France: Selected Issues
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This Selected Issues paper first explains the recent increase in trend growth and then discusses how labor market and tax policies could best sustain it. This study calculates French trend growth estimating simultaneously a Cobb–Douglas production technology and total factor productivity. The main conclusion is that French trend growth indeed increased during the second half of the 1990s to an average annual rate of 2.1 percent, from 1.8 percent in 1993. This was not owing to a recovery of total factor productivity growth.

Abstract

This Selected Issues paper first explains the recent increase in trend growth and then discusses how labor market and tax policies could best sustain it. This study calculates French trend growth estimating simultaneously a Cobb–Douglas production technology and total factor productivity. The main conclusion is that French trend growth indeed increased during the second half of the 1990s to an average annual rate of 2.1 percent, from 1.8 percent in 1993. This was not owing to a recovery of total factor productivity growth.

I. Potential Growth of the French Economy1

A. Introduction

4. Most industrial countries experienced a slowdown in trend growth after 1973. During the second half of the 1990s, however, there was a revival largely attributed to the IT revolution in the United States but also reflecting policy changes in several European countries as from the beginning of the decade. For France, Doisy (2002) concluded that trend growth increased from 2 percent to 2.5 percent in the second half of the 1990s as a result of an increase in structural employment, and capital accumulation (Figure I.1). Productivity, measured as business sector output per hour worked (PPP adjusted), remained high and second only to the United States (Figure I.2). On the other hand, French labor force growth has been declining, and is expected to become negative in 2006, and the labor force participation rate remains one of the lowest in Europe (Figure I.3). Also, since 1998, the introduction of the 35-hour workweek, while accompanied by cuts in social security contributions and a reorganization of labor market practices, detracted further from the contribution of labor. In sum, these factors are weighing negatively on French trend growth.

Figure I.1.
Figure I.1.

France: Total Employment and Net Capital Slock

(Annual Percent Change)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE.
Figure I.2.
Figure I.2.

France: Business Sector Output per Hour Worked PPP

(1995 Prices)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: OECD, Economic Outlook
Figure I.3.
Figure I.3.

France; Labor Force Growth and Participation Rate

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE.

5. This chapter asks whether French trend growth increased in the second half of the 1990s. Trend growth is estimated using a Cobb-Douglas production technology, with total factor productivity growth treated as an unobservable variable. The main novelty is the use of the Banque de France’s (2000) measure of the intensity in the use of capital to adjust the net stock of capital for its weekly operating time. The use of that measure eliminates the effect of cyclical components in total factor productivity growth, and thus removes the downward bias in its measurement caused by the underestimation of excess capacity. The chapter’s main conclusion is that French trend growth indeed increased during the second half of the 1990s. This was not due to a recovery of total factor productivity growth, however, which remained at its lowest level since the late 1970s. The recovery of French trend growth seems instead due to an increase in trend employment as well as to a deepening of capital made possible via investment and also, in a minor way, by increased recourse to shift work. These developments were facilitated by a gradual move in the early 1990s toward policies intended to make the labor market more flexible, and by an environment of low real interest rates. Looking forward, policies that further enhance labor market flexibility, increase incentives to participate in the labor force, and promote domestic and foreign investment, inter alia through modifications in the tax system, would help sustain the revival in trend growth—all the more needed to counter the adverse effects on growth of the reduction of the workweek, which occurred mostly beyond the sample period used in this chapter, and the impending demographic shock.

B. Production Function Approach to Estimating Trend Growth

6. The production function approach to estimate output trend growth is an extension of growth accounting.2 It has been favored by those interested in analyzing the economic forces behind output developments, including changes in the net capital stock, the intensity in its use, labor force participation, demographics, and so on (European Commission, 2002). Such analysis hinges crucially on the assumption that the country’s production process can be represented by an aggregate production function. The technology postulated in the production function has to be justified: with a Cobb-Douglas production technology, for instance, the assumption of constant returns to scale, the measurement of the capital stock, and the determination of the natural level of inputs pose theoretical and empirical challenges.3 Finally, as the production function approach often derives total factor productivity as a residual, empirical work usually treats as exogenous a non-negligible part of overall growth.

7. This chapter calculates French trend growth estimating simultaneously a Cobb-Douglas production technology and total factor productivity. Following Lucas’ (1970) insight, the stock of capital is adjusted to proxy a measure of intensity of capital services by using variations in the weekly operating time of equipment in French industry obtained from the Banque de France’s annual survey.4 Both the assumption of constant returns to scale, and the stability of the parameters over the sample are tested and accepted. Possible endogeneity problems are addressed by testing for cointegration between output, labor, and capital. Having accepted that there is no cointegration, the production function is simultaneously estimated with total factor productivity growth as a latent variable.

8. The Cobb-Douglas production function with constant returns to scale is defined in terms of the flow of services of the factors labor (N) and capital (Z). Labor services are represented by the total number of hours worked by the labor force (L = N Hn). The services of the net capital stock are represented by the number of hours the capital stock is used (K=Z Hz). Formally5:

Y = A ( N H N ) α ( Z H Z ) β , ( 1 )

where Y is output, and A is total factor productivity. Therefore, when the factors of production are properly measured in a competitive equilibrium, A summarizes technical progress, including the degree of efficiency in the utilization of the factors of production (total factor productivity). The exponents a and p represent the relative shares of total output accruing to labor services and to capital services, respectively. When α + β = 1, the production function is the Cobb-Douglas linear production function which exhibits constant returns to scale.

9. Since Solow’s (1967) work, a standard practice in the calculation of A has been, first, to either compute a and p from national accounts as the shares of output accruing to the factors of production, or to estimate a Cobb-Douglas production function with constant returns to scale. In either case, the residual has then been viewed as a proxy for total factor productivity, and has been dubbed the “Solow residual.” The production function has usually been estimated in the first differences of the logarithms of output and measures of labor and capital services because the series are often not cointegrated:

Δ Y t = α Δ ( N t H N t ) + ( 1 - α ) Δ ( Z t H Z t ) + t . ( 2 )

The next section analyzes the statistical properties of the time series used in this paper.

Data issues

10. Output is annual real GDP, and labor services Lt are actual hours worked. Both time series are from INSEE, the French statistical office. Services from the capital stock are proxied using the French stock of net capital from the Annual Macroeconomic Data Base (AMECO), and the series on the weekly operating time of capital in French industry published by the Banque de France.6 The sample period is 1978–1999.

11. Total economy net capital stock services are obtained as follows: the business sector net capital stock ZB, t is removed from the total economy net capital stock ZTt, and then it is added back once it has been adjusted by the intensity in the use of capital in industry. Formally,

Z t = Z t T - λ Z t B + λ Z t B H z t , ( 3 )

where λ is the weight given to the adjustment, i.e., when λ = 1, the adjustment of the total net capital stock assumes that the intensity in the use of capital in the business sector is exactly the same as in industry. Annex 1 displays a sensitivity analysis to gauge the importance of this assumption. It shows that results are not much altered even assuming that only one-tenth of the net capital stock in the business sector is subject to the same intensity in the use of capital as industry.

12. Tests for stationarity and cointegration suggest that a first difference specification is preferable for the purpose of estimating the production function. While the levels of all time series are nonstationary, when a constant and a time trend are included in the alternative hypothesis (Table I.1),7 the rates of change of all variables are stationary when the alternative hypothesis includes a constant. The model in the levels of output, labor, and capital services is not properly identified. The cointegration tests reject the null hypothesis of no cointegration at the 95 percent confidence level, and accept that there is one cointegrating vector (Table I.2).8 Residuals are normal, and there is no serial correlation. Full identification of the model with one cointegrating vector requires two common trends (i.e., two weakly exogenous variables). A weak exogeneity test accepts that real GDP and net capital stock services are weakly exogenous. The weak exogeneity of real GDP is difficult to explain. Moreover, the test of exclusion from the cointegration space is accepted for all variables. In order to accept that all variables belong to the cointegration space, there should be two cointegrating vectors, a hypothesis already rejected.9

Table I.1.

France: Elliot, Rothenberg, and Stock Test for Unit Roots1 Statistics for ρ=0

(1978-1999)

article image
Source: Fund staff estimates.

All variables are measured in natural logarithms. Lags are determined according to Schwarz information criterion and checking that the residuals are white noise.

The DFGLSτ has a null of unit root with a constant and a linear trend. The 5 percent critical value is -2.89.

The DFGLSτ has a null of unit root with a constant. The 5 percent critical value is -1.95.

Table I.2.

France: The Johansen-Juselius Maximum Likelihood Test for Cointegration

(1978-1999)

article image
Source: Fund staff estimates. The models include a drift term in the variables but not in the cointegration space.

Column r refers to the number of cointegrated vectors.

The λ max and the trace statistics critical values are corrected for small samples using Cheung and Lai (1993).

This is a test of long-run exclusion of the relevant variable from the cointegration space. It is distributed as a chi square variable with r degrees of freedom.

This is a test of weak exogeneity of the relevant variable. It is distributed as a chi square with r degrees of freedom.

It is a multivariate version of the Shenton-Bowman test for normality of individual series.

The LM are Lagrange multiplier tests. The p values are between parentheses.

The econometric estimation

13. The model estimated in the first differences of the logarithm of the series is:

Δ Y t = Δ A t + α Δ L t + β Δ K t + t . ( 4 )

14. Total factor productivity growth (i.e., the unobserved variable ΔAt) is modeled as an autoregressive process of order one.10 This model choice implies that shocks to total factor productivity growth will not have permanent effects, although they could be persistent. Formally, and with ρ < 1:

Δ A t = ρ Δ A t - 1 + v t . ( 5 )

15. Equations (4) and (5) are put in state-space form, and the model is estimated using the maximum likelihood estimator based on the prediction error decomposition generated by the Kalman filter. As the model is just identified, the maximum likelihood estimator provides the same results as instrumental variables (Hamilton, 1994), the standard approach to simultaneity in non-cointegrated models. The simultaneity concern is further mitigated because it is unlikely that current output shocks influence current investment in such a way that both current output and the current capital stock are simultaneously affected.

16. Estimates of the model with capital services taking into account the operating time of capital yield results consistent with constant returns to scale technology and output elasticities of capital and labor in line with factor shares. In the unrestricted model (model 1), these elasticities are about 0.8 and 0.3, respectively (Table I.3), and their sum is not statistically different from one.11 The autoregressive coefficient of total factor productivity growth is 0.91, and is highly statistically significant, suggesting persistence in total factor productivity growth. When restrictions are imposed (model 2), the coefficient on labor falls to about 0.7. Moreover, a likelihood ratio test shows that the model estimated with the restriction that the parameters sum to one (model 2) is not statistically different from the unrestricted model 1.

Table I.3.

France: Parameter Estimates of the Cobb-Douglas Production Function with TFP as a Latent Variable

(1978-1999)

article image
Source: Fund staff estimates.

The Kolmogorov-Smimov statistic is 0.31 at the 10 percent level.

The sum of the coefficients in the Cobb-Douglas production function is restricted to one.

Chow test using a dummy variable equal to one from 1992 onward and zero otherwise distributed as an F statistic with 3,14 degrees of freedom. The 95 percent critical value is 3.34.

Chow test using a dummy variable equal to one until 1991 and zero otherwise distributed as an F statistic with 3,14 degrees of freedom. The 95 percent critical value is 3.34.

The value of the likelihood ratio test that the unrestricted and restricted models are equal is 2.71 at the90 percent confidence level.

17. The level of the residuals is white noise although the square of the residuals is not.12 Chow tests for the stability of the coefficients in the unrestricted model indicate that the parameters are stable over the sample period. Model 2 is thus the preferred model, and henceforth we shall refer to it unless otherwise stated.

18. These results confirm Lucas’ (1970) insight and subsequent findings in the literature on the importance of taking into account variations in the intensity of capital stock utilization; they contrast sharply with estimates in which capital services are measured by the capital stock only. In the latter case, the unrestricted production function estimation (model I) yields labor and capital shares of about 0.9 and 1, respectively, which are clearly excessive. As in Mankiw, Romer, and Weil’s (1992) paper, unadjusted capital services result in an elasticity of capital services much higher than what is implied by the share of capital in national accounts, and the autoregressive coefficient describing total factor productivity growth is not statistically different from zero.13 In this model, total factor productivity growth ranges between 0 and 0.2 percent per annum, which is inconsistent with most observers’ view on total factor productivity developments in France during the sample period (e.g., Doisy, 2002).14

Estimated total factor productivity

19. Total factor productivity growth (as measured by the Solow residual) is higher when the net stock of capital is adjusted by the intensity in its use than when it is left unadjusted. Total factor productivity growth has fallen from about 1.7/1.6 percent per annum at the beginning of the 1980s to about 0.5 percent per annum in 1999.15 When compared with the adjusted Solow residual, estimated total factor productivity growth is clearly free from cyclical components (Figure I.4). This suggests that net capital stock measures understate excess capacity, generating unrealistically high input shares and, consequently, unrealistically low total factor productivity growth. As a result, unobserved input movements such as changes in the intensity in the use of capital are bound to be interpreted as changes in total factor productivity growth.16 These results accord well with Finn (1995), Shapiro (1996), Baxter and Farr (2001), Chen (1997), and others.

Figure I.4.
Figure I.4.

France: TFP Growth: Estimates and Adjusted Solow Residual

(Annual Percent Change)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE; Bank of France: and Fund staff calculations.

20. Given that total factor productivity growth has been estimated as a latent variable, it is desirable to assess its plausibility further by relating it, as well as the Solow residual (unadjusted and adjusted), to other work in the area. First, it seems that the intensity of use of the net capital stock can account for most of the observed cyclicality of total factor productivity growth, without having to make reference to increasing returns to scale in production.17 Second, a regression of the unadjusted Solow residual on the intensity in the use of capital measure transforms the residual in white noise.18 Stressing this point, the correlation between output growth and the unadjusted Solow residual is 77 percent; it drops to 48 percent when the Solow residual is adjusted. Instead, the correlation between GDP growth and estimated total factor productivity growth is insignificant.

21. The volatility of the adjusted Solow residual is 1.1 while the volatility of the estimated total factor productivity growth is about half of that. Such a reduction in volatility compares with reductions of between 15 to 23 percent for the industrial sector alone reported for Canada and the United States by Baxter and Farr (2001) using various proxies for the intensity in the use of the capital stock.

22. A final comparison of estimated total factor productivity growth is with Bernanke and Giirkaynak’s (2001) results. The authors have shown that a constant, national savings, and labor force growth explain 48 percent of total factor productivity growth in their crosscountry growth-accounting exercise comprising the sample period 1980-1995. Similarly, 51 percent of the estimated French total factor productivity growth is explained by national savings and hours worked.19 Growth of the labor force is, instead, not statistically significant.

C. Trend Growth Calculation

23. The trend growth rate for France is calculated as follows:

Y t ¯ = N t P t ¯ ( 1 - Nairu t ) α K ¯ t 1 - α A ¯ t , ( 6 )

where bars over variables represent trends, and all variables are in annual growth rates. Yt is natural trend growth, Nt is the population of working age, Pt is trend in the participation rate, Kt is trend growth in capital stock services, and Āt, is trend in total factor productivity growth. The calculation of French trend growth is done using constant returns to scale because, as stated above, the hypothesis that α + β = 1 cannot be rejected.

24. The calculation of trend output and trend output growth assumes that all factors of production are used at their natural level. As indicated above, the correction of the net capital stock by the intensity in its use removes most of the cyclicality of total factor productivity. It is to be expected, however, that there is still a relevant difference between actual and potential capital stock services, and actual and potential labor effort. For instance, the hours worked used in the estimation have been affected by changes in the rate of labor force participation, changes in the age structure of the population or in the labor force growth rate, and changes in patterns of shift work and part-time work, possibly both as a result of preference changes as well as policy changes. It is therefore necessary to assess the natural level of this factor of production, and this implies determining the trends of the participation rate, and the unemployment rate.

25. The approach taken here is to calculate time series trends using the ideal band-pass filter developed by Ouliaris (2001).20 The filter only requires to take a view on the business cycle duration range. This duration range is defined for France as comprising between two and seven years, which is consistent with the analysis of French business cycle characteristics in Nadal-De Simone (2002) using Harding and Pagan’s (2002) methodology. This filtering procedure is applied to the capital stock services, to estimated total factor productivity, and to the labor force participation rate.21

26. Finally, the definition of the potential or natural contribution of employment to output is made consistent with the non-accelerating inflation rate of unemployment (Nairn). The Nairn time series was kindly provided by the European Commission. The Nairn series is the one used by the institution to calculate member countries’ output gaps.22

27. The French trend growth rate averaged 2.5 percent per annum in the period 1979-1999 (Figure I.5). The trend growth rate, however, shows three distinct periods. The first period comprises 1979-1989, during which France experienced an average annual trend growth rate of 2.8 percent. During the second period, which started in 1990, trend growth rates fell and bottomed at 1.8 percent in 1993. Finally, in the rest of the sample period, France recorded an acceleration of trend growth to an average annual rate of 2.1 percent.

Figure I.5.
Figure I.5.

France: Growth and Trend in French Real GDP

(Annual Percent Change)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE; Bulk of France, and Fund staff calculations.

28. French trend growth clearly increased during the second half of the 1990s. One advantage of the production function approach to trend growth estimation is the possibility of analyzing the macroeconomic relations between short-run departures of inputs growth as well as GDP growth from their trends. Based on the analysis of this chapter, it can be argued that there was indeed a rise in French trend growth in the second half of the 1990s in a context of a persistent decline in total factor productivity growth since the late 1970s. It is true that the rate of decline in total factor productivity decelerated during the second half of the 1990s, but its contribution to French trend growth was nevertheless small.

29. Therefore, the recovery of French trend growth in the second half of the 1990s is to be attributed to increases in the average use of factors of production, as suggested by Doisy (2002). Judging from the analysis of trends in factor inputs, however, it is difficult to ascribe the increase in trend growth to capital accumulation. Although French capital stock growth accelerated in the second half of the 1990s, it was still well below the peak of the 1980s. Instead, there was a clear acceleration in trend growth in the intensity of the use of the capital stock (Figure I.6).23 Similarly, trend growth in employment and hours worked increased since 1993 (Figure I.7), as well as trend growth in the labor force and the trend participation rate (Figure I.8).

Figure I.6.
Figure I.6.

France: Capital Stock Growth and the Work Week of Capital

(Annual Percent Change, Hours per Week)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE; Bank of Fiance; and Fund staff calculations.
Figure I.7.
Figure I.7.

France: Employment and Hours

(Annual Percent Change)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE and Fund staff calculations.
Figure I.8.
Figure I.8.

France: Labor Force Growth and Participation Rale

(Annual Percent Change)

Citation: IMF Staff Country Reports 2003, 335; 10.5089/9781451813548.002.A001

Source: INSEE and Fund staff calculations.

D. Conclusion and Policy Implications

30. This chapter asked whether French trend growth rates increased in the second half of the 1990s. Trend growth was estimated using a Cobb-Douglas production technology, with total factor productivity growth treated as an unobservable autoregressive process of order one. The main novelty was the adjustment of capital services to take into account capital operating time. This resulted in estimates of the production function more aligned with factor shares and total factor productivity growth lost basically all its cyclical components. The use of adjusted capital services made the estimation of total factor productivity growth more robust.

31. The main conclusion is that French trend growth indeed increased during the second half of the 1990s to an average annual rate of 2.1 percent, from 1.8 percent in 1993. This was not due to a recovery of total factor productivity growth, however, which remained at its lowest level since the late 1970s. The recovery of French trend growth seems instead due mostly to an increase in trend employment and trend hours worked, and in a minor scale to a deepening of capital made possible via investment. The increase in the intensity in the use of capital was associated with a rising trend in the labor force participation rate, and in a small part with changes in labor organization that reduced the cost of shift work and continuous work (although the full impact of the introduction of the 35-hour week is outside the sample period used in this study). A gradual move in the early 1990s toward policies intended to increase labor market flexibility facilitated the process. Social security contributions were lowered first for part-time employees and subsequently for minimum-wage workers, a reduction that was gradually extended up the pay-scale in the context of the reduction of maximum workweek.

32. Looking forward, a key policy question is whether the upward change in French trend growth in the late 1990s will be sustained. The question takes a particular relevance because the sample period used in this study does not include developments that have the potential to affect trend growth either negatively or positively. An illustration of policy measures that can offset, at least partially, the observed revival in trend growth is the full implementation of the reduction in the workweek to 35 hours; on the structural front, a major event is the looming negative growth of the labor force expected after 2006. On the other hand, examples of policy changes expected to have a positive effect on growth are: the recent pension reform with its beneficial effect on the labor participation rate; the relaxation of the implementation of the 35-hour workweek for small- and medium-size enterprises and the increased flexibility of overtime rules; further cuts in social security contributions; and active policies to promote business employment. In summary, the sustainability of the revival in French trend growth is contingent on the implementation of policies that further enhance labor market flexibility, increase incentives to participate in the labor force, and promote investment.

Annex I France: Sensitivity of coefficient estimates of a Cobb-Douglas production funding for the French economy to adjustments to the net capital stock by the intensity of its use1

article image
Source: Fund staff estimates PS: Coefficients that are not statistically significant at least at the 90 percent confidence level are shown as zero.

The factor of correction F took the values 1, 0.5 and 0.1. The capital stock series for the whole economy was adjusted consequantly. The sensitivity of total factor productivity growth, the estimated input elasticities as well as the AR(1) coefficient was tested by running the same econometric model with the different meaures of capital services. The table shows that correcting the capital stock to measure better the services it provides to the production process is crucial to obtain elasticities and total factor productivity growth that accord with factual evidence on factor shares. The results are quite robust to the share of the net capital stock adjusted.

The bias and inconsistency due to error in measurement in one regressor is directly proportional to the variance of the measurement error. If all the measurement error were corrected by the adjustment to the capital stock growth rate by using the intensity-of-use measure, the variance in measurement error would be 2.8 in case of full adjustment and 1.8 in case of adjustment by a factor of 0.1.

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1

See France: Selected Issues, IMF Country Report No. 02/249, November 2002.

1

Prepared by Francisco Nadal De Simone.

2

See Guarda (2002) for a recent survey of methods to estimate potential output, Fare et al (1994) for a detailed survey on production frontiers work, and Temple (1999) for a related survey on the empirical research on growth.

3

There are also econometric issues such as simultaneity, and the possible instability of the parameters of the function as policy changes affect consumers’ and firms’ optimal choices.

4

In his 1970 paper, Lucas argued that if empirical estimates of Cobb-Douglas production functions are to be consistent with the lack of factual evidence of diminishing returns to labor, and the absence of countercyclical real wage movements, they have to take into account the fraction of the production period over which capital is used.

5

For an analysis of the decentralized equilibrium of an economy with this type of production function, see Dupaigne (1998, 2002), and for an extension that links intensity in the use of the capital stock to shift work, see Garofalo and Vinci (2000).

6

Given the difficulties involved in directly measuring the operating time of heterogeneous capital equipment, the survey conducted by the Banque de France takes an indirect approach. It computes capital operating time as the product of the number of hours worked per week per employee and the weighted mean of the number of shifts per week. Thus, while the length of the contractual workweek and the organization of labor are the structural determinants of capital operating time, the latter will also reflect the rate of capacity utilization without and with new hiring, which is also calculated by the survey. The rate of capacity utilization without new hiring will proxy changes in the duration of the workweek over the cycle—through overtime and temporary lay-offs—and will affect the measure of capital operating time. The rate of capacity utilization with new hiring—when more or less machines are brought on stream—which does not necessarily affect the duration of the workweek or the organization of labor, will also be reflected in the measure of capital operating time.

7

The unit root test is the augmented Dickey-Fuller test proposed by Elliott, Rothenberg, and Stock (1996). Lags are determined according to Schwarz information criterion, and checking that the residuals are white noise.

8

Confidence levels are corrected for small sample bias (Cheung and Lai, 1993).

9

Mindful of the effect of the low power of currently available unit root tests on cointegration analysis, the long-run elasticities of the Cobb-Douglas production function (i.e., in the levels of the variables) were also estimated using the nonlinear dynamic least squares estimator of Phillips and Loretan (1991). However, long-run factor elasticities had no relationship with values expected from national accounts data.

10

Two other models of total factor productivity growth were estimated. First, the autoregressive process of order one with a constant produced the same results as the ones reported for the autoregressive process of order one without a constant; the constant was statistically insignificant. Second, lag two of the autoregressive process of order two was insignificant.

11

To the extent that the test of a “good” production function estimate is elasticities near labor’s and capital’s income shares, these results are encouraging.

12

The hypothesis that serial correlation in the square of the residuals could be due to business cycle asymmetries by which shocks to the economy affect output differently depending on whether the economy is expanding or contracting was rejected. This remains an issue for future research, however.

13

This finding led Mankiw et al (1992) to consider a variant of the Solow model in which human capital as well as physical capital is accumulated.

14

Bernanke and Gürkaynak (2001) test a Solow model with a proxy for human capital using Summers-Heston database in a cross-country framework, and find that although the coefficient on human capital takes on reasonable values (between 0.3 and 0.4), the coefficient on physical capital becomes unreasonably low, and sometimes even not significantly different from zero.

15

See Everaert and Nadal-De Simone (2003) for an estimation of total factor productivity growth in the French business sector which shows a similar pattern of behavior in the period 1970-2001.

16

The extent of the bias is large if we take the variance of the error in measurement as reflected by the difference in growth rates of the net capital stock unadjusted and adjusted. The variance is 2.8 with full adjustment of the capital stock, and 1.3 with an adjustment factor for the capital stock of only 10 percent of the workweek of capital.

17

For example, while the correlation between changes in capacity utilization (used here as a proxy for the business cycle) and the unadjusted Solow residual is 43 percent, it drops dramatically, and becomes non significant statistically, either in the case of the adjusted Solow residual or estimated total factor productivity growth. Notice that given the sample size, any correlation below 43 percent is not significantly different from zero.

18

The estimated regression is: Unadjusted Solow residualt = 0.004 Workweek of capital,. + rest, with a t-statistic for the slope of 7.71. Residuals are white noise.

19

The estimated regression is: ΔAt = 0.006 + 0.05 Δsavingst - 0.30 Δlabor hourst + rest, with t-statistics 4.79, 3.37, and -4.48, respectively, and R2 = 0.51. Bernanke and Giirkaynak’s (2001) national savings elasticity is similar, 0.07, and their labor force elasticity is -0.50.

20

This filter is not affected by leakage from the zero frequency component of nonstationary series. Importantly for practitioners, in contrast to Baxter and King’s band-pass filter, the filter does not involve the loss of observations at either end of the series, and it is consistent. The standard Hodrick-Prescott filter was not used because it is bound to introduce spurious cycles, and it suffers from end-of-sample bias (Cogley and Nelson, 1995).

21

The application of the filter to estimated total factor productivity growth left the series practically unchanged, as it contained no significant cyclical component.

22

The European Commission calculates the Nairn as a Kalman filter estimate that assumes that the deviation of unemployment from the Nairu is negatively related to the change in wage inflation after controlling for temporary shocks to wage inflation such as the terms of trade. Thus, wage inflation is linked to the cyclical component of unemployment plus other exogenous or predetermined variables using a Phillips curve relationship.

23

Everaert and Nadal-De Simone (2003) argue that the intensity in the use of capital also had a major role in the increase in trend growth in the business sector during the second half of the 1990s.

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France: Selected Issues
Author:
International Monetary Fund
  • Figure I.1.

    France: Total Employment and Net Capital Slock

    (Annual Percent Change)

  • Figure I.2.

    France: Business Sector Output per Hour Worked PPP

    (1995 Prices)

  • Figure I.3.

    France; Labor Force Growth and Participation Rate

  • Figure I.4.

    France: TFP Growth: Estimates and Adjusted Solow Residual

    (Annual Percent Change)

  • Figure I.5.

    France: Growth and Trend in French Real GDP

    (Annual Percent Change)

  • Figure I.6.

    France: Capital Stock Growth and the Work Week of Capital

    (Annual Percent Change, Hours per Week)

  • Figure I.7.

    France: Employment and Hours

    (Annual Percent Change)

  • Figure I.8.

    France: Labor Force Growth and Participation Rale

    (Annual Percent Change)