Optimal Innovation : Evidence from the U.S. Manufacturing Industry

Transcription

1 Optimal Innovation : Evidence from the U.S. Manufacturing Industry Sungmin Han Texas A&M University Abstract The purpose of this paper is to investigate the relationship among firm growth, firm size and firm behavior in the U.S. manufacturing industry between 2000 and This study first considers the manufacturing industry and extends the model to the retail trade and accommodations industries. As others have found, firm size is negatively related to firm growth and positively correlated with firm survivability in the manufacturing industry. These findings are consistent with those of a theoretical model including an innovation process. It also finds that Gibrat s Law holds for large firms. R&D investment representing product innovation has a significantly positive effect on firm growth and survivability in the same industry. The results are robust to different classification of firm size and different time. In the services industry, advertising investment causes a reverse effect on firm growth. This suggests that innovative activities should vary depending on the characteristics of each industry. Department of Economics, Texas A&M University, College Station, TX shan@econmail.tamu.edu 1

2 I. Introduction A great deal of study has been devoted to the effect of firm size on firm growth. Less attention has been given to other factors affecting firm growth. Firms grow by making innovations in their products. Innovations can be attained by firm s investments. Therefore, innovations through investments are the basis on firm growth. This study investigates how firm behavior affects firm growth over time and interacts with an innovation process of its competitors. It is based on a theoretical stochastic model with the innovation process for an individual firm and empirically examines the relationship between firm growth and innovative activities related to firm investment strategy in manufacturing and service industries from 2000 to I focus on i) whether the theoretical model is consistent with the empirical results by testing the law of diminishing returns to scale for R&D and service oriented industries, ii) identifying the roles of innovative activities - R&D, advertising and capital investments, on firm growth and iii) the pattern of firm growth dynamics. This paper first analyzes the manufacturing industry and extends the model to the retail trade and accommodations industries. Firm growth has been a longstanding issue in economics. Gibrat (1931) first claimed that a firm s expected growth should be proportional to its current size. It implies that a firm s expected growth rate should be independent of its size. Gibrat s Law, called the Law of Proportionate Effects, has been taken as an assumption by economists. Lucas (1978) assumes Gibrat s Law to prove the existence and uniqueness of an equilibrium of the size distribution of firms. A number of economists have empirically tested it to show the relationship between firm growth and size. These studies found out the existence of the decreasing returns to scale in economy by rejection of Gibrat s Law. Most of the earlier studies mainly focused on identifying the relationship between firm growth and size in the manufacturing industry. However, a recent trend in endogenous firm growth theory emphasizes the importance of innovation measured by R&D investment level as well as firm size on firm growth. Therefore, this article first investigates whether the theoretical model derived from endogenous firm growth theory is consistent with the empirical results including innovative activities on Gibrat s Law in the US manufacturing sector. Innovation (the advent of new products) plays a major role for firm growth (Mansfield, 1962). It is also related to firm s investment which involves the expenditure of considerable resources. Hall (1987) investigates that firm growth is related to the degree of capital investment in the US 2

3 manufacturing sector. The study describes the difference in innovative activities to affect firm growth. It is found that R&D investment needs only half of the physical investment to obtain the same effect on firm growth. Does the result happen because manufacturing firms concentrate more on R&D activity? Is it enough to explain the firm growth? In the services industries, firms focus more on advertising investment rather than R&D investment. Then, is the advertising investment also related to firm growth? Therefore, we need to investigate different innovative activities according to different industries. First, how can we define innovation 1? Innovation is generally defined as introducing something new. If we consider innovation as the introduction of a new good (product innovation), it is certain that firm s R&D investment plays a vital role to produce it. The firm can gain a competitive advantage by introducing a new product, which allows it to increase mark-ups. Hence, it can be one of the critical factors to explain the relationship between innovative activity and firm growth. If we consider innovation as the change in equipment (process innovation), capital investment to improve production or gain a cost advantage over its competitors is associated with firm growth. Furthermore, if we interpret innovation as a new marketing method (marketing innovation), advertising investment influences innovation since it involves significant changes in product promotion which involves promotional efforts made by firms to improve their products image or to increase awareness of their products. It normally results in competitive advantage. In this regard, advertising investment may also represent firm behavior. However, each industry has its own characteristics. Most firms in manufacturing industry concentrate on R&D investment to innovate, while firms in services industry spend more money on advertising or capital investment in general. Hence, this study focuses on identifying the roles of various investments - capital, advertising and R&D investments, on firm growth depending on different industries. Finally, this study analyzes the pattern of firm growth dynamics. As pointed out above, it focuses on the effect of different investments on firm growth. Here, an interesting question may arise. How does firm behavior affect firm growth with the passage of time? This analysis examines the effects of R&D investment and firm size on firm growth in the manufacturing industry during the seven year period. 1 The OECD s Oslo Manual defines an innovation as the implementation of a new or significantly improved product or process, a new marketing method, or a new organizational method in business practices, workplace organization or external relations (OECD, 2005, p.46), Appendix A supports general classification on innovation. 3

4 The aim of this work is to fill the gap of the existing firm growth literatures. Many theorists and empirical economists have concentrated on identifying the relationship between firm growth, size and age without considering other factors to affect firm growth. They did not believe that there was a causal relationship among them. However, it is found that there is a negative(positive) relationship between firm size(age) and growth. Recently innovation is a critical factor for firm growth. This study is based on the endogenous firm growth theory generated by innovation process to check the effect of firm investment s level on firm growth. There has been much discussions of the importance of the endogenous firm growth. However, literatures regarding endogenous firm growth theory showed simple empirical findings regarding the relationship between R&D investment, firm size and firm growth after proving the optimal level of investment from the theoretical model. This article captures which investment is more related to firm survivability and firm growth rate. It also finds whether there exists the decreasing returns to scale in economy. Furthermore, it describes the effect of different innovative activities on firm growth according to the size distribution of firms. For the empirical part, this paper uses cross-sectional analysis to show the dynamics of the firm growth in three sectors - manufacturing, retail trade and accommodations & food services sectors from 2000 to This paper is organized as follows. Section II presents theoretical model. Section III represents datasets used in this study. Estimation is developed in Section IV. Section V summarizes the results. Extension to other industries describes in Section VI. Conclusion is drawn in Section VII. A. Related Literature The first empirical test for Gibrat s Law was examined by Simon and Bonini (1958). They investigated the distribution of growth rates according to different firm sizes - small, medium and large firms. They found that the distributions of those firms were equal if they were above the minimum efficient size level. Gibrat s Law holds under this condition. Mansfield (1962) studied specific industries - steel, petroleum and rubber tires - to show whether Gibrat s Law holds according to the different time periods in the early 1900s. Also, the study tests whether a successful innovation has an impact on a firm s growth rate. With respect to Gibrat s Law, it generally fails to hold for all firms including firms that leave the industry. On the contrary, it holds for survival firms in six of ten cases. The result regarding innovations indicates that there is no tendency for the 4

5 successful innovators to grow more rapidly before introducing their innovations. However, after introducing them, the mean growth rate for innovators exceeds that of non innovators. Another analysis of different industries and periods is examined by Hart (1962). He investigates the average, dispersion and distribution of proportional growth rates for large, medium and small firms in a brewing, cotton and drink industry from 1930 to It is found that all firms have the same average proportionate growth rate and the same dispersion of growth rates over the average. It is consistent with Gibrat s Law. Log normal distribution implies that the relative dispersion of the sizes of firms tends to increase over time. Until 1982, most economists tried to find only stylized facts which meant the relationship between firm size and growth. The relationship could be negative or positive according to particular periods and industries when applied to real data. Jovanovic (1982) discovered that firms could learn about their efficiencies from the realizations of costs during operation in the industry. It implies that there exists the decreasing returns to learning in economy. That is, young firms grow faster than older firms. Afterwards, many economists have tried to show the relationship among size, age and firm growth. Evans (1987a) analyzed firm growth, firm survival and the variability of firm growth with a larger sample for young and old firms in manufacturing sector. The study examines econometric issues which early literatures have not focused on by controlling for sample selection bias and heteroscedasticity. It is found that there is a negative relationship between firm growth and size which is not consistent with Gibrat s Law. This contradicting result is due to a larger and more comprehensive sample of firms and control for sample censoring arising from firm exit. Moreover, the probability of firm survival increases with firm size and firm age. Finally, there is also a negative relationship between the variability of firm growth and firm age. This paper considers age as a crucial determinant of firm growth. It can be described that this negative relationship is consistent with the learning model predicted by Jovanovic. Therefore, the paper describes the existence of a diminishing returns to scale and learning in economy. Evans (1987b) also tested two theories, Jovanovic s Theory and Gibrat s law. The findings are the same as the previous literature. However, it focuses on more econometric issues. The paper considers nonlinearity, sample censoring, heteroscedasticity and the level of statistical significance on the relationship between firm growth and size. He explains these issues by testing higher order logarithmic expansion, White s heteroscedasticity test, jointly estimating the probit of survival and the firm growth by maximum likelihood 5

6 estimation and Bayesian approach by Leamer (1978). In the late 80s, most of the empirical papers have checked the two theories using a large number of data sets for various industries, especially manufacturing and service sectors. However, they did not consider other factors to affect firm growth. As discussed above, they focused only on the relationship among them. There are few papers that considered other factors on firm growth. Hardhoff, Stahl and Woywode (1998) consider legal forms for the determinants of firm growth. Other researchers began considering various factors such as R&D activities, consumer decision behaviors and ownership structure as the determinants of firm growth. In the early 2000s, economists started developing methodologies to solve the econometric issues. They use the panel unit root tests to unravel cross sectional correlation problems emerged due to the short panel and the quantile regressions to see if acceptance or rejection of Gibrat s Law depends on the level of firm growth. Recent trend on the analysis of firm growth has moved to dynamics of an individual firm. Innovation such as R&D activity has been a critical issue on firm growth. Klette and Griliches (2000) presents the pattern of firm growth with a quality ladder model which represents that the quality of the product is increased through cumulative innovations. They derive the optimal level of investment from a Bellman equation. It is found that under the steady state level, R&D intensity and firm growth is independent of firm size. Klette and Kortum (2004) which is based on this study, set up the valuation model for an individual firm. They investigated ten stylized facts proved from the previous studies on the firm level studies of innovation. It first described the dynamics of individual firms and extended a general equilibrium model for aggregate innovation. They showed a positive relationship between productivity and R&D and between patents and R&D with the Poisson hazard rate of innovation occurrence. However, it is found that R&D is not strongly related to the productivity growth and the expected firm growth rate is independent of its size. II. Theoretical Model As discussed above, innovative effort is represented by R&D, capital and advertising investments depending on industry characteristics. This section examines the theoretical results regarding the effects of R&D investment and firm size on firm growth. The first purpose of this study is to discuss whether empirical results are consistent with the results derived from a theoretical model. 6

7 Unfortunately, there have not been many theoretical models in early studies on firm growth theory since researchers focused only on the empirical testing. Klette and Kortum (2004) focus on a theoretical stochastic model with product innovation measured by R&D investment to explain firm growth. A value function is used to obtain the optimal level of R&D investment. They derive the relationship between firm growth, firm size and R&D investment from the model. It is a departure for this study. The model assumes that a firm of size n chooses an innovation policy, I(n). Firm s R&D investment determines the Poisson rate, I at which a firm s next product innovation arrives. A firm s innovation intensity, λ, is denoted as I(n)/n. To see the investment decision for a firm, we need to consider other firms innovative activity. The incumbent firm can lose the good from its portfolio if other firms will innovate on a good it is currently producing. This event can be represented by the Poisson hazard rate per good, λ. To derive the relationship among firm growth, firm size and R&D investment, consider the probability of becoming a firm of size n. Let p n (t, n 0 ) denote the probability that a firm size is n at t given n 0. At any instant of time, a firm will be in three different situations to be a firm of size n: i) if the firm had n 1 products, it becomes a firm of size n by innovation, ii) if the firm had n + 1 products, it loses a good by other firm s innovation and iii) if the firm already had n products, it might innovate or lose a good. The rate at which this probability changes over time is p n (t, n 0 ) = (n 1)λp n 1 (t, n 0 ) + (n + 1) λp n+1 (t, n 0 ) n(λ + λ)p n (t, n 0 ), n 1 (1) The probability of exit is p 0 (t, n 0 ) = λp 1 (t, n 0 ) (2) Equation (1) and (2) can be solved by the probability generating function 2. In this section, we focus on the economic implications of that solution. Let the firm growth rate from date 0 to t be 2 Calculation is described in Appendix B. 7

8 denoted by G t = (N t N 0 )/N 0. Klette and Kortum show : [ ] Nt N 0 E[G t N 0 = n 0 ] = E N 0 = n 0 N 0 = 1 N 0 E[N t N 0 = n 0 ] 1 = 1 np n (t, n 0 ) 1 N 0 n=1 = e ( λ λ)t 1 (3) In equation (3), the expected firm growth rate given initial size is independent of its initial size, which is consistent with Gibrat s Law. However, it is dependent on innovation intensity. A firm s expected growth rate increases with its own innovation intensity given other firms fixed innovation rate. However, if we consider firms that exit during the period, we can derive the expected growth rate conditional on survival. The probability that a firm of size n 0 at date 0 survives to date t is 1 p 0 (t; n 0 )=1 p 0 (t; 1) n 0. 3 The probability that a firm exits is high when λ is less than λ. Hence, the survivability increases with initial size. The expected growth rate conditional on survival is E[G t N t > 0, N 0 = n 0 ] = e ( λ λ)t 1 [p 0 (t; 1)] n 0 1 (4) Equation (4) can be interpreted differently depending on the initial size. As for large firms, the expected growth rate is independent of its size since the probability of exit to date t is close to zero. However, it has a negative relationship with its size for small firms, which contradicts Gibrat s Law. In both cases, the innovation intensity measured by R&D investment intensity affects firm growth. It is not possible to derive an exactly same form for estimation from equation (4) due to the complexity of the probability of firm exit. Nevertheless, we can derive a meaningful estimation model which represents the relationship between firm size, innovative activity and growth. Based on this model, I estimate the empirical model to check whether the theoretical results derived from (4) are consistent with the empirical ones. Even though this model is derived from a dynamic process, a cross sectional analysis is more appropriate because an innovation intensity is much different across firms than across time. 4 3 p 0(t; n 0)= [ λ λe ( λ λ)t λ λe ( λ λ)t ] n0 4 The average of R&D intensity is in 2000 and is in The ratio of the increment between the two periods is 5.8%. But the standard deviation for R&D intensity in 2000 is

9 III. Data Information for various investments is required to investigate the effects of innovation on firm growth. Most firms publicly disclose this information through the balance sheet, income statement and financial statement every year. The term of XRD is used for R&D investment in this study. This information can be obtained from each firm s supplementary income statement. More accurate definition for variables is described in Appendix C. This paper focuses on the relationship between firm investment and firm growth. Hence, other investments - advertising and capital expenditures, are also considered to see the effects of firm investment on firm growth for the analysis of different industries. Each variable for firm investment is defined in COMPUSTAT as follows 5 : XRD is all costs incurred during the year that relate to the development of new products or services. XAD is the cost of advertising media and promotional expenses. CAPX is the amount spent for the construction and/or acquisition of property, plant and equipment. Each variable can be obtained from the balance sheet and income statement. I gather these data from CRSP/Compustat Merged Database. It provides researchers with information of individual firms in the U.S., especially financial statement. It is comprised of CRSP and Compustat data together with the link and link-history references between these two databases. It covers stock market data on major stock exchanges even if Compustat covers basically accounting data for public and private companies. However, CRSP has many missing data in some industries. Therefore, this study discovered possible industries without many missing data for more precise estimation. I first investigated the largest nine industries to avoid missing data. The ratio of missing data to total observations for each industry during seven years is described in Appendix D 6. The investigation is distinguished by two digit NAICS Codes. Most of the missing data 7 come from XAD and XRD since many firms report no formal R&D and advertising activities. Some firms do not report only these information even if they report all other information except them. It is difficult to know the reason why a firm has no R&D or advertising information. It does not really 5 Appendix C provides more detailed definition. 6 The variables of interest, XAD and XRD are highlighted. 7 It is expressed by (dot), in the data set. 9

10 invest in R&D or report R&D activity due to firm s business strategy even though they invest in R&D. If firm does not report it, CRSP treats it as a missing value. [Table 1 about here.] Hence, missing values are excluded due to the difficulty of obtaining the information about them, but zero R&D activity is included. In other industries except manufacturing, retail trade and accommodations & food services, the ratio of missing data for these variables is over 70 percent. Hence, the analysis for these industries may produce unreliable results. Consequently, manufacturing, retail trade and accommodation & food services are used for this analysis. As pointed out above, R&D and capital investments are first considered to estimate their effects on firm growth in the manufacturing sector. Afterwards, the model is extended to the services sector to investigate the effect of advertising and capital investments on firm growth. This study uses the longitudinal data from 2000 to In the theoretical model, firm size is defined as the number of products. However, it is not possible to obtain this data regarding how many products a firm have. A suitable proxy variable is needed. Hence, the data for size is collected through employment information same as the conventional way that most literatures have considered. Information for employment are also described in Appendix C. We can obtain each firm s growth rate from the difference of employment size between the two periods, 2000 and All data is distinguished by NAICS code. The descriptive statistics on the variables used in this paper are in Table 1. The statistics are presented separately by manufacturing, retail trade and accommodation & food services sectors. [Figure 1 about here.] Table 1 reports the number of surviving firms in 2006, the average annual growth rate of employment between 2000 and 2006 for surviving firms and the average expenditures of capital, advertising and R&D investments for all firms in Zero employment values are treated as missing values since firms might not operate without employment. As discussed above, all missing values are excluded in all industries. The means of R&D investment in retail and accommodation industries are very low because most firms do not invest in R&D activity. Hence, R&D investment is not considered when this paper investigates the services industries since it might cause biased estimators. It is 8 The growth rate is S t = (N t N t0 )/(t t 0). Where N t and N t0 are the employment size at time t and the initial time. 10

11 one of the reasons why this study focuses on the manufacturing sector. When we consider the employment in manufacturing industry, the mean is 7754 and the standard deviation is The range for firm size is very wide and the distribution of firm size is highly skewed. Figure 1 illustrates it. Hence, we need to divide each firm into size classes. Hall (1987) divided the size into small and large firms by 2500 employees to make equal numbers in each class. However, it is impractical to define firms with over 2000 employees as small firms. Hence, the percentage distribution of firm size is used to classify firm sizes classes in this study. It can be a good measure to determine the size class. [Table 2 about here.] Table 2 illustrates the average employment, the standard deviation and the number of firms according to the percentage distribution of firm sizes in all industries. The first column indicates the smallest group within the 0-10 th percentile in all industries. The mean of employment is 36 and the standard deviation is 18 in the manufacturing industry. However, in retail trade and accommodations industries, the means of employment are 108 and 324 respectively. It describes that there are a number of small firms in manufacturing industry compared to other industries. In the second column, the average employment within the th percentile in the manufacturing industry is also lower than other industries. The same trend appears in the other groups over the 25 th percentile. In the next section, an estimation for firm sizes classes is executed in the manufacturing industry. Based on this percentage distribution, this study considers small firms as the firms within the 0-25 th percentile and large firms as the firms within over the 25 th percentile. 9 In the theoretical model, it is said that Gibrat s Law holds for large firms, while it fails for small firms. Hence, we can anticipate that the coefficient of firm size is significantly negative in the manufacturing industry due to a large number of small firms when we estimate the model. Insignificant results are expected in accommodations industries, which represents that firm growth is independent of its size. In retail trade, the results can be significant or insignificant. 9 The range of the employment for small firms is up to 154 in the manufacturing industry. Firms with over 155 employees are classified as large firms. In this study, firms only in manufacturing industry are considered as small and large firms. 11

12 IV. Estimation A. Traditional Model A number of literatures used the simple regression model to test Gibrat s Law as below. conventional model to see the relationship between firm growth and size is The ln(s it ) = β 0 + γ 1 ln(s it 1 ) + ɛ it 1 ln(s it ) ln(s it 1 ) = β 0 + (γ 1 1) ln(s it 1 ) + ɛ it 1 ln(s i ) = β 0 + β 1 ln(s it 1 ) + ɛ it 1 (5) Equation (3) of the theoretical model predicts that firm growth is independent of its size. In equation (5), if β 1 = 0, then it is consistent with those theoretical results. That is, Gibrat s Law holds. If β 1 < 0, then Gibrat s Law fails. It implies that small firms grow faster than larger firms. Otherwise, larger firms grow at a higher rate than small firms. 10 However, prior to the estimation, econometric issues should be unraveled. Next section describes this problem. B. The Regression Model In the theoretical model, expected growth rate is dependent upon innovation intensity. Hence, all expenditure variables are divided by 2000 employment size. In the data section, I mentioned the variables to be considered as the determinants on firm growth. The regression model 11 to explain the effect of firm behavior on firm growth in manufacturing industry is ln(s i ) = α i + β 1 ln(s it 1 ) + β 2 ln(cap XV it 1 /S it 1 ) + β 3 ln(r&d it 1 /S it 1 ) + ɛ it 1 (6) Where i is an individual firm and α i is a firm specific term. CAP XV it 1 is the investment of property, plant and equipment. R&D it 1 is R&D expenditure and ɛ it 1 is a normally distributed 10 After Jovanovic mentioned the learning effect of firm efficiency, researchers started considering firm age. However, the purpose of this paper is to identify the roles of firm investments on firm growth derived from innovation process. Therefore, I add investment variables without considering firm age. 11 Hall (1987) considered firm size, capital expenditures, R&D investment and dummy variables for growth function and Tobin s Q for probit function. 12

13 error term with mean zero and variance σ In the theoretical model, equation (3) represents that firm growth is independent of its size and dependent on the level of firm investment. However, as I mentioned in the previous section, a critical econometric problem may occur. The growth rate for each firm is not always observed because some firms do not exist in the industry any more during the sample period. There are some reasons. A firm may bankrupt or merge. It is impossible to distinguish the explicit reasons why firms do not exist in the dataset. ln(s i ) is observed if firm i is observed both in 2000 and 2006 sample. Let us express this status as SUR it = 1. If firm i is not observed in 2006 sample but in 2000, the status is expressed as SUR it = 0. Then we can define the selection function as follows. SUR i,t = θ 0 + θ 1 ln(s it 1 ) + θ 2 ln(cap XV it 1 /S it 1 ) + θ 3 ln(r&d it 1 /S it 1 ) + ν it 1 (7) 1 if SURi,t SUR i,t = 0 (8) 0 if SURi,t < 0 Where ν it 1 is a normally distributed error term with mean zero and variance 1. The appropriate econometric method to deal with the selection problem, equation (6) and (7), is the two step procedure suggested by Heckman. The error terms (ɛ it 1, ν it 1 ) are assumed as below. Heckman Two Step Procedure ( ɛit 1 ν it 1 ) N (( ) 0, 0 ( σ 2 )) ρσ ρσ 1 We can observe a dependent variable of interest, ln(s i ) if firm i is observed both in 2000 and 2006 sample, but this variable is unobserved if firm i is not observed in 2006 but in Then a selection problem may occur. The following model describes this problem. ln(s) = Xβ + ɛ (9) SUR = 1[Zθ + ν > 0] (10) 12 When we estimate this model, we may encounter 0 values. In this case, we can add 1 to make log(1) = 0 since any firm does not invest only $1. 13

14 Where X is the explanatory variables in the growth function, (6), and Z is the explanatory variables in the survival function, (7). Since ln(s i ) is observed only when SUR i,t = 1, we should estimate E( ln(s) X, SUR = 1). E( ln(s) ln(s) is observed) = E( ln(s) SUR > 0) = E( ln(s) Zθ + ν > 0) = E(Xβ + ɛ Zθ + ν > 0) = Xβ + E(ɛ Zθ + ν > 0) = Xβ + E(ɛ ν > Zθ) = Xβ + ρσλ(zθ) = Xβ + γλ(zθ) (11) Where λ(zθ) = φ(zθ)/φ(zθ) is the inverse Mills ratio. φ(zθ) and Φ(Zθ) denote the normal density and cumulative distribution respectively. We can consistently estimate β and θ using the selected sample by regressing y on X and λ(zθ). A consistent estimator of θ is available from the first stage probit estimation of the selection equation. V. Results From the theoretical model, equation (4), it is found that a firm s expected growth rate is independent on its initial size for large firms, but not for small firms and dependent of an innovative activity. To prove these theoretical results, the regression model is estimated by Heckman method. The estimation results in the manufacturing sector are described in Table 3. [Table 3 about here.] Table 3 describes the results of three different estimations with and without considering R&D investment. Each panel of the table is organized as follows. The top panel represents OLS and probit estimation in firm growth and survival functions, equation (6) and (7) of the empirical model. The bottom one is estimated by the sample selection model, equation (11) of the empirical model. In the first column of the growth function, (1), the coefficient of firm size is and significantly negative at the 5% level. As for the survival function, (1), the coefficient of firm size is and 14

15 significantly positive at the same level. The first result describes that Gibrat s Law fails, which is consistent with the theoretical model since there are a number of small firms in the manufacturing sector. It implies that small firms grow faster than larger firms since they tend to increase their size to survive in a market. In the next table, the model is estimated separately for small and large firms to observe the difference between them. As discussed above, this study regards small firms as firms whose employment size distribution is less than the 25 th percentile. Firms whose size distribution is over the 25 th percentile are regarded as large firms. The second result indicates that firm survivability has the significantly positive relationship with its size. These results are similar to those already stated in the previous research (Evans 1987a). The results of the sample selection model, (1), are similar to those of growth and survival function. The second and fifth columns, (2), show the estimation results of the relationship between R&D investment and firm growth under the control of firm size. From these columns, we can see the negative relationship between firm size and growth even when taking account of the effect of R&D. The failure for Gibrat s Law is still confirmed. The results of OLS and probit are not much different from those of the sample selection model in these columns. It means that the variation in growth rates across firms which remains after controlling for size is uncorrelated with the probability of survival. That is, growth rates do not seem to be related to survival. Therefore, it is said that selection bias of this kind does not seem to account for the negative relationship between growth and size. Hall (1987) found that correcting for attrition bias had very little effect on these results. Next, we proceed to the relationship between firm growth and innovative activity. The coefficient of R&D expenditure is and significantly positive at the 5% level. If we connect it with the theoretical model, it can be said that product innovation by R&D investment is positively related to firm growth. It influences on firm survivability as well as firm growth. Firm survivability is highly correlated with firm R&D investment. In the third and last columns, capital investment variable regarded as a process innovation is added. This variable is considered to see whether another investment can significantly change the results. Capital investment is not significantly positive, but it confirms the significantly positive relation among R&D investment and firm growth. It did not change the size and R&D coefficients in both equations very much. Consequently, R&D investment plays a vital role for firm growth and survivability in the manufacturing sector. R&D might be more highly correlated with future success of the firm since it is more forward looking (Hall, Griliches 15

16 and Hausman [1986]). [Table 4 about here.] Table 4 reports the effect of R&D investment on firm growth for small and large firms. All results are estimated by the sample selection model. In the case of the small firms, the coefficient of firm size of the growth function is and significantly negative at the 5% level. The growth rate is dependent of its size for small firms, which is consistent with the theoretical results, equation (4). However, as for the large firms, the coefficient of its size of the growth function is insignificant. The result is consistent with equation (4), which implies that firm growth is independent of its size. In the theoretical model, the likelihood of survival increases with firm initial size. As for the survival function, the coefficients of its size are and However, it is insignificantly positive for small firms. It is because that the probability of survival to date t is close to one for initially large firms. The coefficients of R&D investment for the growth function are insignificant for small firms although Table 3 reports that it is positively related to firm growth. However, it is significantly positive for large firms. It is difficult to connect these results with the theoretical results. It may happen due to the classification of firm size. Nevertheless, we can infer that R&D investment is more important for firm growth as firm size gets larger. Finally, R&D investment is positively related to firm survivability for small firms, but not for large firms. Table 5 illustrates the relationship among firm size, R&D investment and firm growth during the different periods. All results are estimated by the sample selection model. [Table 5 about here.] The number of exiting firms has increased during the period between 2000 and Each column represents the effect of R&D investment on firm growth during the two periods. All growth rates are actually measured in annual terms in order to make the coefficients comparable. Comparing these results to the previous ones, we can obtain similar interpretations. As regards the survival function, the coefficient of its size has increased over time from during 2000 and 2001 and during 2000 and The likelihood of survival has increased by 56%. The number of exiting firms has increased by almost 6% annually since Firm size for survival firms becomes 13 In table 3, as for the survival function, the coefficient of its size is between 2000 and

17 a more important factor for firm survivability over time. 14 Also, the coefficients of R&D investment are significantly positive at the 5% level in all cases except the period of 2000 and 2002, but decline after It also tells us that R&D investment plays a crucial role for firm survivability and becomes less important over time. As for the growth function, Gibrat s Law fails except the first and third columns. Nevertheless, it is consistent with the previous theoretical and empirical results. Here, there is an interesting implication for R&D investment. The coefficients of R&D investment are significantly positive in four out of six cases including the period of 2000 and 2006 in Table 3. The coefficient of R&D investment between 2000 and 2001 is even higher than any other period. We can infer that R&D investment has a significant effect on firm growth in the subsequent year. However, it does not have a long lasting effect on firm growth. It is found that R&D investment significantly influences on firm growth and firm survivability even if it becomes less important over time. R&D investment is a more important predictor for firm growth in the immediate future. VI. Extension Section V showed that the empirical results regarding the relationship among firm size, firm investment and firm growth were consistent with the theoretical results. However, we have merely observed the effect of R&D investment on firm growth in the manufacturing sector since the theoretical model considers product innovation. If I include advertising investment for the manufacturing regressions, significant results can not be obtained. Estimation results for this specification are available from the author upon request. Many firms in other industries also innovate, but use different methods such as process or marketing innovation as mentioned before. Hence, considering other innovative activities in different industries may be more effective to understand the relationship between firm behavior and firm growth. In retail trade and accommodations industry, firms mainly use process or marketing innovations. In this section, these results are not derived from a theoretical model. It merely describes the magnitude of the correlation between different innovative activities and firm growth in retail trade and accommodations industries. They do not generally focus on R&D investment. [Table 6 about here.] 14 Similar results are found when time dummies are included. 17

18 It is not simple to find appropriate variables to represent such innovative activities for estimation. As discussed in the data section, in terms of reducing costs and gaining competitive advantage, capital and advertising investment is respectively used in this analysis. Table 6 and 7 report different estimations with considering different investments. In the first column of Table 6, as regards the sample selection model, the coefficient of firm size is and insignificant at the 5% level. However, if we add an advertising variable, the coefficient of firm size is significantly negative, which fails Gibrat s Law. In the third and fourth columns, (3) and (4), advertising and capital investments are considered. The coefficient of capital investment is significantly positive, but advertising investment coefficient is significantly negative at the same level in (4). These findings describe that capital investment positively affects firm growth, but advertising expenditure tends to be negatively correlated with firm growth. It is said that firm growth increases with capital expenditure, while advertising expenditure can cause a reverse effect on firm growth in retail trade industry. From this result for advertising investment, we can infer two things. [Table 7 about here.] First, this study focuses on firm behavior represented by innovative activity on firm growth. In this industry, product innovation is not a major innovative activity. 15 Most firms invest in advertising. Therefore, advertising expenditure can be an innovative activity. It can be used for marketing innovation in this analysis. Nevertheless, it might not be enough to explain an innovative activity. Secondly, advertising investment might not really affect firm growth. There might be a positive effect to advertise its products in terms of gaining competitive advantage over its competitors. However, a firm needs a lot of money to invest in advertising. If an advantage from advertising does not directly appear, it can cause costs to increase. Consequently, increasing costs results in a negative effect on firm growth. It is concluded that in the retail trade industry, capital investment is a more important factor for firm growth rather than advertising investment. The results of the sample selection model are almost similar to growth and probit model since ρ is insignificant. Table 7 reports the results for accommodations industry. Like the preceding, advertising and capital expenditures are considered. In table 2, firm size in this industry is relatively high - even the mean of the 10% group is 324. It implies that most firms are large in this industry. Hence, 15 In the data set, only 10% of the firms in this industry invests in R&D. 18

19 it is expected that the coefficient of size is insignificant, which is consistent with the theoretical model. As for the growth rate function and sample selection model, the coefficient of size is and insignificant at the 5% level. As predicted, firm growth is independent of its size. In all cases, the coefficients of firm size are not significant. As for the survival function, firm size still plays an important role for firm survivability. Large firms have a higher probability of survival. If we add the advertising and capital investment variables, the coefficient of capital investment is not significant. However, the result for advertising investment is the same as the retail trade. Advertising expenditure is negatively correlated with firm growth. This finding can be explained by similar reasons mentioned in the previous case. VII. Conclusion In this paper, the relationship among firm size, firm behavior and firm growth rate in the US manufacturing, retail trade and accommodations is analyzed using CRSP/Compustat merged data between 2000 and The first analysis is to find the relationship between firm size and firm growth, called Gibrat s Law. In the theoretical model, firm growth rate is independent of its initial size for large firms and dependent on its size for small firms. In the empirical model, we can derive the similar results to the theoretical ones. The result obtained here is that firm size has a significant negative effect on firm growth in general. Especially, the coefficient of firm size is significantly negative in the manufacturing industry. It is found that small firms grow faster than larger firms since they struggle to obtain the optimal size. Furthermore, firm size has a significant positive effect on firm survivability in most industries. The likelihood of survival is high for larger firms, which holds for the theoretical results. The second objective of this paper is to see the influence of various types of innovations on firm growth. This study mainly focuses on the manufacturing sector. In this industry, R&D investment plays a crucial role for firm growth. It can be the determinants of firm growth. However, in the retail trade and accommodations industries, advertising investment is negatively related to firm growth. Capital investment influences on firm growth only in the retail trade industry. As mentioned above, the result can be due to the inappropriate explanatory variables. Nonetheless, we can interpret that it has a negative effect on firm growth due to the significant cost change. 19

20 Finally, this study investigates how firm behavior affects firm growth in the manufacturing industry. R&D investment is positively correlated with firm growth and survivability over time. However, as time passes, the effect of R&D investment declines. In the following year, R&D investment has a great effect on firm growth. Further analysis for the accumulation of R&D investment over time may be effective. As for innovation, this study mentions three different innovation - product, process and marketing innovation. However, so far, only product innovation is considered in the theoretical model. For future work, it might be a creative work to set up the model for the different innovations. Further investigation is expected. REFERENCES Almus, M., and Nerlinger, E. (2000), Testing Gibrats Law for Young Firms - Empirical Results for West Germany, Small Business Economics, 15(1), Alper, A (2008), Testing Gibrat s Law: Empirical Evidence from Panel Unit Root Tests of Turkish Firms, International Research Journal of Finance and Economics, 16, Audretsch, D.B., Klomp, L., Santarelli, E., and Thurik, A.R. (2004), Gibrat s Law: Are the Services Different?, 24, Chen, J. and Lu, W. (2003), Panel unit root tests of firm size and its growth, Applied Economics Letters, 10(6), Dunne, Paul and Alan Hughes (1994), Age, Size, Growth and Survival: UK companies in the 1980s, Journal of Industrial Economics 43(2), Dunne, T., Roberts, M. J., and Samuelson, L. (1989), The Growth and Failure of U.S. Manufacturing Plants, The Quarterly Journal of Economics, 104(4), Evans D.S.(1987a), The Relationship between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries, Journal of Industrial Economics, 35, (1987b) Tests of Alternative Theories of Firm Growth, Journal of Political Economy, 95, Francesca, L., Enrico, S., and Marco, V. (2001), The Relationship between Size and Growth: the Case of Italian Newborn Firms, Applied Economics Letters, 8,

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22 the Semiconductor Industry, The American Economic Review, 83(2), Papers and Proceedings of the Hundred and Fifth Annual Meeting of the American Economic Association, May 1993, Megna, Pamela and Mueller, Dennis(1991), Profit Rates and Intangible Capital, Review of Economics and Statistics, November 1991, 73, Oliveira, B., and Fortunato, A. (2006), Testing Gibrats law: Empirical evidence from a panel of Portuguese manufacturing firms, International Journal of the Economics of Business, 13(1), P.A.Geroski, S. Lazarova, G. Urga, and C.F. Walters (2003), Are Differences in Firm Size Transitory or Permanent?, Journal of Applied Econometrics, 18(1), Sutton, J. (1997), Gibrat s Legacy, Journal of Economic Literature 35, Yasuda, T (2005), Firm Growth, Size, Age and Behavior in Japanese Manufacturing, Small Business Economics, 24, Appendix A The Oslo Manual is the foremost international source of guidelines for the collection and use of data on innovation activities in industry. The general definition of innovation defined in the Oslo manual is as follows: Product Innovation represents the introduction of a good or service that is new or substantially improved. It includes significant improvements in technical specifications, components and materials. Process Innovation represents the introduction of a new or significantly improved production or delivery method. It includes significant changes in techniques, equipment and software. It can be intended to decrease unit costs of production, to increase quality or to produce significantly improved products. Marketing Innovation reflects the implementation of a new marketing method involving significant changes in product design or packaging, product promotion or pricing. New marketing methods in product promotion involve the use of new concepts for promoting a firm s goods and 22