This Selected Issues paper on Germany reviews investment trends and business capital stock in Organization for Economic Co-operation and Development (OECD) countries. Sharp wage increases are found to boost capital formation in the short term as employers substitute capital for labor at a rate that adjusts to the higher relative price for labor. To limit the political economy biases to fiscal policy, the paper explores options to strengthen budgetary institutions, notably more transparency; stronger budgetary rules; and more room for Länder governments to mobilize revenue and tailor spending to local circumstances.

Abstract

This Selected Issues paper on Germany reviews investment trends and business capital stock in Organization for Economic Co-operation and Development (OECD) countries. Sharp wage increases are found to boost capital formation in the short term as employers substitute capital for labor at a rate that adjusts to the higher relative price for labor. To limit the political economy biases to fiscal policy, the paper explores options to strengthen budgetary institutions, notably more transparency; stronger budgetary rules; and more room for Länder governments to mobilize revenue and tailor spending to local circumstances.

I. Investment Trends and Business Capital Stock in OECD Countries: Long-Term Developments and Future Prospects 1

A. Introduction

7. By almost any measure—capital stock or net investment rate—the pace of capital accumulation has been declining steadily in Germany over the past several decades (Figure I-1). This phenomenon has been a source of concern to policymakers, since it directly affects the long-run ability of the German economy to produce goods and service. The Deutsche Bundesbank (1998, page 36), for example, wrote “… the current capital stock is not sufficient to absorb the existing supply of labor. To create the necessary jobs, more corporate investment is urgently necessary.” Since the Bundesbank wrote those words in 1998, capital accumulation has slumped further.

Figure I-1.
Figure I-1.

Germany: Investment Trends, 1960-2002

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Source: OECD, European Commission; and IMF staff calculations.

8. These trends are shared by a number—but not all—OECD countries (Figure I-2). Investment trends have been similar to Germany’s experience in several European countries, such as France, Italy, the Netherlands, and Switzerland, and in Japan. Capital growth declines were somewhat sharper in the Nordic countries (Denmark, Finland, Norway, and Sweden) and in Greece in the early 1990s, but appear to have recovered somewhat in recent years. In contrast, there are a number of countries with fairly stationary investment rates and capital growth rates, with the most stable trends seen in Anglo-Saxon countries: Australia, Canada, New Zealand, the United Kingdom, and the United States. Finally, there also is a group of European countries where growth rates have stabilized in recent years.

Figure I-2.
Figure I-2.

Selected OECD Countries: Business Capital Growth Trends, 1960-2002

(Percent change)

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Source: OECD, European Commission; and IMF staff calculations.

9. Although the economic literature offers several possible explanations, there is no agreement on the causes of these trends. The following explanations have been put forward:

  • First, standard neoclassical growth theory, which relies on a balanced growth path, predicts that the long-run, steady-state growth rate of the capital stock should equal the sum of total factor productivity (TFP) growth and labor force (LF) growth. Both of these components have slowed for many countries in recent years.

  • Second, the capital-to-labor ratio was relatively low for some countries after World War II, particularly in France, Germany, Italy, Japan, and the United Kingdom. Thus, convergence could account for the relatively high levels of investment in those countries during the 1960s and 1970s. Moreover, there was additional “catch-up” investment in Germany in the 1990s following reunification.

  • Finally, there are a number of factors that alter the trade-off between capital and labor, such as the real interest rate, the rate of capital depreciation, wage rates, and tax rates on capital and labor. While these factors can temporarily affect the growth rate of capital during the transition period, they cannot affect the long-run growth rate. Broadbent, Schumacher, and Sachels (2004) have argued that countries with a large presence of public sector banks—particularly Germany—have relatively lower rates of return on capital and larger capital-to-labor ratios. With EMU and a decreasing presence of public sector banks in recent years, interest rate spreads among public sector banks have been on the rise and could explain part of the recent slowdown in investment. Many countries with declining capital accumulation rates have also been saddled with high unemployment rates, following increases in labor market protection and real wages in the 1970s and early 1980s. Blanchard (1997, 1998) has argued that excessive wage growth initially stimulates capital growth in the short run (as firms substitute away from labor) but this diminishes the marginal product of capital and investment rates in the medium term. The persistence—and perhaps permanency—of these effects is still an unsettled question. Daveri and Tabellini (2000) have argued that higher labor taxes have been an important source of increased labor costs—thereby leading to both higher unemployment and slower capital growth. But, the importance of this explanation for capital stock growth rates is questionable, as tax policy is generally considered to have a negligible effect on the long-run growth of an economy (see Mendoza, Milesi-Ferretti, and Asea for a recent study on this issue), although it can affect the levels of capital and labor utilization.

10. This paper examines the empirical importance of these explanations, using a panel data set of 21 OECD countries. The paper is organized as follows: Section B provides a more extended discussion and examines the stylized facts of each explanation. Section C presents econometric test results for the various theories. Section D concludes.

B. Stylized Facts and Possible Explanations

11. This section compares the stylized facts to those implied by various theoretical explanations. All the explanations that have been offered can be viewed as extensions to the neoclassical growth model, so that model is used as the benchmark for evaluating various alternatives2. The next section then presents a more rigorous evaluation using econometric techniques.

12. The paper focuses only on capital accumulation—the growth rate of business capital—which has advantages and disadvantages for economic analysis. First, the growth rate of the business capital stock is an important component of the potential growth rate of the economy—along with total factor productivity and labor force growth rates. That is, the capital growth rate is helpful in understanding income growth, but it is not useful for understanding the relative importance of using capital—relative to labor, for example—or for understanding per capita income3. Second, the net investment rate—an alternate measure of capital accumulation—is more commonly cited in the literature, largely because it is easily constructed from national accounts data. Still, this measure includes private residential construction and public investment; the former has little direct impact on the productive capacity of the economy, and the latter may not be a perfect substitute for private investment.4 Finally, all of the above measures rely on calculations for capital consumption, which, in turn, rely on assumptions for depreciation and scrap rates. Countries use different methodologies to calculate capital consumption, so these measures are not strictly comparable across countries.

13. Particular emphasis is placed on four countries—Germany, Sweden, the United States, and Spain—each representing a member of the four groups of countries shown in Figure I-2.

Long-run determinants of capital accumulation

14. According to the neoclassical growth model, the growth rate of the capital stock (and GDP) is determined by the sum of the growth rate of the labor force and the growth rate of total factor productivity (TFP). In the long run, the factors of production are supply-determined. In the standard neoclassical growth model, TFP growth (which is labor-augmenting) and changes in the labor supply are exogenously determined and are the sole drivers of potential GDP; assuming a balanced growth path, the capital stock must grow in line with these components.5 As it turns out, these two factors explain only part of the long-run trends in most countries (Figure I-3). Fundamentals (shown as dashed lines in each panel) show a relatively close correlation with the growth of business capital in the U.S. However, in Germany and Sweden, the capital stock grew faster than fundamentals in the 1960s and 1970s, with capital accumulation falling more in line with fundamentals more recently. In Spain, capital accumulation continues to exceed the pace of fundamentals.

Figure I-3.
Figure I-3.

Selected OECD Countries: Business Capital Stock Growth and Neoclassical Fundamentals, 1965-2000

(HP filtered, percent change)

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Source: OECD, European Commission; and IMF staff calculations.

15. There are several factors (shocks) that could disrupt the long-run relationship between the growth rate of capital and its fundamental determinants. First, the actual capital-to-labor ratio might be lower than the desired level. As a result, the marginal product of capital will be high, which will encourage high rates of investment and capital accumulation until the economy reaches the steady state. Similarly, changes in real rates of return, depreciation rates, or tax policies will change the optimal level of capital relative to other factors, such as labor. Again, this will involve permanent changes in the capital-to-labor ratio and the net investment rate but will generate only temporary changes in the capital stock growth rate, until the economy reaches the new steady state.

16. The literature suggests that the transition period to a new steady-state capital stock, and hence deviations from the fundamentals, could be very long. It finds that convergence rates are between 2 percent and 3 percent per year. This means that it could take between 25 and 35 years to accomplish only ½ of the necessary adjustment. In other words, the long-run trends that are seen in Figures I-1 through I-3 could actually be long-run adjustments to age-old shocks. This possibility is examined in the remainder of this section.

Capital stock convergence

17. Assume, for the moment, that there are no real differences among countries with regard to TFP or labor force growth and that there have been no changes to production possibilities, consumer preferences, or government policy in several years. In this case, the steady-state determinants of capital stock growth rates would be the same for all countries, and all countries would have the same steady-state growth rate. Suppose, however, that countries differ in their initial endowments of capital, with some having too little capital relative to the steady-state level. Standard growth theory predicts that investment and savings rates will increase temporarily until the steady-state capital stock is reached.

18. There is a fairly strong negative correlation between measures of capital accumulation and per capita GDP (Figure I-4). Assuming a Cobb-Douglas production function, per capita GDP is proportional to the capital-to-labor ratio. As seen in the figure, there is a great deal of dispersion at low income levels (low capital-to-labor ratios) compared to higher income levels. Much of the dispersion at low-income levels is due to two countries—Japan (which had very high investment rates) and Ireland (which had very low investment rates).

Figure I-4.
Figure I-4.

Selected OECD Countries: Capital Accumulation and Per Capita GDP, 1960-2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Source: OECD, European Commission; and IMF staff calculations.

19. Focusing on Germany, Sweden, the United States, and Spain, the convergence hypothesis appears to have some merit in explaining investment trends (Figure I-5). Germany, for example, had a relatively low level of per capita income and per capital stock after WWII and was investing heavily in 1965; subsequently, the capital stock growth rate converged to levels closer to those in the United States in 2000. However, the fall is much steeper than for other countries, suggesting additional explanations. Although Sweden’s capital stock growth rate slowed along with U.S. rates, Sweden’s net investment rate has slowed much faster. Spain also had a relatively low level of per capita income in 1965 but invested less than Germany; more recently, its investment trends are in line with the convergence hypothesis. Thus, while the fit is not perfect, the convergence hypothesis appears to have some merit.

Figure I-5.
Figure I-5.

Selected OECD Countries: Capital Accumulation and Per Capita GDP, 1965 and 2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Source: OECD, European Commission; and IMF staff calculations.

Lending rates

20. Broadbent, Schumacher, and Sachels (2004) have argued that Germany has significantly lower rate of return on capital than other European countries. They attribute this feature to a relatively large presence of public sector banks. Low cost of capital encouraged overinvestment and, more recently, slow capital stock growth. Although the authors do not provide an explicit estimate of the investment overhang, they imply that it is substantial. In contrast, analysis below does not suggest a strong correlation between lending rates and the presence of public sector banks.

21. Real rates of return on capital are notoriously difficult to calculate for cross-country comparisons. The necessary data are often not available, or the data are not comparable across countries. As a crude approach, one can calculate the “real” rate as an interest spread of lending rates over short-term government rates and compare them to the share of banking assets that are government controlled (Figure I-6). The government banking shares are from La Porta and others (2002) for 1995, and the interest rate spreads are average spreads from 1995-2000 from the International Finance Statistics. There is a slight positive correlation between these two measures. While it is true that lending rate spreads are somewhat low in Germany compared to other continental European countries, they are not low compared with a broader sample of countries, and there is no strong evidence suggesting that there is a link between these spreads and the role of public sector banks.

Figure I-6.
Figure I-6.

Selected OECD Countries: Government Ownership of Banks and Lending Spreads, 1995-2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Sources: IMF, International Financial Statistics; and La Porta and others, 2002.

Excessive wage growth

22. Blanchard (1997, 1998) has argued that excessive wage growth—relative to inflation and changes in labor productivity—is the primary reason for persistently high unemployment in Europe. In Blanchard’s model, firms are monopolistically competitive, and, therefore, can earn positive economic profits. Workers can extract some of these profits through collective wage bargaining agreements. Workers are assumed to be less aggressive when unemployment rates are high. The so-called wage curve can be written as:

ΔlogWt^=λΔlogut+ut(1)

where Wt^ is the efficiency wage rate, ut is the unemployment rate, λ is a slope of the wage curve (<0), and vt is a temporary labor supply shock (measured in wage rate terms) that results in permanent changes to the level of efficiency wages. A very large literature finds that λ is fairly constant across countries, regions, and time periods, at a value of about -0.1.

23. Relatively high labor costs—as a result of negative labor supply shifts—lead to changes in the optimal mix of capital and labor. In Blanchard’s model, the effects of excessive wage growth are temporary. Initially, they stimulate capital growth, as firms substitute away from labor. In the medium-term, however, capital growth diminishes the marginal product of capital and investment rates, and thus capital accumulation. Kaas and von Thadden (2001) formalized and provided a more thorough discussion of the Blanchard model; they showed that the persistence of the effects of labor supply shocks depends critically on the elasticity of substitution between labor and capital. Blanchard also hinted at the possibility of permanent effects on the capital-to-labor ratio, and Acemoglu (2000) has formalized this explanation. The basic idea is that firms not only substitute away from labor in response to adverse wage shocks, but they also invest in labor-saving capital. Nevertheless, it should be stressed that the effects, whether temporary or permanent, only affect the long-run levels of capital, labor, and income and not their growth rates.

24. The correlation between efficiency wage growth and capital accumulation is somewhat weak (Figure I-7). A detailed look at Germany, Sweden, the United States, and Spain also suggests that excessive wage growth is unlikely to be an important explanation for the stylized facts observed earlier (Figure I-8). Indeed, in many cases, it appears that slowing capital growth went hand-in-hand with efficiency wage growth, which suggests a common explanation rather than causality from labor to capital.

Figure I-7.
Figure I-7.

Selected OECD Countries: Capital Accumulation and Efficiency Wage Growth, 1960-2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Sources: OECD, European Commission; and IMF staff calculations.
Figure I-8.
Figure I-8.

Selected OECD Countries: Business Capital Stock and Efficiency Wage Growth, 1965-2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Sources: OECD, European Commission; and IMF staff calculations.

The role of labor and capital taxation

25. Daveri and Tabellini (2000) argue that higher taxes on labor income can have important effects on employment and capital. The intuition for this result is very similar to the arguments made by Blanchard and others in the context of efficiency wages. If workers have monopolistic power because of collective bargaining arrangements, then the burden of higher labor taxes can be passed on (to some extent) to firms. This has two effects. First, real wages will be higher, resulting in lower employment. Second, firms will also substitute toward capital. As before, capital growth speeds up and then falls as the marginal product of capital is pushed down. In the long-run, the economy has higher unemployment, a higher capital-to-labor ratio, lower per capita income, and an unchanged capital stock growth rate.

26. Net investment rates and capital accumulation will also be affected by the tax rate on capital income. Higher taxes on capital income will lower the steady-state capital-to-output ratio and the net investment rate. In addition, capital accumulation will slow until the new steady state is reached.

27. The correlation between capital accumulation and tax rates are shown in Figure I-9. As seen in the top panel, there is a small negative correlation between capital growth rates and tax rates on capital, in line with the notion that capital accumulation slows with higher taxes and that the transition period is very long. The evidence on the effects of labor taxes is also consistent with the theory (bottom panel). That is, with higher taxes and lower subsequent output, both capital and labor are adversely affected in the medium-term (over the 5-year intervals).

Figure I-9.
Figure I-9.

Selected OECD Countries: Capital Accumulation and Taxation of Capital and Labor, 1960-2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Sources: OECD, European Commission; and IMF staff calculations.

28. With respect to specific countries, the time-series evidence also suggests that tax rates are playing a role in observed investment trends (Figure I-10). The United States has had relatively high and fairly constant tax rates on capital, in line with relatively low and constant capital stock growth rates. Moreover, tax rates on labor have edged up over time, which may help explain the small slowdown in capital accumulation over the sample period. In contrast, tax rates have been relatively low but increasing in Spain, where investment rates have been significantly higher. Tax rates were very high and increasing in Sweden, until very recently, and capital accumulation edged down over this period as well. Germany is a bit harder to explain with a tax rate story, given the relatively large fall in the capital stock growth rate relative to changes in taxation. Still, higher taxes on both capital and labor may have contributed to the decline.

Figure I-10.
Figure I-10.

Selected OECD Countries: Business Capital Stock Growth and Taxation of Capital and Labor, 1965-2000

Citation: IMF Staff Country Reports 2004, 340; 10.5089/9781451810455.002.A001

Sources: OECD, European Commission; and IMF staff calculations.

C. Econometric Results

29. This section of the paper examines several explanations for movements in capital stock growth rates using econometric analysis. As reviewed in the previous section, economic growth theory points to two main determinants of the capital stock growth rates in a steady state—the growth rate of TFP and the labor force. Changes in these determinants result in a new steady-state, along with transitional dynamics to the steady-state. In addition, there are several shocks that could temporarily raise or lower the growth rate and require transition back to the steady state. Changes in the level of the capital stock, the real interest rate, the depreciation rate, tax rates on capital or labor, or the efficiency wage are some of the many factors that could have temporary affects on capital accumulation. The econometric approach to testing these possibilities involves two steps. First, the theory implies a co-integrating relationship among capital stock, TFP and labor force growth rates. In the second step, deviations from the long-run level—that portion that cannot be explained by fundamentals—is then regressed on proxies for the various explanation and also allowing for transitional dynamics.

30. Measures for the determinants of the capital stock growth rates are problematic. First, one should use total hours worked rather than the labor force to measure the labor component, but this variable is not widely available over time or across countries. This, in turn, affects the measure of TFP growth and efficiency wages, which calculated as a residual, after accounting for labor and capital inputs. Second, households and firms respond to effective marginal tax rates, which are difficult to measure. Instead, this study uses effective average marginal tax rates on labor and capital income. Third, there are many ways to calculate real interest rates and efficiency wage rates. With respect to real interest rates, this paper uses the 3-month interest rate less actual GDP inflation.6 With respect to wage growth, the “wage” rate is measured by estimating total compensation for all workers in the economy, using the relationship in equation (1). Finally, capital depreciation rates, as discussed earlier, are measured differently across countries, and, sometimes, across time.

31. This paper uses a panel data set of 21 OECD countries from 1961-2000. Since there is a great deal of business cycle volatility in these data and the emphasis is on long-run developments, five-year averages of the data were constructed (1961-65, 1966-70, and so forth). This provides (at most) 168 observations for each variable in the panel.

The econometric approach

32. The results of estimating the long-run, steady-state relationship is as follows:

Δkt=α+0.58(1.89)*ΔTFPt+1.37(3.35)*ΔLFt+εt(2)

where t-statistics are shown in parenthesis and εt represents temporary, but persistent, deviations from the steady state. The hypothesis that the co integration coefficients are both equal to one cannot be rejected. Henceforth, this restriction will be imposed. The next econometric challenge is to explain these deviations:

εt=μ+γXt+ηt(3)

where Xt denotes a vector of variables that could have a temporary effect on the capital stock growth rate.7 Note that these variables are, by assumption, stationary, since they cannot have permanent, long-run effects on the steady-state capital stock.

33. The econometric results of estimating second-stage regression are presented in Table I-1 Four specifications are presented in the table. Each specification contains country and time dummies, as well as a reunification dummy for Germany. The first regression is the most general, while other specifications progressively remove variables that are statistically unimportant. The results are fairly consistent with theory, but some puzzles exist:

  • Several lag structures were evaluated, although the number of lags was limited by the short time series component of the panel data set. One lag was found to be sufficient to capture dynamics. This implies a fairly short adjustment period compared to other studies, as discussed in Section B.

  • The proxy for the capital-to-labor ratio (per capita income) has the wrong sign, but is not significantly different from zero. This could indicate that it is not a good proxy, that countries are not converging to the same capital-to-labor ratio, or that other changes (such as tax rate policy) that are correlated with increases in per capita income provide better explanations for capital growth rates.8

  • The real interest rate and the depreciation rate do no have statistically significant effects. Both of these measures are difficult to construct and likely accounts for this outcome. The tax rates on capital and labor and the wage rate have statistically significant effects on the change in the capital stock growth rate. The most parsimonious regression in column (4) indicates that higher taxes on labor or capital results in decreases in capital accumulation while increases in the efficiency wage boosts capital growth, suggesting a substitution of capital for labor.

Table I-1.

Selected OECD Countries: Determinants of Business Capital Growth Rates, 1960-2000

(Dependent variable is “excess” capital growth)

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Notes: Data are 5-year averages of annual observations. Each regression also includes country and time dum and a reunification dummy for Germany. Standard errors have been corrected for heteroskedasticity.***, **, and * indicate significance from zero at the 1, 5 and 10 percent level, respectively.

Decomposition of long-run developments

34. The final step in the analysis is to decompose capital stock growth rates into contributing categories. This done by multiplying the regression coeffecients by the appropriate time-series value, using the right-most regression in Table I-1. Tables I-2A through I-2D show the decomposition of change in the capital stock growth rate for the four countries from the 1970s to the 1990s. The first line shows the actual change in the average growth of the capital stock for each country. The next three rows show developments in fundamentals, leaving “excess” capital growth to be explained. The final rows show the amount of excess capital growth—the deviations from the steady state in equations (2) and (3)—that can attributed to changes in tax rates on capital and labor and to increases in the efficiency wage rate. The results can be summarized as follows

  • As noted earlier, fundamentals make only a partial contribution in explaining the decline in the capital stock growth rates.

  • A large part of Germany’s rapid capital stock growth rate in the early 1970s and in the period following reunification can be attributed to large increases in the efficiency wage rate. Increases in taxation, especially labor taxation, had a negative effect on capital accumulation.

  • Sweden and Spain also experienced increases in efficiency wages in the 1970s. These increases were smaller than Germany’s, and they were almost exactly offset by developments in taxation of capital and labor.

  • The amount of “excess” capital growth is very small in the United States relative to the other countries. Small declines in the efficiency wage rate were offset by the effects of higher taxes on capital and labor.

  • Finally, the “unexplained” portion of excess capital growth—the last line of each table—has mostly declined over the last three decades for Germany, Sweden, and (to a lesser extent) the United States, suggesting that convergence may have played a role in these countries but was not adequately captured by the convergence measures used in the regression analysis. In contrast, the unexplained growth for Spain has remained relative high over the entire sample period, as was seen in Figure I-5.

Table I-2A.

Germany: Decomposition of Capital Stock Growth Rates, 1961-2000

(in percentage points)

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Table I-2B.

Sweden: Decomposition of Capital Stock Growth Rates, 1961-2000

(in percentage points)

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Table I-2C.

United States: Decomposition of Capital Stock Growth Rates, 1961-2000

(in percentage points)

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Table I-2D.

Spain: Decomposition of Capital Stock Growth Rates, 1961-2000

(in percentage points)

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D. Summary and Policy Conclusions

35. This study has examined possible explanations for the decline in capital accumulation rates that have been observed in several countries. In addition to changes in fundamentals, the possibility of convergence in capital-to-labor ratios, changes in factors that affect the underlying capital-to-labor ratios and investment rates (real interest rates, depreciation rates, and the taxation of capital and labor), and changes in the supply of labor (proxied by the growth rate of the efficiency wage rate) were examined.

36. While TFP growth and the labor force growth rates have abated over the last several years, the results suggest that other factors were also important in explaining the slowdown in capital accumulation. A large part of the explanation lies in excess wage growth during the 1970s. Results for Germany, for example, show that about half of the rapid growth in business capital in the 1970s can be attributed to increases in the efficiency wage. Wage increases had a much smaller effect in Sweden. These developments were offset, to some degree, by increases in tax rates on capital and labor. Somewhat surprisingly, the evidence found in favor of the convergence hypothesis is relatively weak, although there is certainly a strong negative raw correlation between capital-to-labor ratios and capital growth rates, suggesting that countries in the sample are not converging to the same capital-to-labor ratio or have different rates of convergence.

37. Focusing on Germany, these results have several important implications for future capital accumulation and potential GDP growth. Fundamentals during the late 1990s suggest a long-run capital stock growth rate of about 2 percent. However, over the medium term, it is likely that the growth of the capital stock will slow further—along with the growth rate of potential GDP.

  • First, capital accumulation will likely slow further over the next several decades in line with expected decreases in the labor force due to aging of the population. In addition, while reforms are underway to improve labor force participation, slippages in this area would lead to further slowdown in the growth rate of the capital.

  • Second, wage rates have shown a downward trend in Germany in recent years, as in other European countries, which is positive for employment prospects but can slow capital accumulation in the short run. It is difficult to assess how much further wage moderation will occur in the future.

  • Finally, after some decades of very high capital accumulation, convergence appears to have been largely achieved in Germany (Table I-2A); that is, capital-to-labor ratios should now be close to their fundamental long-run equilibrium.

38. The results are preliminary. Capital stock measures and proxies for their determinants are imprecise and difficult to obtain. In addition, this study examined the capital stock in isolation, rather than looking at the simultaneous determination of capital and labor, which could be an interesting project for the future.

Appendix: Capital Accumulation in a Neoclassical Growth Model

39. This appendix describes a simple, benchmark closed-economy neoclassical growth model and its implications for capital accumulation. The economy is characterized by a representative firm and a representative household. Although the closed-economy assumption is not directly defensible for the countries analyzed in this paper, Barro and others (1992) have shown that such a model has essentially the same steady-state properties, if capital is a composite of physical capital and human capital and if only physical capital can be used as collateral for international borrowing.

The representative firm

40. The representative firm hires labor and rents capital to produce a single good. The production function is:

Yt=F(Kt,AtLt)=A0Ktα(AtLt)1α

where Yt is output; A0 is an arbitrary constant; At is the level of labor-augmenting technology; Kt is the level of the capital stock; Lt is the size of the labor force, respectively; and a is the share of output paid to capital.9 Technology and the labor force are assumed to grow exogenously at a constant rates over time:

At+1/At=(1+γA)
Lt+1/Lt=(1+γL)

Since technology and the labor force grow over time, it is convenient to transform the growing economy into one that is stationary, by dividing through by At Lt:

Yt/AtLt=yt^=A0(Kt/AtLt)α=A0kt^α

Note that output and the capital stock are now expressed relative to “effective” labor.

41. The firm is assumed to choose capital in each period in order to maximize the firm’s profits, which can be written as:

πt^=A0Kt^αvtKt^wt^

where wt^ is the efficiency wage rate (wt /At) and vt is the rental rate of capital. The optimal choice for capital and the zero-profit condition imply that:

αA0kt^α1=vt(A1)
(1α)A0kt^α=w^t(A2)

Both conditions state that the firm rents capital and hires labor up to the point where their marginal products are equal to their effective marginal costs.

The representative household

42. The representative household is comprised of Lt workers, earns income from renting capital and providing labor to firms, pays taxes, and derives utility from consumption and leisure. The household budget constraint is:

Ct+[Kt+1(1δ)Kt]=(1τk)vtKt+wtLt+Tt

where τk is the tax rate on capital income, δ is the depreciation rate of capital, and Tt is a lump-sum transfer from the government.10 In effective labor units, the household budget constraint is:

ct^+(1+γA)(1+γL)k^t+1(1δ)k^t=   (1τk)vtk^t+w^t+t^t(A3)

43. The household chooses consumption and the amount of capital to be carried into the next period, so as to maximize household utility:

Ut=Σt=0βtLtU(c^t)

subject to the budget constraint in equation (A3). Finally, the utility function is:

U(c^t)=(c^t1θ1)/(1θ)

The optimal capital choices is:

(1+γA)[c^t+1/c^t]θ=β[(1τk)vt+1+1δ](A4)

The equation states that the relative willingness of households to postpone consumption increases with an increase in the discount rate or the rate of capital, and decreases with an increase in the tax rate on capital or the depreciation rate. In addition, the household budget constraint in equation (A3) must hold.

The government

44. In this model, the government simply collects taxes and redistributes them to the household, so the lump-sum transfer can be written as:

t^t=τkvtk^t(A5)

Steady-state equilibrium

45. The equilibrium conditions for the economy are summarized by equations (A1) through (A5). These conditions—which determine output, capital, and consumption expressed in efficiency units—can be further simplified as:

y^t=A0k^tα
c^t+(1+γA)(1+γL)k^t+1(1δ)k^t=y^t
(1+γA)[c^t+1/c^t]θ=β[(1τk)αA0k^t+1α1+1δ]

46. In the steady state, the model has the following implications for capital accumulation:

  • The capital stock and output grow at the exogenous rate of γL + γA.

  • The capital-to-output ratio is:

    KY=αβ(1τk)A0(1+γA)+β(1δ)

    which states that the optimal ratio is larger with increases in the share of output paid to capital, the discount rate, and the depreciation rate, and is smaller with increases in the tax rate on capital income, and the growth rate of technology. Note that changes in these factors would change the level of the capital stock, but they would not affect the long-run growth rate of the capital stock nor the long-run growth rate of the economy.

  • The net investment (NI) rate is:

    NIY=[(1+γA)(1+γL)1]KY=[(1+γA)(1+γL)1]αβ(1τk)A0(1+γA)+β(1δ)

    which has essentially the same properties as the optimal capital-to-output ratio, except that the effect of faster technology growth is ambiguous, but faster labor force growth raises the optimal net investment rate.

47. In summary, the model suggests that the capital stock growth rate should be determined by the growth rates of TFP and the labor force. However, temporary deviations from the steady state in response to factors that determine the underlying the capital-to-output and net investment rates, such as changes in real interest rates, tax rates, and depreciation rates. In addition, extensions to the neoclassical model also suggest that fundamental changes in the labor market—changes in the rents captured by labor, for example, could also have temporary effects on capital accumulation. These changes are evaluated in the empirical section of the paper.

References

  • Acemoglu, Daron, 2000, “Labor- and Capital-augmenting Technical Change,Working Paper No. 7544, National Bureau of Economic Research.

    • Search Google Scholar
    • Export Citation
  • Barro, Robert J., N. Gregory Mankiw, and Xavier Sala-i-Martin, 1992, “Capital Mobility in Neoclassical Models of Growth,Working Paper No. 4206, National Bureau of Economic Research.

    • Search Google Scholar
    • Export Citation
  • Blanchard, Olivier, 1997, “The Medium Term,Brookings Papers on Economic Activity, (2), pp. 89158.

  • Blanchard, Olivier, 1998, “Revisiting European Unemployment: Unemployment, Capital Accumulation, and Factor Prices,Working Paper No. 6566, National Bureau of Economic Research.

    • Search Google Scholar
    • Export Citation
  • Broadbent, Ben, Dirk Schumacher, and Sabine Sachels, 2004, “No Gain without Pain—Germany’s Adjustment to a Higher Cost of Capital,Global Economics Paper No. 3, Goldman Sachs.

    • Search Google Scholar
    • Export Citation
  • Daveri, Francesco, and Guido Tabellini, Unemployment and Taxes: Do Taxes Affect the Rate of Unemployment?,Economic Policy, (April), pp. 49104.

    • Search Google Scholar
    • Export Citation
  • Deutsche Bundesbank, 1998, “Trends in and Structure of the Overall Capital Stock,Monthly Report, (November), pp. 2537.

  • Kaas, Leo and Leopold von Thadden, 2001, “Unemployment, Factor Substitution, and Capital Formation,Discussion Paper 01/01, Economic Research Centre of the Deutsche Bundesbank.

    • Search Google Scholar
    • Export Citation
  • La Porta, Rafael, Florecio Lopez-de-Silanes, and Andrei Schleifer, 2002, “Government Ownership of Banks,Journal of Finance, Vol. LVII (1), pp. 265301.

    • Search Google Scholar
    • Export Citation
  • Mendoza, Enrique, Gian Maria Milesi-Ferretti, and Patrick Asea, 1997, “On the Effectiveness of Tax Policy in Altering Long-run Growth: Harberger’s Supernuetrality Conjecture,Journal of Public Economics, Vol. 66, pp. 99126.

    • Search Google Scholar
    • Export Citation
  • Romer, Paul M., 1998, “Capital Accumulation in the Theory of Long-Run Growth,in Modern Business Cycle Theory, (edited by Robert J. Barro), Cambridge, MA: Harvard Unversity, pp. 51127.

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    • Export Citation
1

Prepared by Allan Brunner.

2

See the Appendix for a brief discussion of the neoclassical growth model. See Romer (1989) for an extended discussion of capital accumulation and long-run growth.

3

For example, a permanent change in the tax rate on capital income could have important effects on the capital-to-labor ratio or the net investment rate—as labor is substituted for capital—but such a policy change would likely have little impact on the long-run growth rates for capital, labor, or income.

4

The literature is somewhat ambiguous as to whether public investment is a substitute or a complement for private investment.

5

Henceforth, the sum of TFP growth and labor force growth will be referred to as “the fundamentals.” Also, note that changes in employment rates and hours worked will be reflected in changes in TFP, since the labor force is being used as the measure of labor supply.

6

Ideally, one would like to use longer-term real interest rates. However, long time series on such measures were not available for most countries in the sample.

7

This model could have been set up as an error-correction model, but the presence of a lagged dependent variable would complicate the decomposition analysis in the next section.

8

Several other proxies for the capital-to-labor ratio were used with similar results.

9

The Cobb-Douglass production function assumes that the elasticity of substitution between capital and labor is one. This assumption has important implications for rate of capital accumulation when the economy is not in steady-state, as discussed in the main section of the paper.

10

There is no labor-leisure choice in the model, so there is no distortionary role for the taxation of labor.

Germany: Selected Issues
Author: International Monetary Fund
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    Germany: Investment Trends, 1960-2002

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    Selected OECD Countries: Business Capital Growth Trends, 1960-2002

    (Percent change)

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    Selected OECD Countries: Business Capital Stock Growth and Neoclassical Fundamentals, 1965-2000

    (HP filtered, percent change)

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    Selected OECD Countries: Capital Accumulation and Per Capita GDP, 1960-2000

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    Selected OECD Countries: Capital Accumulation and Per Capita GDP, 1965 and 2000

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    Selected OECD Countries: Government Ownership of Banks and Lending Spreads, 1995-2000

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    Selected OECD Countries: Capital Accumulation and Efficiency Wage Growth, 1960-2000

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    Selected OECD Countries: Business Capital Stock and Efficiency Wage Growth, 1965-2000

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    Selected OECD Countries: Capital Accumulation and Taxation of Capital and Labor, 1960-2000

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    Selected OECD Countries: Business Capital Stock Growth and Taxation of Capital and Labor, 1965-2000