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Challenges for France in the emerging international environment: a dynamic analysis.


France has recently been beset with economic headwinds on many fronts as it tries to restructure its economy. The hallmark of the international economic scene has recently been one of change, with substantial newly emerging economies, the implementation of the European Monetary Union (EMU), the expansion of the European Union (EU), and the advent of other trading blocs. As a result of these events, the economies of individual countries are becoming much more intertwined with and challenged by international markets than in previous years. However, the available economic policy alternatives for an individual country in the EMU are more restricted than prior to the formation of the EMU. For example, the press has recently reported widespread concerns that France and Germany are not complying with and may not be able in the near future to meet EMU economic stabilization requirements. As a result, these countries are putting pressure on the organization to relax the rules of the stability and growth pact, actions that have resulted in frustration on the part of other European countries, particularly smaller ones, that have made spending cuts to bring their budgets in compliance. In addition, domestic pressures have erupted as France attempts economic reforms. (1)

The current budgetary difficulties of both France and Germany are ironic in that these nations were initially among those most insistent on fiscal discipline. While both countries are making efforts at economic reform, domestic resistance to these efforts has been extensive, especially in France. Yet, if these countries are to accomplish their expressed goals of economic stability and growth, it is essential that both France and Germany succeed in implementing reforms that will make their economies more efficient and sensitive to these emerging international market forces. In this article, we concentrate on the French economy and examine elasticity of input demand estimates to see if there is evidence consistent with progress to a structure characterized by greater international market responsiveness. We then examine the implications of these findings for the French economy in the new international environment.

This study uses the technology of an aggregate dynamic translog cost function with inputs of capital, labor, and imports to explore the likely impact of this continuing international integration on the French economy. (2) The use of a dynamic translog function and quarterly data, rather than a static model and annual data, allows one to estimate both short- and long-run direct price elasticities of input demand as well as cross-price elasticities for each input pair. Although a static model is simpler, some scholars have criticized the limitations of that model because it implies adjustment to equilibrium values during each time period covered by a data point. (3)


An aggregate production possibility frontier for the case of one output, Y, and three inputs (labor, capital, and imports) can be expressed in the following form:

(1) F(Y, [X.sub.K], [X.sub.L], [X.sub.M], T) = 0,

where Y is the aggregate output of goods and services, [X.sub.K] is capital, [X.sub.L] is labor, and [X.sub.M] is imports and T represents time-related components, including technological change. (4) If the transformation function has a strictly convex input structure then there exists a unique cost function,

(2) TC = [Florin](Y, [P.sub.K], [P.sub.L], [P.sub.M], T),

where [P.sub.K] is the price of capital, [P.sub.L] is the price of labor, and [P.sub.M] is the price of imports. (5)

The exact cost function (2) can be approximated with the familiar static translog cost function:


where i, j = K, L, and M (Berndt and Christensen, 1973a, 1973b; Christensen, Jorgenson, and Lau, 1973; Guilkey, Lovell, and Sickles, 1983, p. 615). The minimum requirements for the cost function to describe a "well-behaved" technology are that it be (1) linearly homogeneous in input prices, (2) positive and monotonically increasing in input prices and output, and (3) concave in input prices (Brown, Caves, and Christensen, 1979, p. 257; Ryan and Wales, 2000, pp. 254-256). The transformation function is homogeneous of degree [([alpha]).sup.-1], and it follows that the maintained assumption of aggregate constant returns to scale requires [alpha] = 1.

Kohli (1991, p. 14) has argued that a revenue or variable profit function is preferable in the context of international trade because those functions imply that the quantity of domestic inputs and output prices are exogenous, whereas the cost function approach implicitly assumes that the output mix and input prices are exogenous. However, the cost function approach could be considered appropriate in a Keynesian context where input usage is determined by the level of aggregate demand and input prices are rigid or at least exogenously determined. Reported aggregate unemployment figures between 1970 and 1997 in France ranged from a low of 2.6% in 1973 and 1974 to 12.5% in 1994 and 1996 and 12.6% in 1997 (Institut National de la Statistique et des Etudes Economiques, 2000, p. 28). From 1979 onward, reported unemployment rates were at least 6% and trending toward the higher end of the range after 1983. Thus, during nearly all the study period, additional workers were certainly available for employment. The presence of substantial unemployment and extensive government involvement in the economy allow the assumption that both the level of output and input prices are exogenously determined to be plausible.

Given perfect competition in the input and product markets, the parameters of the trans-log cost function can be estimated indirectly by estimating the coefficients of the input cost share equations. These cost share equations, [S.sub.i] = [partial derivative]In [TC/[partial derivative]In] [P.sub.i] (where i = K, L, M), are as follows:

[S.sub.i] = [[beta].sub.i] + [summation over (j)][[gamma].sub.[ij]]ln [P.sub.j] + [[rho].sub.[iY]]ln Y + [[gamma].sub.[it]]ln T, and (j = K, L, M).

Given the restriction of linear homogeneity in factor prices on the cost function and the additional assumption of a homogeneous transformation function, the values of [[rho].sub.[iY]] as well as [[alpha].sub.YY] in the cost equation are 0. As stated above, with the added maintained assumption of constant returns to scale, the value of [[alpha].sub.Y] in the aggregate cost function is restricted to 1 (Kohli 1991, pp. 21-22, 63, 64, 210-212).

To some extent, the assumption of perfect competition may be out of place in the French economy. However, the historical system of extensive government involvement, or dirigisme, in the economy and labor union influence have resulted in some characteristics of perfect competition in the sense that certain prices appear fixed from an individual firm point of view. For example, by the end of 1982, nationalized firms produced 22% of total value added and comprised 31% and 21%, respectively, of industrial investment and employment and extended to such key industries as heavy metals, motor vehicles, electronics, chemicals, telecommunications, and aerospace. Government interventionist measures have included, for example, the use of selective price controls, limits on business firm access to financial credit and foreign exchange, import regulation, and restriction of employee layoffs. While in some respects governmental control of the French economy has lessened in recent years, a substantial amount still persists (Adams, 1989, pp. 99-106; Ardagh, 1982, pp. 32-34; Organisation for Economic Co-operation and Development, 2000, pp. 73-103; Tuppen, 1988, p. 102).

In this article, we extend the above static model by using a dynamic translog cost model, patterned after those developed by Allen and Urga (1999) and Urga (1996, 1999), which allows us to distinguish between short-run and long-run elasticities of demand for the three inputs. We use quarterly data from 1971 to 1997. (6) As Allen and Urga (1999, p. 406) and Anderson and Blundell (1983) have stated, a dynamic autoregressive distributed lag of order 1 (ADL(l, l)) process for the actual input shares [S.sub.t] can be written as:

[S.sub.t] = [AS *.sub.t] + [BS *.sub.[t-1]] + [CS.sub.[t-1]],

where S * denotes the optimal share, there are n inputs, and A, B, and C are ([n - 1] x [n - 1]) matrices of adjustment coefficients. (7) However, to estimate short-run elasticities of demand as well as coefficients reflecting neutral technological change, a translog cost function with both equilibrium and disequilibrium coefficients must be added to the above system of share equations (less one). The dynamic translog function used in this study is given by:


where [TC *.sub.t] is the static cost function described above.

The corresponding input shares system is:

[S.sub.t] = m[S *.sub.t] + (1 - m)[S.sub.[t-1]] + B([S *.sub.[t-1]] - [S.sub.[t-1]]),

where m is a scalar and B is a 3 x 3 matrix of adjustment coefficients. Since the sum of the input shares must be equal to 1, the share equation corresponding to one of the inputs must be eliminated during the estimation process. The cost function and capital and labor input share equations are estimated by using the iterative Zellner-efficient method (Barten, 1969, pp. 24-25; Oberhofer and Kmenta, 1974; Zellner, 1962).

With aggregate data, both prices and quantities could be considered endogenous variables and, as a result, one could argue that it would be more appropriate to use an iterative three-stage least squares procedure with instrumental variables. However, this method presents the problem that the results may be sensitive to the set of instrumental variables employed, and there are no straightforward decision criteria to determine which variables should be included. Moreover, Applebaum (1978, p. 94) compared the I3SLS results of Berndt and Christensen (1973a) with those of his model using the maximum likelihood method and found that they were very similar. (8)


The estimated values of the parameters of the long-run or static cost function as well as the adjustment parameter m are shown in Table 1. (9) While these estimated values are not necessarily of importance in and of themselves, the corresponding calculated mean short- and long-run elasticity estimates are definitely of interest and are given in Table 2. As Table 2 shows, the mean estimates of the long-run direct price elasticities were all negative, consistent with the Law of Demand, while those of the input cross-price elasticities were positive, consistent with a substitutes relationship between each input pair. A bootstrap procedure (Eakin, McMillen, and Buono, 1990) produced the results that all the mean long-run direct and cross-price elasticity estimates were significantly less than or greater than zero, respectively, at least at the 5% level of significance.

Estimates of French Dynamic Translog Cost Function Parameters

Parameter Estimated Value (t values for
 estimated m parameter values)

[a.sub.0] 0.401 (6.868)
[a.sub.T] -0.047 (-2.146)
[a.sub.TT] -0.001 (-0.057)
[[beta].sub.K] 0.841 (3.878)
[[beta].sub.L] 0.026 (5.992)
[[gamma].sub.KK] 0.006 (1.777)
[[gamma].sub.LL] 0.043 (8.756)
[[gamma].sub.RL] 0.013 (4.291)
[[gamma].sub.[KM]] -0.020 (-7.066)
[[gamma].sub.RT] -0.019 (-1.563)
[[gamma].sub.LT] 0.024 (2.174)
M 1.970 (17.025)
[R.sup.2] .994

The signs of the mean estimated short-run elasticities were the same as their respective long-run values, with the exception of [[member of].sub.[LM]] and [[member of].sub.[ML]]. However, only four of the mean short-run elasticity estimates were significantly less than or greater than zero at the 5% level of significance, while [[member of].sub.[KM]] was significantly greater than zero at the 10% level of significance.

The mean estimated long-run direct price elasticities of demand for capital and labor are similar in value to the corresponding elasticity estimates of an earlier paper using a static model (Truett and Truett, 2005). However, the estimated long-run direct price elasticity of demand for imports is much higher (-0.412 compared with -0.075) in absolute value with the current model. The result here is consistent with a much greater responsiveness of the French economy to import prices.

As Table 2 indicates, the estimated long-run direct price elasticities are also higher in absolute value than the corresponding short-run elasticity estimates, as the Le Chatelier principle would require. (10) We again used a bootstrap procedure to produce the results that these differences are statistically significant for each respective input, except for [[member of].sub.KK] The particularly large difference between the long- and short-run elasticity estimates for imports suggests that the estimates of the direct price elasticity of demand for imports in the earlier study with a static model did not fully capture the total (long run) response of imports to their own price changes. It follows that the impact of a change in import prices on the quantity demanded of imports is substantially greater in the long run than in the short run.

French Aggregate Elasticities Estimates

 Mean Direct and Cross-Price Elasticities of Input Demand:
[[member of].sub.[js]] = [[partial derivative] [(ln [X.sub.j])]/
 [partial derivative] [(ln [P.sub.s])]]

Parameter Long Run Short Run Difference
 (Long - Short)

[[member of].sub.[KK]] -0.672 **** -0.646 **** -0.026
[[member of].sub.[LL]] -0.426 **** -0.336 **** -0.090 ****
[[member of].sub.[MM]] -0.412 **** -0.026 -0.386 ****
[[member of].sub.[KL]] 0.541 **** 0.577 **** -0.036 ****
[[member of].sub.[LK]] 0.347 **** 0.369 **** -0.022 ****
[[member of].sub.[KM]] 0.131 **** 0.069 * 0.062 ****
[[member of].sub.[MK]] 0.214 **** 0.112 0.102 *
[[member of].sub.[LM]] 0.078 **** -0.033 0.111 ****
[[member of].sub.[ML]] 0.198 ** -0.086 0.284 **

*. **, and ****Significantly less than or greater than zero at the 10%,
5%, and 0.5% levels of significance.

As stated above, the mean long-run cross-price elasticity of demand estimates for the various input pairs, especially for capital and labor, are consistent with the hypothesis that all the inputs are substitutes for one another in the long run. Moreover, the mean long-run cross-price elasticity of demand estimates are statistically significantly greater than the corresponding short-run estimates, with one exception. (11) An intriguing result is that the mean short-run estimates of [[member of].sub.[KL]] and [[member of].sub.[LK]] are greater than the corresponding long-run estimates by a small but statistically significant amount. These violations of the Le Chatelier principle imply that the short-run adjustments are (slightly) larger than the long-run adjustments with respect to the sub-stitutability of capital and labor. One possible explanation for this outcome might be that firms try to adjust quickly to changes in the quantity of labor needed by hiring (or laying off) temporary workers where possible. French labor market regulations tend to make firms more cautious in adding "permanent" workers and make it more difficult for them to reduce the number of those employees. Also, a firm might attempt to lay off workers in the short run but be forced to reemploy them later. Thus, it may make sense, given French labor market restrictions, that the long-run elasticities could be somewhat smaller than those in the short run.

The estimated long-run cross-price elasticities involving a domestic input and imports are all significantly greater than those for the short run, consistent with the Le Chatelier principle. Thus, as would be expected, these results strongly suggest that the demand for imports is more responsive to both own and other input price changes in the long run than in the short run.

It is interesting to note that the mean estimated values of [[member of].sub.[LM]] and [[member of].sub.[ML]]. in the short run are negative, while the long-run estimates are positive. These estimated cross-price elasticities of demand for imports and labor may reflect the situation discussed by Griffin and Gregory (1976, p. 846), with respect to energy and capital. In that article, the authors argued that a complementary relationship might exist between inputs in the short run, while in the long run, they would be substitutes. Here, we see a similar situation with respect to labor and imports, with the short-run (negative) estimates of [[member of].sub.[LM]] and [[member of].sub.[ML]] implying that imports and labor are complements, while the long-run (positive) estimates are consistent with a substitutes relationship. (12)

We also used a bootstrap procedure to ascertain if the estimated elasticity coefficients changed significantly in a statistical sense over the period of study and found that the absolute values of the (long run) direct price elasticities of the domestic inputs as well as that for imports increased significantly between 1970 and 1997. The results with respect to the cross-price elasticity estimates were varied. The estimated values of both [[member of].sub.[KL]] and [[member of].sub.[LK]] significantly between 1970 and 1997. The values of [[member of].sub.[KM]] and [[member of].sub.[MK]] increased between 1970 and 1997, but only the increase in [[member of].sub.[KM]] was statistically significant. However, the estimated values of both [[member of].sub.[LM]] and [[member of].sub.[ML]] increased significantly over this period.

Thus, the results of this last bootstrap procedure are consistent with the hypothesis that the absolute values of all the direct price elasticities increased over the period of study, as did the values of the cross-price elasticities involving a domestic input and imports. On the other hand, the values of [[member of].sub.[KL]] and [[member of].sub.[LK]]. both decreased significantly.

These findings strongly suggest that the quantity demanded of each of the inputs was more responsive to a change in its own price in 1997 than in 1970, consistent with the hypothesis that certain impediments to market adjustments in the French economy have diminished at least to some extent over time. Moreover, similar conclusions can apparently be drawn with respect to the input pairs consisting of a domestic input and imports. However, the finding that both [[member of].sub.[KL]] and [[member of].sub.[LK]] decreased significantly over time raises concerns that there are increasing rigidities in the French economy that inhibit substitution of domestic capital for labor and vice versa. If restrictions to market adjustments are increasing in the domestic input markets, as these results imply, this development will surely make it more difficult for France to compete in the international marketplace and stay within the budgetary and other regulations of the EMU stability pact. Although enacted after the period covered by this study, the country's 35-hour workweek law, imposed in 1999, certainly increased labor market rigidities rather than helped to reduce them. (13) In addition, the international community has observed the recent difficulties the French government has encountered as it tried to implement small reforms in the domestic labor market. (14) Recently, however, France has been reducing the limits placed on businesses by the 35-hour workweek policy, a step toward enhancing domestic market forces. On the other hand, Italy and France recently expressed their opposition to further lowering trade barriers to developing countries who did not reciprocate by opening their markets. (15)


In this article, we used a dynamic aggregate translog cost function and quarterly data to examine the effects of the emerging international markets on the French economy and to highlight the challenges these changes will create. A harbinger of the changes that these developing markets will bring are the price elasticities of demand for inputs, especially those for imported inputs, and we estimate both the long- and the short-run direct and cross-price elasticities of demand for French inputs. All the long-run direct price elasticity estimates were negative, consistent with the Law of Demand. The long-run cross-price elasticity estimates in this study are consistent with the hypothesis that all the inputs (domestic capital and labor and imports) are substitutes for one another. Moreover, all the mean long-run direct and cross-price elasticity estimates were significantly less than or greater than zero, respectively, at the 5% level of significance. In addition, the estimated long-run direct price elasticities for each input and, with three exceptions, the estimated long-run cross-price elasticities between each input pair increased significantly over the period of study. One exception is the increase in the estimated value of [[member of].sub.[MK]], which was not statistically significant.

The estimates of the long-run direct and cross-price elasticities in this study were similar to those of an earlier effort using a static model. However, the estimates of the long-run direct price elasticity of demand for imports were higher in absolute value with the dynamic model, as were the estimates of the cross-price elasticity of demand for a domestic input and imports pair. These results strongly suggest that the French economy is becoming more and more sensitive to changes in import prices. Thus, the continuing integration of the world economy and the newly emerging players in the international economic arena are likely to pose some very substantial challenges for France unless the country continues with the domestic market reforms recently undertaken, particularly during this past year.

Two exceptions to statistically significant increasing elasticity estimates over time involved the estimates of [[member of].sub.[KL]] and [[member of].sub.[LK]], which actually decreased significantly over the period of study. Such decreases are particularly troubling in the new environment of greater internationalization since they suggest increasing rigidities in the markets for domestic inputs, especially with respect to labor. Although enacted after the period covered by this study, the country's 35-hour workweek law increased labor market rigidities rather than helped to reduce them. Recent efforts by the Sarkozy government to enact market reforms appear to be a step in the right direction. However, as noted above, these efforts have been met with a great deal of resistance. Moreover, the government has been reluctant to further reduce international trade barriers for developing countries.

All the short-run elasticity estimates were consistent with the Le Chatelier principle except for the cross-price elasticities involving only capital and labor, [[member of].sub.[KL]] and [[member of].sub.[LK]]. Again, as discussed earlier, these results may point to impediments to adjustments in the markets for the domestic inputs. Thus, firms may try to make adjustments in the short run that are not maintained in the long run because of governmental labor policies.

Finally, it is interesting to note that the short-run cross-price elasticity estimates of [[member of].sub.[LM]] and [[member of].sub.[ML]] were consistent with a complementary relationship between labor and imports, while the long-run elasticity estimates indicated that they are substitutes. These results are similar to those described by Griffin and Gregory (1976) with respect to capital and energy.

Clearly, the findings of this study suggest that the emerging international marketplace will have a larger impact on the French economy in the coming years. President Sarkozy faces many challenges as he tries to introduce more flexibility into the labor market as well as implement other economic reforms. Given France's current substantial unemployment and budget deficit problems and the rules of the EMU stability pact, French policy makers are likely to have their work cut out for them in the near future. Further research using data from this study and extended until perhaps 2015, after the effects of these changes have had some time to be reflected in the French economy, would be an interesting future project.


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EMU: European Monetary Union

EU: European Union

Online Early publication May 18, 2009

doi: 10.1111/j.1465-7287.2009.00170.x


* We very much appreciate the helpful comments and suggestions of Dr. Hamid Beladi, Dr. Wade Martin, and two anonymous referees on earlier drafts of the article. The research on this article was partially supported by a summer research grant from the College of Business at The University of Texas at San Antonio.

L. J. Truett: Professor, Department of Economics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249-0633. Phone (210) 458-5300, Fax (210) 458-5837, E-mail

D. B. Truett: Professor, Department of Economics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249-0633. Phone (210) 458-5313, Fax (210) 458-5837, E-mail

(1.) See, for example, Buck (2002, p. 2), Parker, Bickerton, and Major (2002, p. 4), Parker and Guerrera (2002, p. 1), Parker, Major, and Mallet (2002, p. 4), Rhoads, Mitchener, and Champion (2004, p. All), Rhoads and Sims (2003, pp. A1, A14), Schwammenthal, Echikson, and Sims (2003, p. A8), Sciolino (2006, pp. 1, 8), Shine (2006, p. 37), and Thornhill and Tait (2008, p. 8).

(2.) Many other researchers have recognized the role of imports as a factor of production. In a seminal study, Chenery and Strout (1966, p. 679). argued that "that inflow of external resources ... has become virtually a separable factor of production. ..." For other examples of this approach, see Kohli (1983, 1993), Aw and Roberts (1985), and Burgess, (1974).

(3.) See, for example. Norsworthy and Harper (1981, pp. 178-80), Anderson and Blundell (1983, pp. 1559-1560), and Friesen (1992, pp. 240-241).

(4.) See Kohli (1991, pp. 103-106) for a discussion of using a time index to model technological change.

(5.) See Brown, Caves, and Christensen (1979, pp. 257-258). For a discussion of the duality of production and cost functions, see Shephard (1953).

(6.) It has been suggested by the referees that it would be useful to extend the data set a few more years. However, the authors believe that extending the data set at the present time would not add much value to the paper. We believe that the results with these data are still representative of current input relationships and therefore can inform current policy decisions in France and the eurozone.

(7.) Since the sum of the input shares must be equal to 1, the system of shares is singular unless one share relationship is eliminated.

(8.) The following data were used in estimating the total cost function and the share equations. The price of labor was given by the salaire horaire: ensemble des secteurs marchands (in centimes). The data series used for the price of capital was the government bond yield for France. The price of imports was given by indice de prix (1980 = 100) of importations. The data for nominal output and the indice de prix (1980 = 100) of the gross output were used to calculate the real value of output. Wages paid to labor was given by compte de revenue de I'ensemble des menagesresources: remunerations des salaries. Total profit was calculated as produit interieur brut less (net indirect taxes and wages). Total cost was equal to total wages plus total profit plus importations in current prices, in millions of francs. The data sources, Institut National de la Statistique et des Etudes Economiques, 1998, 2000 and the International Monetary Fund, 1991 and 1998 (interest rate data), are listed in the bibliography.

(9.) With this model, and the elimination of one share equation, it appears not possible to estimate a unique value for each of the [b.sub.[ij]] terms. The regularity conditions were violated at 14 of the early data points (out of 108). Nevertheless, this fact does not preclude translog estimates of the elasticities from being informative. See Wales (1977) and Caves and Christensen (1980) for a discussion of the implications of violations of the second-order conditions.

(10.) The Le Chatelier principle is that long-run elasticities should be greater in absolute value than the corresponding short-run elasticities. See Allen and Urga (1999, pp. 408, 410), Urga (1996, p. 208, 1999, p. 508) for a discussion of this relationship.

(11.) Also, the difference between the mean long- and short-run estimates of [[member of].sub.[MK]] was significantly greater than zero at only the 10% level of significance.

(12.) One example of an industry where these relationships may have occurred is the French automobile industry. In an earlier study (Truett and Truett. 2007), using a static model yielding long-run elasticity estimates, the authors found that labor and imported intermediate goods were substitutes for this industry. However, a review of the quarterly data suggests that labor and imported intermediate goods may be complementary inputs in the short run.

(13.) See, for example, Rossant (2003. p. 58).

(14.) See Sciolino (2006, pp. 1, 8).

(15.) See Gauthier-Villars (2008, p. A9), and Dinmore (2008, p. 2).
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Author:Truett, Lila J.; Truett, Dale B.
Publication:Contemporary Economic Policy
Article Type:Report
Geographic Code:4EUFR
Date:Oct 1, 2009
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