This Selected Issues paper attempts to analyze the end-point problem and improve the quality of potential GDP estimates for Germany. It projects that Germany’s potential GDP growth will slow over the coming decade, mainly because of declining labor input. The paper focuses on a long-term fiscal scenario for Germany based on current policies. The paper also attempts to construct a preliminary public sector balance sheet for Germany, and analyzes the performance of its nonfinancial corporate sector.


This Selected Issues paper attempts to analyze the end-point problem and improve the quality of potential GDP estimates for Germany. It projects that Germany’s potential GDP growth will slow over the coming decade, mainly because of declining labor input. The paper focuses on a long-term fiscal scenario for Germany based on current policies. The paper also attempts to construct a preliminary public sector balance sheet for Germany, and analyzes the performance of its nonfinancial corporate sector.

I. Long-Run Growth in Germany1

1. Potential or trend GDP is crucial for short-term economic analysis. The size of the output gap and possible inflationary consequences depend critically on the level of potential GDP. Equally important, potential GDP and its components determine the level of the structural fiscal balance and hence the assessment of fiscal policies.

2. However, potential GDP analysis is sensitive to estimation errors in the present and near future. The reason for this is the so-called “end-point problem” of smoothing methods such as the HP filter. Calculating potential GDP invariably involves some smoothing of time series, either of total factor productivity (TFP), labor and capital input, or GDP itself. Since the HP filter assigns greater weight to more recent observations, their quality determines to a large extent the quality of the HP trend estimate. Recent observations are prone to revisions, and projections of the immediate future may be ad-hoc or in turn depend on estimates of potential GDP, creating circular logic. Thus, conventional estimates of potential GDP are least reliable in present years, where they would matter most.

3. This paper attempts to get around the end-point problem and improve the quality of potential GDP estimates for Germany. It uses demographic projections to push out the end-point problem to 2050, where it matters less for present analysis. Demographic variables move slower and in a more predictable way than economic ones, making them a convenient anchor of the projections. A simple yet analytically rigorous production function model is then used to calculate GDP, taking demography and productivity as the main exogenous variables. The note presents the main ideas in a mostly visual fashion.

A. Main Quantitative Results

4. Potential GDP growth is declining faster than anticipated, mainly because of slowing labor input. Potential growth is now estimated to be around 1¼ percent a year, rather than 1¾ percent in previous calculations. This new “benchmark” may still be optimistic because the model does not include a feedback from taxes to labor supply. As aging pushes payroll taxes up, labor input and growth may be reduced further, absent other policy changes.


Potential GDP Growth

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001

5. Potential growth is projected to slow further to only 1 percent over the coming two decades, as aging shrinks the labor force. The table below details the results of the calculations, and shows that total hours worked decline most strongly in the 2020s. As a result, returns on investment decline as well, and capital accumulation slows down. However, the picture is better in per-capita terms, as productivity is assumed to hold up well.

Table 1.

Germany: Potential Output Growth 1/

article image
Source: IMF staff calculations.

Arithmetic average growth rates

B. The Method in Brief

6. The calculation uses a neoclassical growth model with an endogenous capital stock response. This is a general equilibrium framework, the appropriate setting for analyzing long-term growth. In particular, we use a calibrated Solow model, which is probably the simplest general equilibrium structure. The main relations are the production function,


the savings-investment relation,


and the capital accumulation equation


7. Two exogenous variables and six parameters have to be determined outside the model: (1) labor input Nt, (2) total factor productivity At, (3) the savings/investment rate s, (4) the capital income share α, (5) the participation rate, (6) the unemployment rate, (7) average hours worked, and (8) the depreciation rate δ. Endogenously determined variables are output Yt, the level of investment It, and the capital stock Kt. The sections below explain in detail how these parameters are determined from past observations and demographic projections. Given the numerical values of the parameters and exogenous variables, potential GDP is calculated as follows:

  • In a first step, past and future input factors are calculated: TFP, labor and capital.

  • In a second step, a raw GDP series Yt is calculated by applying the production function to the input factors. Since capital accumulation is endogenous and investment derives from calculated GDP, there is a feedback loop to step (1). The recursive nature of equation (3) ensures that the model does not become circular.

  • Finally, a HP filter is passed through Yt to obtain a smooth potential GDP path.

8. Clearly, the assumptions of this model contain strong simplifications. Total factor productivity and labor input may not be completely exogenous. Labor input in particular depends on the incentives provided by payroll taxes and labor market institutions such as unemployment benefits and collective wage bargaining. Also, the elasticity of substitution between capital and labor may differ from one, as postulated by the model. Nevertheless, the Solow model has worked quite well for an analysis of growth in industrialized countries in the past, and may be a robust benchmark for potential GDP projections.

C. Total Factor Productivity (TFP)

Source: Timmer, Ypma and van Ark (2003), updated June 2005

9. TFP cannot be observed directly and has to be estimated. This is done by subtracting historical labor and capital inputs from GDP. The resulting time series is the so called Solow residual, which shows a cyclical pattern, and reached a peak during German unification. The average growth rate of TFP over the past 35 years was about 1½ percent per year, but this has declined to below 1 percent in the present decade.

10. Going forward, we assume TFP growth to be at 1 percent per year, in line with the average for the EU15 and the U.S. for the past three decades. Projecting productivity growth is fraught with uncertainties. A modest improvement is possible due to the implementation of new information technologies, as witnessed e.g. in the United States. However, this may be offset by the effects of an aging labor force.2 An older labor force may be less innovative and prefer stability over risk taking: new business startups tend to be undertaken by individuals under 40 years of age. Also, the structure of demand changes further from manufacturing to services as a country ages, including health and long-term care. Productivity gains in services may be more limited than in manufacturing, so overall TFP increases could suffer. On the other hand, the work experience of older people may lead to a more efficient use of existing technology and to fewer investment failures.

11. Finally, there may be trade-offs between productivity gains and higher labor force participation, as the example of Spain shows. When the country lowered its unemployment rate from 24 percent in the early 1990s to less than 10 percent at present, it added mostly jobs at the lower end of the pay scale and TFP growth turned negative. In the absence of strong indications in either direction, we assume a conservative increase of productivity growth from the recently observed rate of 0.8 percent to 1 percent a year. This corresponds to the average TFP growth in the EU15 and the U.S. since 1980, as estimated by Timmer and others (2003), in work done by the Groningen Growth and Development Center.

D. Labor Input

12. The variable used for labor input is total hours worked, which is the product of four factors:

article image

13. Germany has reached a demographic peak, and its population will start to decline within the next 10 years. Simple extrapolations from the past are thus inappropriate to derive future labor input. The most recent demographic projection from the Federal Statistical Office (2003) predicts in a “central scenario 5,” that the working-age population will decline by over 20 percent until 2050. This comes despite a steady stream of immigration assumed at 200,000 people per year.

14. The participation rate is assumed to increase somewhat as more women enter the labor force. This variable translates working-age population into the labor force. An IFO projection assumes that the effect of women offsets weaker demographics for the coming few years. After 2010, however, no further contribution from participation is projected. Fluctuations are then purely mechanic, driven by changes in the age composition of the population.


Working Age Population

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001


Participation Rate

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001

15. The equilibrium unemployment rate (or NAIRU) is assumed to decline to around 8 percent. This is a more conservative assumption than IFO (2005), which sees unemployment falling to 3.3 percent over the medium term (as mentioned in section 7). In this paper, we project a baseline model with unchanged policies and argue that unemployment would behave as the past in the absence of further reforms. Over the past three decades, unemployment has been highly persistent in Germany, rising in recession, but failing to decline much in upswings. The last section explores the sensitivity of the results to falling unemployment, as assumed by IFO. While potential growth might be higher, productivity growth could temporarily suffer as in the case of Spain over the past 10 years.

16. Average hours worked have declined steadily since 1970. Some of it was due to shorter workweeks, but increasingly part-time jobs also played a role. Part-time work will continue expanding in the near future, in particular if more women enter the labor force. However, the shortening of the workweek may have reached a limit, and is even reversing to a small extent. For projections, we assume that average hours worked will continue to taper off until 2030 and then stay constant.

17. Total hours worked will decline rapidly after 2010. They are the final labor input in the production function, being the product of the four factors discussed above. After a stagnation during the present decade, total hours start declining after 2010. The decline accelerates during the 2020s, when demographic transition will be in full swing, and slows somewhat thereafter. However, from here to 2050, labor input will diminish potential GDP growth. The feedback through capital accumulation only reinforces this effect.


Hours Worked per Employee

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001


Total Hours Worked

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001

E. Capital Input

18. The production input of capital is the capital stock in use:

Capital input = Capital stock X Utilization rate

The future capital stock is calculated according to equation (3), also called the “perpetual inventory method.” The capital stock of the following period obtains from the present capital stock by adding investment and subtracting depreciation.


Investment Rate

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001


Capital Stock

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001

19. The model assumes a recovery of the investment rate to around 20 percent of real GDP. To simplify, the German economy is assumed to have a balanced current account, with savings equal to investment. A constant investment rate, as assumed in the Solow model, also obtains in more complex intertemporal models, provided that preferences are logarithmic3. On trend, however, the German investment rate has been declining over the past three decades, as discussed in Brunner (2004). Values have been particularly low in years of stagnation such as the past ones. Going forward, it is assumed that the investment rate recovers somewhat and settles at around 20 percent of GDP. The constant investment rate links the capital stock to past GDP. Capital formation is thus endogenized, and as GDP growth slows, capital accumulation slows as well. Over time, output and capital tend to move together, limiting fluctuations in the real interest rate.

20. The calculation assumes that the depreciation rate and capital utilization remain constant at their post-unification average. Data show that the rate of depreciation has been fairly constant at around 5 percent of the capital stock since unification. This number is used for the projections as well. Capacity utilization in industry fluctuated over the business cycles, but has a strong tendency towards an average value. To include the service sector, capacity utilization in industry is scaled for the share of industry in GDP. All other sectors are assumed to have a capacity utilization of 1. In the projections, capacity utilization is assumed to increase slightly to 96.5 percent, as the economy approaches potential.

F. Capital Income Share

21. The calculations assume a constant share of capital income in GDP (a) of around 40 percent. This share is a crucial parameter of the production function, but it is hard to observe. “Capital income” in the national accounts includes the income of self-employed workers, which is mostly labor income. Thus, raw measures tend to overstated the capital income share. Gollin (2002) proposes to scale capital income by the share of the self-employed in total employment. The adjusted measure of the capital share is around 0.4 in Germany right now. It has been trending up since the late 1970s, with a downward break after unification. Blanchard (1998) observed this trend in a wider European context, but not in the US and Switzerland. He argues that it is mostly due to rising unemployment over this period. Since we assume a constant unemployment rate in our projections, keeping the capital share constant seems justified.


Capital Income Share

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001

G. Alternative Models

22. Labor market developments can be key to potential growth in the near future. A recent study by Werding and Kaltschütz of IFO (2005) found a more benign slowdown in growth, particularly over the near future if a more optimistic assumption is used for unemployment. In the IFO model, the unemployment rate is assumed to decline to 3.3 percent over the coming 20 years, instead of keeping it at 8 percent as in this paper. However, Werding and Kaltschiitz admit that this is optimistic and depends on further decisive reforms. Also, there is no feedback from the capital stock and payroll taxes, which creates an upward bias to growth in the face of aging. They present a “risk scenario” with no decline in unemployment and growth rates very similar to ours. However, their model is still partial equilibrium and allows for no feedback from aging to either the capital stock or labor supply.

23. A more complete general-equilibrium model is likely to yield even lower growth, because of the high fiscal costs of aging. The model above abstracts from government finances and labor supply. The labor force is assumed to respond to demographic trends, but not to economic incentives. The government is not present in equations (1) - (3). While this is a useful starting point, public finances and the labor supply can interact with aging in a way that further slows GDP growth.


Sensitivity Analysis

Citation: IMF Staff Country Reports 2006, 017; 10.5089/9781451810509.002.A001

24. This is particularly true if the costs of aging are financed by increasing payroll taxes, as in Germany. The costs of aging could also be financed by higher public debt. Debt financing may temporarily postpone higher taxes, but will raise real interest rates over time as the risk of default increases. In the case of Germany, emerging imbalances in the social security finances have led to pressures to increase payroll taxes although there is no immediate legal mandate to do so. A section in last year’s Selected Issues dealt with this outlook in depth (IMF country report No. 04/340, chapter III: Pensions and Growth). Higher taxes will deter labor supply and lead to a further reduction in GDP growth, possibly close to zero in the 2020s. It is thus likely that the GDP growth rates above are still optimistic.

H. Conclusions

25. This chapter projects that Germany’s potential GDP growth will slow over the coming decade, mainly because of declining labor input. This result is based on demographic projections, current policies and a general-equilibrium macro model. Potential growth for the coming years is now estimated to be around 1¼ percent a year, slowing to only 1 percent after 2010, as aging shrinks the labor force. However, the picture is better in per-capita terms, as productivity is assumed to hold up reasonably well.

26. Government policies can improve this outlook, in particular if they encourage labor utilization. Growth rates could be boosted significantly during demographic transition if labor market reforms succeeded in bringing down Germany’s high unemployment rate. Raising the effective retirement age would also have a high payoff for economic growth. Even total factor productivity should not be seen as being out of reach for public policies, as recognized, for example, by the Lisbon Agenda. Indeed, past experience demonstrates that Germany is capable of significant productivity sprints, and this could well occur again in the future.


  • Barro, R. Sala-i-Martin, X., (2003), Economic Growth. Cambridge: MIT Press.

  • Brunner, A., (2004), Investment Trends and Business Capital Stock in OECD Countries:Long-Term Developments and Future Prospects. IMF Country Report No. 04/340– Germany: Selected Issues.

    • Search Google Scholar
    • Export Citation
  • Faruquee, H., (2002), Population Aging and its Macroeconomic Implications: A Framework for Analysis. IMF Working Paper WP/02/16.

  • Gollin, D., (2002), Getting Income Shares Right, Journal of Political Economy, vol. 110, pp. 458474.

  • Timmer, M., Ypma, G., Ark, B. , (2003), IT in the European Union: Driving Productivity Divergence? GGDC Research Memorandum GD-67, University of Groningen, Appendix Tables, updated June 2005.

    • Search Google Scholar
    • Export Citation
  • Werding, M., Kaltschütz, A., (2005), Modellrechnungen zur langfristigen Tragfähigkeit der öffentlichen Finanzen. IFO Beiträge zur Wirtschaftsforschung (17). Munich: IFO.

    • Search Google Scholar
    • Export Citation

Prepared by Benedikt Braumann.


See Faruquee (2002) for a discussion of age-earning profiles.

Germany: Selected Issues
Author: International Monetary Fund