Industry dynamics and the distribution of firm sizes: a nonparametric approach.

1. Introduction

Ever since the seminal works of Herbert Simon and his coauthors (Simon and Bonini 1958; Ijiri and Simon 1974, 1977) the distribution of firm sizes (FSD) has received considerable empirical attention. Previous studies have typically found that the FSD is reasonably well described by a lognormal distribution at both the industry and the economy-wide level, implying that the distribution is right skewed. This piece of evidence is consistent with the so-called Law of Proportionate Effect, also known as Gibrat's (1931) Law. As Simon and Bonini (1958, p. 609) point out, if one "incorporates the law of proportionate effect in the transition matrix of a stochastic process, ... then the resulting steady-state distribution of the process will be a highly skewed distribution."

Recent evidence, however, based on more complete data sets, suggests that Gibrat's Law is not confirmed for either new entrants or established firms tracked for a five-year or longer time period (cf. the surveys by Mata 1994; Geroski 1995; Audretsch et al. 2002; Lotti, Santarelli, and Vivarelli 2003) since smaller firms grow more than proportionally with respect to larger ones. This decreasing relationship between size and growth suggests that the distribution of firm sizes is not stationary over time and may differ from the lognormal distribution.

We use quarterly data from Italy for 12 cohorts of new manufacturing firms to examine the evolution of the FSD over time in the case of young firms. Moreover, we try to reconcile our empirical evidence with the predictions of three complementary views of industry dynamics, drawing on theoretical work of Jovanovic (1982), Audretsch (1995), and Ericson and Pakes (1995). Section 2 contains a review of the empirical evidence about Gibrat's Law and the FSD as well as an overview of some recent explanations of industry dynamics. Section 3 describes the data and the methodology used, whereas Section 4 summarizes the main empirical findings. Finally, Section 5 contains some concluding remarks.

2. Theory or Stylized Facts?

Gibrat's Law, applied to the analysis of market structure, is the first attempt to explain in stochastic terms the systematically skewed pattern of the size distribution of firms within an industry (Sutton 1997). The Law of Proportionate Effect can be empirically tested in at least three different ways. First, one can assume that it holds for all firms in a given industry, including those that have exited the industry during the period examined (setting the proportional growth rate of disappearing firms equal to -1). Second, one can postulate that it holds only for firms that survive over the entire time period. If survival is not independent of firm's initial size--that is, if smaller firms are more likely to exit than their larger counterparts--this empirical test can be affected by a sample selection bias, and estimates must take account of this possibility. Third, one can state that Gibrat's Law applies only to firms large enough to have overcome the minimum efficient scale (MES) of a given industry (e.g., Simon and Bonini 1958 found that the law was confirmed for the 500 largest U.S. industrial corporations).

In effect, the law cannot be rejected if (i) firm growth follows a random process and is independent from initial size and (ii) the resulting distributions of firms' size are approximately lognormal. Of course, when identifying a FSD skewed to the right, one cannot a priori exclude that the skewness is the result of turbulence, namely, the presence of new entrants in the right tail of the distribution. Although from a theoretical viewpoint labeled "unrealistic" since Kalecki's (1945) study on the size distribution of factories in U.S. manufacturing, this result was initially consistent with some empirical studies dealing with incumbent, large firms (Hart and Prais 1956; Simon and Bonini 1958; Hymer and Pashigian 1962). In recent years, most studies have instead identified an overall negative relationship between initial size and postentry rate of growth. (1) Nevertheless, Lotti, Santarelli, and Vivarelli (2001a, b) have shown that, in the case of newborn firms, the growth rates are negatively correlated with their initial size only during their infancy: Gibrat's Law fails to hold in the year(s) immediately following start-up, when smaller firms have to rush in order to reach a size large enough to enhance their likelihood of survival; but in the subsequent years, the patterns of growth of entrants do not differ significantly from the landscape of the industry as a whole.

In the present paper, we argue that explanation of this phenomenon of self-selection should more carefully consider the firms' learning and evolution processes theorized by Jovanovic (1982), Audretsch (1995), and Ericson and Pakes (1995). According to these authors, entrants are uncertain about their relative level of efficiency, and only once they are in the market do they learn about their possibilities of survival and growth. The main advantage of these theories is that they allow for (i) heterogeneity among firms, (ii) idiosyncratic sources of uncertainty and discrete possible events, and (iii) entry and exit. In particular, these complementary views of firm and industry dynamics provide a role for uncertainty in entrant decisions and selection mechanisms, which imply changes in the size distribution of an entering cohort over time.

Jovanovic (1982) proposes a Bayesian model of noisy selection, according to which efficient firms grow and survive, whereas inefficient firms decline and fall. In particular, Jovanovic's model of passive learning deals with a small industry in which the product is homogeneous, the time path of the demand for the product is deterministic and known, and the factors are supplied at a constant price. In this competitive environment, firms are initially endowed with uncertain, time-invariant characteristics (i.e., efficiency parameters), and for each firm the mean of its costs is a proxy of its "true cost." Thus, in every period each firm has to decide its strategy: whether to exit, continue with the same size, grow in size, or reduce its productive capacity. Because of a particular kind of selection process in this model, the most efficient firms survive and grow, while the others are bound to shrink or to exit from the market. Under the hypotheses of small industry size and product homogeneity, there is no room for pursuing niche strategies characterized by different paths of convergence to the lognormal distribution. In particular, as a new firm with a suboptimal scale discovers that its true costs are low, it adjusts its size as rapidly as it can through accelerated growth. Within this perspective, one expects to observe a "strictly monotone" convergence, with the size distribution of survivors increasing stochastically from period to period.

Like the passive learning model, Ericson and Pakes's (1995) model of active learning assumes that all the decisions taken by firms are meant to maximize the expected discounted value of the future net cash flow, conditional on the current information set. In this model, a firm knows both its own characteristics and those of its competitors, along with the future distribution of industry structure, conditional on the current structure. Jovanovic's assumptions concerning small industry size and product homogeneity are instead relaxed in Ericson and Pakes's model, in which new entries may either adjust their size to the MES level of output of the "core" of the industry or choose/find a niche within which the likelihood of survival is relatively high even though the firm does not grow fast. The model of active learning can be usefully employed in explanation of "entry mistakes" (as defined by Cabral 1997), namely, the fact that in every period and every industry more firms enter than the market can sustain: Within an active learning perspective, such mistakes occur because of lags in observation of rivals' entry decision or just because entry investments take time (Cabral 1997). In an industry with similar dynamics, therefore, convergence to the lognormal distribution of firm sizes is a process that might take more time and will eventually occur non-monotonically.

In a subsequent work, Pakes and Ericson (1998) examined two cohorts of firms from Wisconsin belonging to the retail and the manufacturing industries and found that the structure of the former industry was compatible with Jovanovic's passive learning model, while that of the latter was compatible with their model of active exploration (learning). After eight years the retail cohort seems to have reached the size distribution of the industry as a whole, while the manufacturing cohort, even though it achieved higher growth rates, was still far from the size distribution of the entire industry after the same number of years. Such marked differences in the speed of convergence are not surprising since the manufacturing aggregate is much less homogeneous than the retailing one, which to some extent displays the features of Sutton's (1997, 1998) "strategic dependence" hypothesis of homogeneous submarkets. Moreover, Pakes and Ericson (1998) claim that the major nonparametric difference between the two models relates to the distinction between heterogeneity and the phenomenon of state dependence (Heckman 1981). Accordingly, the passive learning model implies that the stochastic process generating the size of a firm is characterized by a form of heterogeneity, while the active learning model implies that such stochastic process is generated by a general form of state dependence, even if with ergodic characteristics.

Audretsch (1995; cf. Audretsch and Fritsch 2002) expanded the passive learning approach put forward in Jovanovic's (1982) theoretical work into an evolutionary perspective, which emphasizes the interindustry differences in the likelihood of survival of newborn firms. Following the evolutionary tradition initiated by Nelson and Winter (1982) in their attempt to reconcile the so-called "Schumpeter Mark 1" and "Schumpeter Mark 2" views of the technological innovation/economic development relationship, Audretsch assumes that both new firm start-ups and large incumbent firms are likely to contribute to economic development but not in all industries and at all times. With the purpose of explaining industry heterogeneity in terms of the evolution of the size distribution of new entrants, Audretsch distinguishes between an entrepreneurial regime, more favorable to innovative entry and unfavorable to innovative activity by established firms, and a routinized regime, characterized by the opposite conditions. The resulting "growth regimes" approach suggests that "in some industries small firms clearly have the innovative advantage, which is consistent with the entrepreneurial regime. In other industries large enterprises exhibit the innovative advantage, which is consistent with the routinized regime" (Audretsch and Fritsch 2002, p. 115). Accordingly, industry-specific characteristics, such as scale economies and the endowment of innovative capabilities (cf. Agarwal and Audretsch 2001), exert a significant impact on entry, exit, and the likelihood of survival of newborn firms. For example, in industries characterized by higher MES levels of output, smaller firms face higher costs that are likely to push them out of the market within a short period after startup. Thus, only the most efficient of newborn firms will survive and grow, whereas the others will be forced to exit the market (cf. Audretsch, Santarelli, and Vivarelli 1999b). In this case, the presence of more potential entrants than firms with a significant likelihood to survive in the long run can bring about a shakeout (Klepper and Miller 1995). In turn, a shakeout occurring at a certain point in the industry's history is likely to affect the long-run size distribution of firms within the same industry, depending on "how the opportunities vacated by exited firms are reallocated among surviving firms" (Sutton 1998, p. 260; Klepper and Graddy 1990; Klepper and Simons 2000; Carree and Thurik 2001). Conversely, in industries with a lower MES level of output, the likelihood of survival will be independent of the firms' ability to grow (Amaral et al. 1977; Brock 1999). Within this perspective, industry- and firm-specific factors affect convergence to the lognormal distribution of firm sizes: The speed of convergence will be higher in those industries in which smaller entrants have the innovative advantage, lower in those in which the innovative advantage is held by established firms.

With this theoretical and empirical background in mind, we look at the evolution of 12 cohorts of newborn firms in selected industries in order to analyze the process of convergence of the firm size distribution, in terms of number of employees, with respect to the overall industry landscape. The aim of this analysis is to show (i) whether the findings by Herbert Simon and his coauthors concerning the skewness to the right of the FSD are confirmed also in the case of newborn, small firms; (ii) how the FSD evolves over time as firms age; and (iii) whether the FSD resulting from application of the kernel density estimator demonstrates the heterogeneity of industries in terms of different speed of convergence to the lognormal distribution of firm sizes.

3. Data and Methodology

Data and Descriptive Statistics 

We use a data set from the Italian National Institute for Social Security (INPS), comprising 12 cohorts of new manufacturing firms (with at least one paid employee) born in each month of 1987, and their follow-up until December 1992. Since all private Italian firms are compelled to pay national security contributions for their employees to INPS, the registration of a new firm as "active" signals an entry into the market, while the cancellation of a firm denotes an exit (this happens when a firm finally stops paying national security contributions). For administrative reasons--delays in payment, for instance, or uncertainty about the current status of the firm--some firms are classified as "suspended." In the present work we consider 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 that have stopped their activity only temporarily were included again in the sample once they became active again. (2) We also performed a careful cleaning procedure aimed at identifying internal inconsistencies and entry or exit due to firm transfers and acquisitions. As regards acquisitions, these am denoted as "extraordinary variations" in the INPS database, and firms involved in such activities could therefore be easily identified and canceled from the database itself. Correct identification of firms that have disappeared via acquisitions ensured that acquiring firms were not drawn disproportionately from the low end of the size distribution. As pointed out by Sutton (1998; see also Hart and Prais 1956; Hymer and Pashigian 1962), this would have caused a violation in the proposed bound and altered the significance of the overall analysis.

We focused our analysis on 12 monthly cohorts of start-up firms in four five-digit industries--bread, office machinery (comprising both its hardware and its software branches), radio and TV equipment, and footwear--and this for mainly two reasons: The first concerned their very different market structure in terms of cost of entry (sunk costs), and the second was the fact that the bread and the footwear industries are not as technologically progressive as office machinery, whereas the radio and TV equipment industry is more mature than the three other industries. These differences among the four industries would allow us to draw some conclusions on whether the FSD is sensitive to structural and technological factors. As far as technological factors are concerned, however, one cannot help but note that most firms in the Italian footwear industry tend to cluster in industrial districts and that clustering itself can be regarded as a type of technology.

To examine the effect of firms' age on the distribution of their employment sizes, we studied each cohort of new entrants at each quarter after start-up or their first six years in the market. Thus, we had 21 observations for the follow-up of each cohort. In order to assess the relative importance of newborn firms over the whole industry, we computed monthly birthrates during the start-up period (from January to December 1987). As one can see from Table 1, the two traditional industries, bread and footwear, exhibit birthrates almost constant over time. In the case of the bread industry, newborn firms represent more than the 2% of the incumbent firms, while this proportion is much smaller (0.5%) if we look at the footwear industry. The relative importance of newborn firms in the office machinery industry proves to be decreasing over time, even if at the end of the relevant period newborn firms still constitute nearly 1.8% of the active firms. The radio and TV equipment industry shows a similar pattern: decreasing over time but with lower levels.

Some descriptive statistics are reported in Tables 2 and 3. In general, all industries experience a shakeout period during which the number of survivors, among new entrants, declines by 40% or more. Table 2 shows that, on average, the survival rate at the end of the period (i.e., after 21 quarters) is much higher within the cohorts belonging to the office machinery and the radio and TV equipment industries than in the case of the bread and footwear industries. Thus, consistent with the theoretical hypotheses summarized in section 2, industry-specific characteristics seem to set in motion a preentry selection mechanism that enhances the likelihood of survival solely of those start-ups whose idiosyncratic endowment of innovative capabilities is a possible competitive advantage. For example, if one follows both Ericson and Pakes (1995) and Pakes and Ericson (1998), the presence of large sunk costs of entry in one industry pushes down entry itself (if demand is similar), unless it is counterbalanced by an expected rate of return high enough to induce more entry.

In such a framework, higher rates of return, ex post, will lead to higher survival rates. Besides, if one follows Jovanovic (1982), in industries characterized by different variances in the distribution of shocks, it will take longer, on average, to learn a firm's true cost and hence longer, on average, for exit to occur in the industry with higher variance. In other words, for some functional forms of the shocks, the passive learning model implies that it takes more time to accumulate the information necessary to ensure that exit is optimal.

It is evident from Table 3 that the standard error of average firm size is much higher at the end of the relevant period than it is in the first quarter, with the partial exception of the bread industry. Dispersion of firm sizes tends therefore to widen as surviving firms reach the MES level of output and specialize in one of the many clusters of products that--according to Sutton's (1998, pp. 597-605) "independent submarkets" hypothesis--characterize each industry. In turn, firm size increases along with its age only for the radio and TV equipment and the footwear industries (albeit, for the latter, only during the first 19 quarters). The office machinery and the bread industries experience increasing firm size only for the first 12 quarters, which roughly correspond to the period between December 1989 and January 1991. (3)

Econometric Methodology

Machado and Mata (2000) use the Box--Cox quantile regression method to estimate the distribution of firm sizes and, accordingly, to analyze industry dynamics in Portugal. This approach consists in modeling each quantile as a function of a number of industry characteristics that are expected to affect firm size. Since our database did not provide any details about industry characteristics, in the present study we instead used a nonparametric approach. The intention was to determine whether, with the passing of time, the empirical distribution of firm sizes converges toward a lognormal distribution, under the hypothesis that this represents the limit distribution. Following a long-standing tradition in the empirical analysis of the FSD, in our analysis we use the logarithm of the size variable. Thus, provided that the logarithmic transformation reduced positive skewness because it compressed the upper end of the distribution while stretching out the lower tail, we were interested in identifying whether the logs of size converge toward a normal distribution. In this search for empirical regularities and stylized facts, we employed a simple nonparametric technique of density estimation. The advantage of this methodology is that no specified functional form of the density under examination is required. When this approach is used, the density is estimated directly on the data and represents the most natural way to compare, also graphically, the empirical distribution to some a priori known distribution. To characterize the distribution, we used the kernel density estimator (Pagan and Ullah 1999).

Let f(x) be the unknown density to be estimated. In such a nonparametric approach, there is no need to postulate the true parametric distribution off, while f(x) is directly estimated through the data. As a consequence, the estimates will have a stepwise nature.

The general formulation of a kernel density estimator is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the kernel function K(*) is defined in such a way that

[[integral].sup.[infinity].sub.-[infinity]] K([[psi].sub.i])d[psi] = 1 and [[psi].sub.i] = ([x.sub.i] - x)/h,

with h denoting the window width (or the smoothing parameter, or bandwidth) and n the size of the sample. There are several ways to estimate a distribution nonparametrically: We used the Gaussian distribution as kernel function (as in Cabral and Mata 2003). We also used different kernel functions, such as the Epanechnikov kernel, but found that the shape of the nonparametric estimate of the FSD was not sensitive to the choice made.

More crucial is the choice of the bandwidth parameter. Some criteria are usually followed: minimizing the integrated squared error or the integrated mean squared error or cross-validation techniques. We used a bandwidth parameter, given by the formula

h = 0.9m/[5th root of (n)],

where n is the number of observations in the sample and

m = min([square root of (var(x)], interquartile range (x)/1.349).

Heuristically, according to Silverman (1986), this automatic bandwidth parameter performs very well in the case of unknown densities that are a mixture of normal distributions or heavily skewed or bimodal.

Accordingly, for each quarter and each industry, we estimated the distribution of the logarithm of the firms' size and checked if a tendency toward a normal distribution emerged. The results are shown in Figures A1-A4 in the Appendix. Moreover, in order to test statistically the conformity of the empirical distribution to the normal, we estimated the skewness and kurtosis statistics since these are very good descriptive and inferential indexes for measuring normality. The skewness and the kurtosis indexes are the third and the fourth standardized moments of the distribution.

In particular, the literature refers to the skewness index as

[square root of ([[beta].sub.1]) = [E(X - [mu]).sup.3]/[[sigma].sup.3]

and to the kurtosis index as

[[beta].sub.2] = [E(X - [mu]).sup.4]/[[sigma].sub.4],

where [mu] and [sigma] are the mean and the standard deviation of the distribution under exam. Since for a normal distribution they are equal to 0 and 3, respectively, a natural way to evaluate the non-normality of a distribution is to look at the difference of such empirical moments from those values.

The skewness index measures the degree of symmetry of a distribution: [square root of ([[beta].sub.1]) > 0 corresponds to skewness to the right, while [square root of ([[beta].sub.1]) < 0 corresponds to skewness to the left. On looking at Table 4, one notes that for three industries out of four (the only exception being the footwear one), the FSD tends to become more symmetric over time, with different speeds of convergence. But even after 21 quarters, the FSD in the bread, office machinery, and radio and TV equipment industries is still skewed to the right, while in the footwear industry, starting from a distribution skewed to the right, it is skewed to the left.

The kurtosis index represents a measure of the curvature: Distributions with [[beta].sub.2] > 3 have thicker tails than the normal distribution and tend to exhibit broader peaks in the center of the distribution, whereas distributions with [[beta].sub.2] < 3 tend to have lighter tails and to have higher peaks than the normal distribution. (4) For all industries (see Table 4), the kurtosis index shows a convergence toward the normal distribution.

In order to evaluate the pattern of convergence to a normal distribution, we computed also different tests for normality. First, we used a simple test based on the skewness and kurtosis indexes (D'Agostino, Balanger, and D'Agostino 1990), which allow the null hypothesis, [H.sub.0]: [square root of ([[beta].sub.1]) = 0 and [H.sub.0] : [[beta].sub.2] = 3, to be tested statistically. The results are reported, in terms of significance, in the first two rows of Table 4. The third row reports the results from the Kolmogorov-Smirnov (5) test, which we used to compare statistically the empirical distribution to the normal distribution. Subsequently, two omnibus tests were computed: the Shapiro-Wilk W-test (Shapiro and Wilk 1965) and the D'Agostino-Pearson [K.sup.2] test (D'Agostino and Pearson 1973). By "omnibus," we mean, following D'Agostino, Balanger, and D'Agostino (1990), a test able to detect deviations from normality due to either skewness or kurtosis.

The results suggest a strong departure of the distribution of the logarithm of the firm's sizes from normality for all industries during their infancy. With the passing of time and the mechanism of self-selection, the office machinery and the footwear industries show a certain degree of normality at the end of the relevant period. Normality is reached by following a slower path in the case of the radio and TV equipment industry, while no significant convergence emerges for the bread industry.

4. Empirical Findings

The different paths and speeds of convergence toward the normal distribution are consistent with alleged structural and technological differences among the industries examined. In general, the empirical evidence resulting from the kernel density estimates demonstrates industry heterogeneity in terms of the evolution of the firm size distribution of new entrants.

More in detail, the convergence toward the normal distribution begins to emerge after the 13th quarter in the case of the office machinery and the footwear industries (see Figures A2 and A4 in the Appendix). As the logarithm of firms' sizes approaches the normal distribution, Gibrat's Law holds when the age of firms exceeds three years. This observation suggests that the FSD changes relatively rapidly as firms learn about their efficiency compared with their competitors.

[FIGURES A2-A4 OMITTED]

Conversely, for the bread and the radio and TV equipment industries, the pattern of convergence is much less clear-cut. For the bread industry, in particular, no significant pattern of convergence emerges (see Figure A1 in the Appendix): After six years of observations, this industry is still far from the limit distribution, and, moreover, the distributions of firm sizes are bimodal. In the bread industry, therefore, the shakeout after entry is not particularly drastic, and this can explain why, at the end of the relevant period, the FSD exhibits two modes: One is likely to identify the "core" of the industry, while the second, which is located at the fringe of the industry, suggests the existence of an evolutionary process of active learning that enables firms below the MES level of output to survive and grow. This result is consistent with Ericson and Pakes's model, and this implicitly corroborates Sutton's (1997, 1998) assumption that any industry, as conventionally defined in official statistics, will contain different clusters of products, some of which compete closely whereas other do not compete at all. (6)

[FIGURE A1 OMITTED]

For the radio and TV equipment industry, convergence instead comes about only after 17 quarters. It should be pointed out, however, that during the relevant period, this industry was characterized, in Italy, by a consolidation process--typical of the mature stage of an industry's life cycle and consistent with Audretsch's routinized regime--largely unfavorable to innovative entry by small firms.

A possible explanation of the contrasting results obtained for the two groups of industries is that the selection and learning processes are much slower in traditional consumer goods and in mature industries than in technologically progressive industries like office machinery and in an industry that typically exploits the externalities of industrial districts like footwear. In both cases, technology makes the difference. In the office machinery industry, innovative entry by small firms brings about the overall innovation process; in other words, new firms learn quickly whether their innovations are competitive, and this makes the convergence more rapid. In the footwear industry, the network embedded in the local cluster is itself a technology able to give greater viability to small firms that would otherwise be vulnerable if they were operating in an isolated context (Audretsch, Santarelli, and Vivarelli 1999a). As a result of their specific features, both the office machinery and the footwear industries therefore follow a passive learning dynamics.

In the bread industry, which from this perspective exhibits a dynamics that is consistent with the active learning model, entry and sunk costs are particularly low, and, as a consequence, smaller firms do not have to "rush" to achieve a higher likelihood of survival. (7) By definition, firms in this industry operate in very small markets (neighborhoods rather than municipal areas) that in most cases are characterized by the presence of a single firm. (8) Thus, even new entrants with a very small start-up size are likely to operate at the MES level of output of their submarket and do not need to adjust as rapidly as they can through accelerated growth. Accordingly, in this industry the process of industry dynamics has to run for more periods before a convergence to the lognormal distribution begins to emerge.

These results are consistent with those emerging from study of the patterns of evolution of the skewness and kurtosis indexes and from application of the normality tests (see Table 4): The patterns of the evolution of the size distribution of firms change from industry to industry, with some of them converging earlier to the lognormal distribution.

5. Conclusions

In this paper we have examined the firm size distribution and its evolution over time for 12 cohorts of newborn firms. Our analysis allows us to draw some conclusions about the different selection mechanisms that may be in operation in different industries and to reconcile our empirical evidence with the predictions, in terms of size distribution of new firms, of some selected models of industry dynamics. In general, the process of convergence toward the limit distribution appears to be merely a matter of time, although our data set unfortunately allowed us to follow the postentry performance of these firms only for their first six years in the industry.

We have examined four industries that differ greatly in terms of (i) the productive capacity required for entering the market at the MES level of output and (ii) their technological content and characteristics. Differences in industry-specific characteristics concerning the levels of sunk costs and the rate of entry engender differences in the way that a convergence toward a lognormal distribution does or does not arise. This Bayesian perspective helps explain the differing speed of convergence of the FSD to a lognormal distribution. In particular, it is consistent with our empirical finding that only in the most technologically advanced industry (office machinery) and in the one (footwear) that is characterized by the widespread presence of industrial districts--both of them industries in which smaller entrants tend to invest in their capacity more rapidly after exploring their efficiency level with respect to their competitors--does a convergence toward the lognormal distribution clearly emerge a few quarters after start-up. Conversely, in the most traditional industry, represented in our analysis by the bread industry, and in an aging, mature industry, represented in our analysis by the radio and TV equipment industry, the speed of convergence is much slower. It will be possible to determine whether this is due to the fact that selection and learning processes are much slower in traditional and mature industries than in technologically progressive ones. Also in industries using a particular production technology like that connected to location within industrial districts, the speed of convengence could be detected only when and if new data are forthcoming that enable a thorough analysis of the behavior of newborn firms in these industries beyond their 21st quarter in the market.

Table 1. Monthly Birthrates (%), All Industries

                    Office Machinery:
                        Hardware         Radio and
            Bread     and Software      TV Equipment   Footwear

Jan. 1987   2.422         2.208            0.828        0.533
Feb. 1987   2.391         2.168            0.815        0.530
Mar. 1987   2.374         2.107            0.807        0.528
Apr. 1987   2.329         2.071            0.804        0.526
May 1987    2.322         2.043            0.796        0.527
Jun. 1987   2.294         1.993            0.784        0.529
Jul. 1987   2.279         1.954            0.780        0.532
Aug. 1987   2.270         1.943            0.782        0.537
Sep. 1987   2.288         1.899            0.769        0.533
Oct. 1987   2.285         1.854            0.759        0.533
Nov. 1987   2.273         1.816            0.753        0.533
Dec. 1987   2.273         1.799            0.751        0.535

Source: Own calculation on the Italian National Institute
for Social Security (INPS) database. The monthly birthrate
is computed as the ratio of the number of newborn firms to
the total number of active firms in each month of 1987.

Table 2. Number of Newborn Firms, Number of Firms Still Active
at the End of the Period, and Survival Rate, All Industries

                         Bread

                       Number of
         Number of   Firms Active
          Newborn     at the End     Survival
Cohort     Firms     of the Period   Rates (%)

1            17            6           35.29
2            10            5           50.00
3             9            5           55.56
4            14            7           50.00
5             7            3           42.86
6             9            4           44.44
7            12            7           58.33
8             4            2           50.00
9             3            2           66.67
10            7            3           42.86
11           12            4           33.33
12           13            7           53.85
Total       117           55           47.01

         Office Machinery:
         Hardware and Software

                       Number of
         Number of   Firms Active
          Newborn     at the End     Survival
Cohort     Firms     of the Period   Rates (%)

1            38            28          73.68
2            20            19          95.00
3            25            19          76.00
4            20            15          75.00
5            18            13          72.22
6            24            11          45.83
7            22            14          63.64
8             9             7          77.78
9            23            17          73.91
10           24            16          66.67
11           21            14          66.67
12           17             9          52.94
Total       261           182          69.73

         Radio and TV Equipment

                       Number of
         Number of   Firms Active
          Newborn     at the End     Survival
Cohort     Firms     of the Period   Rates (%)

1            52            38          73.08
2            32            22          68.75
3            27            16          59.26
4            16            12          75.00
5            26            13          50.00
6            37            26          70.27
7            17            12          70.59
8            10             5          50.00
9            36            25          69.44
10           30            20          66.67
11           19            12          63.16
12           24            17          70.83
Total       326           218          66.87

                       Footwear

                       Number of
         Number of   Firms Active
          Newborn     at the End     Survival
Cohort     Firms     of the Period   Rates (%)

1            76            41          53.95
2            39            20          51.28
3            34            16          47.06
4            30            17          56.67
5            31            19          61.29
6            23            13          56.52
7            32            13          40.63
8            24            13          54.17
9            32            16          50.00
10           32            18          56.25
11           37            22          59.46
12           21            10          47.62
Total       411           218          53.04

Table 3. Average Size and Its Standard Error, Average Growth Rate
and Its Standard Error, and Number of Firms Active at the End of
Each Quarter, All Industries

                                Q1      Q2      Q3      Q4      Q5

Bread
  Average size                  2.44    2.85    2.69    3.07    3.34
  Standard error of
    average size                4.18    4.36    4.62    4.56    5.07
  Average growth rate          --      27.12    5.00    2.29   12.64
  Standard error of
    average growth rate        --      72.69   35.36   38.45   52.97
  Number of
    active firms                 117     111     106      97      93

Office machinery:
Hardware and software
  Average size                  5.00    6.95    9.25   11.16   11.96
  Standard error of
    average size               23.80   28.70   34.04   39.06   42.12
  Average growth rate          --      61.42   42.19   18.32   16.73
  Standard error of
    average growth rate        --     126.33   79.84   50.22   50.44
  Number of
    active firms                 261     259     255     254     249

Radio and TV equipment
  Average size                  7.04    9.35   10.40   10.89   11.12
  Standard error of
    average size               36.10   40.14   40.41   40.77   38.51
  Average growth rate          --      79.69   23.45    9.20   13.25
  Standard error of
    average growth rate        --     166.66   76.66   30.28   37.82
  Number of
    active firms                 326     325     317     309     305

Footwear
  Average size                  8.40   11.24   12.66   14.16   15.33
  Standard error of
    average size               13.84   18.75   20.82   24.74   26.25
  Average growth rate          --      71.77   21.06   29.54   13.15
  Standard error of
    average growth rate        --     188.82   83.48  247.19   65.73
  Number of
    active firms                 411     395     378     361     348

                                Q6      Q7      Q8      Q9     Q10

Bread
  Average size                  3.42    3.66    3.84    4.09    4.34
  Standard error of
    average size                5.24    5.41    5.69    5.66    6.17
  Average growth rate           3.66    9.41    3.24    8.54   10.19
  Standard error of
    average growth rate        32.08   39.87   29.13   32.40   32.94
  Number of
    active firms                  90      84      80      74      73

Office machinery:
Hardware and software
  Average size                 12.63   13.75   15.24   16.02   16.33
  Standard error of
    average size               43.15   47.60   52.00   54.43   56.19
  Average growth rate           8.85   12.88    8.89   10.69    2.62
  Standard error of
    average growth rate        28.43   44.80   26.31   39.87   24.71
  Number of
    active firms                 246     244     238     235     231

Radio and TV equipment
  Average size                 12.07   12.85   13.10   13.37   13.63
  Standard error of
    average size               42.07   42.91   42.58   42.23   41.99
  Average growth rate          11.97   11.73   10.26    6.14    4.31
  Standard error of
    average growth rate        45.50   39.87   40.98   33.61   38.44
  Number of
    active firms                 297     291     285     279     276

Footwear
  Average size                 16.14   17.17   17.53   18.34   18.53
  Standard error of
    average size               28.15   30.42   30.76   33.21   33.63
  Average growth rate          15.64    7.64    7.29   11.78    5.13
  Standard error of
    average growth rate        84.60   66.37   70.43   62.46   31.71
  Number of
    active firms                 338     323     311     301     292

                               Q11     Q12     Q13     Q14     Q15

Bread
  Average size                  4.61    4.53    4.49    4.41    4.44
  Standard error of
    average size                6.22    6.17    6.22    6.31    6.24
  Average growth rate           8.57   -2.46   -0.68   -1.64    3.11
  Standard error of
    average growth rate        33.27   21.86   18.68   24.99   40.46
  Number of
    active firms                  72      69      67      67      63

Office machinery:
Hardware and software
  Average size                 16.81   17.17   16.90   14.35   14.77
  Standard error of
    average size               57.20   58.37   57.75   49.27   49.66
  Average growth rate           8.20    3.66    2.97    0.55    4.54
  Standard error of
    average growth rate        33.59   25.16   43.49   28.39   35.45
  Number of
    active firms                 224     218     215     206     203

Radio and TV equipment
  Average size                 14.46   14.79   14.89   15.01   15.63
  Standard error of
    average size               43.02   44.50   44.50   45.57   47.60
  Average growth rate           5.40    3.52    5.74    2.32    3.05
  Standard error of
    average growth rate        28.54   27.30   64.83   24.57   27.42
  Number of
    active firms                 262     256     254     247     241

Footwear
  Average size                 19.77   20.40   20.61   20.98   21.50
  Standard error of
    average size               41.55   43.34   44.49   42.54   43.22
  Average growth rate           3.75    2.80    2.62    4.83    1.86
  Standard error of
    average growth rate        31.49   49.71   27.49   30.19   24.14
  Number of
    active firms                 280     270     264     261     254

                               Q16     Q17     Q18

Bread
  Average size                  4.24    4.41    4.32
  Standard error of
    average size                5.93    6.24    5.82
  Average growth rate          -2.79    3.62    4.21
  Standard error of
    average growth rate        19.03   41.80   26.15
  Number of
    active firms                  62      61      61

Office machinery:
Hardware and software
  Average size                 15.17   15.39   15.80
  Standard error of
    average size               50.65   48.95   49.22
  Average growth rate           6.09    4.30   16.64
  Standard error of
    average growth rate        25.26   65.10  233.89
  Number of
    active firms                 201     195     193

Radio and TV equipment
  Average size                 15.99   15.98   16.05
  Standard error of
    average size               49.13   49.15   48.41
  Average growth rate           3.87    4.93    8.69
  Standard error of
    average growth rate        32.59   51.26   83.05
  Number of
    active firms                 236     232     231

Footwear
  Average size                 21.90   22.77   23.07
  Standard error of
    average size               47.14   50.31   50.25
  Average growth rate          -0.69    0.49    1.78
  Standard error of
    average growth rate        20.64   19.22   27.19
  Number of
    active firms                 247     239     233

                               Q19     Q20     Q21

Bread
  Average size                  4.59    4.44    3.83
  Standard error of
    average size                6.30    6.36    5.47
  Average growth rate           1.75   -8.00   -3.03
  Standard error of
    average growth rate        20.97   28.51   33.13
  Number of
    active firms                  58      55      55

Office machinery:
Hardware and software
  Average size                 16.23   17.12   17.33
  Standard error of
    average size               49.39   51.22   48.78
  Average growth rate           0.65    2.82    1.16
  Standard error of
    average growth rate        22.18   23.62   54.44
  Number of
    active firms                 188     183     182

Radio and TV equipment
  Average size                 16.56   16.68   16.52
  Standard error of
    average size               48.89   49.49   48.53
  Average growth rate           2.96   -0.30    0.03
  Standard error of
    average growth rate        34.39   18.97   30.75
  Number of
    active firms                 224     220     218

Footwear
  Average size                 22.88   22.94   22.71
  Standard error of
    average size               49.86   52.56   52.70
  Average growth rate          -1.09    0.19    0.09
  Standard error of
    average growth rate        26.41   24.49   22.77
  Number of
    active firms                 227     222     218

Table 4. Test for Normality for Each
Quarter Following Birth, All Industries

                            Q1          Q2          Q3          Q4

Bread
  Skewness (a)            1.22 ***    0.79 ***    0.82 ***    0.77 ***
  Kurtosis (b)            3.10        2.11 ***    2.19 **     2.07 ***
  Kolmogorov-Smirnov      0.43 ***    0.34 ***    0.33 ***    0.29 ***
  Shapiro-Wilk            0.88 ***    0.90 ***    0.89 ***    0.88 ***
  D'Agostino             17.68 ***   16.43 ***   14.08 ***   14.60 ***
Office machinery:
Hardware and software
  Skewness (a)            0.94 ***    0.48 ***    0.28 *      0.22
  Kurtosis (b)            2.49 **     1.90 ***    1.87 ***    1.78 ***
  Kolmogorov-Smirnov      0.30 ***    0.21 ***    0.17 ***    0.18 ***
  Shapiro-Wilk            0.93 ***    0.95 ***    0.96 ***    0.95 ***
  D'Agostino             27.37 ***   61.80 ***   66.05 ***   64.56 ***
Radio and TV equipment
  Skewness (a)            0.75 ***    0.31 **     0.26 *      0.23 *
  Kurtosis (b)            2.09 ***    1.72 ***    1.71 ***    1.71 ***
  Kolmogorov-Smirnov      0.28 ***    0.20 ***    0.19 ***    0.18 ***
  Shapiro-Wilk            0.94 ***    0.94 ***    0.95 ***    0.95 ***
  D'Agostino             49.22 ***   51.54 ***   50.76 ***   61.23 ***
Footwear
  Skewness (a)            0.12       -0.11       -0.15       -0.17
  Kurtosis (b)            1.57 ***    1.56 ***    1.58 ***    1.62 ***
  Kolmogorov-Smirnov      0.17 ***    0.15 ***    0.16 ***    0.16 ***
  Shapiro-Wilk            0.93 ***    0.92        0.93 ***    0.93 ***
  D'Agostino             56.48 ***   55.67 ***   58.12 ***   61.49 ***

                            Q5          Q6          Q7          Q8

Bread
  Skewness (a)            0.62 **     0.69 ***    0.56 **     0.54 ***
  Kurtosis (b)            1.90 ***    2.01 ***    1.88 ***    1.81 ***
  Kolmogorov-Smirnov      0.26 ***    0.25 ***    0.22 ***    0.21 ***
  Shapiro-Wilk            0.90 ***    0.89 ***    0.90 ***    0.89 ***
  D'Agostino             18.35 ***   14.27 ***   16.75 ***   19.17 ***
Office machinery:
Hardware and software
  Skewness (a)            0.22        0.16        0.18        0.17
  Kurtosis (b)            1.82 ***    1.77 ***    1.79 ***    1.85 ***
  Kolmogorov-Smirnov      0.16 ***    0.17 ***    0.18 ***    0.20 ***
  Shapiro-Wilk            0.95 ***    0.95 ***    0.95 ***    0.96 ***
  D'Agostino             65.12 ***   63.24 ***   68.36 ***   68.68 ***
Radio and TV equipment
  Skewness (a)            0.17        0.18        0.15        0.14
  Kurtosis (b)            1.71 ***    1.74 ***    1.78 ***    1.80 ***
  Kolmogorov-Smirnov      0.16 ***    0.16 ***    0.14 ***    0.13 ***
  Shapiro-Wilk            0.94 ***    0.94 ***    0.95 ***    0.96 ***
  D'Agostino             58.43 ***   55.98 ***   59.93 ***   71.28 ***
Footwear
  Skewness (a)           -0.22       -0.19       -0.18       -0.21
  Kurtosis (b)            1.66 ***    1.71 ***    1.70 ***    1.68 ***
  Kolmogorov-Smirnov      0.18 ***    0.15 ***    0.17 ***    0.18 ***
  Shapiro-Wilk            0.92 ***    0.93 ***    0.94 ***    0.93 ***
  D'Agostino             60.20 ***   62.39 ***   63.99 ***   67.84 ***

                            Q9          Q10         Q11         Q12

Bread
  Skewness (a)            0.38        0.29        0.24        0.25
  Kurtosis (b)            1.64 ***    1.69 ***    1.68 ***    1.66 ***
  Kolmogorov-Smirnov      0.21 ***    0.17 ***    0.15 *      0.16 *
  Shapiro-Wilk            0.90 ***    0.91 ***    0.92 ***    0.91 ***
  D'Agostino             30.26 ***   27.78 ***   24.26 ***   23.56 ***
Office machinery:
Hardware and software
  Skewness (a)            0.19        0.18        0.11        0.13 ***
  Kurtosis (b)            1.86 ***    1.83 ***    1.82 ***    1.87 ***
  Kolmogorov-Smirnov      0.18 ***    0.20 ***    0.19 ***    0.18 ***
  Shapiro-Wilk            0.95 ***    0.95 ***    0.96 ***    0.96 ***
  D'Agostino             63.30 ***   70.25 ***   72.09 ***   53.08 ***
Radio and TV equipment
  Skewness (a)            0.14        0.15        0.15        0.16
  Kurtosis (b)            1.89 ***    1.89 ***    1.90 ***    1.92 ***
  Kolmogorov-Smirnov      0.12 ***    0.14 ***    0.13 ***    0.15 ***
  Shapiro-Wilk            0.96 ***    0.96 ***    0.96 ***    0.96 ***
  D'Agostino             65.42 ***   64.54 ***   56.85 ***   49.92 ***
Footwear
  Skewness (a)           -0.15       -0.18       -0.21       -0.20
  Kurtosis (b)            1.68 ***    1.73 ***    1.77 ***    1.79 ***
  Kolmogorov-Smirnov      0.13 ***    0.12 ***    0.13 ***    0.12 ***
  Shapiro-Wilk            0.94 ***    0.93 ***    0.94 ***    0.94 ***
  D'Agostino             69.23 ***   67.49 ***   68.43 ***   69.95 ***

                            Q13         Q14         Q15         Q16

Bread
  Skewness (a)            0.27        0.29        0.24        0.26
  Kurtosis (b)            1.58 ***    1.60 ***    1.66 ***    1.66 ***
  Kolmogorov-Smirnov      0.18 **     0.21 ***    0.18 **     0.16 **
  Shapiro-Wilk            0.90 ***    0.90 ***    0.91 ***    0.91 ***
  D'Agostino             32.37 ***   28.60 ***   19.35 ***   18.39 ***
Office machinery:
Hardware and software
  Skewness (a)            0.11        0.08        0.07        0.07
  Kurtosis (b)            1.82 ***    1.75 ***    1.75 ***    1.79 ***
  Kolmogorov-Smirnov      0.16 ***    0.14 ***    0.15 ***    0.14 ***
  Shapiro-Wilk            0.95 ***    0.94 ***    0.94 ***    0.95 ***
  D'Agostino             65.53 ***   68.95 ***   64.25 ***   68.34 ***
Radio and TV equipment
  Skewness (a)            0.13        0.11        0.12        0.14
  Kurtosis (b)            1.96 ***    1.89 ***    1.87 ***    1.78 ***
  Kolmogorov-Smirnov      0.16 ***    0.14 ***    0.15 ***    0.15 ***
  Shapiro-Wilk            0.97 ***    0.96 ***    0.96 ***    0.95 ***
  D'Agostino             40.93 ***   56.06 ***   61.09 ***   63.56 ***
Footwear
  Skewness (a)           -0.19       -0.17       -0.17       -0.18
  Kurtosis (b)            1.81 ***    1.85 ***    1.86 ***    1.82 ***
  Kolmogorov-Smirnov      0.11 ***    0.10 ***    0.11 ***    0.13 ***
  Shapiro-Wilk            0.95 ***    0.95 ***    0.95 ***    0.94 ***
  D'Agostino             71.89 ***   72.09 ***   65.39 ***   68.46 ***

                            Q17         Q18         Q19

Bread
  Skewness (a)            0.25        0.32        0.25
  Kurtosis (b)            1.67 ***    1.79 ***    1.71 ***
  Kolmogorov-Smirnov      0.17 *      0.15        0.16
  Shapiro-Wilk            0.91 ***    0.92 ***    0.91 ***
  D'Agostino             16.63 ***   12.15 ***   14.10 ***
Office machinery:
Hardware and software
  Skewness (a)            0.05        0.09        0.09
  Kurtosis (b)            1.75 ***    1.73 ***    1.74 ***
  Kolmogorov-Smirnov      0.15 ***    0.16 ***    0.16 ***
  Shapiro-Wilk            0.94 ***    0.94 ***    0.93 ***
  D'Agostino             65.42 ***   63.51 ***   64.26 ***
Radio and TV equipment
  Skewness (a)            0.09        0.07        0.04
  Kurtosis (b)            1.75 ***    1.78 ***    1.79 ***
  Kolmogorov-Smirnov      0.15 ***    0.13 ***    0.13 ***
  Shapiro-Wilk            0.94 ***    0.95 ***    0.94 ***
  D'Agostino             61.04 ***   62.13 ***   60.26 ***
Footwear
  Skewness (a)           -0.19       -0.18        0.00
  Kurtosis (b)            1.83 ***    1.85 ***    1.69 ***
  Kolmogorov-Smirnov      0.15 ***    0.13 ***    0.17 ***
  Shapiro-Wilk            0.95 ***    0.95 ***    0.94 ***
  D'Agostino             72.09 ***   58.00 ***   65.37 ***

                            Q20         Q21

Bread
  Skewness (a)            0.27        0.21
  Kurtosis (b)            1.64 ***    1.62 ***
  Kolmogorov-Smirnov      0.19 **     0.16
  Shapiro-Wilk            0.90 ***    0.91 ***
  D'Agostino             15.23 ***   14.56 ***
Office machinery:
Hardware and software
  Skewness (a)            0.10        0.06
  Kurtosis (b)            1.77 ***    1.76 ***
  Kolmogorov-Smirnov      0.16 ***    0.18 ***
  Shapiro-Wilk            0.94 ***    0.94 ***
  D'Agostino             67.04 ***   68.68 ***
Radio and TV equipment
  Skewness (a)            0.00        0.00
  Kurtosis (b)            1.76 ***    1.79 ***
  Kolmogorov-Smirnov      0.15 ***    0.14 ***
  Shapiro-Wilk            0.95 ***    0.95 ***
  D'Agostino             65.41 ***   73.47 ***
Footwear
  Skewness (a)           -0.01       -0.02
  Kurtosis (b)            1.66 ***    1.66 ***
  Kolmogorov-Smirnov      0.18 ***    0.18 ***
  Shapiro-Wilk            0.94 ***    0.94 ***
  D'Agostino             63.24 ***   64.42 ***

(a,b) The values are the skewness and kurtosis indexes. We reported
the significance level of the D'Agostino, Balanger, and D'Agostino
(1990) test.

***, **, * mean statistically significant at
[alpha]=0.01, [alpha]=0.05, and [alpha]=0.10. respectively.

This paper is part of the research project "The Post-Entry Performance of Italian Firms: Technology, Growth and Survival," cofinanced by the Italian MIUR (protocol #MM13038538_001). Previous versions were presented at the Econometrics Seminars at the University of California, Riverside; the XXVIII Annual E.A.R.I.E. Conference; the 5th Annual EUNIP Conference; and seminars held at Erasmus University Rotterdam. NBER, University of Trieste, and University of Pavia. Helpful suggestions were made by Andrea Bonaccorsi, Giovanni Dosi, Samuel Kortum, Jose Mata, Markus Mobius, Lnigi Orsenigo, Ariel Pakes, Jack Porter, Roy Thurik, Aman Ullah, and, in particular, Marco Vivarelli, coeditor Robert A. Margo, and two anonymous referees. The authors thank Ettore Romagnano for assistance in data collection. The opinions expressed by Francesca Lotti do not necessarily reflect those of the Bank of Italy.

(1) Compare, among others, Mata (1994) and Hart and Oulton t1999); for opposite results, compare Del Monte and Papagni (2001).

(2) In this case, if firms were active in years t - 1 and t + 1, we considered them to be active in year t, assigning the employment size of the last month before suspension.

(3) In effect, since the 12 cohorts include firms born in each month of 1987, each column in Table 2 deals with all firms and all cohorts.

(4) The literature refers to them as "leptokunic" distributions in the former case and as "platykurtic" in the latter.

(5) We computed this test even though we were aware of its poor properties when testing for normality.

(6) Using data on the complete demography for the period 1986-1994, we observed that, differently from the other sectors, the bread industry exhibits net entry rates close to zero but a very high degree of market turbulence: Every year, the sum of exits and entries is between 10% and 11% of the population of active firms. This is a clear indication of the low level of sunk costs in this industry.

(7) As clearly shown by the low growth rate of new entries in this industry (cf. Table 3).

(8) More than any of the other industries taken into account in the present paper, the bread industry is typically one in which "there are many submarkets each large enough to support exactly one product (or plant)" (Sutton 1998, p. 597).

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Received November 2001; accepted February 2003.

Francesca Lotti * and Enrico Santarelli ([dagger])

* Research Department, Bank of Italy, Via Nazionale, 91, 00184 Roma, Italy; E-mail lotti.francesca@insedia. interbusiness.it.

([dagger]) Department of Economics, University of Bologna, Strada Maggiore, 45, 40125 Bologna, Italy; E-mail [e-mail]; corresponding author.