows from traded to nontraded sectors could be smaller than in partner countries despite an apparently larger price incentive.
However, one cannot say this unambiguously unless labor and capital shares are similar in the two sectors. One also has to assume that labor markets are effectively integrated. To the extent that wage increases are different across sectors, then one may not be able to compare the development of r across sectors from PVN and PVT.
The effect of capital reallocation in response to a change in the productivity adjusted internal terms of trade is to offset, at least in part, the original change in this terms of trade.
The analysis focuses on Belgium, Denmark, France, Italy and the Netherlands. The 1988 cut-off point was for data reasons; comprehensive 1989 data were not available for all the countries when the calculations were made.
The term “exogenous” is used here to mean that the productivity growth is not the result of changes in the capital: labor ratio.
Some attempt might be made through the analysis of sectoral capital stocks; however, the availability of data to pursue such an analysis is limited for most countries.
The Fund does publish measures of RERULC adjusted and unadjusted for relative cyclical positions. However, to carry out cyclical adjustments for the wide range of indicators used here would have been a major exercise which would have contributed little to the central purpose of the study.
The examination of bilateral rates comes not from any belief that such rates are in themselves of importance; rather it was felt that the varied factors which impinge on the interpretation of RERs could be most effectively understood by analyzing bilateral rates. The bilateral analysis for countries other than Italy was included in an earlier version of the paper and is available from the authors upon request.
Variables are defined such that an increase in RER indicates a real appreciation of the lira against the deutsche mark.
Normalizing by relative GDP growth rates helps take into account the likelihood that producers in each country have a large share in their home market.
As noted, these adjusted data should be interpreted carefully as they do not control for differences in productivity growth due to changes in capital: labor ratios.
A second factor contributing to the larger appreciation of RERGDP than RERULC is the widening of profit margins in Italian manufacturing relative to the FRG.
Belgium, Denmark, France, Italy, and the Netherlands. The results would not have been materially affected by including Ireland and Luxembourg (the other members of the ERM during the period), as these two countries have relatively small weights in the FRG’s external trade.
Take for example the experiences of France and the FRG. Between 1985 and 1987, expressed in deutsche mark terms, the price of manufacturing production fell by 6 1/2 percent in France and by 3 3/4 percent in the FRG; the declines reflected the lower price of intermediate inputs, particularly oil, and value added deflators increased. The difference in the behavior of value-added deflators was, however, significantly greater--in deutsche mark terms, the value added deflator for manufacturing in the FRG grew by 10 1/2 percent while in France it rose by less than 1 percent. The implication is that the FRG manufacturing benefited to a greater extent from declining prices of intermediate inputs.