The size-growth relationship in the European manufacturing sector

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The size-growth relationship in the European

manufacturing sector

Jan-Joost Snijder

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Abstract

This paper examined the relationship between firm size and firm growth in the European manufacturing sector. In this study firm-level data is used for a large sample of 217,035 companies in 25 countries. The ordinary least squares regression method is used for investigating the impact of firm size on firm growth in cross section analyses for the year 2003. Two regression models were used with different measures of firm growth. In the first model it is measured by the average sales growth over the next two years and in the second model by the average employee growth over the next two years. The results of this research indicate a U-shaped relation between firm size and firm growth in the European manufacturing sector. However, the regression models in this study explain only a marginal part of the variation of firm growth rates and leave much to randomness. The conclusion of this paper is that increasing firm size leads to decreasing firm growth at a decreasing rate followed by a positive growth rate.

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1 Introduction

An important question in the market structure literature is to what extent firm size is related to firm growth. So far the existing literature does not provide one clear answer. For instance, Robert Gibrat (1931) explains in an early study about this subject that the proportionate growth of a firm is randomly determined. Therefore this ´law of proportionate growth´ assumes that firm growth follows a stochastic process. Many years later Jovanovic (1982) and Ericson and Pakes (1995) developed different learning models which assume that firm size and firm growth are negatively related. Besides the theoretical models also different relationships were found in previous empirical studies. In general, the early empirical studies show that size and growth follow a stochastic process which is in line with the ‘law of proportionate growth’. However, positive relations are reported in later studies with sample periods till the 1970s. After this period more empirical studies reported a tendency for a negative size-growth relationship.

Due to the different results from theoretical and empirical studies, this paper investigates the size-growth relationship empirically for a large sample. The relationship between firm size and firm growth is already studied for a long time but previous empirical research was mainly focused on industrial firms in the United States and the United Kingdom. This paper tries to narrow the gap in the literature by examining a large set of European manufacturing companies. In this research annual firm-level data will be used of 217,035 manufacturing companies in 25 European countries. Besides the large sample size this research contributes to the existing literature by using an up to date dataset which contains firm data from the year 2003. Further, this paper does not limit the empirical research to a specific group of companies within the manufacturing sector but includes all active firms operating in the manufacturing sector in Europe.

Based on the most recent empirical studies and the theoretical models of Jovanovic (1982) and Ericson and Pakes (1995), it is expected that there will be a negative relationship between firm size and firm growth in the European manufacturing sector. Therefore increasing firm size should lead to decreasing firm growth.

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4 the results from the empirical research and section 5 will present the conclusions that can be drawn from the empirical results.

2 Literature review

It is well known that firm growth is an important indicator for the economic success of a company. That is why firm growth plays a significant role in the existing market structure literature since many years. In the large amount of studies about firm growth different theoretical views and models are investigated extensively. To structure these developments, this section will start with a chronological overview of the most important theories of firm growth. The second part will describe several empirical results of the size-growth relationship.

Robert Gibrat (1931) introduced in 1931 the first formal model for the growth rate of firms. He introduced this model in his book ‘Inégalités Économiques’ and is also known as the ‘law of proportionate effect’ which represents a stochastic approach to firm growth. This law states that the proportionate growth of a firm is randomly determined. This model holds three important implications. The first implication of the model is that small and large firms should have equal average proportionate growth rates. Secondly the variation in the growth rates of firms should be equal for the different size classes. In other words, the mean growth rate of small companies should be equal to the mean growth rate of large companies. Finally, there should be no correlation between previous and current firm growth rates. This means that historical growth rates have no value in predicting future growth (Sutton, 1997).

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5 more efficiencies can be gained. That is why the model states that small companies will grow faster than large companies. The result of this learning model is that an inefficient company will decline in growth or go bankrupt while on the other hand an efficient company will grow and thereby survive. Therefore, it is expected that the degree of efficiency of a firm has a positive influence on its growth rate where the size of a firm is expected to have a negative influence on its growth rate.

In 1995 a refinement of the passive learning model of Jovanovic (1982) was introduced by Ericson and Pakes (1995). In their model, firms are no longer passively submitted to efficiency but firms can gain competitive advantage in the market by making additional investments in for instance research and development, product renewal and advertisement. The passive learning model of Jovanovic (1982) assumes that firms that enter the market are not aware of their cost efficiency compared to other firms. As firms become more aware of their relative efficiency, a selection will take place where low efficient firms will leave the market and efficient firms will continue to grow until they reached maturity. In the active learning model of Ericson and Pakes (1995) entrants in the market must learn to compete with products and processes to survive. A firm can meet this requirement by actively exploring opportunities in the market to improve its productivity. Regardless of the differences between the passive and active model they both predict that small firms will grow faster than large firms. In table 1 an overview is presented on the expected relationship between firm size and growth based on the above described theoretical views.

Since the start of the 1950s an enormous amount of empirical research is conducted to test the relationship between firm size and firm growth. The early studies were generally focused on testing Gibrat’s Law. Till the 1970s several studies turned out to support this law of proportionate effect. In 1956 Hart and Prais (1956) reported that overall no relationship was found between firm size and firm growth for quoted companies in the United Kingdom. They investigated companies in the mining, manufacturing and distribution sector for the period 1885 till 1950. Only for the period 1939 till 1950 small quoted firms were found to grow faster than large quoted firms. This Table 1 Theoretical relationship between firm size and firm growth

Theory/ model Introduced by Introduced in Firm size-growth relation

Gibrat's Law Robert Gibrat 1931 none

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6 was related to the non-linearity in the regression. Hart and Prais (1956) argued that this could be the result of wartime controls which favored smaller firms in this period.

In addition, Aaronovitch and Sawyer (1975) also did not find a systematic relationship between firm size and firm growth. In their study, quoted and unquoted non-financial firms in the United Kingdom were analyzed for the period 1958 until 1967. Although they used a small sample of 233 companies, no significant size-growth relationship was observed. Therefore, the law of proportionate effect could not be rejected.

On the other hand, positive relationships between firm size and firm growth were found by Hart (1965), Samuels (1965), Utton (1971), Prais (1976) and Singh and Whittington (1975). This means that in these studies larger firms were growing faster than small firms. Hence, this implies a rejection of Gibrat’s Law. In the study by Utton (1971) 1,527 quoted companies in the manufacturing sector were investigated in the United Kingdom from 1954 until 1965. He argued that the main reason for the observed significant positive relationship between size and growth was due to the large amount of mergers in the dataset. Further, Singh and Whittington (1975) pointed out that the correlation of growth rates with itself over time is the main factor for the positive relationship between firm size and firm growth. They analyzed almost 2,000 quoted companies in the United Kingdom from 1948 until 1960.

Since 1970 most of the studies indicated a weak trend that large firms do not grow as fast as small firms (Kumar 1985, Hall 1987, Evans 1987, Storey et al. 1987, Dunne and Hughes 1994, Hart and Oulton 1996). These studies were mainly focused on the manufacturing sector and showed that firm growth and firm size are negatively related. Hence, this is in line with the expected relation of the learning theories of Jovanovic (1982) and Ericson and Pakes (1995). For instance, the results of Hall (1987) confirm the negative relation for companies in the United States for the period 1972 until 1983. In the sample of this research 1,800 publicly traded companies in the manufacturing sector were investigated. Hall (1987) concludes that this negative relationship is caused by the observed phenomenon that large firms were getting smaller and smaller firms were getting larger over time. According to Mansfield (1962), Hall (1987) weakly rejects Gibrat’s Law for small firms and accepts it for large firms.

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7 manufacturing firms located in the United States. In this sample, which covered the period 1976 till 1982, large companies were oversampled. Further, no distinction was made between internal growth and external growth of a company because merger and acquisition data were not taken into account. Since this study also showed a significant negative relation between firm size and firm growth, Evans (1987) rejects Gibrat’s Law as well. However, he proves that the reason for this rejection is not caused by a sample selection bias, as proposed by Mansfield (1962). Further, the relation between firm size and firm growth is found to be non-linear because the size-growth relationship showed large variations over the firm size distribution.

Furthermore, Dunne and Hughes (1994) indicated the same relationship between size and growth as Evans (1987). Only in this more recent study small firms were found to grow faster in the United Kingdom. Dunne and Hughes (1994) investigated almost 1,700 quoted and unquoted companies in the manufacturing sector for the period 1980 until 1985. Since they did not provide a clear reason for the observed relationship, they pointed out that further research is necessary for explaining the size-growth relation. Nevertheless, Dunne and Hughes (1994) did provide general arguments for the shift in the observed relationship between size and growth since the 1960s. They state that in the 1960s and 1970s growth rates were heavily influenced by increased instability compare to growth rates in the 1950s. The first reason for this instability is the increase in merger and acquisition activity during this period. Secondly, they point out that firm growth rates could be influenced by the increase of international trade in the 1960s and 1970s.

In a study by Hart and Oulton (1996) the same size-growth relationship is observed as in the paper of Dunne and Hughes (1994). Hart and Oulton (1996) argue that the negative relationship between size and growth is probably caused by eliminating non-surviving firms from the sample. This would favor the growth rates of small firms because non-surviving firms are likely to have large negative growth rates. Next to that, they also mentioned that the relation could be influenced by the fact that it is more difficult for a company with fifty employees to double its size than it is for a company with just one employee. Therefore employee growth rates are likely to be higher for smaller companies.

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8 Table 2 Relationship between firm size and firm growth

Study Period Country Sample firms Sector

Size

measure Observations

Estimated coefficient 1

Hart and Prais

(1956) 1885-1896

United

Kingdom Quoted

Mining, manufacturing and distribution Market valuation 60 0,95 1896-1907 250 0,91 1907-1924 571 1,09 1924-1939 726 0,92 1939-1950 1712 0,75* Mansfield (1962) 1945-1952 United States Quoted and

unquoted Tires Employment 31 0,97

1945-1954 Steel Capacity 69 1,00

1947-1957 Petroleum Capacity 106 0,94

Hart (1965) 1958-1960

United

Kingdom Quoted Manufacturing sector Net Assets 1312 1.02* Non-financial companies 2515 1.03* Samuels

(1965) 1950-1960

United

Kingdom Quoted All sectors Net Assets 322 1.07*

Utton (1971) 1954-1965

United

Kingdom Quoted Manufacturing Net Assets 1527 1,06* Samuels and

Chesher (1972)

1960-1965

United

Kingdom Quoted All sectors

Capital Employed 183 0.96* 1960-1969 183 1.03 Aaronovitch and Sawyer (1975) 1958-1967 United Kingdom Quoted and

unquoted Non-financial Net Assets 233 0.99 Singh and

Whittington (1975)

1948-1960

United

Kingdom Quoted Manufacturing, construction, distribution and miscellaneous service Net Assets 1955 1,06* Prais (1976) 1951-1958 United Kingdom Quoted and

unquoted Manufacturing Employment 4300 1.08*

Kumar (1985) 1960-1965

United

Kingdom Quoted

Manufacturing and a limited

range of services Net Assets 1747 0,96*

1966-1971 including wholesale, 1021 0,96

1972-1976 retail and transport 824 0,93*

Hall (1987) 1972-1979

United States

Quoted and

unquoted Manufacturing Employment 1349 0,99

1976-1983 1098 0,99

Evans (1987) 1976-1982

United

States Age 0-6 Manufacturing Employment 4343 0,96*

Age 7-20 6124 0,95* Age 21-45 5412 0,98* Age 46+ 1520 0,98* Storey et al. (1987) 1971-1975 United Kingdom Quoted and

unquoted Manufacturing Net Assets 265 0.81*

1985-1990 308 0.90* Dunne and Hughes (1994) 1980-1985 United Kingdom Quoted and

unquoted Manufacturing Net Assets 1696 0,93* Hart and

Oulton (1996) 1990-1993

United Kingdom

Independent

companies All sectors Employment 29230 0,84*

Sales 34774 0,83*

Net Assets 55098 0,83*

1

Estimated coefficient is calculated with the formula: log Si,t = α + β log Si,t-1 + εi,t where S = firm size measure and β = (1+ estimated

coefficient)

* Significantly different from 1 at a 5% significance level

a _{Gibrat’s Law holds when the estimated coefficient is equal to 1. If the estimated coefficient is lower than 1, small firms grow faster}

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3 Data and methodology

For the compilation of the dataset for this study, firm-level data were used from the AMADEUS1 database. This database from Bureau van Dijk Electronic Publishing is chosen for this research because it provides the required firm-level financial information for more than 9.5 million public and private companies over 41 pan-European countries. For the final sample, the data from the original AMADEUS database were reduced with the following two restrictions: The first restriction was aimed at limiting the data to active companies in the manufacturing sector2. The use of manufacturing data is in line with many other papers studying firm growth and avoids data measurement problems for non-manufacturing sectors. Secondly, to avoid missing data, only companies with a known value for sales (2003 and 2005), total assets (2003), number of employees (2003) and the year of incorporation were selected. The data were reduced to the year 2003 because of a severe global recession in 2001 and 2002. This is in line with the study of Evans (1987) where also a sample period is chosen after a recession period. Firms that have been merged with another company or have been acquired in the period 2003-2005 are not included in the dataset. The same applies to firms that have gone bankrupt, did not have at least one employee or were no longer active in that same period.

To ensure that the sample is a good representation of the population (all European firms) no further limitations were used. After eliminating the data according to these restrictions the sample ends up with annual firm-level data for 217,035 companies in 25 countries. In appendix 1 an overview is presented of the number of firms per country. It should be noted that due to the data restrictions the sample becomes not very representative of the total population. As a result, the number of manufacturing companies in each country shows a mixed picture of the distribution of manufacturing companies across Europe. Furthermore, the absence of some European countries in the sample may bias the interpretation of the results.

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The AMADEUS database from the full version DVD with update number 152 for May 2007

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10 For calculating one of the control variables in this research also a second database is used. This ‘Worldwide Governance Indicators: 1996-2006’ database of Kaufmann et al. (2007) provides six governance indictors which evaluates the governance of different countries. More details about the ‘Worldwide Governance Indicators: 1996-2006’ database can be found in the paper of Kaufmann et al. (2007) which also provides a comprehensive description about the calculations behind the indicators.

This study examined how well size, age, assets and country governance explains future firm growth. Firm growth is therefore the dependent variable in the study and is measured in terms of sales growth and employee growth. These definitions are chosen because they are commonly mentioned as good indicators of firm growth (Hart and Oulton 1996, Sutton 1997). Next to that, the use of both definitions makes it possible to carry out a sensitivity analysis on firm growth. For measuring the average firm growth rate per year this paper uses the following calculations for sales growth (SGROW) and employee growth (EGROW):

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The independent variable firm size (SIZE) is determined by the natural logarithm of the number of full-time employees. Although firms hire more part-time workers nowadays, these numbers were not incorporated in the number of employees used in this study due to a lack of data. Nevertheless, the full-time employee proxy for firm size commonly appears in more recent literature and is assumed to be an important indicator for the development of a business. Therefore this paper used the number of full-time employees to define firm size. In line with other studies also a quadratic variable of SIZE (SIZESQ) is introduced in order to test a non-linear relationship between firm size and firm growth.

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11 reason, firm age is also included in this study. Since firm age (AGE) is not normally distributed it is measured by the natural logarithm of the value 1 plus the number of

years the firm exists. In this case a company incorporated in 2003 is (2003 – 2003 +1)

one year old. With adding the value of one an error is avoided by calculating the natural logarithm of a company incorporated in 2003. Another variable which is added to the regression model is total assets. The total assets (ASSETS) of the firm is a control variable which is calculated by the logarithm of the total assets (in thousands of Euros) of the firm in the year 2003.

Finally, a country variable is introduced which measures the overall level of governance in a country. This governance variable (GOVERN) is an indicator which is calculated by taking the average of the six governance indicators described by Kaufmann et al. (2007). The indicator is calculated for the year 2003 and can take a value from -2.5 to +2.5. In this case, the higher the value of the indicator the better the governance is. In table 3 a summary is provided of the variables which are used in the regression analyses.

3.1 Regression models

The regression models are based on the empirical growth equations from Hall (1987) and Evans (1987). In this study the model is extended with the variables ASSETS and GOVERN. This results in the following two models:

Table 3 Summary statistics

Variable Obs. Mean Std. Dev. Min Max

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12 SGROW i,j = α + b1 (SIZE i,j) + b2 (SIZESQ i,j) + b3 (AGE i,j) + b4 (ASSETS i,j) + b5

(GOVERN j) + ε

EGROW i,j = α + b1 (SIZE i,j) + b2 (SIZESQ i,j) + b3 (AGE i,j) + b4 (ASSETS i,j) + b5

(GOVERN j) + ε

where in the equations firm growth is a function of SIZE, SIZESQ, AGE, ASSETS and GOVERN3. The dependent variable in the first model is the sales growth and in the second it is the employee growth of a firm. The error term (ε) in the model captures those effects which are caused by the incompleteness of the model or measurement errors in determining the variables. Further the subscripts refer to firm i in country j.

This study used a linear regression analysis because the relation between the dependent and the combination of independent variables is expected to be linear. To explain the influence of the independent variables on the dependent variable a clustered robust OLS regression is performed which accounts for the clustering of the 25 countries in the database. The clustered robust method is used because the observations are likely not to be independent of each other in each country. The average firm growth rates for sales and the number of employees (over the period 2003 till 2005) are examined by using cross section data for the year 2003. The regression analysis itself is carried out by the statistical computer program STATA (version 10.0) from StataCorp LP.

It is expected that the coefficient on ‘SIZE’ is significantly negative and that the coefficient on ‘SIZESQ’ is not significant. This expectation is based on the learning models of Jovanovic (1982) and Ericson and Pakes (1995) together with recent empirical research which assume a negative relation between firm size and firm growth. According to Jovanovic’s passive learning model the coefficient of AGE is expected to be significantly negative since he assumed that only young firms can get more efficient by learning by doing. Hence, this would mean that in general younger firms have higher growth rates than older firms. Alternatively, when no significant relation is found between firm size, age and growth, it is not possible to reject Gibrat’s Law which means that the law of proportionate growth would still hold.

The fact that only firms are included in the sample that survived the period 2003 until 2005 denotes that there could be some bias in the results. Since the firms that did

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13 not survive were likely to report a negative growth, it is expected that with eliminating these firms from the sample the results could show some distortion. On the other hand, Dunne and Hughes (1994) did not find a significant difference in outcomes when making adjustments for the possible bias in sample selection. Therefore, no corrections were made for this sample selection effect in this study.

In table 4 the correlation matrix is presented for the sales growth regression model. The table makes clear to what degree two variables are correlated with each other and in which direction they are correlated (positive or negative). In table 5 the correlations are presented for the employee growth regression model. The value 1 is shown in the matrix when the variable is correlated with itself. Due to a difference in the number of observations for both models, two separate correlation matrices are displayed.

4 Results

In this section the results are presented of the two regression models which were introduced in the previous section. It is assumed that in both ordinary least square regressions the mean value of the error term is equal to zero because an intercept term is used in the regressions. Since a performed White’s test reported a non-constant Table 4 Correlation matrix 1

(obs.=215851)

SGROW SIZE SIZESQ AGE ASSETS GOVERN

SGROW 1 SIZE -0.0631 1 SIZESQ -0.0338 0.9387 1 AGE -0.1013 0.3498 0.3096 1 ASSETS -0.0972 0.7269 0.6734 0.4355 1 GOVERN -0.0783 -0.0960 -0.1293 0.1884 0.2918 1

Table 5 Correlation matrix 2

(obs.=184527)

EGROW SIZE SIZESQ AGE ASSETS GOVERN

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14 variance of the error term all standard errors are corrected for heteroskedasticity. The clustered robust method, with country clusters, is used for both models to get robust standard errors and to relax the requirement that all observations need to be independent. Due to the large sample in this research, the clustered robust method is assumed to be the most correct and accurate remedy for the heteroskedastic error terms. Therefore, no variables were redefined and no weighted least squares method is used. Further, no outliers were removed because this would unfairly bias the results of this study.

The first model that is analyzed is the sales growth model. The results of the OLS regression for this model are presented in table 6.

Table 6 OLS results sales growth model

Dependent variable: SGROW

1 2 3 4

Variable Coefficient Coefficient Coefficient Coefficient

SIZE -.0119911 (0.031*) -.1599887 (0.001*) -.18365 (0.023*) -.1476844 (0.003*) SIZESQ .023469 (0.010*) .0239344 (0.019*) .0226804 (0.013*) AGE -.1203811 (0.020*) -.1261858 (0.008*) -.1156829 (0.032*) ASSETS -.0230537 (0.426) -.0361404 (0.143) -.0251516 (0.355) GOVERN -.1243777 (0.004*) -.1227165 (0.005*) -.141688 (0.000*) -.106236 (0.008*) (Cons) .7532987 (0.000*) .6921878 (0.000*) .8642194 (0.000*) .8837787 (0.000*) R2 0.0161 0.0167 0.0197 0.0201 F 64.24 167.52 63.54 162.71 Number of firms 215851 215853 216394 215851

P-values are reported between brackets. All p-values are robust and adjusted for 25 country clusters. * indicates significance at 5% level

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15 Sometimes it happens when adding an insignificant linear and an insignificant squared term simultaneously in a regression model they both become significant. For that reason also regressions are performed with only one of these terms in the regression model. The result of the regression without the variable SIZESQ is displayed in column 1 of table 6. When the variable SIZESQ is eliminated it turns out that SIZE is still negatively significant on a 5 percent significance level. On the other hand, SIZESQ remains significantly positive on a 5 percent significance level when SIZE is eliminated. Therefore the observed influence of SIZE and SIZESQ on sales growth is assumed to be reliable.

Additionally, in column 2 and 3 of table 6 the regression results are displayed of the sales growth model without respectively AGE and ASSETS. These regressions are performed to ensure that the observed results are not influenced by the presence of multicollinearity between the independent variables. When looking at these results it becomes clear that even with the separate elimination of the variables AGE and ASSETS from the sales growth model, the direction of the coefficients and the statistical significance stay the same for the remaining variables in the model. This indicates a robust relation between size and growth.

Since a U-shaped relation is found between firm size and firm growth it is interesting to determine the bottom of this parabola. When looking at the value of the coefficients of SIZE (-.1476844) and SIZESQ (.0226804) it becomes clear that the slope leading downwards is much steeper than it is in the upward move. For calculating the turning point of the U-shaped curve, the first derivative of the sales growth equation is set equal to 0.

Solving this equation yields SIZE = 3.2557715. Since SIZE is determined as the natural logarithm of the number of employees, the turning point of the curve is at

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16 a firm reaches 26 employees. After that point, every increase in the number of employees should lead to increasing future sales growth rates. When sorting the observations for SIZE in ascending order it turns out that 150,322 observations (69.64 percent) lie below the turning point and 65,529 (30.36 percent) lie above it.

The significant negative coefficient of the variable AGE implies that younger firms

have higher growth rates than older firms. This is consistent with the view of Jovanovic (1982) who argues that young firms grow faster than older firms. Another variable that has a significant negative coefficient is the governance indicator (GOVERN). This control variable was measured for each country by the average of six different country governance indicators. The only independent variable that is not significant in this regression is ASSETS. Therefore it can be said that the total assets of a company does not remarkably influence the firm growth. Further it is important to notice that the regression only explains a very small part the variation of firm growth. The R2 indicates that the independent variables only explain two percent of the variation in firm growth rates measured by sales.

In table 7 the regression results are presented for the employee growth model. Table 7 OLS results employee growth model

Dependent variable: EGROW

1 2 3 4

SIZE -.1162752 (0.000*) -.211422 (0.000*) -.1363018 (0.000*) -.2036791 (0.000*) SIZESQ .0148431 (0.000*) .0151033 (0.000*) .0143788 (0.000*) AGE -.0726252 (0.000*) -.0478568 (0.002*) -.0695907 (0.000*) ASSETS .0680223 (0.000*) .0602901 (0.000*) .0665689 (0.000*) GOVERN -.1304338 (0.000*) -.128951 (0.000*) -.022786 (0.227) -.1183054 (0.000*) (Cons) .2229659 (0.000*) .1922269 (0.001*) .4058954 (0.000*) .307713 (0.000*) R2 0.0663 0.0693 0.0490 0.0776 F 14.70 14.09 39.05 13.54 Number of firms 184527 184529 185118 184527

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17 It is remarkable that the regression of the employee growth model shows consistent results compared to the sales growth model. Since the p-value of the F statistic is lower than 0.05 for both regressions the overall models are statistically significant. Apart from the fact that in table 7 the variable ASSETS becomes positively significant all other explanatory variables keep the same coefficient sign and their significance in both models. Even when the squared term of size is deleted from the model, the variable SIZE keeps its negative significance. However, SIZESQ loses its positive significance and becomes negative significant when the variable SIZE is deleted. Further it should be noticed that the goodness-of-fit (R2) of the model is improved to 7.76 percent. This means that the independent variables explain a higher percentage of the variation in firm growth measured by the number of employees than when it is measured by sales. Even though the R2 is improved, the variables still explain a small part of the future firm growth.

From the results shown above, it is can be concluded that Gibrat’s Law does not hold for European manufacturing firms. To be more specific it should be noted that this study can only reject one of the three versions of Gibrat’s Law which are described in the economic literature. The first version claims that Gibrat’s Law holds for surviving firms and firms that exit the market. The second one claims that it only holds for surviving firms and the third version claims that the law holds for large firms that operate above the minimum efficient scale. Since this study uses data of surviving firms and does not make a distinction between firms operating under or above the minimum efficient scale, only the second version can be rejected. The fact that both regressions report a significant relation of firm size with firm growth provides enough evidence to assume that the law of proportionate growth does not hold for surviving manufacturing firms.

Also the learning theories of Jovanovic (1982) and Ericson and Pakes (1995) do not hold. This is primarily caused by the significant positive squared term of size, implying increasing growth rates when firms become larger. Some caution should be noted because the squared term loses its significance in the employee growth model when SIZE is deleted. The fact that the age of a firm is negative related with firm growth is still in line with the learning model of Jovanovic (1982).

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18 larger it is likely that the growth rate is negatively affected, amongst others, by; the motivation of employees, the effectiveness of communication lines, the coordination of activities and the extra management layers. To explain the observed U-shaped relation between firm size and firm growth this study assumes that till the turning point all negative factors which influence firm growth outweigh all positive factors. Exactly at the bottom of the U-shape the influence of the positive and negative factors should cancel each other out. After this turning point the positive factors which influence firm growth should outweigh the negative factors when firm size increases further.

To check the sensitivity of the results, this study examines two shorter data samples. For the first examination firm data from the first seven countries, in alphabetic order, are deleted from the sample4. This means that 12,592 (5.80 percent) firms are deleted from the original sample. Due to missing data the effect is that the sales growth model and employee growth model are reduced with respectively 12,575 (5.83 percent) and 12,352 (6.69 percent) observations. For the second examination the data of firms located in Western Europe5_{, as defined by the United Nations, is excluded. This results}

in a data reduction of 37,756 (17.49 percent) observations for the sales growth model and 37,072 (20.09 percent) observations for the employee growth model. The results of the sensitivity analyses are presented in table 8. Apart from the fact that in the sales growth model AGE loses its significance on a 5 percent significance level in both regressions, the same conclusions can be drawn as from the basic regression analyses. Therefore the regression results in this study are assumed to be robust.

Finally, this study describes some data weaknesses which could affect the reliability of the results. For instance, the exclusion of firms from the sample that went bankrupt between the year 2003 and 2005. This makes it more likely that the observed growth rates in this study are higher than expected. Furthermore, firms which were taken over or were merged with another company between 2003 and 2005 also did not end up in the sample. On the other hand, mergers and acquisitions will result in unusual changes in growth rates for the purchasing company. Next to that it is possible that some (large) diversified firms were not included in the sample because they are not labeled as manufacturing firms according to the NACE Rev. 1.1 code. Besides that, no distinction is made between firms which are fully or partly owned by the government and

4

Countries excluded: Austria, Belgium, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic and Estonia.

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19 Table 8 Sensitivity analyses

Dependent variable: SGROW Dependent variable: EGROW

1 2 1 2

SIZE -.1510954 (0.005*) -.1813433 (0.001*) -.205386 (0.000*) -.226062 (0.000*) SIZESQ .0232958 (0.018*) .027876 (0.008*) .0147793 (0.000*) .0167326 (0.000*) AGE -.1125506 (0.051) -.1346625 (0.068) -.0626573 (0.001*) -.0836793 (0.001*) ASSETS -.0264901 (0.368) -.0283285 (0.351) .0642238 (0.000*) .0693253 (0.000*) GOVERN -.1129392 (0.009*) -.0951287 (0.043*) -.1203065 (0.000*) -.1182846 (0.000*) (Cons) .8931364 (0.000*) .985849 (0.000*) .3016399 (0.000*) .3658884 (0.000*) R2 0.0206 0.0214 0.0783 0.0851 F 262.45 356.70 11.87 17.23 Number of firms 203276 178095 172175 147455 Number of countries 18 19 18 19

P-values are reported between brackets. All p-values are robust and adjusted for country clusters. * indicates significance at 5% level

Countries excluded in regression 1: Austria, Belgium, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic and Estonia. Countries excluded in regression 2: Austria, Belgium, France, Germany, Netherlands and Switzerland

the ones without government ownership. A government-owned firm is likely to grow faster because it is expected that these firms have easier access to capital markets for raising money. Another weakness is the restricted time span of this research. Since economic cycles can cause large fluctuations in economic growth, it is possible that the conclusions that are made in this research will not be robust over time. Finally, it should be mentioned that excluding part time workers from the number of employees working at a firm results in misinterpretations of the relationship between firm size, measured in number of FTE’s, and firm growth. In this case it is obvious that the firm size measured in FTE’s is not representative for a company with many part time workers.

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5 Conclusions

The purpose of this research is to analyze the influence of firm size on the future growth rate of the firm. This size-growth relationship is tested using a large sample of 217,035 manufacturing companies in 25 European countries. From regressions performed with the ordinary least squares method with clustered robust standard errors it becomes clear that firms size has a negative influence on firm growth and the squared term of firm size has a positive influence on firm growth. Therefore the regression results indicate that firm size has a U-shaped relation with firm growth. In this research firm size is measured by the number of full time employees and firm growth is measured by sales growth and employee growth.

The observed size-growth relationship is not supported by leading theories in the existing market structure literature. This means that the results can not be explained by the active and passive learning models of Jovanovic (1982) and Ericson and Pakes (1995). Also Gibrat´s Law is rejected since the results are significant on a 5 percent significance level which means that firm growth of surviving manufacturing firms is not based on a stochastic process.

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Appendix 1

Country Number of firms

1 Austria 18

2 Belgium 2460

3 Bosnia and Herzegovina 504

The size-growth relationship in the European manufacturing sector