Jens ; Krüger
email: jens.krueger@wiwi.uni-jena.de

Uwe Cantner

Jens J Krüger

Kristina Von Rhein

Knowledge Compensation in the German Automobile Industry by

Keywords: L10 -General &lt, L1 -Market Structure, Firm Strategy, and Market Performance &lt, L -Industrial Organization, L62 -Automobiles|Other Transportation Equipment &lt, L6 -Industry firm survival, patents, innovation, automobile industry, hazard rates JEL classification: L10, L62, O33, C41 firm survival, patents, innovation, automobile industry, hazard rates

In studies looking at firm survival over the industry life cycle knowledge is one of the most important determinants. Different kinds of knowledge, namely post-entry experience, preentry experience, and knowledge acquired by innovative activity positively influence the survival chances. This paper investigates how the kinds of knowledge are able to compensate each other. Therefore, a statistical survival analysis is performed for the German automobile industry which applies an estimation approach that links instrumental variables with the Cox regression. The results highlight that innovative activity is able to compensate for lacking post-entry experience, supporting Schumpeterian creative destruction.

Introduction

Knowledge is an important aspect of economic life, but has received only a crude treatment in scientific economic analyses. This treatment frequently consists of the consideration of knowledge as an accumulable factor of production that contributes in the production function in addition to and just like labor, capital, materials, etc. by shifting the production function over time [START_REF] Griliches | Issues in Assessing the Contribution of Research and Development to Productivity Growth[END_REF]). In the growth models of [START_REF] Romer | Endogenous Technological Change[END_REF] and [START_REF] Aghion | A Model of Growth through Creative Destruction[END_REF] microfoundations are provided that explain the (aggregate) effects of knowledge either by an increasing variety of intermediate products which are used to assemble the final product or by increasing the quality of these intermediate products.

In evolutionary economics knowledge acquired by agents in an cumulative process is conceived as incomplete. There are differences of the accumulated knowledge between the actors of an economy, so that they are heterogeneous. A detailed discussion of the role of knowledge in evolutionary economics can be found in [START_REF] Loasby | Knowledge, Institutions and Evolution in Economics[END_REF]. There it is explored how the limitations of human knowledge create opportunities as well as problems in a modern economy.

In general, knowledge can be divided in knowing that (knowledge of facts, relationships and theories) and knowing how (ability to perform appropriate actions to achieve a desired result). [START_REF] Loasby | Knowledge, Institutions and Evolution in Economics[END_REF] describes the evolution of knowledge as a path-dependent process in which the acquirement of new knowledge depends on the knowledge accumulated before. Furthermore differences in knowledge arise from learning-by-doing in different activities as a result of the division of labor. In the following we restrict the notion knowledge to the knowing-how aspect.

In the present article we deal with this aspect of knowledge as a key determinant of firm survival in the German automobile industry. The life-cycle literature distinguishes between knowledge that is already available in the firm at the time of entry (pre-entry experience), the knowledge that is accumulated during the operation in the market since entry (post-entry experience) and the knowledge that is explicitly associated with innovative activities (innovative experience). In this article we build on the work of [START_REF] Klepper | Entry, Exit, Growth, and Innovation over the Product Life Cycle[END_REF]Klepper ( , 2002a,b) ,b) who uses survival analyses for the investigation of the life cycle of various U.S. industries, including the automobile industry. We apply this approach and assess the role of knowledge over the life cycle of the German automobile industry in the period 1886 to 1939. Our earlier results reported in 3 [START_REF] Cantner | Firm Survival in the German Automobile Industry[END_REF][START_REF] Cantner | Knowledge and Creative Destruction over the Industry Life Cycle: The Case of the German Automobile Industry[END_REF] show that each of the three types of knowledge has an independent effect on firm survival, even if all are included in the statistical analyses simultaneously.

To extend these results, the specific focus of this article is an investigation of whether and to which extent the three forms of know-how are able to compensate each other. In particular, we are interested in assessing whether an early entry in the industry which is associated with relatively more opportunities to accumulate post-entry experience is able to compensate for lacking pre-entry experience and likewise whether innovative experience since entry is able to compensate for lacking pre-or post-entry experience, respectively. Analyses of this type also appear in [START_REF] Klepper | Industry Shakeouts and Technological Change[END_REF] as part of their evaluation of the empirical validity of different theoretical explanations for industry shakeouts.

Following these introductory remarks we treat the three forms of compensation (pre-entry versus post-entry experience, pre-entry experience versus innovative experience and postentry experience versus innovative experience) in the next three sections. A particularly illuminating interpretation in terms of Schumpeterian creative destruction is associated with the compensation of lacking post-entry experience as a result of late entry into the industry by innovative experience since entry. Section 5 concludes. Two appendices deal with the data sources, the definition of the variables and the solution to the simultaneity problem that arises in the econometric analysis.

Compensation I: Pre-Entry versus Post-Entry Experience

Starting with the compensation of pre-entry and post-entry experience we divide the firms of our sample into four disjoint groups. It is assumed that pre-entry experience exists if a firm is either an experienced entrepreneur, a spinoff or a diversifying firm. Post-entry experience is assumed to be associated with the time of entry as quantified by the division of the firms into four entry cohorts. Firms that entered in the first (from 1886 to 1901) or second entry cohorts (from 1902 to 1906) are classified as early entrants and firms that entered in the third (from 1907 to 1922) or forth cohorts (from 1923 to 1939) are classified as late entrants. Based on that we divide our sample of firms into the group of firms that entered early and are endowed with pre-entry experience (early experienced firms), the group of firms that entered late and are endowed with pre-entry experience (late experienced firms), the group of firms that en-F o r P e e r R e v i e w 4 tered early and are not endowed with pre-entry experience (early inexperienced firms) and finally the group of firms that entered late and are not endowed with pre-entry experience (late inexperienced firms). Appendix A contains the relevant information about the data sources and the definition of the indicators for pre-entry and post-entry experience, as well as the indicator of innovative experience that will be required further below. This classification into early and late as well as experienced and inexperienced firms is typically used in a statistical survival analyses to assess the impact of the different knowledge types on the survival rate or the exit hazard of the firms. The methods applied there consist of the nonparametric Kaplan-Meier estimator of survivor curves [START_REF] Kaplan | Nonparametric Estimation from Incomplete Observations[END_REF]) and the semiparametric Cox regression for the hazard rate [START_REF] Cox | Regression Models and Life Tables[END_REF]). Both methods are able to take account for the right censored nature of the data. Since space considerations prevent a detailed discussion of these methods, we refer the interested reader to [START_REF] Kiefer | Economic Duration Data and Hazard Functions[END_REF] or [START_REF] Lancaster | The Econometric Analysis of Transition Data[END_REF] for more general treatments of methods for survival analysis and references to economic applications. More exact statements about the compensation of pre-entry and post-entry experience can be gained from an application of the Cox regression. In this method, the hazard rate of firm i out of a sample of n firms that survives for at least i t years

n i t h t h i i i ,..., 1 , ) exp( ) ( ) ( 0 = ⋅ = β x can be divided into the baseline hazard rate ) ( 0 i t h
depending exclusively on the duration of survival and a second part depending on the values of the explanatory variables for firm i, contained in the row vector i x , mediated by the exponential function. The method of partial maximum likelihood estimation allows to estimate the parameters in the vector β without requiring to estimate the baseline hazard rate which gives the whole procedure a distinct semiparametric flavor (see again [START_REF] Kiefer | Economic Duration Data and Hazard Functions[END_REF] or [START_REF] Lancaster | The Econometric Analysis of Transition Data[END_REF] for the details). In the present case the vector i x contains the three dummy variables indicating the affiliation to the groups of the early experienced, late experienced and late inexperienced firms, respectively. Since the four group classification of the firms is exhaustive, one category has to be omitted from the regressions. Here, this omitted category is the group of the early inexperienced firms so that the parameter estimates represent the differences of the hazard rates of the other groups relative to that reference group. All three possibilities to divide the firms in the four entry cohorts into early and late entrants are explored and the results for the Cox regressions are shown in the columns of table 1. Accordingly, in model (A) the firms are divided between the first and the second entry cohorts, so that the firms of the first cohort are considered as the early entrants and the firms of the second, third and forth cohorts are considered as the late entrants. Analogously, in model (B) the division is between the second and the third entry cohorts (as in figure 1) and in model (C) it is between the third and the forth entry cohorts.

F

Considering the first two rows of the table which show the parameter estimates for the experienced firms, we observe that all parameter estimates have a negative sign. The parameter estimates for the group of early experienced firms are largest in absolute magnitude and statistically different from zero (as is evident from the p-values in parentheses below the parameter ). This implies that the early experienced firms have the lowest exit hazards of all groups. This finding holds irrespective of where the division in early and late entrants has been implemented. Opposed to that, the parameter estimates for the late inexperienced firms are consistently positive and significantly different from zero (on 5 percent level or lower), implying the highest exit hazards and the worst survival chances for the firms in this group.

For the group of late experienced firms the reduction of the hazard rate that is associated with negative parameter estimates which are, however, only significant on a 10 percent level in the case of model (A). Accepting this higher error probability, one can state that firms with preentry experience that entered late into the market are faced with a lower exit risk compared to firms of the reference group that entered early but were not endowed with pre-entry experience if earliness means membership in the first entry cohort. In this case pre-entry experience is able to compensate for the disadvantages of late entry. Unfortunately, this form of compensation is only weakly supported by the data because it is found only in the case of model (A)

and there only on a 10 percent level of significance, but not in the case of models (B) and (C).

Further results reported in the table concern the differences of the exit hazards within the group of experienced firms (comparing the parameter estimates in rows ( 1) and ( 2)) and within the group of late entrants (comparing the parameter estimates in rows (2) and ( 3)). The associated results for the t-statistics of the differences of the parameter estimates show that the parameter estimates are significantly different with essentially zero p-values. This confirms our findings in [START_REF] Cantner | Firm Survival in the German Automobile Industry[END_REF] that pre-entry experience and post-entry experience play their own role in reducing the exit hazard. Related findings are reported in Klepper (2002a) for the U.S. automobile industry. The overall fit of the regressions can be judged from the row R 2 and appears to be quite reasonable in all three regressions.

Compensation II: Pre-Entry Experience versus Innovative Experience

We now turn to the investigation of the relation of the pre-entry experience and innovative experience. Innovative experience is assumed to be associated with patenting (see e.g. Griliches (1990)). Specifically, innovative experience is quantified by a dummy variable that is equal to unity if a firm got granted at least one patent since it entered the automobile industry.

Combining this variable with the information about pre-entry experience we can again divide 8 divide the firms of our sample into four exhaustive groups. We are able to distinguish firms that are endowed with pre-entry experience and have been innovative since market entry (experienced innovators), firms that are not endowed with pre-entry experience and have been innovative since market entry (inexperienced innovators), firms that are endowed with preentry experience but have not been innovative since market entry (experienced noninnovators)

and finally firms that are not endowed with pre-entry experience and have not been innovative since market entry (inexperienced noninnovators).

The graphical analysis of the survival chances of these four groups is shown in figure 2 The inference based on the Kaplan-Meier estimates may, however, be flawed since the assessment of the effect of a firms innovative experience since entry on its hazard rate and therefore on its duration of survival may be associated with a simultaneity problem. The reason is that the longer the duration of survival of a firm, the higher is the probability of receiving at least one patent grant (and the higher is also the expected number of patents granted).

Thus, the patent variable is likely to be jointly determined with the duration. This implies that using any information contained in the patent data that refers to the period in which a firm actually operates possibly leads to inconsistent coefficient estimates. In econometrics, methods of instrumental variable estimation (also referred to as two-stage least squares) have been developed in order to achieve consistent estimates in such situations. To solve the simultaneity problem we combine the idea of instrumental variables estimation with the Cox regression and apply the bootstrap for computing correct standard errors (see appendix B for a detailed description of the approach taken). 10 not be affected by the subsequent events. In particular, as instruments are used the dummy variables for the first three entry cohorts, the dummy variables for the type of pre-entry experience, a dummy variable indicating innovative experience prior to market entry (equal to unity if patents are granted for the founder before the firm enters the automobile industry), the number of patents granted before market entry and its square as well as several interactions of the patent variables with the cohort dummies and the dummies for the type of pre-entry experience.

The results show that the parameter estimates for both groups of innovators are negative, irrespective of their pre-entry experience. Although the estimates are only in the case of the experienced innovators statistically significant on 5 percent level, the magnitude of both parameter estimates is quite similar. Thus, with respect to the omitted reference group of the experienced noninnovators, innovating firms generally tend to have systematically better survival chances. This further supports our findings reported in [START_REF] Cantner | Knowledge and Creative Destruction over the Industry Life Cycle: The Case of the German Automobile Industry[END_REF]. As expected, the inexperienced noninnovating firms are faced with the highest exit hazard, even higher than that of the reference group and statistically significant on 5 percent level. Based on these estimates we have to be a little bit cautious with our conclusions regarding the compensation of pre-entry experience by innovative experience. The parameter that is associated with the dummy variable for the inexperienced innovators and that reflects the difference of the hazard rate to the experienced noninnovators has a p-value slightly above 0.1. Given that this parameter estimate is indeed negative, this would imply that inexperienced innovators have a lower exit hazard than experienced noninnovators. In that case, the disadvantages accruing from lacking experience before market entry can be compensated by innovative experience since the time of entry.

In addition to these results the differences within the group of innovating firms (comparing (1) and ( 2)) and the differences within the group of inexperienced firms (comparing (2) and

(3)) are also tested. The reported t-statistics show that the differences within the group of innovating firms are not statistically significant on conventional levels, but the differences within the group of inexperienced firms are. Thus, for innovating firms the existence of experience before market entry or the lack of that form of knowledge does not make a difference regarding their exit hazards. This may be explained to some extent by the depreciation of preentry experience (analogous to [START_REF] Carroll | The Fates of de novo and de alio Producers in the American Automobile Industry 1885-1981[END_REF]) and further supports the assertion that innovative experience can compensate for lacking pre-entry experience. In contrast, for the

Compensation III: Post-Entry Experience versus Innovative Experience

The final compensation relationship we want to investigate is that between post-entry experience and innovative experience since market entry. Therefore, we again construct four groups of firms: firms that entered early and were innovative since entry (early innovators), firms that entered late and were innovative since entry (late innovators), firms that entered early but were not innovative since entry (early noninnovators) and finally firms that entered late and were not innovative since entry (late noninnovators). Again, the three different possibilities to define early and late entry provided by the four cohorts are explored. Especially the statistically significant difference between the survivor curves of the late innovators and the early noninnovators opens up a very appealing economic interpretation. This difference shows that firms that are faced with the disadvantage of being late in the market but are innovative once entered have better survival chances than firms that have the advantage of entering early but are not innovative since their entry. Thus, the disadvantages of late entry can be compensated by innovative experience which implies that young innovative firms tend to replace old, but noninnovative firms. This pattern resembles exactly the process that [START_REF] Schumpeter | Capitalism, Socialism, and Democracy[END_REF] had in mind when he coined the notion of "creative destruction", which he described as revolutionizing "the economic structure from within, incessantly destroying the old one, incessantly creating a new one" (Schumpeter 1942, p. 83; emphasis in the original).

A possible source of bias that may render the Kaplan-Meier estimates erroneous is the simultaneity problem already discussed at some length in the previous section. To safeguard against this possibility, we again apply the instrumental variable Cox regression to this form of compensation. The set of instrumental variables is the same as that used in the previous section.

Table 3 shows the corresponding results for three regressions with the three alternative divisions of the firms into early and late entrants. In model (E) only the firms of the first entry cohort are considered as early entrants, whereas in model (F) the firms of the first two cohorts and in model (G) the firms of the first three cohorts are considered as early entrants. It is important to note first that all parameter estimates are significantly different from zero, the sole exception being the parameter estimate pertaining to the late noninnovators in model (E). Recall that the parameter estimates in rows ( 1), ( 2) and (3) here again represent the deviations from the hazard rate of the omitted reference group of the early noninnovators. The results confirm that innovating firms have consistently lower exit hazards than noninnovating firms, irrespective of their time of entry. Among the noninnovating firms, those classified as late noninnovators have higher exit hazards than the reference group of the early noninnovators (this finding, however, is not significant in the case of model (E)). Late innovators have substantially better survival chances compared to late noninnovators, as the respective tstatistics for the coefficient difference (2) -(3) show. The hazard rates for the early innovators are slightly lower than that of the late innovators, but this difference is not statistically significant as the respective t-statistics for (1) -( 2) show. These findings parallel the analogous results of Klepper and Simons (2005, table 4) for the U.S. automobile industry regarding sign as well as significance and actually roughly resemble the magnitude of the parameter estimates.

F

Most important is the significantly negative parameter estimate for the late innovators showing that firms that entered late but are innovative since then are faced with lower exit hazards compared to the reference group of the early noninnovators. The finding that innovative experience is able to compensate for the disadvantages of late entry supports the conclusions from the Kaplan-Meier estimates. Moreover, this compensation consistently holds across all definitions of late and early entrants with respect to statistical significance and is also of considerable magnitude. The hazard rate of late innovators is about 78 to 89 percent lower than that of the early noninnovators. All this strongly suggests that the force of Schumpeterian creative destruction appears to be a very robust and quantitatively important finding in the German automobile industry.

Summary and Conclusion

Summarizing the findings discussed above, it can be concluded that firms with pre-entry experience tend to be better off than inexperienced firms, that early entrants tend to be better off than late entrants and that innovative firms (with at least one patent since entry) tend to be better off than noninnovative firms, always expressed in terms of survival chances. Moreover, each of the three knowledge components has a separate effect on the exit hazard as found by [START_REF] Cantner | Knowledge and Creative Destruction over the Industry Life Cycle: The Case of the German Automobile Industry[END_REF]. The value added of this article consists of a detailed examination of the possibility that one knowledge component dominates another knowledge component in that it is able to compensate for the lack of the other knowledge component, again expressed in terms of survival chances. These results are not restricted to the German automobile industry;

the already mentioned article of [START_REF] Klepper | Industry Shakeouts and Technological Change[END_REF] reports similar results for several U.S. industries.

Regarding this compensation issue the results give a rather weak indication for the compensation of post-entry knowledge by pre-entry knowledge, a marginally significant indication of compensation of pre-entry knowledge by innovative experience and a strongly significant indication of compensation of post-entry knowledge by innovative experience. Thus, the relation of the three knowledge components satisfies transitivity with innovative knowledge weakly dominating pre-entry knowledge and pre-entry knowledge weakly dominating postentry knowledge. Furthermore, the results reported above establish that knowledge accumulated by innovative experience is able to compensate for lacking pre-entry and post-entry experience. This gives rise to the conclusion that knowledge accumulated by innovative experience is the single most important type of knowledge for long-run firm survival. This finding is so important because the decision to innovate can be made by the firm itself, whereas pre-entry experience and time of entry are fixed once a firm enters the market. So firms are able to improve their survival chances by engaging in innovative experience, but they can not influence their pre-entry experience or their time of entry. Thus, the survival chances of firms are not fixed at the time of entry because of their founding characteristics, instead they can be actively influenced by their decision about innovative experience. This is another lesson taught by Schumpeter and his successors.

Appendix A: Data Sources and Variable Definitions

The basis of the statistical analyses performed in this paper is a data set of German firms which produce automobiles during the period 1886 to 1939,2 their experience before they entered into the market and the patents they hold. The data set is the same as used in [START_REF] Cantner | Knowledge and Creative Destruction over the Industry Life Cycle: The Case of the German Automobile Industry[END_REF]. We have collected data only for automobile manufacturing firms, excluding their suppliers and trucks producers. The data we gathered pertain to the year of entry (start of the automobile production), the year of exit (due to the stop of the automobile production, mergers or acquisitions). Relevant for the survival analysis is the number of years a firm was actually producing automobiles and not the number of years in which the firm merely existed. We further collected data regarding the type of entry (explained below).

The data are assembled from a multitude of different sources, such as yearbooks, historical and statistical journals and books about veteran cars. The most important sources are [START_REF] Doyle | The World's Automobiles 1862-1962[END_REF], [START_REF] Flik | Von Ford lernen?[END_REF], [START_REF] Köhler | Deutsche Personenwagenfabrikate zwischen 1886 und 1965[END_REF], [START_REF] Kubisch | Deutsche Automarken von A-Z[END_REF], [START_REF] Oswald | Deutsche Autos 1920-1945[END_REF]), Schrader (2002[START_REF] Von Fersen | Autos in Deutschland 1920 -1939, eine Typengeschichte[END_REF][START_REF] Von Fersen | Autos in Deutschland 1885 -1920, eine Typengeschichte[END_REF]) and von [START_REF] Von Seherr-Thoss | Die deutsche Automobilindustrie, eine Dokumentation von 1886 bis heute[END_REF]. From these sources we identified 441 firms that produced automobiles at some time during 1886 to 1939. The data are censored at 1939 after which the German economy became increasingly regulated and adapted to war production. As in [START_REF] Köhler | Deutsche Personenwagenfabrikate zwischen 1886 und 1965[END_REF] The classification of the type of entry is implemented according to Klepper (2002b). He distinguishes experienced firms (firms that diversify into the production of automobiles originating from other industries), experienced entrepreneurs (de novo firms whose founder headed and typically owned a part of another firm before), spinoffs (de novo firms whose founder worked in the automobile industry before) and inexperienced firms. Firms that produced automobiles, were forced to exit and later on produced automobiles again are treated as different firms and are classified as spinoffs when they enter the market a second time.

(2) Post-entry experience

The classification of the entry cohorts is based on Klepper (2002a). He defines the cohorts so that there are at least 15 firms in every cohort which survived for at least 15 years. This procedure results in four entry cohorts, the first with 56 firms ranging from 1886 to 1901, the second with 52 firms from 1902 to 1906, the third with 126 firms from 1907 to 1922 and the fourth with 115 firms from 1923 to 1939. In the fourth cohort there are 11 firms that survived for at least 15 years. Together with the information about the pre-entry experience, a total of 333 observations is available for the survival analysis.

(

3) Innovative experience

The data about a firm's innovative experience are based on the patent grants of these firms.

The search procedure is described in detail by [START_REF] Cantner | Knowledge and Creative Destruction over the Industry Life Cycle: The Case of the German Automobile Industry[END_REF]. Since this procedure was based on the patent documents it is evident that patent grants are used, but recorded in the data set is the year of the application. The reason is that although there is a time lag between the application and the grant (see [START_REF] Griliches | Patent Statistics as Economic Indicators: A Survey[END_REF]), the knowledge represented by the innovation is available for the firm at least since the date of application. Some patents were applied together by two or more automobile firms. These patents were assigned to all applying firms, justified by the argument of [START_REF] Romer | Endogenous Technological Change[END_REF] that the firms can use the associated know-how simultaneously. In the case of mergers and acquisitions, the patents of the merged (respectively acquired) firms were assigned to the new firm. where the prime denotes matrix transposition. This amounts to the calculation of the fitted values of a linear regression of the columns of X on W. Accordingly, since the exogenous regressors are contained in W this operation does not affect the columns of the exogenous regressors but expresses the endogenous regressors as optimal (in the least squares sense) linear combinations of the variables in W. Since all variables in W are predetermined by assumption, the variables in the resulting matrix X ˆ are exogenous as well by the properties of orthogonal projections (see Davidson and MacKinnon (2003, pp. 57ff.) for more on the geometry of orthogonal projections). The matrix X of the original regressors is subsequently replaced by X ˆ for the estimation of the Cox regression in the second step.

(

2) Cox Regression

In this second step the semiparametric Cox regression [START_REF] Cox | Regression Models and Life Tables[END_REF]) is executed in order to estimate the parameters β of the hazard rate

) êxp( ) ( ) ( 0 β x i i i t h t h ⋅ =
specified in proportional hazards form, where ) (

0 i t h
denotes the baseline hazard rate that exclusively depends on the duration of firm i, i t , and i x ˆ denotes the ith row of X ˆ, n i ,..., 1 = .

The parameters are estimated by maximizing the so-called partial likelihood function, which allows us to estimate β independent of the specific functional form of the baseline hazard rate, simultaneously accounting for the effects of censoring. In practice, numerical and tractability considerations lead to the maximization of the log of the partial likelihood function. The ability of the Cox regression to estimate β without requiring the specification of the functional form of the baseline hazard rate underscores the semiparametric character of the procedure.

The resulting estimate is denoted by β ˆ. A brief and illuminating exposition of the reasoning underlying the partial likelihood estimation is given by [START_REF] Kiefer | Economic Duration Data and Hazard Functions[END_REF]. 3

3 A further problem may be suspected in the application of the linear projections of the first stage to dummy variables since the result of the projection operation is unlikely to be a dummy variable itself. However, results reported in Angrist (1999) justify our procedure. Even more forcefully Angrist and Krueger (2001, p. 80) argue that "using a linear regression for the first-stage estimates generates consistent second-stage estimates even with a dummy endogenous variable. Moreover, using a nonlinear first stage to generate fitted values that are plugged directly into the second-stage equation does not generate consistent estimates unless the nonlinear model happens to be exactly right, a result which makes the dangers of misspecification high".

F

  . The survivor curves are again estimated by the Kaplan-Meier estimator. The figure clearly shows that the experienced innovators have by far the best survival chances, whereas the inexperienced noninnovators have the highest exit hazards. The survivor curves of the inexperienced innovators and the experienced noninnovators are rather close and the test of Harrington and Fleming (1982) does not reject the equality of these two survivor curves. Besides this exception all other survivor curves are statistically significantly different from each other.

Figure 2 :

 2 Figure 2: Kaplan-Meier Estimates for Pre-Entry Experience versus Innovative Experience

  is very important to be innovative for achieving improvements of their survival chances.

Figure 3

 3 Figure 3: Kaplan-Meier Estimates for Post-Entry Experience versus Innovative Experience

  we assign 1915 as the year of exit to those firms that exit the market as a cause of World War I. The peak of the number of firms is reached in 1924 with 139 firms. Thereafter the German automobile industry experienced the typical shakeout and the number of firms declined to 26 until the year 1939.

Table 2

 2 Cox Regression for Pre-Entry Experience versus Innovative Experience

	Model (D)

For the instrumental variable estimates of the Cox regression reported in table 2 (model (D)) the set of instruments consists of variables that are fixed at the time of entry and can therefore

Page 13 of 21 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
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Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The history of the German automobile industry started in 1886 with the inventions of Gottlieb Daimler and Karl Benz, who worked independent of each other.

All results reported in this article are based on the sample of the 333 firms for which all required data are available. Mergers and acquisitions are treated as in Klepper (2002a, p. 42). In the cases of mergers the firm with the same name as the new group or the largest firm (if the new group has a new name) is treated as continuing, the others are treated as censored exits.

In the case of acquisitions, the absorbing firm is treated as continuing if it produces automobiles and the acquired firm is treated as a censored exit. If the absorbing firm does not produce automobiles, the acquired firm is treated as continuing.

Appendix B: Cox Regression with Instrumental Variables

Our estimation methodology relies on three basic building blocks. It combines (1) the idea of generalized instrumental variables estimation (GIVE) with (2) the semiparametric Cox regression. Since the standard errors (and therefore t-statistics and p-values) of the regression coefficients obtained from this procedure do not adequately reflect the additional estimation uncertainty that is introduced by the construction of the instrumental variables, corrected standard errors are computed by (3) the design matrix variant of the bootstrap.

(1) Instrumental Variables

In this procedure the endogenous regressors are projected on to the space spanned by the exogenous regressors and the instruments in the first step, which are chosen to assure their uncorrelatedness with the error terms. Considered as instrumental variables are only those variables that represent characteristics of the firms which are fixed once and for all before their entry into the automobile industry. The guiding idea is that such predetermined variables represent information that may have an effect on the duration of survival but are by construction not affected by the duration themselves. Among the data series available, the cohort dummies, the classification of pre-entry experience and the number of patent grants before the recorded time of entry are valid candidates for instrumental variables.

Let n denote the sample size and k the number of explanatory regressors on the right hand side of the regression equation and define X as the n×k matrix of all (exogenous and endogenous) regressors and W as the n×l matrix (with k l ≥ ) containing both exogenous regressors and instruments. Both matrices are assumed to contain a column of ones representing the intercept. Then the linear projection of X on to W is equivalent to the matrix operation

The preceding two steps of our approach will produce consistent estimates of the parameters, but the raw combination of these two methods will result in flawed statistical inference since the regressors used are generated by the projection operation in the first step. To obtain standard errors that are corrected for these biases, the design matrix variant of the bootstrap (alternatively called bootstrapping cases or bootstrapping pairs) is used (see [START_REF] Davison | Bootstrap Methods and Their Application[END_REF] for a general reference on bootstrapping). According to Davison and Hinkley (1997, p. 87) this procedure is also justified in the present case of censored data if the censoring information is included in the process of repeated sample drawing.

The p-values that are reported jointly with the coefficient estimates of the instrumental variables variant of the Cox regression are throughout computed with the aid of the design matrix bootstrap. This approach usually performs well even if some forms of heteroskedasticity are present. The design matrix bootstrap is based on randomly drawn samples (with replacement), each of size n from the rows of the original data ) ,

, where y contains the duration data, i.e. )' ,..


Lukasz Grzybowski
email: lukasz@mushroomski.com.

L41 -Monopolization|Horizontal Anticompetitive Practices < L4 -Antitrust Policy

Keywords: collusion, best-response functions, mobile telephony. JEL Classification: L13, L41, L96

This paper presents a simple method for screening competition in differentiated products oligopoly with a small number of competitors. In many situations, estimation of price elasticities of demand may be impossible due to difficulties in defining demand or missing data on sales. However, even without information on price elasticities, in certain situations it is possible to test for the static non-cooperative Nash-Bertrand equilibrium, which in the case of rejection, may be important screening information for antitrust authorities. The static non-cooperative Nash-Bertrand equilibrium may be rejected when demand is linear and in the estimation of best-response functions, the coefficients on the competitors' prices are statistically greater than 0.5. The application of this method is illustrated by the example of German mobile telephony using monthly data between January 1998 and December 2002.

According to the estimation results, the observed prices in the segment of low-users cannot be the outcome of a static non-cooperative Nash-Bertrand equilibrium.

Introduction

This paper is concerned with competition in the mobile telecommunications industry. A simple method for testing static non-cooperative Nash-Bertrand equilibrium is presented and applied to mobile telecommunications industry in Germany using monthly data between January 1998 and December 2002.

In general, mobile telecommunications industries are oligopolies with a small number of competitors and institutionally regulated entry. Mobile telephony seems to be also characterized by other necessary and important ingredients for collusion to be sustainable (see Rey (2000)).

Firms interact frequently and may react quickly to changes in competitors' prices, i.e. a new tariff may be marketed within a very short period of time, probably even a month. The innovation, which is observed in mobile telecommunications industry, such as the introduction of pre-paid cards, SMS, MMS, etc. can be very quickly imitated by competitors. Furthermore, there are structural links between network operators, because they have to sign bilateral interconnection agreements. In many countries we may also observe symmetry of market shares. However, the asymmetry of shares is not uncommon and network operators may significantly differ in cost structure, which may disturb incentives for collusion. 1 Because of these structural characteristics the mobile telecommunications industry is perceived as an industry in which tacit or explicit collusion may be suspected. 2 Detection of collusion and cartels is one of the critical issues in antitrust and there is an overwhelming number of theoretical and empirical studies on this subject. This paper presents a simple method for testing static non-cooperative Nash-Bertrand equilibrium. It is based on a stylized framework for differentiated products competition with linear demand functions and uses market level data. 3 When there is a change from competition to collusion, the slopes of best-response functions become steeper and the intercepts move towards the origin. The noncooperative Nash-Bertrand best-response functions should not in general be too steep and, in particular, their slopes cannot be greater than 0.5. When firms jointly maximize their profits, in certain situations, best-response functions may have slopes greater than 0.5. 4 Therefore, when in the estimation of best-response functions the coefficients of competitors' prices are statistically greater than 0.5, one may state that the observed prices do not result from the static non-cooperative Nash-Bertrand equilibrium. Importantly, this framework does not require estimation of price elasticities of demand, which in many situations may be impossible due to difficulties in defining demand or missing data on sales. If information on diversion ratios is not available and the estimates of the coefficients on competitors' prices are smaller than 0.5, static non-cooperative Nash-Bertrand equilibrium cannot be rejected. However, if it is possible to estimate demand functions or get information on diversion ratios from elsewhere, a particular market equilibrium could be tested. This method is then an alternative to the estimation of a structural model of demand and supply.

The application of this method is illustrated on the case of mobile telephony in Germany using monthly data between January 1998 and December 2002. According to the estimation results of the best-response functions, the observed prices cannot result from a static non-cooperative Nash-Bertrand equilibrium. 5 The remainder of this paper is organized as follows. Section 2 presents a literature review.

Section 3 introduces the empirical framework. Section 4 provides an overview of the German mobile telephony and presents the data and estimation results. Section 5 contains the conclusions. This paper refers to studies on competition in the mobile telecommunications industry and detection of cartels. There is a large body of literature on estimation of demand for telecommunications services but studies which assess the degree of competition either by estimating structural models of demand and supply or in other ways are rather scarce. For instance, Grzybowski and Pareira (2007) estimate nested logit demand for aggregate data and simulate a merger in mobile telephony in Portugal. [START_REF] Kim | Consumers' Dynamic Switching Decisions in the Cellular Service Industry[END_REF] uses aggregate data on Korean mobile telecommunications industry to estimate a dynamic structural model of switching decisions between tariff plans and network operators. She finds that the magnitude of switching costs varies across networks and that a change in the variety of optional plans and plan characteristics play a role in the consumer switching decision.

F

Recent reviews of economic research on the detection of cartels may be found in [START_REF] Porter | Detecting Collusion[END_REF] and [START_REF] Harrington | Detecting Cartels[END_REF]. In general, collusion may be detected if there are structural breaks in the market data. For instance, sharp changes in the price cannot be typically explained by changes in cost and demand. They are inconsistent with competitive theory but consistent with theories of collusive pricing under imperfect monitoring (see [START_REF] Green | Noncooperative Collusion under Imperfect Price Information[END_REF]).

According to [START_REF] Harrington | Detecting Cartels[END_REF] the empirical methods for cartel detection may be classified as screening and verification methods. Screening methods provide evidence that firms do not behave competitively but do not provide evidence of collusion. Verification methods directly contrast competition and collusion as alternative explanations for the observed behavior of firms. There is a large body of empirical studies of both types. In particular, screening methods were developed and applied for empirical analyses of procurement auctions. These studies commonly estimate reduced form bidding equations by regressing price on cost and demand shifters. Bidding equations for suspected cartel members should be statistically different from bidding equations for non-colluding firms. Afterwards, one may check whether bidding by noncolluding firms is consistent with a competitive model and bidding behavior of colluding firms is consistent with a model of collusion. Examples of such studies are: [START_REF] Porter | Detection of Bid Rigging in Procurement Auctions[END_REF] on the procurement auctions for high-way-paving jobs, [START_REF] Porter | Ohio School Milk Markets: An Analysis of Bidding[END_REF] for school milk, [START_REF] Bajari | Deciding Between Competition and Collusion[END_REF] for seal coating. Many other studies, reviewed in [START_REF] Harrington | Detecting Cartels[END_REF], try to screen industries for the presence of cartels by analyzing the patterns of prices and market shares. In particular, under certain conditions, the variance of price is lower for collusion. [START_REF] Abrantes-Metz | A Variance Screen for Collusion[END_REF] develop a screening method in terms of price variance. Moreover, parallel price movements are commonly perceived as a collusive marker, which, however, may not be true, as illustrated by [START_REF] Buccirossi | Does Parallel Behavior Provide Some Evidence of Collusion?[END_REF].

The literature mentioned above and others suggests that detecting collusion is very difficult.

The empirical methods at hand are data demanding and often limited.

Empirical Model

A differentiated products industry is considered, in which firms strategically choose prices and play static Nash-Bertrand game. The profits of a single product firm j in period t may be written as:

Π jt (p jt , p -jt ) = (p jt -mc jt )D jt (p jt , p -jt ) -F jt , (1)
where p jt represents price, mc jt is marginal cost, D jt (.) is the demand, F jt represents fixed cost of firm j and p -jt is a vector of prices of competitors. 6 The first order condition may be written as:

D jt (p jt , p -jt ) + (p jt -mc jt ) ∂D jt (p jt , p -jt ) ∂p jt = 0. ( 2
)
Demand functions are assumed to be linear:

D jt (p jt , p -jt ) = a jt + J k=1 b jk p kt , (3)
for which

∂D jt (p jt ,p -jt ) ∂p kt = b jk .
For given demand function, the system of FOCs (3) may be written as a system of j Nash-Bertrand best-response functions in the form: In the case of an industry in which some firms collude, the best-response functions for colluding firms may be written as:

p jt = - a jt 2b jj + mc jt 2 - 1 2b jj k =j b jk p kt , (4)
p jt = - a jt 2b jj + mc jt 2 - 1 2b jj k∈cartel (b jk + b kj )p kt - 1 2b jj k cartel b jk p kt + 1 2b jj k∈cartel b kj mc kt , (5)
while the best-responses for non-colluding firms are given by equation ( 4). Once, firms start colluding, their best-response functions become steeper and the intercepts move towards the origin.

The coefficients of the competitors' prices b jk 2b jj in the non-cooperative best-response equation ( 4) represent a diversion ratio divided by 2, which in theory must be smaller than 0.5. 7 For an industry with a small number of competitors it should be possible to estimate a system of bestresponse functions given by ( 4) or ( 5), or a mixture of these two. If the coefficient of the prices of competitors is statistically greater than 0.5, then a static non-cooperative Nash-Bertrand equilibrium may be rejected. Thus, observed prices can be generated by the steeper cooperative best-response functions given by equation ( 5).

Mobile telecommunications services are commonly perceived as horizontally differentiated products. Empirical studies typically model demand for mobile access using discrete choice framework. In this study, a stylized linear differentiated products demand functions are used.

The assumption of the functional form of demand is critical for the validity of the test. It is responsible for the appearance of a 2 in the denominators of equations ( 4) and ( 5), which results in a boundary value for the estimates of coefficients on competitors' prices, based on which competition and collusion may be distinguished. The consequence of the assumption of the functional form of demand on testing for market power in homogenous products framework is discussed by [START_REF] Bulow | A Note on the Effect of Cost Changes on Prices[END_REF]. They show that a monopolist facing a linear demand curve will pass to consumers 50% of cost changes, while in general pass through rates can be higher or lower depending on the shape of the demand curve. The other underlying assumption is that cross-price effects are smaller than own-price effects, which is a common premise in theoretical models. 7 As in [START_REF] Shapiro | Mergers with Differentiated Products[END_REF], diversion ratio from product A to product B is the fraction of sales lost by product A which is captured by product B due to a price increase of product A. It may be also interpreted as the proportion of people buying product A who consider product B as their second choice. Network operators may sell services to consumers directly or indirectly through independent service providers (ISPs). In general an ISP resells airtime on a third party's mobile telecommunications network by providing billing and customer care services under its own brand name.

In Germany network operators can commercially decide whether to sign an ISP agreement. According to the German Telecommunications Act the agreements between network operators and ISPs have to be non-discriminatory and assure fair competition between retailers. Typically, the tariffs offered by ISPs reflect tariffs of the network carriers.

In 2003, there were four network operators -T-Mobile, D2 Vodafone, E-Plus and O2 -and about twelve ISPs. Only O2 did not reach any agreement with ISPs. Out of these firms, only eight had significant market shares -network operators: T-Mobil (29.9%), D2 Vodafone (27.7%), E-Plus (9.3%), O2 (6.3%) and ISPs: Debitel (12.7%), Mobilcom (6.5%), Talkline (3.2%), Drillisch (2.4%). The remaining ISPs accounted for only about 2.0% of subscribers. 9 Be-8 This technology allows data to be transferred at much higher rates in order to satisfy the demands of multimedia applications.

Data

The estimation of best-response functions requires data on firm-specific prices, marginal costs and demand factors, as given by equations ( 4) and ( 5). Such a detailed firm-level information is not available publicly. The Federal Statistical Office (FSO) in Germany provides separate CPI indices for fixed line and mobile telephony. Four different price indices are computed for mobile telecommunications services -three different user profiles: infrequent, average and frequent users, and an aggregate index.

Firm-specific price indices used in this study are computed based on user profile methodology, which is similar to the one used by the FSO (see [START_REF] Beuerlein | New computation of the consumer price index for telecommunications services on base 1995[END_REF]. 10 Tariff information for Germany was collected from the price listings published in telecommunications magazine "Connect" and on the Internet in the time period January 1998 -December 2002. The price indices are computed for a consumer who uses mobile telecommunications services infrequently so that he is interested in purchasing a pre-paid tariff rather than a contract. The number and length of phone calls, as well as distribution of calls among destination networks and time-zones are randomized. Moreover, the simulation accounts for price discrimination between on-net and off-net calls.

The following algorithm is used for the calculation of firm-specific price indices. An infrequent mobile telephony user is assumed to make on average 15 calls per month (uniform distribution from the interval [10,20]). An average length of a call is 2 minutes (Poisson distribution with λ = 20 seconds multiplied by 6). The distribution among destination networks is proportional to the market shares. The peak time is assumed to be the same for all tariffs, between 8am and 8pm on weekdays. The distributions over days and hours of the day are uniform. Then, for the first draw, for all tariffs available on the market in a given month, the expected bill value Low-end prices for mobile services:

The FSO provides also country-level information on potential marginal cost factors, such as the cost of labor, capital and electronic equipment (see Table (1)), which are used as exogenous explanatory variables in the regression of best-response functions. Moreover, the time trend may be a component of the cost function and could be interpreted as technological innovation.

As described in the previous section, two market entries took place in the time period of this analysis. The first one, of O2, took place in November 1998 and the second one, of Quam, in November 2001. Prices of these firms are not used in the regressions but instead, the bestresponse functions are allowed to react to entries through parallel shifts. on the market sufficiently long to provide coverage for the whole country area. Thus, it may be expected that there were no significant changes in the network quality between January 1998 and December 2002. Other important issues are handset subsidies and advertising. Unfortunately, due to lack of data on these factors, they cannot be accounted for in this analysis. Potentially, the improving quality of handsets may show up in the time trend as stimulating demand. On the other hand, firms tend to reduce their subsidies over time, which may have a negative impact on the demand.

A number of empirical studies suggest the presence of network effects in mobile telecommunications industry. The demand for mobile telecommunications services could be stimulated by the number of current users. In particular, consumers may value to subscribe to a larger network more than to a smaller one. Thus, lagged own network market shares are used in the regressions as a proxy for firm-specific network effects. Since network effects are supposed to stimulate demand, they should show up with a positive sign in the regressions of best-response functions. Moreover, if there are high switching costs in mobile telecommunications industry, greater market shares may induce firms to charge higher prices to exploit locked-in consumers.

The information on market shares in terms of subscriptions was provided by the Federal Network Agency.

The best-response prices are regressed on the variables discussed above and the prices of competitors, which are endogenous and require instrumental variables estimation method. The exogenous explanatory variables from the model are used as instrumental variables. Cost factors are commonly used instrumental variables for prices. Entries of O2 and Quam were regulated and may be considered as exogenous. Price index for fixed line services is assumed to be exogenous. Fixed line markets in Germany were liberalized on January 1st, 1998. There has been an increasing number of entries and competition in the national and international markets, in particular. Moreover, lagged penetrations for mobile telecommunications services in Germany and dummies for third and fourth quarters are used as instruments. We also use the average Prices of mobile telecommunications services in France and Germany may follow a common trend due to similarity of cost structures. Then, industry-level price is constructed by weighting the individual prices by market shares. 13 List prices in these periods may be the same for all four network operators but, for instance, in 2003, the share of E-Plus was 14.3% and of O2 only 6.3%. has the same effect on collusive and non-collusive prices. Therefore, in general, it is not possible to distinguish between collusive and non-collusive best-response prices as long as information on own and cross-price elasticities is not available.

Estimation

The network operators T-Mobile, Vodafone and E-plus are numbered by 1,2 and 3, respectively. Since the observed prices of T-Mobile and Vodafone are basically the same, we may substitute p 2t = p 1t in the FOCs. In the case of competition we have a system of FOCs given by equation ( 4). In the case of collusion among all three network operators we use equation ( 5).

When only T-Mobile and Vodafone collude and E-plus maximizes profits non-cooperatively we have a system of equations ( 5) for the first two operators and equation ( 4) for E-plus. 14 Thus, in a general form, we have a following system of three equations to estimate:

         p 1t = α 1 x 1t -β 1 p 3t + ε 1t p 2t = α 2 x 2t -β 2 p 3t + ε 2t p 3t = α 3 x 3t -β 3 p 1t + ε 3t (6)
where x it are the vectors of demand and cost factors and ε it represent normally distributed error terms. 15 The slopes in these three situations take the following values: When demand functions are not estimated and information on diversion ratios is missing, it is not possible to test which equilibrium fits best the data. However, as already discussed, if in the estimation of best-response functions, some slopes on competitors' prices are greater than 0.5, 14 It is assumed that mobile network operators set their prices independently to the prices of fixed-line services.

         β 1 = b 13
In the case of a price increase by one network operators, the second choice would be almost certainly subscription to another network. There are very few consumers who completely give up the usage of mobile telecommunications services. Also the European Commission in a number of decisions has established that mobile telecommunications services cannot be regarded as a substitute to fixed line telephony services.

15 Given that p 2t = p 1t , the first two equations are the same. Nevertheless, both equations are estimated. The estimation results are presented in Table (2) for SURE estimation and in Table (3) for GMM estimation. According to the Hausman J test the exogeneity of the prices of competitors may be rejected. In the regression of prices of T-Mobile and Vodafone on the prices of E-plus, the coefficients are significantly greater than 0.5, which rejects the static non-cooperative Nash-Betrand equilibrium and the case of collusion between T-Mobile and Vodafone only. This may be an important screening information for the German Competition Authority. In fact, these coefficients should be smaller than 1. In all three regressions in Table (3) their equality to values smaller than 1 cannot be rejected.

The regressions show some dependence of the best-response prices on the cost factors: the cost of labor and electronic equipment, in the case of T-Mobile and Vodafone. Pricing by E-plus seems not to be determined by the cost factors. There is even a negative dependence, which is counterintuitive. Greater lagged market share leads to lower current period prices in the case

Conclusions

This paper presents a simple method for testing static non-cooperative Nash-Bertrand equilibrium and illustrates its application to mobile telephony in Germany.

In many situations estimation of price elasticities of demand may be impossible due to difficulties in defining demand or missing data on sales. However, even without information on price elasticities, in certain situations it is possible to test for a static non-cooperative Nash-Bertrand equilibrium.

When there is a change from competition to collusion and demand functions are linear, the slopes of best-response functions become steeper and the intercepts move towards the origin. and, in particular, their slopes cannot be greater than 0.5. Therefore, if in the estimation of bestresponse functions the coefficients on the competitors' prices are statistically greater than 0.5, it may be definitely stated that the observed prices do not result from a static non-cooperative Nash-Bertrand equilibrium. Moreover, when it is possible to estimate demand functions or get information on diversion ratios from elsewhere, a particular equilibrium can be tested. This method is then an alternative to the estimation of a structural model of demand and supply.

The application of this method is illustrated on the example of German mobile telephony

4

  Page

  Telephony in GermanyIn 1992, Telecom Mobilnet and Mannesmann Mobilfunk started to provide mobile telecommunications services in Germany using digital networks. The first one was a subsidiary of state-owned telecommunications incumbent Deutsche Telekom, which was later privatized and transformed into T-Mobile. The second one was a private company, which was later taken over by Vodafone.In 1993 a third license was granted to E-plus, which began to provide mobile telecommunications services one year later. Another license was granted in 1997 to Viag Interkom (later called O2) which started providing mobile telecommunications services in November 1998.In 2000, six companies received licenses to develop UMTS networks: Group 3G (Quam), T-Mobil, Mannesmann-Vodafone, Auditorium, Mobilcom Multimedia and O2. 8 One of the license winners, Quam, entered the market in November 2001 by signing roaming agreements with active network operators. It acquired about 200,000 consumers but subsequently went bankrupt one year later.

  market structure and pricing dependence, it is assumed that only network operators compete with each other.

  Figure (1)).

  Figure 1:

11 11

 11 As can be seen on the Figure (1), prices of T-Mobile and Vodafone did not react to these entries, while E-plus reacted by price decreases. Apart from cost determinants, the regressions should also include demand factors. Demand for mobile telecommunications services may depend on the network quality, i.e. reception quality and coverage. By January 1998 all three network operators: T-Mobile, Vodafone and E-plus were

  telecommunications services in France as an instrument for prices in Germany.12

Figure ( 1

 1 Figure (1) shows that prices of mobile telecommunications services set by T-Mobile and Vodafone are almost identical with correlation of 0.998. Only between January 2002 and April 2002 pricesdiffered by a negligible value. This means that these firms were able to form perfect conjectures about the prices set by the competitor in the next month. They lowered prices exactly in the same month and by the same value. The prices set by E-plus also match perfectly the prices of competitors for most of the time but, in addition, E-plus reacted to entries of O2 and Quam by lowering prices. The prices set by the entrant O2 also do not differ significantly from the prices of competitors. The differences visible in prices of E-plus and O2 in the form of a parallel shift upwards are partly due to differences in on-net and off-net prices and the distribution of calls according to market shares.13 The observed parallelism and the coordination in lowering prices by T-Mobile and Vodafone looks suspicious and may potentially indicate coordination of strategies. However, based on equation (4), one cannot exclude that identical prices result from a static non-cooperative Nash-Bertrand game. We may observe that two networks set identical non-collusive prices when demand factors, marginal costs, and own and cross-price elasticities with the other networks are very similar. T-Mobile and Vodafone have almost identical market shares since the startup of mobile telecommunications industry in Germany, which may be due to similar cost structure. The collusive best response prices given by equation (5) may be similar under the same conditions. Also, lack of reaction of T-Mobile and Vodafone to the entry of O2 and Quam does not allow to distinguish collusive and non-collusive price setting. Entry has no effect on the best-response 12 First, price indices for the network operators in France are computed in an analogous way as for Germany.

  2b 11 +b 12 , β 2 = b 23 2b 22 +b 21 , β 3 = b 31 11 +b 12 ) , β 2 = b 23 2(b 22 +b 21 ) , β 3 = b 31 b 33 only T-Mobile and Vodafone collude; β 1 = b 13 +b 31 2(b 11 +b 12 ) , β 2 = b 23 +b 32 2(b 22 +b 21 ) , β 3 = b 31 +b 13 b 33 all collude.

  of non-cooperative Nash-Bertrand equilibrium and collusion between T-Mobile and Vodafone can be rejected.

  of T-Mobile and Vodafone, but higher for E-plus. The entry of Viag and Quam was basically ignored by T-Mobile and Vodafone, while E-plus reacted with price decreases. Finally, prices of fixed line services are insignificant in the GMM estimation and time trend is significant in the case of T-Mobile and Vodafone.

  The non-cooperative Nash-Bertrand best-response functions should not in general be too steep 13

  using monthly data between January 1998 and December 2002. According to the estimation results, observed prices for the segment of low-users cannot be the outcome of static noncooperative Nash-Bertrand equilibrium. This may be important market screening information for the German Competition Authority.

11 Page 11 of 18 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  function when it does not change own-price elasticity and the cross-price elasticity with the entrant is close to zero, i.e. the diversion ratio is almost zero. Basically, a non-collusive entry

	Submitted Manuscript
	F o r
	P
	e
	e r
	R
	e
	v i e
	w

If the price elasticities may be estimated in a trustable way, the main problem remains lack of information on marginal costs. However, when the determinants of marginal costs are observed, markups may be estimated and a collusive market conduct can be tested against the competitive one (for a literature review and discussion seeBresnahan (1987) andReiss and Wolak (2006)).

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

L40 -General < L4 -Antitrust Policy < L -Industrial Organization< L -Industrial Organization, L96 -Telecommunications < L9 -Industry Studies: Transportation and Utilities < L -Industrial Organization


Christian Pierdzioch
email: c.pierdzioch@mx.uni-saarland.de

Jan-Christoph Rülke

Georg Stadtmann
email: stadtman@whu.edu

Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods, F37 -International Finance Forecasting and Simulation < F3 -International Finance < F -International Economics, G15 -International Financial Markets < G1 -General Financial Markets < G -Financial Economics

Keywords: Ruelke, Jan-Christoph Pierdzioch, Christian C32 -Time-Series Models < C3 -Econometric Okunዊps law, Forecasting, Panel-data model JEL classification: C32, F37, G15 Okun's law, Forecasting, Panel-data model JEL classification: C32, F37, G15 Okun's law, Forecasting, Panel-data model

Introduction. In particular, we now present the results reported by Mitchell and Pierce (2007a) on Page 1.

• We next turn to the data description. Remark 2: It would be appropriate to describe the Consensus economic INC. In other words, why is the panel data reliable?

As a robustness check, we now report in Tables 2 and4 the estimation results we obtained when we used forecasts made in April. In the new Footnote 1, we explain that the results for the other months are not reported, but are available upon request. The results of the robustness checks confirm the results reported in Tables 1 and3. In addition, the results show that the magnitude of the estimated Okun coefficient shows some variation over the year. Below, we summarize some more results based on forecasts made in July.

• We next turn to the econometric methodology and results. I think that the econometric methodology is not sufficiently detailed. Remark 3: The null hypothesis of common constant for all professionals (and for the countries?) is tested but results are not reported. What test is used?

The Hsiao homogeneity test?

Thanks for pointing this out. In the revised version of our paper, we describe the econometric methodology in more detail. Specifically, we now describe on Page 5 that we used an F-test to test for a common constant across all professional forecasters. We present the results of this test in tables in the row entitled "Test statistic: Fixed effects (Fvalue)".

• Remark 4: A model with time fixed effects is estimated but results are not reported. The time stability is however a critical assumption in the model.

Time stability is in fact crucial for our econometric analysis, and we appreciate this comment very much. All tables now include the results of a test on time-fixed effects in the row entitled "Test statistic: Time effects". The results suggest that the time-fixed effects specification is • Remark 5: The results indicate that there is a cross country heterogeneity. Could the authors explain why Okun's coefficient for the UK (Japan) is largest (smallest) in an economic point of view?

Following your suggestions, we have added a discussion of the potential economic forces driving the differences between Okun's coefficients across countries. Our discussion focuses on the role played by differences in labor-market institutions across countries (Page 7). For example, the labor market in the United Kingdom is relatively flexible as compared to the Japanese labor market, and this flexibility may explain why we estimated a large (small) Okun coefficient for the United Kingdom (Japan). Because the magnitude of the estimated Okun coefficient shows some variation over the year (Table 2), we also emphasize that this interpretation should not be stretched too far.

• Remark 6: The linear version of Okun's law is robust but empirical evidence of asymmetries over the business cycle is less clear-cut. I understand the econometric result via gamma but what are the economic explanations of this result?

In the revised version of our paper, we explain on Page 5 that, in economic terms, the coefficient γ renders it possible to trace out how the correlation between the expected rate of change in the unemployment rate and the growth rate of real output differs in times of economic downturns and economic booms.

=

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8206

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8157

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6553

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8407

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9378

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4703

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9465

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Note:t-statistics in parentheses. *** (**, *) denotes significance at the 1 (5, 10) percent level. [START_REF] Knoester | Okun's Law Revisited[END_REF][START_REF] Kaufman | An International Comparison of Okun's Law[END_REF]and 1999[START_REF] Holmes | Okun's Law, Asymmetries, and Jobless Recoveries in the United States: A Markov-Switching Approach[END_REF], Mitchell/Pearce (2007a) have reported evidence of a significant negative correlation between forecasts of changes in the rate of unemployment and forecasts of the growth rate of real output. They also have found that the expected correlation is significantly lower than the realized correlation implied by the data.

We go beyond the study by Mitchell/Pearce (2007a) in two important respects. First, we report empirical results for the G7 countries. Second, we tested whether professional economists' forecasts reflect asymmetries in Okun's law over the business cycle. Evidence of asymmetries has been reported by [START_REF] Lee | The robustness of Okun's law: Evidence from OECD Countries[END_REF], [START_REF] Harris | Testing for Asymmetry in Okun's Law: A Cross-Country Comparison[END_REF], and [START_REF] Holmes | Okun's Law, Asymmetries, and Jobless Recoveries in the United States: A Markov-Switching Approach[END_REF]. We describe our data in Section 2, and our empirical model in

Data Description

We used data from survey studies conducted by the Consensus Economic Inc.

The Consensus Economics Forecast (CEF) survey regularly asks professional forecasters about their projection of several financial and macroeconomic variables, including the unemployment rate and the growth rate of real output. Because professional economists' forecasts of the unemployment rate are only available for the G7 countries, we carried out our empirical analyses for Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States.

The CEF data have at least two advantages as compared to other survey data. First, professional economists who participate in the CEF poll do not only take a stance on the direction of the expected change of a macroeconomic variable. Rather, they also forecast the level of a macroeconomic variable. Second, individual forecasts are published together with the name of the employer of a forecaster, implying that it is relatively easy to evaluate the accuracy of a professional economist's forecast. The accuracy of forecasts is likely to have an effect on the reputation of a forecaster. The survey takes place on a monthly basis. In every survey, the professional economists are asked for their forecasts of a large number of economic variables including the yearly growth rate of real output and the average unemployment rate over the year. This implies that uncertainty in forecasts should by highest in January and lowest in December. For instance, for the United States, the standard deviation of forecasts of the unemployment rate in January is more than four times higher as compared to the standard deviation of forecasts made in December. The forecasts made in January, therefore, should give a conservative answer to the question of whether professional economists' forecasts reflect Okun's law. For this reason, and in order to avoid problems due to overlapping forecast horizons, we focus on the forecasts published in January for the respective year. As a robustness check, however, we shall also report in Section 3 the results we obtained when we used the forecasts published in April. Our baseline empirical model is given by the following version of Okun's law [START_REF] Moosa | A Cross-Country Comparison of Okun's Coefficient[END_REF]):

E t,i [u t+1 ] -u t = α + βE t,i [∆y t+1 ] + t,i , (1)
where α denotes an intercept term, β denotes a slope coefficient, E t,i denotes the forecast of economist i in year t, u t denotes the unemployment rate in year t, ∆y t+1 denotes the growth rate of real output in year t + 1, and t,i denotes a forecaster-specific stochastic disturbance term. Given the empirical support for Okun's law, one would expect α > 0 and β < 0, where β is referred to as the Okun coefficient. A positive value for α can be expected in countries in which the unemployment rate has increased over time. Equation ( 1) is a widely used approximation of Okun's law. This approximation is built on the assumptions that both the natural rate of unemployment and the growth rate of real potential output are constant.

Data on the current unemployment rate, u t , are from Thompson Financial Datastream. 2

Based on realized changes in the unemployment rate and realized growth rates of real output for various countries, the empirical estimates of the Okun coefficient reported by [START_REF] Paldam | How Much Does One Percent of Growth Change the Unemployment Rate? A Study of 17 OECD Countries, 1948 -1985[END_REF], [START_REF] Moosa | A Cross-Country Comparison of Okun's Coefficient[END_REF][START_REF] Freeman | Panel Tests of Okun's Law for Ten Industrial Countries[END_REF] vary roughly between -0.15 and -0.90. 3 If professional economists believe in Okun's law, we should observe that our estimates of the Okun coefficient that are based on expected changes in the unemployment

2 The Mnemonic codes are as follows: Canada (CNOUN015Q), France (FROUN015Q), Germany (BDOUN015Q), Italy (ITOUN015Q), Japan (JPOUN015Q), United Kingdom (UKOUN015Q), United States (USOUN015Q).

3 [START_REF] Okun | Potential GNP: Its Measurement and Significance[END_REF] found a value of β of about -0.30, implying that an increase in the rate of unemployment leads to a more than proportionate change in output. [START_REF] Okun | Potential GNP: Its Measurement and Significance[END_REF] argued that changes in unemployment are associated with changes in labor force participation and capital utilization, which lead to a more than proportional response of output. rate and expected growth rates of real output are of a comparable magnitude.

We estimated Equation (1) as a fixed-effects panel-data model and tested by means of an F-test whether the null hypothesis of a common constant for all participating professional economists cannot be rejected. In case of an insignificant F-test, we used a pooled OLS estimator to estimate Equation (1).

We then proceeded and tested the null hypothesis that the intercept term is constant over time. Because the null hypothesis was rejected for all countries in our sample, we estimated all regressions as a time-fixed effects model. Finally, we tested for asymmetries in Okun's law over the business cycle.

In a recent empirical study, [START_REF] Silvapulle | Asymmetry in Okun's law[END_REF] have analyzed Okun's law using data for the United States and have found evidence in favor of asymmetries. They have reported Okun coefficients of -0.25 and -0.61 with respect to increases and decreases in cyclical output. In order to test whether the CEF forecasts reflect asymmetries, we estimated the following model:

E t,i [u t+1 ] -u t = α + βE t,i [∆y t+1 ] + γI(E t,i [∆y t+1 ])E t,i [∆y t+1 ] + t,i , (2)
where the indicator function I(.) assumes the value one whenever the expected growth rate of real output is below its sample average, and zero otherwise.

In economic terms, the coefficient γ renders it possible to trace out how the correlation between the expected rate of change in the unemployment rate and the growth rate of real output differs in times of economic downturns and economic booms. The magnitude of the Okun coefficient varies considerably across the G7 countries. For example, we estimated the largest (smallest) Okun coefficient of about -0.34 (-0.11) for the United Kingdom (Japan). For Japan this implies that the professional economists expect a fall in the unemployment rate by 0.11 percent if they expect, at the same time, a one percent increase in real output. In his analysis of realized Okun's law for the sample time period [START_REF] Okun | Potential GNP: Its Measurement and Significance[END_REF]-1995[START_REF] Freeman | Panel Tests of Okun's Law for Ten Industrial Countries[END_REF] has found a value of about -0.25 for Japan, which is the lowest out of ten industrialized countries. Also, [START_REF] Moosa | A Cross-Country Comparison of Okun's Coefficient[END_REF] has reported that the value for Japan is the lowest one. He has analyzed the same countries and the same sample period as Freeman, but has extracted the cyclical components of output and the unemployment rate. [START_REF] Moosa | A Cross-Country Comparison of Okun's Coefficient[END_REF] has reported a value of -0.37 for the United Kingdom, which is close to the value -0.34 reported in Table 1. 4 We also used real time data from the Philadelphia Federal Reserve Bank rather than revised data for the unemployment rate. The results, however, are similar to those reported in Table 1 andTable 2. It is tempting to interpret the cross-country heterogeneity in the Okun coefficient in terms of cross-country differences in labor-market structures and institutions. According to [START_REF] Lee | The robustness of Okun's law: Evidence from OECD Countries[END_REF], the relatively small Okun coefficient in the case of Japan can be attributed to substantial institutional rigidity in the Japanese labor market in general and to lifetime job security typical of the Japanese labor market in particular. By the same token, the substantial flexibility of the British labor market may explain the relatively large Okun coefficient of about -0.34 estimated for the United Kingdom. The British labor market is the least regulated one in the European Union [START_REF] Moosa | A Cross-Country Comparison of Okun's Coefficient[END_REF]. The flexibility of the labor market implies that employers can easily reduce (expand) their workforce during an economic downturn (boom). As a result, the correlation between changes in the unemployment rate and the growth rate of real output and, thus, the estimated Okun coefficient is large.

Estimation Results

The results summarized in Table 2 suggest that this labor-market-based interpretation of the cross-country variation of the Okun coefficient should not be stretched too far. The results in Table 2 are based on forecasts made in April. Corroborating the results reported in Table 1, the Okun coefficient has the expected negative sign and is statistically significant in all countries, with Germany being an exception. As compared to the results based on the forecasts made in January, however, the relative magnitude of the coefficients has changed. The Okun coefficient estimated for the United Kingdom is now smaller in absolute terms than the Okun coefficients estimated for Canada, the United States, and France. The smallest Okun coefficient is still the one estimated for Japan. Only the coefficient estimated for Germany is smaller, but this coefficient is not significant.

-Include Table 2 about 3 summarizes the results for the empirical model featuring asymmetries, where the results are based on the forecasts made in January. The Okun coefficient always has the expected negative sign. The coefficient, γ, which captures potential asymmetries, is not significant. Table 4 summarizes the estimation results we obtained when we used the forecasts made in April. Again, the Okun coefficient has the expected negative sign and the coefficient that captures potential asymmetries is not significant. The coefficient γ is significant only in the case of the United States, a result which is in line with the evidence of asymmetries in Okun's law reported by [START_REF] Silvapulle | Asymmetry in Okun's law[END_REF]. However, because the significance of the coefficient depends upon which forecasts (January versus April) we used for estimating the model, the evidence of asymmetries in the case of the United States is not particularly strong.

-Include Tables 3 and4 about here. -

Conclusion

Our results suggest that, for the G7 countries, professional economists' forecasts reflect Okun's law. We found a significant negative relationship between the expected change in unemployment rate and the expected growth rate of real output. While the magnitude of the Okun coefficient shows some variation over the year, the estimated coefficients are significant and largely comparable in size to those found in studies based on realized data. Professional economists, however, do not believe in potential asymmetries of Okun's law over the business cycle. This result may reflect that, while empirical evidence in support of the classic linear version of Okun's law is robust, empirical evidence of asymmetries in Okun's law over the business cycle is less clear-cut and often involves difficult econometric issues concerning the appropriate specification and testing of an empirical model (see, for example, [START_REF] Lee | The robustness of Okun's law: Evidence from OECD Countries[END_REF].

  should have a relatively strong incentive to make "good" rather than strategic forecasts.

  our results suggest that, in the G7 countries, professional economists believe in and, thus, adopt the classic linear version of Okun's law to forecast macroeconomic developments.

  give t-statistics in parentheses. *** (**, *) = significant at the 1 (5, 10) percent level.

  give t-statistics in parentheses. *** (**, *) = significant at the 1 (5, 10) percent level.

  give t-statistics in parentheses. *** (**, *) = significant at the 1 (5, 10) percent level.

  give t-statistics in parentheses. *** (**, *) = significant at the 1 (5, 10) percent level.

Table 1 :

 1 Estimation Results for the Baseline Model (July forecasts)

	Country Canada France Germany Italy Japan UK USA	Method Fixed Effects Fixed Effects Fixed Effects Fixed Effects Fixed Effects Pooled OLS Fixed Effects	α .5844*** .6576*** 1.100*** 3.5641*** .3145*** .5597*** -.7767***	(8.88) (3.21) (4.06) (13.81) (3.97) (10.62) (-16.82)	β -.2011*** -.0932 -.0258 -.2123** -.0710*** -.1845*** -.0746***	(-5.57) (-1.54) (-.39) (-2.37) (-4.72) (-7.29) (-2.94)	Observations (No. of groups) 268 (35) 318 (37) 490 (46) 233 (37) 354 (44) 466 (61) 512 (66)	Test statistic: Time effects (F-value) 54.67*** 25.33*** 133.03*** 97.18*** 17.62*** 74.83*** 490.39***	.8388 .6866 .8362 .9239 .5198 .7798	Goodness of Fit .7040 .3440 .9380 .9761 .1928 R 2

Table 2 :

 2 Estimation Results for the Model Featuring Asymmetries (July forecasts)

	Country Canada France Germany Italy Japan UK USA	Method Fixed Effects Fixed Effects Fixed Effects Fixed Effects Fixed Effects Pooled OLS Fixed Effects	-.7863*** .5439*** α .5807*** .6436*** 1.100*** 3.6060*** .3202***	(-15.94) (9.33) (8.22) (3.12) (4.05) (13.52) (3.86)	-.0755*** -.1821*** β -.2014*** -.0889 -.0256 -.2264** -.0721***	(-2.97) (-7.12) (-5.55) (-1.46) (-.38) (-2.45) (-4.56)	.0106 .0060 γ .0027 .0235 -.0158 .0409 .0042	(.55) (.52) (.15) (.84) (-.37) (.64) (.23)	512 (66) 466 (61) Observations (No. of groups) 268 (35) 318 (37) 490 (46) 233 (37) 354 (44)	486.79*** 71.71*** Test statistic: Time effects (F-value) 51.35*** 25.17*** 127.20*** 81.62*** 16.36***	.7800 .8389 .6874 .8362 .9241 .5199	R 2 = .8107 Goodness of Fit .8032 .3369 .9176 .9763 .1919	.9464 .7730 .8157 .6560 .8406 .9379 .4701	Note:t-statistics in parentheses. *** (**, *) denotes significance at the 1 (5, 10) percent level.

(WSJ) reflect Okun's law. Using semiannual data for the United States covering the sample periods

1 1

 1 The results for the other months are not reported, but are available upon request.

	4
	3 The Empirical Model
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  It is interesting to note that the Okun coefficient we estimated for the United States is somewhat smaller than the coefficients reported in the earlier literature.4 This result is in line with the finding ofMitchell/Pearce (2007a), who have reported that, in the case of the United States, the expected Okun coefficient is lower than the realized value.

	consistent with the magnitude reported by researchers who have analyzed
	the link between realized changes in the unemployment rate and realized
	growth rates of real output. Hence, our estimation results reveal that the
	forecasts made by professional economists for the G7 countries are consistent
	with Okun's law.
	-Include Table 1 about here. -
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	Table 1 summarizes the results for the baseline empirical model without
	asymmetries. All coefficients have the expected sign and are highly sig-
	nificant. The Okun coefficient is negative, and its magnitude is roughly

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Yearly data are used and January is used because uncertainty. What would happen if an other month was used? Have you