Gibrat's Law and Market Selection in the Radio, TV & Telecommunications Equipment Industry

Lotti, Francesca; Santarelli, Enrico; Vivarelli, Marco Working Paper Gibrat's Law and Market Selection in the Radio, TV & Telecommunications Equipment Industry Quaderni - Working Paper DSE, No. 478 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lotti, Francesca; Santarelli, Enrico; Vivarelli, Marco (2003) : Gibrat's Law and Market Selection in the Radio, TV & Telecommunications Equipment Industry, Quaderni - Working Paper DSE, No. 478, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4816 This Version is available at: https://hdl.handle.net/10419/159319 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/ GIBRAT’S LAW AND MARKET SELECTION IN THE RADIO, TV & TELECOMMUNICATIONS EQUIPMENT INDUSTRY* by Francesca Lotti Bank of Italy, Research Department Enrico Santarelli University of Bologna, Department of Economics; and Free University of Bozen/Bolzano, School of Economics and Management Marco Vivarelli Catholic University of Piacenza, Department of Economic and Social Sciences; ILO, Geneva; and IZA, Bonn Abstract According to Gibrat’s Law of Proportionate Effect, the growth rate of a given firm is independent of its size at the beginning of the period examined. In contrast to the previous literature on the subject, this paper seeks to test the Law by taking account of both the entry process and the role of survival/failure in reshaping a given population of firms over time. It does so by focusing on the entire population of firms (including newborn ones) in the Italian Radio, TV & Telecommunications equipment industry and tracking them over seven years. Consistently with the previous literature, it finds that - in general - Gibrat’s Law is to be rejected, since smaller firms tend to grow faster than their larger counterparts. However, the paper’s main finding is that this rejection of Gibrat’s Law may be due to market dynamics and selection. In other words, it is due to the entry process and the presence of transient smaller firms. Indeed, whilst it is found that Gibrat’s Law has to be rejected over a seven-year period during which both incumbent and newborn firms are considered, for both sub-populations of surviving firms a convergence towards Gibrat-like behavior over time can be detected. Thus, market selection “cleans” the original population of firms and the resulting industrial “core” (mature, larger, well-established and most efficient firms) does not seem to depart from a Gibrat-like pattern of growth. JEL codes: L11, L60. Keywords: Gibrat’s Law; manufacturing; industrial dynamics; entry; survival; selection bias. This version: 14 July 2003 Corresponding author: Enrico Santarelli Department of Economics University of Bologna Strada Maggiore, 45 40125 Bologna Italy [email protected] * This paper was presented at the International Workshop on “The Post-entry Performance of Firms: Technology, Growth, and Survival” (Bologna, 22 and 23 November 2002), and the 30th Annual E.A.R.I.E. Conference (Helsinki, 24-26 August 2003). We thank the participants, and in particular Vivek Ghosal, Josè Mata, Alessandro Sembenelli, Ken Simons, and Peter Thompson for their helpful suggestions. Financial support from MIUR (Year 2000; protocol #MM13038538_001; project leader: E. Santarelli) is gratefully acknowledged. 2 Introduction The debate on Gibrat’s Law of Proportionate Effect is a rather old one (see, amongst others, the surveys by Sutton, 1997; Geroski, 1999; Lotti et al., 2003). A commonly accepted interpretation of the Law formulated by Robert Gibrat (1931) is that the growth rate of a given firm is independent of its size at the beginning of the period examined. In other words, “the probability of a given proportionate change in size during a specified period is the same for all firms in a given industry - regardless of their size at the beginning of the period” (Mansfield, 1962, p. 1031). From an empirical viewpoint, the Law can be tested in two ways: either by using a sample of firms continuously active during a given period (balanced panel analysis), or by using a population of firms and testing the Law with sample attrition taken into account, since a portion of firms alive at the beginning of the period do not survive until the end of the same period (unbalanced panel analysis).1 Both approaches have some shortcomings. Tracking only incumbent surviving firms is by definition equivalent to considering only a sub-sample of the firms’ population and to neglecting important elements of industrial dynamics, i.e. entries and failures. If Gibrat’s Law is not a feature of the best incumbent firms, but a general pattern of industrial dynamics, it should be tested over the entire population of firms in a given time span (with the inclusion of new entries and firms that may exit the market in the subsequent periods). It is probably for this reason that the most recent estimates of the Law2 have used the second methodology. Yet, neither in this case do most studies specifically consider newborn firms and they deal with the survival/failure phenomenon by taking account only of sample attrition due to exit. Most of previous studies, in fact, pool large incumbents, newborn firms and small transient firms together, although estimates over a given time period are corrected for sample bias. By contrast, this paper attempts to consider both the entry process and the role of selection mechanisms in reshaping a given population of firms over time. It consequently differs from the previous literature in that it tries 1) to take joint account of both incumbents and newborn firms and 2) to consider the selection process as it occurs both over the entire period and year by year. Repeating the test of Gibrat’s Law year by year enables one to consider what happens when the original heterogeneous population is gradually reshaped in favor of larger, most efficient and wellestablished firms. Indeed, whilst most of the previous literature has found that Gibrat’s law must be rejected, since smaller firms tend to grow faster than their larger counterparts, no previous study 1 Fotopoulos and Louri (2001) is an example of the first approach, and Goddard, Wilson, and Blandon (2002) of the second. 2 See for example Becchetti and Trovato (2002), Hesmathi (2001), Fotopoulos and Louri (2001), Almus and Nerlinger (2000), Harhoff et al. (1998). 3 has attempted to determine whether this result is robust once industrial dynamics are taken fully into account. More specifically, in this paper we deal with the Italian Radio, TV & Telecommunications equipment industry in January 1987 (including 122 newborn firms). During the period examined, this industry was a rather mature one in Italy and still lagging behind in the technological revolution brought about by the passage from analog to digital signals.3 Many small firms in the industry operated in one of its three sub-markets, whereas only a few large multiproduct firms competed against each other in all of those sub-markets. Consequently, this study is affected by a certain degree of arbitrariness in its definition of the industry’s boundaries which, according to Sutton (1998), is likely to make it impossible to take account of the fact that each industry contains a number of sub-markets between which rivalry is less intense than it is within each (cf. also Giorgetti, 2003; Roberts and Thompson, 2003). Nonetheless, it is less severely affected by this arbitrariness than are studies which focus on several different industries. Gibrat’s Law is tested by using a sample selection procedure (augmented with age) for all firms, incumbent firms and newborn firms respectively, both over the entire period (1987-1994) and year by year. This set of estimates will enable us to answer the following questions: a) Is Gibrat’s Law valid in general (that is for all firms and over the entire period)? b) Is Gibrat’s Law less valid for new entries than for incumbent firms (smaller sub-optimal firms are relatively more common among new entries)? c) Is there any convergence towards a Gibrat’s like pattern of growth over time (due to market selection particularly adverse against smaller firms)? The empirical findings support the following string of answers: NO/YES/YES. Our interpretation is that previous results rejecting Gibrat’s Law have been partially determined by incomplete consideration of the entry and selection processes. More specifically, Gibrat’s Law fails to hold because a given population of firms is characterized by the presence of both newborn firms and “fragile” firms (which will subsequently fail). Smaller firms are over-represented in both categories, but it is precisely the presence of smaller fast-growing firms that leads to the rejection of Gibrat’s Law. As a result of market selection, surviving larger firms tend to behave in accordance with Gibrat’s Law and this holds for both incumbents and newborn firms. Hence, if these results are correct, and if they are confirmed by other studies, Gibrat’s Law and industrial dynamics are interrelated and it is incorrect either to assume or to deny Gibrat’s Law a priori. Although the Law is not confirmed in general, it may be an accurate representation of the pattern of growth assumed 3 In fact, the leading Italian firms in the industry proved unable to cope with this technological revolution, with a consequent contraction of the entire industry in the following years. In this connection, the Italian Radio, TV & 4 by a mature population of well-established firms, that is, a population already selected by market forces. The paper is organized as follows. Section 2 presents the dataset and deals with some methodological issues related to the estimation of Gibrat’s Law; Section 3 discusses the econometric results and Section 4 summarizes the main findings of the study. 2. Data and methodology In this paper we use a unique data set from the Italian National Institute for Social Security (INPS). This data set identifies all incumbents and newborn firms with at least one paid employee in the Radio, TV & Telecommunication equipment industry in Italy, and tracks their employment performance at yearly intervals from January 1987 to January 1994.4 The original INPS file was checked in order to identify entry and failure times correctly and to detect inconsistencies in individual tracks due to administrative factors, and cancellations due to firm transfers, mergers and take-overs. This cleaning procedure reduced the total number of firms in the database to 3,285, of which 122 were new entries in January 1987. The central relationship tested in this study is the original logarithmic specification of the Law: log Si,t = β0 + β1 log Si,t-1 + εi,t (1) where Sit, is the size of firm i at time t, Sit,−1 is the size of the same firm in the previous period and εi,t is a random variable distributed independently of Sit,−1. Following Chesher (1979, p.404), if both sides of equation (1) are exponentiated, it becomes clear that if β1 is equal to unity, then growth rate and initial size are independently distributed5 and Gibrat’s Law is in operation. By contrast, if β1 < 1 smaller firms grow at a systematically higher rate than do their larger counterparts, while the opposite is the case if β1 > 1. If - as in the majority of previous studies - growth and exit are not treated as homogeneous phenomena (that is, on the disputable hypothesis Telecommunication industry can be regarded, in the period under examination, as an aging one. 4 All private Italian firms are obliged to pay national security contributions for their employees to INPS. Consequently, the registration of a new firm as “active” signals an entry into the market, while the cancellation of a firm denotes an exit from it (this happens when a firm finally stops paying national security contributions). For administrative reasons - delays in payment, for instance, or uncertainty about the actual status of the firm - cancellation may sometimes be preceded by a period during which the firm is “suspended”. The present paper considers these suspended firms as exiting from the market at the moment of their transition from the status of “active” to that of “suspended”, while firms which have halted operations only temporarily during the follow-up period, and which were “active” in January 1994, have been treated as survivors. 5 Following a random walk (with drift) stochastic process. 5 that exit is equal to a minus one rate of growth), empirical estimates need only deal with surviving firms, obtaining results conditional on survival. Let χi,t be an indicator function which takes value 1 if firm i is still alive at time t and 0 otherwise. Accordingly, observed data on firm size can give only the conditional expectation of Si,t given Si,t-1 and χi,t=1, i.e. according to our specification, ( ) ( ) 1,|log1,| ,1,,1,10,1,, =++== −−− tititititititi SESSSE χεββχ (2) If the conditional expectation of εt is zero, the regression function for the selected sub-sample is the same as the population regression function, the only drawback being a loss of efficiency due to the smaller number of observations available. But if this is not true, the last term of equation (2) need to be included in the regression function. It is for this reason that a rule for χt is required, and the most natural way to deal with this kind of selection is to use a survival equation (i.e. a probit model), given that we can exactly identify when a firm exits the market. In a more general formulation, this is the same as saying that: Prob(χi=1) = Φ(α’zi)Probit Selection Equation (3a) { yi = β’ xi + εiobserved only if χi=1 (3b) If we denote the residual of equation (3a) with µi,t and if we assume that the error terms are normal, respectively () ε σε ,0~ N i and ( ) µ σµ ,0~ N i with () ρµε = ii corr , , we can reformulate equation (2) as: ( ) ititititi SSSE λρσββχ ε ++== −− 1,10,1,, log1,|(4) where () () i i iz z ' ' α αφ λ Φ = is the inverse of the Mills’ ratio.6 The two-step estimation procedure requires one to estimate the probit selection model first. Once λi has been obtained for each observation, the growth equation (4) is estimated, augmenting the observations with the Mills’ ratio 6 We use Φ to denote the cumulative density function of the Normal distribution and φ to denote its density function. 6 inverse, to obtain an additional parameter estimate ε σρβ ˆ ˆ = M from which we can simply recover the two-step estimate of ε σ β ρ ˆ ˆM =. We used Maximum Likelihood estimation7 with heteroskedasticity robust standard errors. Table 1 – Number of Active Firms, Average Size and its Standard Deviation. ALL FIRMS Year Number of Active Firms Average Size of Surviving Firms Standard Deviation 1987 3285 35.99 285.14 1988 3216 37.07 277.46 1989 2893 44.34 343.17 1990 2743 44.89 337.04 1991 2564 46.10 336.10 1992 2347 45.11 368.56 1993 2149 46.31 346.37 1994 1933 45.83 378.60 INCUMBENTS Year Number of Active Firms Average Size of Surviving Firms Standard Deviation 1987 3163 36.94 290.43 1988 3095 37.97 282.61 1989 2786 45.36 349.46 1990 2646 45.81 342.89 1991 2476 47.00 341.73 1992 2265 46.00 374.84 1993 2078 47.18 352.00 1994 1871 46.76 384.66 NEWBORN FIRMS Year Number of Active Firms Average Size of Surviving Firms Standard Deviation 1987 122 11.38 41.61 1988 121 14.10 52.70 1989 107 17.55 61.11 1990 97 19.82 67.45 1991 88 20.74 70.39 1992 81 20.12 67.90 1993 71 20.83 65.76 1994 62 17.76 54.91 Consistently with most previous studies, both the main and the selection equations were augmented with the age variable (which is obviously only relevant to incumbent firms). 7 Since Heckman's (1979) estimator may be inefficient and biased for small samples. 7 Regressions were run separately for all firms, all firms with a dummy for newborn ones, only incumbent firms and only newborn firms. The same specifications were tested over the entire period (1987-1994) and year by year (7 separate estimates for each group of firms). The descriptive statistics in table 1 confirm the importance of market selection: only 59% of incumbents and 51% of newborn firms survive until the end of the 7 years period. This selection, as it is evident from the average sizes of surviving firms, is dramatically biased towards smaller firms (especially in the first years). 3. Results Tables 2 and following present the regressions results over the entire period examined (1987-1994) and year by year. The model specification is reported in the headline, while coefficients estimates are presented together with robust standard errors and level of statistical significance (*=90%; **=95%; ***=99%). Estimates of the Gibrat’s coefficient β1 are also coupled with a Wald test, whose null is β1=1 (that is the Law is not rejected). After the coefficients estimates of the sample equation have been presented, some overall diagnostic tests are reported, among which the estimate of the correlation between the residuals of the two models (ρ) and the related significance level of the corresponding Likelihood Ratio test,8 and a Wald test for the overall validity of the model. As can be seen from all tables, the need for the sample selection model has been confirmed, especially in the first years of the period examined. Finally, the reader can follow the market selection process by looking at the number of observations, the decrease of which marks the incidence of firms’ failures. Examination of table 2 (all 3,285 firms operating in January 1987) prompts a number of considerations: 1) consistently with previous studies (see Section 1), Gibrat’s Law is rejected, with a β1=0.847 significantly different from 1; smaller firms seem to grow faster than their larger counterparts. Moreover, an initial larger size improves the likelihood of survival, although in a non-linear fashion (this result is also consistent with previous empirical studies); 8 The test statistic is LR = 2 (log LU - log LR), where log LU and log LR are the log-likelihoods for the unrestricted and restricted versions of the model, that is distributed as a χ2 statistic with 1 degree of freedom under the null hypothesis that the restriction ρ = 0 is valid. Table 2 – Estimates for all firms, basic model. ALL FIRMS Growth equation. ln Si , t=β0+β1ln Si , t-1+εi , t Selection equation Pr(δi , t=1)=F(ln Si , t-1, ln Si , t-1 2, const) 1987-94 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 β1 0.847*** (0.023) 0.959*** (0.005) 0.968*** (0.005) 0.973*** (0.007) 0.988*** (0.007) 0.986*** (0.008) 0.986*** (0.008) 0.982*** (0.011) Growth Equation β0 0.360** (0.168) 0.183*** (0.011) 0.155*** (0.013) 0.091*** (0.017) 0.020 (0.018) -0.006 (0.021) -0.019 (0.020) 0.028 (0.030) Wald Test β1=1 44.50*** 78.44*** 42.27*** 13.69*** 3.15* 3.07* 2.79* 2.58 α1 0.227*** (0.040) 0.298*** (0.081) 0.411*** (0.050) 0.334*** (0.066) 0.319*** (0.062) 0.332*** (0.060) 0.374*** (0.064) 0.240*** (0.063) α2 -0.025*** (0.008) -0.029** (0.014) -0.041*** (0.008) -0.027*** (0.009) -0.035*** (0.010) -0.040*** (0.009) -0.035*** (0.011) -0.031*** (0.010) Selection Equation α0 -0.066 (0.047) 1.690*** (0.088) 0.758*** (0.060) 1.140*** (0.085) 1.072*** (0.084) 0.928*** (0.082) 0.826*** (0.084) 0.965*** (0.087) ρ0.467 0.054*** 0.109*** 0.049** 0.073 0.045 0.077 -0.012 λ0.344 0.018 0.036 0.015 0.023 0.014 0.024 -0.004 Wald χ21360.97*** 42470.04*** 38275.57*** 17548.49*** 19762.35*** 15749.22*** 14505.59*** 7358.87*** log L -4372.26 -1343.91 -1897.21 -1180.25 -1340.00 -1346.80 -1233.71 -1251.28 Number of observations 3285 3285 3216 2893 2473 2564 2347 2149 Censored 1352 69 323 150 179 217 198 216 Uncensored 1933 3216 2893 2743 2564 2347 2149 1933 15 incumbent firms. Nevertheless, among newborn firms as well, there is evident convergence towards Gibrat’s Law (question c). In sum, the passage of time enables the market “to clean” a given population of firms12 and the surviving industrial core (mature, larger, well-established and most efficient firms) does not seem to depart from a Gibrat-like pattern of growth. This result reconciles the recent literature with the very early studies on Gibrat’s Law (see Hart and Prais, 1956; Simon and Bonini, 1958; Hymer and Pashigian, 1962) which tended to confirm the Law on the basis of samples comprising very large, old and well-established firms. If these results are confirmed by future research, Gibrat’s Law should no longer be considered a representation of overall industrial dynamics, but rather as a way to describe the growth behavior of mature, large and well-established manufacturing firms. References Almus, Mathias and Eric A. Nerlinger, 2000, “Testing Gibrat’s Law for Young Firms. 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