Abstract

The events of the past year have focused attention on the troubled state of east Germany’s economy. At the same time, the prospect of a fast pace of integration of the two German economies has raised the question of what is needed to bring labor productivity in east Germany close to that prevailing in the western part of the country. In this chapter, a framework for analyzing the supply side of east Germany’s economy is developed, in which productivity growth is linked to capital accumulation and improvements in the efficiency with which labor and capital services are utilized. This is then used to provide illustrative calculations for the investment needs based on assumptions relating to the initial conditions in east Germany, the behavior of factor efficiency, and the speed with which the productivity gap between east and west Germany is narrowed.

Donogh McDonald and Günther Thumann

The events of the past year have focused attention on the troubled state of east Germany’s economy. At the same time, the prospect of a fast pace of integration of the two German economies has raised the question of what is needed to bring labor productivity in east Germany close to that prevailing in the western part of the country. In this chapter, a framework for analyzing the supply side of east Germany’s economy is developed, in which productivity growth is linked to capital accumulation and improvements in the efficiency with which labor and capital services are utilized. This is then used to provide illustrative calculations for the investment needs based on assumptions relating to the initial conditions in east Germany, the behavior of factor efficiency, and the speed with which the productivity gap between east and west Germany is narrowed.

The approach is, thus, a macroeconomic one. It involves estimating the capital required to achieve a specified productivity level relative to west Germany and comparing this with an estimate of the current capital stock in east Germany. Some examples of the former calculation are easily given. Assuming the same potential supply of services per unit of labor and capital as in west Germany, the achievement of a productivity level in east Germany on par with that in the west would require a similar capital-labor ratio and elimination of inefficiencies in the economic system. Actually, this would probably overstate the capital requirements, as capital in east Germany would be on average much newer than in the west. A lower productivity target would, of course, reduce the capital needed and indeed, more than proportionately, given the ability to substitute labor for capital in the production process. Estimates of the present value of the capital stock in east Germany are more difficult, since they involve evaluating current output in terms of what can be sold in open markets. They also depend on the extent to which productivity can be increased with a more efficient use of existing resources. Illustrative calculations are provided for initial productivity levels of 30 percent and 35 percent of the west German level, and a range of values for the efficiency of factor use in east Germany at the time of German economic, monetary, and social union (GEMSU).

Given the nature of the calculations, it is necessary first to map out a scenario for the economy of west Germany; this is provided in the next section. Then the supply framework for east Germany is discussed in greater detail. These two sections form the basis for the numerical illustrations of the investment requirements in east Germany. The calculations show that the investment needs are large but also rather sensitive to the assumptions made. Assuming an initial productivity level in east Germany that is 30 percent of the level in west Germany, net investment of some DM 1,100 billion (in terms of 1990 prices) would be required over the period 1991—2000, under the central scenario, in order to reach a productivity level that is 80 percent of the west German level by the year 2001. This net investment would amount to about 60 percent of net national product in west Germany in 1990 and involve an increase in the net capital stock in the east of about 170 percent from its end-1990 level, compared with an assumed increase in west Germany’s net capital stock of about 40 percent over the same period. To close the productivity gap with the west completely would require, perhaps, an additional DM 600 billion in net investment.

Supply Conditions in West Germany

Initial Conditions

It is assumed that value added in west Germany is determined according to a CES (constant elasticity of substitution) production function:

V=[pLLSλ+pkKSλ]1/λ(1)

where V is real (net) value added, KS and LS are the supplies of capital and labor services, pK and pL are constants,1 and λ is σ/(l − σ) with σ being the elasticity of substitution between capital and labor services. Technical change is assumed to be labor augmenting and is incorporated in LS; there is therefore no need in equation (1) for a variable denoting total factor productivity. Supplies of factor services at time (t) can be characterized as follows:

KSWt=KWt(2)
LSWt=TAWtTKWtLWt(3)
TAWt=(1+A)t(4)
TKWt={1+f[(KLWt/KLW0)1]}(5)

TAWt and TKWt are terms describing technical change; technical change is assumed to be, in part, exogenous (TAWt) and, in part, related to the speed with which the capital-labor ratio increases (TKWt), where K/L denotes the capital-labor ratio. Purely as a normalization convenience, 1990 is designated t0 and KSW and LSW in 1990 are set equivalent to the actual levels of capital (K) and labor (L).2 The production function (1) is parameterized so as to make it consistent with supply conditions in the west German economy in 1990. It is assumed that the elasticity of substitution between KS and LS is 0.5,3 that firms are profit maximizing, and that the labor market is in equilibrium (in the sense that the marginal product of labor is equal to the real wage). On this basis, information on factor shares in net national product can be used to derive the parameter values in (1). A profile of key supply-side elements for the west German economy in 1990 is provided in Table 1.

Table 1.

West Germany: Key Supply-Side Data1

(Evaluated at constant 1990 prices)

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Authors’ estimates for 1990 and model calculations for 2001. The estimates for 1990 were made in the summer of 1990. Later revisions, which are shown in Table 1 of Chapter II, have not been incorporated here or in the modeling exercises in Chapters VVI. If the more recent estimates had been incorporated, the effects on the calculations of capital requirements presented in this chapter or on the scenarios presented in the next two chapters would have been negligible.

Beginning of the year; includes residential structures and public infrastructure.

Assuming that the average labor income of the self-employed is the same as that for employees.

Compensation of capital relative to the net capital stock, including public infrastructure and residential property.

Medium-Term Assumptions

The next step is to construct a scenario for the evolution of the supplies of labor and capital services so as to provide a picture of production conditions in the west German economy in 2001. The broad outlines of the scenario are as follows. The labor force is assumed to rise in total by 4½ percent, with most of this occurring in the first half of the scenario under the influence of immigration from east Germany and Eastern Europe; the increase in employment is a little larger, as the unemployment rate falls from 6½ percent in 1990 to 6 percent in 2001. With respect to the capital stock, the key consideration is what happens to the rate of return to capital. In the scenario adopted, the rate of return to capital declines by about ½ of 1 percentage point, implying an increase in the capital-output ratio. The fall in the rate of return is founded on the premise that in 1990, based on real interest rates prevailing prior to the announcement of GEMSU, the rate of return is above equilibrium, that is, the capital stock in 1990 has not yet adjusted fully to the sharp unexpected decline in the labor share (rise in the profit rate) that occurred in 1987-90.4 This disequilibrium has probably been offset, at least in large part, by the rise in real interest rates associated with GEMSU. In later years (as the effect of GEMSU on the cost of capital recedes), the disequilibrium would reemerge in the absence of a rise in the capital-output ratio. The final element needed to complete the picture of supply conditions in west Germany in 2001 is the behavior of technical change. It is assumed that autonomous labor-augmenting technical change takes place at the rate of 1 percent a year (i.e., in equation (4), A = 0.01) and that labor services per unit of labor input respond to changes in the capital-labor ratio with an elasticity of one half (i.e., ƒ = 0.5).5 This implies that, if there was no change in the capital-output ratio,6 labor productivity would grow at 2 percent a year; half of this productivity growth would reflect exogenous forces and the other half be induced by capital accumulation. In the medium-term scenario adopted here, labor productivity rises somewhat faster (2½ percent a year) owing to the increase in the capital-output ratio. Incorporating the assumed growth in the labor force, output grows at an annual rate of 3 percent and the net capital stock at 3¼ percent.

A Supply-Side Framework for East Germany

In analyzing supply conditions, it is assumed that the production function in east Germany is the same as in west Germany; lower productivity levels in the east reflect, first, a poorer endowment of resources, which results in a lower potential output per worker than in west Germany and, second, inefficiencies in production practices, which lead to a below-potential economic performance. The lower potential output per worker in the east is due, in part, to the mix of factor resources (less capital per worker) but also to the assumption that labor-augmenting technical change is embodied to some extent in capital accumulation; the latter assumption implies there are fewer labor services potentially available per man-hour of work effort than in west Germany. The below-potential performance of the eastern economy is also viewed as having two sources: general inefficiency in the economy, affecting both capital and labor, and labor-specific inefficiency. The first of these can be attributed to poor management and the absence of a well-functioning system of factor allocation. Labor-specific inefficiency is likely to comprise in large part of labor hoarding—lowering the physical quantity of labor used does not lower output as retained labor can be used more efficiently.7 More generally, to the extent that systemic inefficiencies in the economy are not neutral in their effects on the effective supply of capital and labor services, a factor-specific inefficiency term is necessary in the modeling of production. In the context of the modeling approach used here, it seems likely that this non-neutrality term should be attached to labor services both because of the believed importance of labor hoarding and because labor is more mobile.8 These elements are reflected in the following characterization of the supply of factor services in east Germany:

kE=gkw(6)
lE=hg{1+f[(KLE/KLW)1]}lW(7)

Equation (6) relates kE, the supply of capital services (KS) per unit of capital (K) in east Germany, to a general efficiency factor (g) and the amount of capital services provided by a unit of capital in the west (kw).9 Equation (7) states that lE, labor services (LS) per unit of labor (L) in east Germany, depends on the availability of labor services per physical unit of labor in the west (lw),10 the capital-labor ratio in the east relative to the west (KLE/KLw),11 the general efficiency parameter (g), and the labor-specific efficiency parameter (h). The supply of factor services per unit of factor input can be broken into two components: first, what is potentially available and, second, the degree to which this potential is used. In the case of capital services, the potential availability per physical unit of capital is the same as in west Germany12 but actual use of capital services per unit of capital is lower due to the general inefficiencies in the economy (g < 1). In the case of labor services, the potential availability of labor services per man-hour {1 + ƒ · [(KLE/KLW) − 1]} · lw is lower than in west Germany (lw) because of the lower capital-labor ratio. This potential is less than fully used due to the general inefficiency in the economy and to inefficiencies related specifically to labor (h < 1). Thus, the key factors influencing productivity in the east relative to that in the west are changes in the efficiency parameters (h and g) and the relative paths of employment and the capital stock in the two areas.

Initial Conditions in East Germany

In characterizing the initial supply position in the east German economy, the objective is to produce a picture of conditions at the start of GEMSU, that is, before any factor reallocation has taken place. Official data of the German Democratic Republic (GDR) suggested that, in 1988, economy-wide labor productivity was close to half of the level in the Federal Republic of Germany (assuming a 1:1 conversion rate between marks and deutsche mark). All indications are, however, that the underlying position was considerably less favorable. In the months running up to GEMSU, estimates of east German productivity tended to lie in the range of 30–40 percent of the west German level. Developments in the months after GEMSU took effect would suggest that this range should be lowered somewhat.

The approach adopted here is to identify alternative sets of the parameters g, h, and K that would be consistent with the assumed relative productivity level and the employment prevailing in the GDR on the eve of GEMSU. As the notion of productivity being used is based on economic efficiency in the production of a given level of output, the answer depends on relative factor prices. Calculations are made for three different assumptions on the relative factor prices that would result from marginal product pricing; for any level of output, this determines the values of LS and KS. From equations (6) and (7), this leaves two equations in three unknowns (g, h, and K); choosing one of these variables is sufficient to tie down the other two. Tables 2 and 3 show, for various levels of g and of the labor share in national output, the combinations of h and K that would be consistent with productivity at 30 percent and 35 percent of that in west Germany.13

Table 2.

East Germany: Initial Production Conditions Based on 35 Percent Relative Productivity Level

(West Germany = 1)

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Calculated as effective LS per employed person divided by potential LS per employed person.

Table 3.

East Germany: Initial Production Conditions Based on 30 Percent Relative Productivity Level

(West Germany = 1)

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Calculated as effective LS per employed person divided by potential LS per employed person.

To illustrate the calculations, assume an output per worker that is 35 percent of the level in west Germany, broadly in line with perceptions at the time of GEMSU. Consider case B.II in Table 2, where general factor efficiency is only 80 percent of potential, and the labor share 67½ percent of net national product (which corresponds to a gross wage of 31 percent of the west German level, assuming all workers were employed). With producers maximizing profits, labor services per person employed are 39 percent of the western level and capital services per person employed 26 percent of the western level. Reflecting the assumption that, as a result of general inefficiency, actual factor use is only 80 percent of potential factor use, potential capital services per employed person are one fourth higher at 33 percent of the west German level. The lower potential of capital services per employed person than in the west means that the potential labor services per employed person are only 66 percent of the west German level, as labor-augmenting technical change is partially embodied in capital accumulation. Actual use of labor services is only 59 percent of this potential;14 this in part reflects the general inefficiency in factor use (g < 1) but it also involves significant labor-specific inefficiency (h < 1). The level of the capital stock implied by these calculations is DM 728 billion,15 of which DM 582 billion (80 percent) is being effectively used; over time, as the general efficiency of the economy improves, the difference between the potential capital stock and the effective capital stock disappears.

By way of comparison, consider a relative productivity of 30 percent, which seems more in line with recent developments. Case B.II in Table 3 uses the same assumptions on the labor share and general efficiency as in the example just discussed. Since relative factor prices determine the mix of factor services that is efficiently used in production, for any level of g the levels of K and h are proportionately reduced (i.e., they are 86 percent (30 divided by 35) of the level in the example described above); thus, the value of K would be DM 624 billion.

The numerical illustrations in Tables 2 and 3 produce a wide range of estimates for the initial capital stock in east Germany; the calculations assuming a lower general efficiency parameter or higher labor share than in the examples used above produce larger capital stock estimates, while assumptions of higher general efficiency or a lower labor share produce smaller estimates of K. All of these estimates are, however, considerably less than official capital stock data of the GDR.16 This reflects the objective of measuring the capital stock with a view to what is usable in the new environment, with the valuation based on the value of capital in west Germany. The calculations in the remainder of this chapter and in the next chapter narrow the range of estimates by starting from the premise that underlying productivity in east Germany at the time of GEMSU was about 30 percent of the level in west Germany. While significant differences remain depending on the assumptions used, these differences are relatively small when compared with the investment needs in east Germany.

The Capital Stock in 2001

In illustrating the capital needs of east Germany in the year 2001, two scenarios for labor productivity are examined: in the more ambitious one, net domestic product (NDP) per worker reaches the same level as in west Germany; in the other, NDP per worker rises to 80 percent of the western level over this period. The narrowing of the productivity gap is achieved in three ways. First, potential productivity rises faster than in west Germany owing to quicker capital accumulation, which also results in a more rapid rate of labor-augmenting technical change. Second, reduction of inefficiencies in factor use closes the gap between actual and potential output. Finally, favorable “vintage” effects on productivity can be expected as a result of the lower average age of the capital stock in the east.

Consider first the capital stock needed to equalize labor productivity by 2001. Leaving aside vintage effects, for the moment, and assuming that over the next ten years inefficiencies in the use of labor and capital are eliminated, that is, g and h reach the same level as in the west (g = h = 1), the equalization of productivity would require that capital-labor ratios be the same in the two areas at the beginning of 2001.17 The actual level of the capital stock will depend also on employment developments. In what follows, it is assumed that the labor force declines on average at a rate of 1 percent a year and unemployment falls to 6 percent of the labor force.18 On these assumptions, a net capital stock of DM 2, 580 billion would be required in east Germany at the beginning of the year 2001 (case A. 1 in Table 4). In this calculation, however, 85 percent of the capital stock in the east would be less than ten years old in 2001, but this would apply to only 55 percent of the capital stock in west Germany.19 Hence, some favorable vintage effects are to be expected in the east and two alternatives are illustrated in the table: in the first of these, effective labor and capital services per physical unit of factor input are 5 percent higher in east Germany than in the west by 2001 (i.e., g = 1. 05) while, in the second, the assumed vintage effect is 10 percent (g = 1. 1). As can be seen, there is a significant influence on the capital stock needed to equalize productivity levels.

Table 4.

East Germany: Capital Requirements in 20011

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Beginning of the year.

The implications of cutting the target productivity to 80 percent of the west German level are also illustrated in Table 4. Case B. 1 examines the situation of no factor efficiency advantages in the east. The reduction of the target productivity level has a more than proportional effect on the capital stock requirements; the sharper reduction in the terminal capital stock than in the target productivity reflects the ability to substitute between capital and labor (and a similar supply of man-hours under the two scenarios, assuming that labor supply is not responsive to wage rates). Indeed, the decline in the estimate of capital needed would have been even greater were it not for the assumption that technical progress is to some extent embodied in capital accumulation. Again, for this scenario, one must consider vintage effects. However, the vintage effects here are likely to be smaller than in the case where the productivity target is 100 percent; with lower capital accumulation in east Germany, the gap between the average age of the capital stock in east and west Germany would be less favorable to the east than in the calculations for case A. Moreover, offsetting these vintage effects, one must consider the possibility that the gap between productive potential and output has not yet been fully closed by 2001.20 Accordingly, Table 4 presents calculations for the cases of a 5 percent efficiency advantage in the GDR and a 5 percent efficiency disadvantage.

The calculations thus far have assumed that the elasticity of labor services with respect to the capital-labor ratio (the parameter ƒ in equation (7)) is 0. 5. The final part of Table 4 illustrates the implications when the degree to which technical progress is embodied in capital accumulation is lower. A striking feature of these calculations is that east German productivity levels could be remarkably close to those in west Germany with production considerably less capital intensive in the east. While there is no firm basis for setting the parameter ƒ at 0. 5, it is clear that a number closer to half seems more reasonable than one close to zero.

Investment Needs

The analysis of the previous two sections can be used to illustrate the magnitude of the investment needs in east Germany over the next decade. Taking case B. II in Table 3 as a starting point (a relative productivity level of 30 percent in east Germany and a starting capital stock of DM 624 billion), and assuming net investment of DM 25–30 billion in the second half of 1990, the broad conclusion is that to achieve output per worker similar to that in the west by 2001 would require a net investment of DM 1, 500-1, 900 billion (in 1990 prices) over the period 1991 to 2000. Moderating the target to 80 percent of west German productivity levels reduces the needed net investment to the range DM 1, 000-1, 300 billion. One should, of course, bear in mind that, in addition to the assumptions on terminal conditions, the scale of the investment requirement is sensitive to the estimate of the initial capital stock; it is however easy to adapt the calculations to different estimates of the initial capital stock as, in the framework used here, the terminal capital stock is independent of the initial capital stock in the east for a given set of terminal assumptions.

The question arises as to how much of this investment is likely to occur in the public sector. As a guide, one can take the current distribution of the fixed capital stock in west Germany, where about 20 percent is in the general government sector, and assume that the public infrastructure in east Germany is in no worse a state than the capital stock in the remainder of the east’s economy; this would suggest that about 20 percent of the net investment requirements would need to be undertaken by general government. Such an estimate would not include investment by public bodies outside of general government (telecommunications and railways, for example), whose investment will presumably be financed in part by capital transfers from the Government.21 Moreover, the calculations do not take into account expenditures to rectify deterioration of the environment.

1

The parameters pK and pL reflect the feasible technology for combining KS and LS and the units in which KS and LS are denominated. KS is related to the capital stock at the beginning of the year.

2

K is the net capital stock in terms of 1990 prices and L is the labor force in millions of workers.

3

Artus found elasticities of substitution ranging from 0.5 to 0.8 in the major industrial countries (see Jacques R. Artus, “The Disequilibrium Real Wage Rate Hypothesis—An Empirical Evaluation,” Staff Papers, International Monetary Fund (Washington), Vol. 31 (June 1984), pp. 249–302). Lipschitz estimated an elasticity of substitution in the region of one half in the manufacturing sector of the FRG (see L. Lipschitz, “Wage Gaps, Employment, and Production in German Manufacturing” (unpublished; Washington: International Monetary Fund, 1986)). Econometric evidence presented in Chapter IX also suggests an elasticity of substitution in the region of one half.

4

Recent developments in the labor share in west Germany are discussed in Chapter II, section on “Employment, Wages, and Prices.”

5

The implications of alternative assumptions for the parameter ƒ are discussed in the final section.

6

This is equivalent to assuming no change in the ratio of KS to LS.

7

Indeed in the framework used here, there is a positive output effect as labor dishoarding enhances the potential supply of labor services from those remaining in employment, given the assumed link between the capital-labor ratio and labor-augmenting technical change.

8

Inappropriate allocation of capital can be less easily rectified and, to this extent, is reflected in the valuation of capital and not in an inefficiency term.

9

As a normalization convenience, kw is set at 1; see equation (2). For simplicity, the time subscript has been dropped.

10

The parameter lw increases over time as a result of labor-augmenting technical change in the west.

11

This reflects the assumption that labor-augmenting technical change is partially embodied in the capital-labor ratio.

12

Capital in the east is evaluated in terms of capital in the west.

13

An alternative approach would have been to start from assumed values of g and h; these would have been sufficient to determine K and the warranted factor shares. The calculations resulting from this approach would have been entirely consistent with those described above.

14

This is derived by dividing effective labor services by potential labor services.

15

This estimate includes residential structures and public infrastructure.

16

The official data put the total net value of the capital stock in 1988 at M 1,685 billion, expressed in terms of 1986 prices, about three quarters of this being in “productive” sectors. However, these estimates excluded residential capital and public infrastructure.

17

It is assumed that there is no change in west Germany in the parameters g and h. Structural measures to improve the allocation of resources in west Germany would increase g and h. The associated increase in profitability would boost the demand for capital in west Germany. Thus even if these increases in g and h were matched in east Germany, the investment requirements would be larger than calculated in this chapter. It is unlikely, however, that the effects of structural policy measures would significantly affect the broad picture presented here; for example, a 5 percent increase in the estimate of the terminal capital requirements in east Germany would be relatively small in relation to the rise in the capital stock needed over the next decade.

18

The underlying demographic projections are based on Deutsches Institut für Wirtschaftsforschung, Wochenbericht, 23–24/90 (Berlin), Vol. 57, June 14, 1990. Net emigration is assumed to decline to 100,000 in 1991, 50,000 in 1992, 20,000 in 1993, and zero thereafter. Migration to west Germany is assumed to be higher, offset by immigration of ethnic Germans from Eastern Europe. A decline of the female participation rate, which is presently much higher in east Germany than in west Germany, is also assumed. An alternative scenario for migration and the labor force is considered in Chapter V.

19

These calculations include in the new capital stock both net investment in 1991–2000 and replacement investment (depreciation) related to the pre-1990 capital stock. The difference in the average age of the capital stocks would be less marked for machinery and equipment, which has a shorter economic life than structures.

20

The existence of an efficiency gap would seem to be more likely the larger the shortfall of east German productivity from the west German level.

21

Of course, the fact that some activity has been in the public sector in west Germany does not necessarily imply that it will need to be financed by government funds in east Germany. For example, there has been recent discussion on the construction of privately financed toll roads in the east.