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VI Prospects for Self-Sustaining Growth in Eastern Germany

Author(s):
Karl Habermeier, Robert Corker, Robert Feldman, Tessa Van der Willigen, and H. Vittas
Published Date:
June 1995
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Considerable progress has been made in restructuring the economy of eastern Germany. The system of economic planning in existence at the time of economic and monetary union in mid-1990 has been replaced by a social market economy on the west German model. Most west German laws and institutions were extended to eastern Germany at the time of unification, and there has been further institutional convergence since then. Privatization has proceeded quickly; by the end of 1994, virtually all of the former state-owned enterprises had been transferred to private ownership. The transformation has been more profound and complete than in any other country in transition in central and eastern Europe. Eastern Germany now possesses a stable political and legal framework, a substantial private enterprise sector, and a comprehensive social safety net.

These achievements have not been without cost: transfer payments from west Germany increased to about 5 percent of total German GDP by 1993 (Table 6-1). The restructuring process has also been accompanied by a large decline in measured production and a massive shakeout of labor.1 However, the downturn in production bottomed out in 1991, and gross domestic product has been increasing ever since at annual rates of between 5 and 10 percent (Table 6-2).

Table 6-1.Public Transfers to Eastern Germany(In billions ofdeutsche mark)
19911199211993219942
Federal Government37589117119
West German Länder governments
and local authorities4551014
“German Unity” Fund3124155
EC budget4556
Federal Labor Office525241818
Statutory pension insurance funds51212
Gross transfers, total6140152177174
less: Receipts of the Federal
Government in eastern Germany733353943
Net transfers, total107117138132
Source: Deutsche Bundesbank, Monthly Report (September 1993)

Partly estimated.

Estimated.

Including financial assistance to the Federal Labor Office.

Including the waiver of turnover tax revenue as a result of the population-based distribution of this tax.

Corresponds to the share of the deficit incurred in eastern Germany, which is being financed by west German contribution payments.

Excluding tax concessions, interest-subsidized loans, and interest payments due to unification.

Tax revenue and administrative reports.

Source: Deutsche Bundesbank, Monthly Report (September 1993)

Partly estimated.

Estimated.

Including financial assistance to the Federal Labor Office.

Including the waiver of turnover tax revenue as a result of the population-based distribution of this tax.

Corresponds to the share of the deficit incurred in eastern Germany, which is being financed by west German contribution payments.

Excluding tax concessions, interest-subsidized loans, and interest payments due to unification.

Tax revenue and administrative reports.

Table 6-2.Eastern Germany: Basic Economic Indicators
1990199119921993
Output and employment
Real GDP1–18.77.85.8
Employment1–14.9–10.4–3.0
Productivity2–1.922.19.0
Investment
Gross fixed investment328.144.748.149.1
Private323.237.739.741.3
Business315.829.630.230.5
Residential37.58.19.510.8
Public34.97.08.47.8
Business investment per employed person438.480.3116.6141.2
In percent of west German level34.666.296.6132.6
Public investment per capita56.69.114.015.3
In percent of west German level75.497.2141.9160.1
Labor costs
Marginal product of labor613.414.921.225.5
Average gross wage716.721.829.532.9
In percent of west German level39.749.162.768.0
Share of labor income887.6101.999.194.2
Labor market
Employment (millions)8.9237.5906.8016.598
Participants in labor market programs92.0641.7631.463
In percent of employment27.225.922.2
Unemployment rate 102.910.714.714.8
West Germany6.25.55.87.3
Sources: Data provided by the authorities; and IMF staff calculations.

Percent changes.

Real GDP per employed person, percent change.

Percent of GDP.

Gross business investment per employed person (in thousands of deutsche mark).

Per population (in thousands of deutsche mark).

Nominal GDP per employed person (multiplied by normal share of labor).

Gross income from dependent employment per employee (in thousands of deutsche mark).

Gross income from dependent employment as percent of national income.

Retraining, job creation, short-time work, early retirement.

In percent of labor force.

Sources: Data provided by the authorities; and IMF staff calculations.

Percent changes.

Real GDP per employed person, percent change.

Percent of GDP.

Gross business investment per employed person (in thousands of deutsche mark).

Per population (in thousands of deutsche mark).

Nominal GDP per employed person (multiplied by normal share of labor).

Gross income from dependent employment per employee (in thousands of deutsche mark).

Gross income from dependent employment as percent of national income.

Retraining, job creation, short-time work, early retirement.

In percent of labor force.

Nonetheless, the question remains whether growth in east Germany can be sustained. There has been concern that the rapid increase in east German wages, which are now far higher than warranted by productivity, could hamper private investment. Moreover, the increase in output since 1991 has been concentrated in nontraded activities, such as construction and retail trade, which may have been stimulated by growing transfers from west Germany. Manufacturing output and exports of goods, on the other hand, have remained relatively weak, although signs of a stronger upswing were emerging in early 1994.

Inadequate economic growth in east Germany could make the region even more reliant on transfer payments and have serious repercussions for the public finances and macroeconomic performance of Germany as a whole. This chapter reviews in more detail some of the factors affecting prospects for an upswing in east Germany, including institutional arrangements, investment, and conditions in the labor market. On the basis of this analysis, an attempt is made to incorporate the most salient features into a quantitative framework for assessing potential growth. The simulations suggest that the prospects for growth are relatively good but that employment will continue to decline unless supported by policy intervention.

Determinants of Growth Investment

Investment

The standard neoclassical view of economic growth is that in the very long run, when the economy has reached a steady state, the growth rate of per capita income depends on the rate of technological innovation. During the transition to the steady state, when the economy is undergoing a process of capital deepening, the growth rate also depends on the rate at which capital is accumulated.

The east German economy at the time of unification was far from a steady state. The inherited capital stock was of little value in a market economy, and technology lagged behind the west by perhaps two decades. Productivity and per capita incomes were substantially lower than in west Germany.

Neoclassical theory implies that economic growth in east Germany will be driven for a considerable time by capital accumulation. The speed of this process, and hence the rate of economic growth, will depend largely on the amount of new productive investment. The propensity of private enterprises to invest depends, in turn, on a multiplicity of factors affecting the rate of return on capital. These include the degree of political stability, the efficiency and honesty of public administration, the condition of the infrastructure, the availability of a labor force that is technically skilled and diligent, and the level of wages.

An important objective of economic policy in the region, therefore, has been to create an environment conducive to private investment. A considerable effort has been devoted to rebuilding east Germany’s public infrastructure, especially in the critical fields of transportation and telecommunications. Moreover, the Government has made available generous assistance to potential investors in the region, including special tax allowances, accelerated depreciation, and subsidized credit. Several laws were passed to ensure that the property rights of investors took precedence over the restitution claims of former owners. Finally, the Treuhand has required buyers of its enterprises to make a contractual commitment to a specified volume of investment.2

These policies appear to have met with some success, although it is difficult to know how investment would have performed in their absence. There has been a marked increase in gross fixed investment, from less than 20 percent of GDP in 1990 to around 50 percent of GDP in 1993 (Table 6-2). There has also been a shift in the perceptions of investors. Early surveys showed that bottlenecks in public administration, a lack of market opportunities, uncertainty about property rights, and an inadequate transportation and telecommunications infrastructure were seen as important obstacles to investment. In more recent surveys, these concerns have moved to the background.

Wages and Employment

Instead, the high level of wages in east Germany has assumed greater prominence in the surveys on the obstacles to investment. This section examines the relationship among the level of wages, employment, and the incentive to invest.

The sharp increase in wages following unification can be attributed to a desire of labor unions to eliminate the wage differential with west Germany. The ostensible motivations for this policy were equity (“equal pay for equal work”) and the desire to reduce migration to west Germany.’3 As a result, wage rates have been far out of line with productivity. Not only is the average wage rate substantially higher than the marginal product of labor but the share of labor in national income exceeds 100 percent, implying that the aggregate current profitability of the business sector is negative (Table 6-2).

Excessive wages affect both the level of output and the propensity to invest. The effect on the level of output results from the reduction in the demand for labor. Indeed, employment has declined every year since unification (Table 6-2). Although some initial decline in employment was to be expected, if only because labor force participation under central planning was artificially high, employment has continued to fall even though production bottomed out in the course of 1991.

The effect of excessive wages on the propensity to invest, and hence on the growth rate of output in the medium term, is of greater consequence. For any given level of total factor productivity, both the real wage and the real implied return on capital are determined by the capital-labor ratio. When a profit-maximizing firm increases its capital-labor ratio in response to higher wages, which in the short run can be accomplished only by cutting employment, the implied rate of return on capital declines, reducing the incentive to invest. In principle, extremely high wages could completely stifle new investment unless offsetting measures are taken.

As mentioned above, the Government has taken a number of measures to stimulate investment. In addition, direct and indirect labor subsidies are widespread in east Germany. They have helped to mitigate the adverse effect of high wages on investment and growth. Workers in special labor market programs accounted for about one fifth of total employment in 1991-93.4 Moreover, the Treuhand has required buyers of enterprises to make a commitment to maintain employment at a specified level for some years. In exchange for these commitments, the Treuhand provided a subsidy by reducing the price charged to the buyers.5

There is a growing recognition that these measures may not be sufficient and that wage moderation and greater wage flexibility may also be needed to forestall a further significant rise in unemployment and to enhance the incentive to invest in east Germany. Numerous enterprises have left the employers’ associations, and there is evidence that many have been paying wages below the official tariff without much protest from the unions. Moreover, many labor unions have now distanced themselves from the objective of achieving wage parity with west Germany in the next few years. There has also been a somewhat greater willingness on the part of the labor unions to permit the negotiation of special wage concessions at the plant level when jobs are in jeopardy.

Composition of Demand and Output

While the adequacy of aggregate investment and labor market conditions are the most fundamental determinants of economic growth, the composition of demand and output also provides information on the likely pace of economic expansion. Aggregate demand in east Germany currently exceeds output by a wide margin, and there is a substantial trade imbalance (Table 6-3). Demand is sustained by large net transfer payments and by a substantial inflow of capital. The capital inflow partly finances private investment and partly finances the borrowing of state and local governments and the Treuhand.6

Table 6-3.Eastern Germany: Trade and Payments
1990199119921993
(In billions of deutsche mark)
Goods and nonfactor services
Exports35.146.952.154.9
Imports91.6199.2246.8261.6
Foreign balance–56.5–152.3–194.7–206.7
Balance of factor services2.08.010.89.4
Balance of transfers107.0117.0138.0
Current balance–37.3–66.9–59.3
Implicit capital account balance37.366.959.3
(In percent of CDP)
Goods and nonfactor services
Exports16.122.819.818.0
Imports42.196.794.085.7
Foreign balance–26.0–73.9–74.1–67.7
Balance of factor services0.93.94.13.1
Balance of transfers51.944.645.2
Current balance–18.1–25.5–19.4
Implicit capital account balance18.125.519.4
Sources: Daca supplied by the authorities: and IMF staff calculations.
Sources: Daca supplied by the authorities: and IMF staff calculations.

Put differently, east Germany’s massive trade deficit is the necessary counterpart of the inflows of transfers and capital. The domestic tradable goods sector (which consists principally of manufacturing industry) was simply unable to satisfy the surge in demand brought on by these inflows. Moreover, the east German manufacturing sector was uncompetitive. Many goods were of low quality, at least initially, and costs were, and in some cases remain, excessive.7 Compared with 1990, the share of manufacturing in value added has fallen sharply, to less than 20 percent (Table 6-4). Although it has recovered somewhat since 1990, it remains well below the industrialized country norm. In west Germany, for example, the share of manufacturing in value added has been around 30 percent in recent years.

Table 6-4.Eastern Germany: Gross Value Added by Sector
Percent ChangesPercent of Total
1991199219931990199119921993
Agriculture and forestry–66.118.841.12.91.31.41.9
Industry–34.314,311.141.535.837.639.2
Mining and energy–13.8–12.2–5.06.97.86.35.6
Manufacturing–49.117.210.624.416.317.518.2
Construction–12.828.119.210.211.713.815.4
Total services–13.65.43.355.562.961.059.0
Trade and transport–36.9–3.07.518.415.213.613.7
Trade–40.4–0.25.712.69.99 19.0
Transport–29.0–8.211.25.75.34.54.7
Other private services11.316.72.716.323.725.524.5
Public sector, private households.
and nonprofit organizations–12.5–0.51.320.924.021.920.8
Gross value added–23.78.86.7100.0100.0100.0100.0
Source: Dcutsches Institut fur Wirtschaftsforschunsg.
Source: Dcutsches Institut fur Wirtschaftsforschunsg.

The decline in the share of manufacturing and other tradable items was mirrored by a marked shift in the structure of production toward nontradables, such as private services and construction; these activities have made a substantial contribution to the growth of output in east Germany in 1992 and 1993. However, there has been concern that, as transfers to east Germany stabilize, the impetus these transfers have imparted to the nontradables sector will also level off. With little further expansion in the nontradables sector, even a relatively rapid increase in the output of manufactures and other tradables would produce only slow economic growth, given the small share of the tradables sector in overall value added. In sum, there would be a deceleration in economic growth as transfers from west Germany level off or decline.

An assessment of this observation would begin by defining the (disposable) income of the east German economy as the sum of domestic net production and net transfers. It then becomes apparent that in 1992-93, the share of income absorbed by nontradables amounted to only 54 percent, substantially below the comparable ratio for west Germany (64 percent). Hence, there is considerable room for a further expansion of the nontradables sector. The extent to which the slackening of transfer payments to east Germany is likely to constrain economic growth is taken up in the quantitative framework developed below.

Quantitative Framework

In this section, an attempt is made to quantify the interplay among several of the key variables affecting economic growth: output, investment, wages, and employment. The model is based on the neoclassical theory of capital accumulation and growth. At its core are aggregate production functions and investment equations, all of which are calibrated on the basis of the historical experience in west Germany. Labor market conditions are analyzed by deriving labor demand functions using standard marginal productivity conditions.

Overview of the Model

Three sectors are distinguished: tradables, private nontradables, and public nontradables.8 Output in each sector (denoted by i) is represented by a Cobb-Douglas production function and indexed by time period t:

where Qti is output, Ati is total factor productivity, Kti is capital stock, and Lti is labor input. The production elasticities of the factors, denoted by α, are the same across sectors.9 As indicated in the previous section, the overall income of the economy is the sum of output and net transfers:

where Qt is output, TRt are transfers, and the subscripts T, NP, and NG refer to tradables, private nontradables, and public nontradables sectors.

The government sector is assumed to be essentially static, with value added remaining constant in real terms for most of the forecast horizon and increasing in step with value added in the other sectors in the longer run. For the sake of simplicity, the projections also assume that net transfers remain constant in real terms over the entire horizon. Moreover, the share of the nontradables sector in overall income is assumed to converge to the equilibrium share according to a partial adjustment process:

where the parameter σ is chosen to achieve the bulk of the adjustment in 20 years or so. Then, income is determined as

The next task is to determine output in the tradable goods sector, which requires a model of investment and the demand for labor. With this model in hand, overall income and output can be determined, as well as the distribution of factors across sectors.

Derivation of the Investment Function

The investment function is based on the solution to the profit-maximization problem of a representative firm. Profits are maximized subject to the constraint of technology (the production function) but also subject to a term representing costs associated with changes in the capital stock. The solution to this problem (see the Appendix at the end of this chapter for details) produces a formula for investment that can be recognized as a partial adjustment model:

In the limit, assuming rt, goes to r = constant, Kt, asymptotically increases each period by a factor of z and the marginal product of capital equals r + γ, the sum of the real rate of return on capital and the rate of depreciation. It is easy to show that the parameter z – 1 is the steady-state growth rate of the economy: that is, the rate at which the capital-output ratio remains constant.

The investment function was calibrated on the basis of west German data (again, details may be found in the Appendix). For the purposes of the simulations, the following related, and relatively simple, form was used:

It might be noted that calibrating the investment function on the basis of the west German experience may understate the volume of investment that can be expected in east Germany. In particular, investment in east Germany is unlikely to be constrained by the availability of domestic savings as may have been the case in west Germany in the period 1960-90. The estimates also do not take account of the large subsidies for investment available in east Germany and so may again understate the propensity to invest in east Germany.10 On the other hand, the fact that Germany was a net exporter of savings for much of the period suggests that the savings constraint may not have been binding. In any event, it is probably safer to underestimate investment than to overestimate it.

Calibration of the Production Functions

Before proceeding to the more complex task of calibrating the multisector model, it is worth making some observations about the overall situation. Aggregate labor productivity in east Germany, as measured by real GDP per employed person, was about 34 percent of the west German level in 1990. In terms of the Cobb-Douglas production function used here, lower labor productivity can be explained by a lower capital-labor ratio, by lower total factor productivity, or by some combination of both.11 As there is no reliable information on the level of the capital stock in east Germany around the time of unification, it is not possible to determine both the capital-labor ratio and total factor productivity. One or the other will have to be arbitrarily set based on broad considerations of plausibility and consistency. In this connection, it should be noted that for any given level of labor productivity, there is an inverse relationship between total factor productivity and the implied capital stock. Table 6-5 illustrates this point (assuming YIL equals 28.40, the 1990 value for east Germany).

Table 6-5.Range of Initial Conditions in Eastern Germany
Range
Total factor productivity

(in percent of west German level)
20.040.060.080.0100.0
Capital stock (ratio to real GDP)18.73.71.50.70.4

Thus, the range of estimates for the initial capital stock varies by a factor of ten or more. Some of the more extreme estimates are easily ruled out on the basis of plausibility considerations. The well-known inefficiency of resource allocation in east Germany’s planned economy and the outmoded technology widely used there make it unlikely that total factor productivity reached 100 percent, or even 80 percent of the west German level. It is also improbable that the capital-output ratio greatly exceeded comparable values in west Germany, where it ranged from about 1.4 in 1960 to 2.0 in the late 1980s. Plausible estimates would put total factor productivity in east Germany at about 50 to 70 percent of the west German level.

Of course, total factor productivity should be expected to increase quickly from this initial level, eventually converging to the west German standard. Substantially improved technology has begun to be employed, and there has been a large influx of west German specialists in management, marketing, and finance. In the manufacturing sector, there are many examples of new facilities established in east Germany that incorporate the most advanced technology. Indeed, most of these enterprises are more productive than the average west German facility. By contrast, in the nontradables sector, less efficient enterprises may be able to persist for a considerably longer period of time.

In the final analysis, total factor productivity in the initial year (1990) in both the tradables sector and the private nontradables sector was set at 60 percent of the west German level. By 1994, total factor productivity in the severely diminished tradable goods sector is assumed to reach 77 percent of the west German level, and it increases to 100 percent of the west German level over the next 15 years. In the larger nontradables sector, it increases to 70 percent in 1994 and then rises much more gradually, not reaching 100 percent of the west German level until 20 years later. Although these assumptions are somewhat arbitrary, there is no alternative to making judgments of this kind if the objective is to provide a quantitative assessment of the growth prospects in east Germany.

Modeling the Labor Market

The production functions, combined with estimates of the initial level of the capital stock, allow for the derivation of sectoral labor demand functions that take the following form:

where wu, is the real wage.12 As mentioned earlier, the level of employment currently seen in east Germany is higher than would be consistent with this labor demand function; this reflects the operation of various labor market support schemes. For the purposes of the simulation, it is assumed that these support schemes will continue to be phased out during the 1990s. In the model, this is represented by a progressive narrowing of the gap between notional labor demand, given the exogenously determined path of wage adjustment, and the actual level of employment.

Once the labor market gap has been fully eliminated, the pace of wage adjustment is set so as to allow for convergence of the unemployment rate to the NAIRU (assumed to be 10 percent) within a number of years.13 After the NAIRU has been reached, wages are determined endogenously to keep the unemployment rate constant.

Simulation Results and Cautionary Notes

The principal result is that the outlook for self-sustaining growth in eastern Germany seems to be rather good, with growth rates of between 8 and 9 percent for the remainder of this decade (Table 6-6). These growth rates are sustained by investment that is considerably higher than in west Germany and by the gradual convergence of total factor productivity to the west German level. The tradable goods sector, which contracted sharply following unification, is expected to grow more rapidly than the nontradable sector, and there is consequently a gradual increase in the share of tradable goods production in the economy. Beyond the turn of the century, the rate of economic expansion is projected to decrease toward its steady-state value, with GDP growth averaging about 6 percent in 2000-09 and 3 percent in 2010-19.

Table 6-6.Eastern Germany: Growth Scenario
199419951996199719981999
Real GDP8.28.48.88.68.78.9
Tradables9.29.010.611.011.612.3
Nontradables8.08 38.48.08.08.0
Percentage shares in GDP
Tradables20.220.320.621.121.622.3
Nontradables79.879.779.478.978.477.7
Employment–1.8–0.3–0.10.10.30.6
Labor market gap146.242.037.633.028.122.9
Real wage3.72.42.83.03.03.0
Percent of west73.474.975.375.675.976.3
Gross investment224.223.122.221.520.920.4
West Germany13.513.713.914.114.214.4
Source: IMF staff calculations.

In percent of employment.

Nonresidential investment (in percent of GDP)

Source: IMF staff calculations.

In percent of employment.

Nonresidential investment (in percent of GDP)

The outlook for the labor market is considerably less favorable and fraught with risks, which could have adverse repercussions for growth. Wages are much higher than compatible with full employment.14 A pronounced recovery in employment is therefore not likely to occur until after the turn of the century, and an equilibrium in the labor market will not be reached before 2005.15

An indicator of pressure in the labor market is the “gap” shown in Table 6-6. This is the difference between notional labor demand (at the exogenously determined level of wages) and actual employment.16 This measure shows that employment will for some years remain substantially higher than warranted by productivity and wages. In these circumstances, the scenario assumes that a further rapid contraction of employment will be forestalled by active labor market support measures and by the employment guarantees obtained from buyers of enterprises by the Treuhand. Moreover, there are important adjustment costs to reducing the labor force. For example, German labor law makes provision for large severance payments. These adjustment costs, which have not been formally represented in the model, combined with the expectation that the gap between wages and productivity will narrow, may induce employers to maintain employment at a higher level than desirable from a purely short-term perspective. Such calculations, however, are subject to serious risks. If enterprises come to realize that they have overestimated the potential markets for east German products or the pace of productivity improvements, they may decide that a further round of layoffs is indicated. This outcome would dampen the prospects for growth during the period when the layoffs occur.

These risks could be substantially reduced and labor market performance improved if real wages in east Germany were frozen at their 1994 level until 1998. The adoption of this policy by the labor unions would reverse, to some extent, the excessive convergence of east German wages toward west German levels that has taken place since 1990. As a result, the labor market gap would virtually vanish by 1999, with notional labor demand about 1 1/2 million (20 percent of labor force) higher than in the baseline scenario.

The results presented above need to be interpreted with considerable caution, as they are highly sensitive to the assumptions made about production, investment, and labor demand. First, although the volume of investment that has taken place in east Germany is high by any standard, its productivity may be rather different from that assumed in the model. For example, if total factor productivity in the tradables sector reached 100 percent of the west German level in another 5 years rather than in 15 years, the growth rate for the overall economy would be well over 10 percent during the second half of the 1990s.

Second, even if investment were as productive as assumed, the east German manufacturing sector may not be able to gain market share as quickly as the model implies. New entrants and local ventures, in particular, may be at a significant disadvantage compared with established producers in other industrial countries, in that they lack market power, access to proprietary technologies, and an established customer base. It should be remembered, though, that many production facilities in east Germany were purchased or newly established by large and well-capitalized multinational enterprises.

Third, it is also possible that deteriorating conditions in the labor market could prompt measures to sustain employment by expanding the “secondary” labor market—that is, through various job creation schemes. To the extent that these activities discourage work effort or compete with the private sector, they could prove to be an obstacle to profitable private investment and economic growth.

Despite these possible concerns, the growth rates projected by the model are not too high compared with what has been observed in many of the newly industrialized countries of Asia and with Germany’s own economic recovery after the war.17 Although there are risks, especially those stemming from excessively high wages, there is also a possibility that total factor productivity in manufacturing could improve more quickly than anticipated. If the growth rates envisaged in the baseline scenario are achieved, the economic restructuring of east Germany could be considered a success.

Appendix: Derivation and Estimation of Investment Function

Behavioral relationships are derived from the profit-maximization problem of the representative firm

where δt is the discount factor, wt is the real wage, γ is the depreciation rate, rt is the implied real rate of return (inclusive of taxes and subsidies) on enterprise debt (or equity) Dt and the function g(.) represents an adjustment cost to capital formation.18

The Euler equations for this problem are the following (subscripts denote partial derivatives):

Note that in the absence of the adjustment cost terms, the last equation reduces to the well-known marginal condition

In other words, without an adjustment cost or other similar constraint on the speed of capital formation, the capital stock would instantaneously jump to its steady-state level.

Assuming that the adjustment cost function is quadratic,

the difference equation for the capital stock may be written in the form shown in the body of the chapter.

In applying the investment equation, it will also be assumed that the production function takes the Cobb-Douglas form and that total factor productivity is given by an exogenous trend (At = Abt):

Then, it may be shown that the steady-state growth factor is given by

where n is the steady-state growth rate of labor input.

The production function can be estimated in the usual way, using west German data. First, the parameter α is equal to the share of labor. Taking the average of the ratio of gross income from dependent employment to GDP over the period 1960-90 yields 1 – α = 0.57, so α = 0.43. Second, total factor productivity (TFP) was derived as a residual by removing the contributions of capital and labor to output:

A linear trend was fitted to the resulting series (see Chart 6-A1),

Chart 6-A1.West Germany: Output, Productivity, and Capital

Source: Deutsche Bundesbank.

1Adjusted using the Hodrick-Prescott filter (c=100).

2Measured by the variable Z’ defined in the Appendix (change in capital stock in excess of steady-state growth, in percent of GDP)

implying a long-term increase in TFP of about 1 percent a year. Similar results were obtained by adjusting TFP using the Hodrick-Prescott filter and taking percentage changes, although this method of adjustment reveals that there were long swings in the growth rate of TFP, with a sharp decline from the late 1960s to the early 1980s and then an increase that lasted until German unification in 1990. Assuming that total factor productivity grows by 1 percent (or slightly more) and employment by 0.3 percent, this would be consistent with a steady-state growth rate of about 2 percent.19

Assuming a Cobb-Douglas production function and a quadratic adjustment cost function, the difference equation for the capital stock is

The equation and the parameter estimates (using data for 1960 to 1990) are

β1 = 0.99555 (86.3423)

β2 = 71.7808 (0.42747)

β3 = 93.1979 (0.71974)

R2 = 0.9997, DW = 0.4956

This equation has a number of problems. In addition to strong serial correlation in the residuals, severe multicollinearity is present, resulting in unstable parameter estimates when estimated over different time periods. In particular, the estimated steady-state growth rate of capital, 1 percent, is inconsistent with what was derived from the information about the share of labor and the growth of total factor productivity.

The equation was hence reestimated, imposing the earlier estimate of 2.1 percent for the steady-state growth rate and using Zt = Kt – 1.021Kt-1 as the dependent variable. This yielded R2 = 0.6850 and highly significant estimates for β2 and β3. With the Durbin-Watson statistic equal to 0.2984, serial correlation in the residuals remained a problem.

Two approaches were taken to address the serial correlation. The first was simply to adjust the preceding equation using Cochrane-Orcutt. The second was to use a more general dynamic specification that includes lagged values of the dependent variable. The first method gave parameter estimates β2 = 995.466 (7.33627) and β2 = -472.383 (6.97133), with R2 = 0.9585. These estimates can be used to derive a value for ψ and for the steady-state capital-output ratio. In particular, it is known that

and that α = 0.43. An estimate of γ equals 0.05 was obtained from data on the capital stock and depreciation. Solving the equations yields r = 0.154 and ψ = 0.00325, implying that K/Y is 2.11 in the steady state.20 These results need to be treated with some caution, as the calculation assumes that long-term r is exogenous, constant, and inferable from past investment behavior. Rather, it is likely that r depends on longer-term developments in the world economy and on the course of economic policy in Germany and elsewhere, especially tax policy.

The second approach uses Z′t = (Kt – 1.021Kt-1)/Yt-1 as the dependent variable:

The fit of this equation is shown in Chart 6-A1. In the steady state, Z′t = 0. This implies that K/Y = –β0/β3 = 2.08 in the long run, an estimate that is consistent with those obtained earlier. A simpler version of this equation, which collapses the dynamics implied by the lagged dependent variables, was used in the simulations. The equation was also estimated for the period 1960-80, yielding an estimate of 2.05 for the steady-state capital-output ratio, relatively close to the current value (Chart 6-A1).21

1

The size of the drop has most likely been exaggerated. Estimates of pre-unification gross domestic product are too high in that they do not adequately reflect differences in quality between western and eastern products.

2

These commitments have been linked with a commitment to maintain a specified level of employment. See section below.

3

The early wage negotiations in east Germany were dominated by union representatives from west Germany, who may have been eager to avoid low-wage competition from cast Germany, and enterprise management was still predominantly in the hands of officials appointed by the old east German Government, who offered little resistance to union demands. In some cases, for example, in the metals industry, agreements reached a few months following unification provided for a full adjustment of wages in east Germany to west German levels within a few years. Some of the more generous agreements have since been amended.

4

These programs include short-time work, job creation measures, and retraining. Recipients of special early retirement benefits are also counted as employed.

5

Taking into account various subsidies for restructuring, debt relief, and other forms of assistance, the effective price charged to buyers of enterprises was, in many cases, zero or even negative.

6

Public borrowing in east Germany amounted to DM 52 billion in 1993 (about 20 percent of GDP).

7

In the immediate aftermath of unification, east German consumers were reluctant to purchase poorly made domestic products. Producers in east Germany have in the meantime sharply upgraded quality and are beginning to regain the confidence of consumers and to increase their market share. The collapse of trade with the countries of the former socialist bloc has added to the woes of east German manufacturing, as have the difficulties of developing new markets in western Europe and elsewhere.

8

The tradables sector is assumed to consist of manufacturing plus transport and telecommunications. Data limitations prevent a more precise delineation, which would include some other tradable services. It is also assumed that the entire value added of the government sector is nontradable.

9

It is straightforward to show that, provided the market wage and cost of capital faced by each sector are the same, and that the marginal conditions for profit maximization hold, the aggregate production function for the economy as a whole also has the Cobb-Douglas form. In this production function, the aggregate factors of production (capital and labor) are the sum of the factors of production employed in the individual sectors, and total factor productivity is a weighted sum of sectoral total factor productivity, where the weights are the share of labor employed in the individual sectors. Moreover, the marginal conditions for profit maximization hold for the aggregate production function.

10

An attempt can be made to correct for this by changing the steady-slate cost of capital r.

11

Part of the shortfall could also be explained by differences in the production elasticities of capital and labor. More generally, the form of the production function could have been entirely different. A full evaluation of these possibilities is beyond the scope of this study.

12

This wage is defined as nominal gross wages per employed person divided by the output deflator.

13

As will be seen below in the discussion of the quantitative results, the labor market gap will continue to exist for at least the remainder of this decade.

14

Gross wages per employed person increase from 70 percent of the west German level in 1993 to 76 percent by 1999 The growth of real gross wages per employed person in west Germany is assumed to average 2 1/2 percent a year in 1996-99, following a slight decline in 1993-94.

15

Labor market equilibrium is defined as a measured unemployment rate equal to the NAIRU, without a need for policies to maintain employment.

16

This estimate is subject to a large margin of error. If the level of total factor productivity in the nontradable sector were to increase to 85 percent of the west German level by 1999 (instead of 76 percent in the baseline and the same level as in the tradable goods sector), the share of employment not warranted by wages and productivity could decline to less than 15 percent by 1999.

17

During the 1950s, the growth of real GDP in west Germany averaged 8 percent a year, while manufacturing output increased at an annual rate of more than 10 percent.

18

Output Qt is a function of the capital stock Kt labor input Lt, and the level of total factor productivity At (which represents exogenous technological change):

As usual, it is assumed that the production function is homogenous of degree one in capital and labor.

19

The growth of the labor force and employment in wet Germany since the mid-1980s has been substantially faster (about 3/4 percent a year, on average), reflecting high immigration. Whether immigration and labor force growth will continue at this rate over the longer term is an open question. If it did, the steady-state growth rate would be closer to 2 1/2 percent.

20

Using the estimates for ft and ft obtained from the equation that was not corrected for serial correlation yielded similar estimates: r = 0.138, Ψ = 0.00865, and KIY = 2.29, for the implied parameters.

21

A casual inspection of the data seems to confirm the impression that the capital-output ratio is converging to a value somewhat greater than two. However, simply eyeballing the series can be misleading. In the laie 1970s the ratio appeared to be converging to 1.9 and to 1.7 in the late 1960s.

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