# The inter relationship between firm growth and profitability

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## Abstract

There is a widespread presumption that there is a close relationship between firm growth and firm profitability. However, most of the past studies on firm growth and profitability have been conducted without mutual associations. Only a few studies, thus far, have examined the inter-relationship between firm growth and profitability and the results have been inconsistent. The reason for the inconsistency is mainly due to the lag structure of the models in each study. To address the issue, this study conducted panel unit-root tests on firm growth and profitability separately and then made appropriate models using dynamic panel system GMM estimators. Through the analyses of the models, this study found that in restaurant firms the prior year's profitability had a positive effect on the growth rate of the current year, but the current and prior year's growth rates had a negative effect on the current year's profitability. This outcome implies that profit creates growth but the growth impedes profitability in the restaurant industry. More implications are also discussed in this paper.

Keywords: Firm growth; Profitability; Panel unit-root test; Dynamic panel system GMM

## 1. Introduction

The dynamics of firm growth and profitability (or profit rate) is an important issue for industrial practitioners as well as academic researchers (Goddard, McMillan and Wilson, 2006). Theoretically, if firm growth rate is unrelated to firm size and prior growth rate, then firm growth follows random walk and the variance of firm size can increase indefinitely. This is known as the Law of Proportionate Effect (LPE). This stochastic growth process implies unlimited industry growth in the long run. However, if growth rate is inversely related to firm size, firm growth would converge in the long run. On the other hand, Mueller (1977) claimed that firm profitability converges at a certain level due to market competition, which is referred to as Persistence of Profit (POP). The POP literature argues that firm entry and exit are sufficiently free to quickly eliminate any abnormal profit and that the profitability of all firms tends to converge toward the long-run average value.

However, Goddard, Molyneux and Wilson (2004) stated, even though it is generally presumed that firm growth and profitability effect each other, that firm growth and profitability are not necessarily connected. Overall, the impact and direction of this relationship remains ambiguous. The ambiguity is associated with various econometric issues. First, due to the endogeneity it is difficult to capture a clear causality and direction between them. Further, if firm growth and profitability time lags are incorporated into the models the endogenous relationship becomes more complicated due to the unknown effects of different time lags.

Recently, there have been a couple of attempts to investigate the inter-relationship between firm growth and profitability (Coad, 2007; Davidsson, Steffens, and Fitzsimmons, 2009). Although it is worth exploring the relationship, the results of the studies turned out to be inconsistent. In the previous studies, two types of methodologies were used: panel unit-root test and dynamic panel system GMM estimator. The panel unit-root test is appropriate for testing the convergence hypotheses of firm growth and profit rates. It is also useful for finding the significance of the lag term in a simple autoregressive model, but it is difficult to control the endogenous effect in the model. Moreover, the panel unit-root test cannot directly examine the inter-relationship between firm growth and profitability. Dynamic panel system GMM estimator can control for endogeneity and test the inter-relationship, but determining the number of lag terms remains ambiguous.

Thus, in order to address the analysis problems in the previous literature, we first employed the panel unit-root test and subsequently made a testable model for the dynamic panel system GMM estimator. Through those analyses, we intended to investigate the inter-relationship between firm growth and profitability under various time lags. More specifically, the objectives of this study were: 1) to examine the panel unit-root test on the series of firm growth and profitability separately and to find an appropriate lag structure; and 2) to make an appropriate model to investigate the inter-relationship between them through a vector autoregression (VAR) model via dynamic panel system GMM estimator. We used restaurant firms for the study sample and, thus, the results are useful for understanding the dynamics of firm growth and profitability in the restaurant industry.

In the following section, we summarize prior LPE and POP literature and present the potential inter-relationships between firm growth and profitability. Next section outlines the details of the study methodology. The following section shows the results of panel unit-root test and dynamic panel system GMM regarding the inter-relationship between firm growth and profitability. Finally, we conclude this study with managerial implications and suggestions for further studies.

## 2. Literature Review

2.1. Law of Proportionate Effect (LPE) and Persistence Of Profit (POP)

The notion that firm growth rate is independent of firm size and past growth rate is known as the Law of Proportionate Effect (LPE) (Gibrat, 1931). According to the LPE, firm growth happens by chance and thus past growth is not a reliable predictor of future firm growth (Goddard et al., 2006). Hence, deterministic factors of firm growth (i.e., managerial capacity, innovation and efficiency) are randomly distributed across firms. However, recent empirical studies have claimed that there is an inverse relationship between firm growth and firm size, rejecting the LPE (Hall, 1987; Evans, 1987; Dunne and Huges, 1994; Geroski and Gugler, 2004). Most empirical studies of LPE used cross-sectional regression models through a simple autoregressive model (for example, AR(1)), but the models were criticized due to their arbitrariness in choosing lag terms. Recently, Chen and Lu (2003) and Goddard et al. (2006) tested the LPE using panel unit-root models because the LPE assumes non-stationarity in the time series analysis. The benefit of the panel unit-root test on LPE lies in its ability to test a long series effect in non-stationarity, while the weakness of the test is its inability to include control variables that may affect firm growth (i.e., prior profitability, leverage, and market competition).

Conversely, researchers on persistence of profit (POP) argue that firm profitability converges at a certain level across all firms and no firms could achieve an above average profit rate in the long run. Mueller (1977) developed the deterministic time-series model for testing the POP and subsequently (Mueller 1986) demonstrated profit rate convergence through an autoregressive model. Since Mueller (1986), most studies on POP have adopted the autoregressive model. However, Goddard et al. (2006) stated that the typical methodology for POP estimated individual effects and autoregressive coefficients for each firm, so the estimated coefficients were often unreliable and the testing power was low. Hence, Goddard et al. (2006) tested the profit rate convergence hypothesis using a panel unit-root test in order to find the stationarity in a profit rate time series.

2.2. The inter-relationship between firm growth rate and profitability (or profit rate)

As noted earlier, it is widely believed that firm growth and profit rates are related to each other (Goddard et al., 2004). Some prior studies have suggested that profit rate has a positive impact on growth rate. Alchian's (1950) theoretical study argued that fitter firms survive and grow, but less viable firms lose their market share and exit through the evolutionary selection mechanism. Thus, if profit rate reflects the degree of fitness, it is possible to predict that profitable firms will grow. Further, according to the financing constraint hypothesis retained profits can be readily used for investment, whereas firms with low profitability could not grow even if they have positive growth opportunities. This is also consistent with the pecking-order theory, which claims that managers prefer internal capital to external capital, such as debt and equity financing.

However, the influence of growth rate on profitability is inconsistent in theories and empirical studies. A Classical Ricardian perspective claims that if a firm shows high profit rates it would grow to exploit additional growth opportunities that are less profitable but still create additional profits. This notion implies three things. First, the profit rate is converges at zero from a long-term perspective. Second, high profit rates have a positive impact on growth rates until the profit rate is zero. Finally, firm growth has a negative influence on profit rate. Along similar lines, the Neoclassical view argues that firms first exploit their most profitable growth opportunities and then consider less profitable opportunities until the marginal profit on the last growth opportunity is equal to zero. Consequently, profitable firms maximize their overall level of profits through profitable growth opportunities but experience a decrease in profit rates. Even though this argument excludes market competition, it theoretically explains the relationship between firm growth and profit rates. However, managerial growth-maximization hypothesis under market competition (Marris, 1964; Mueller, 1972) claims that the managerial objective of a firm is to maximize growth rather than profit. Thus, this hypothesis proposed that growth and profits are in a competitive relationship with each other, which suggests the possibility that growth victimizes profit.

Nevertheless, there are a number of theoretical claims that growth rate has a positive impact on profit rate. First, the Kaldor-Verdoorn Law in economics (Kaldor, 1966; Verdoorn, 1949) claims that growth increases productivity and in turn the enhanced productivity increases profit rates. This notion is consistent with scale economies (Gupta, 1981). Thus, because firm growth contributes to an increase in firm size, the larger size could gain benefits from an economy of scale and in turn this affects profit enhancement. That is, growth can help increase profitability.

However, empirical studies on the effects of growth rate on profit rate have not always been supportive. Capon, Farley and Hoenig (1990) reported that firm growth is related to high financial performance, but it was significant only in some industries. Chandler and Jansen (1992) and Mendelson (2000) reported a significant positive correlation between sales growth and profit rates, whereas Markman and Gartner (2002) found no significant relationship between growth and profitability. Furthermore, Reid (1995) claimed growth had a negative effect on profitability.

The relationship between growth and profit rates are more complicated when time lags of the two variables are considered. Only a few empirical studies have considered the link between growth and profit rates using various time lag terms. Goddard et al. (2004) found profitability to be important for future growth in European banks. Conversely, through panel data estimates of French manufacturing firms Coad (2007) found that the opposite direction of causation (i.e., growth to profitability) might be true. Both Goddard et al. (2004) and Coad (2007) investigated the relationship between firm growth and profit rates with vector autoregressive models using dynamic panel system GMM estimators. The difference between the two studies was that Goddard et al. (2004) used a one-year time lag but Coad (2007) incorporated three-year time lags in the analysis. More specifically, Goddard et al. (2004) found that a one-year lagged profit rate had a positive significant effect on the current-year's growth rate, but a one-year lagged growth rate did not have a significant impact on the current-year's profit rates. However, Coad (2007) showed that two- and three-year's lagged profit rates have a positive significant influence on the current-year's growth rate and that the current-year's growth rate was positively significant in terms of the current-year's profit rates. As noted, Goddard et al. (2004) and Coad (2007) reported opposing empirical results, which could be attributed to the difference in lag length. Considering the scarcity of past studies on the growth-profitability relationship and the problems with analytic methods, there is a need for a study that can verify this important relationship in a more holistic way. Hence, we intended to address the above research need in this study. A detailed outline of how the study was conducted follows in the next section.

## 3. Data and methodology

The data used in the analysis was collected from the COMPUSTAT database using SIC 5812 (eating places). The data covers fiscal years 1978 to 2007 for U.S. restaurant firms. Profit rate (or profitability) was measured as net income divided by net sales and growth rate was gauged as the difference between the current and prior year's net sales divided by the prior year's net sales. After deleting severe outliers in the two main variables, growth rate and profit rate, this study used 2,927 firm-year observations for the analysis.

As previously indicated, this study first conducted panel unit-root tests on growth and profit rates separately. The Dickey-Fuller unit-root test was set up for testing the stationarity of a time series. For example, if Ï†1 is equal to a unit in equation (1), the series is non-stationary. Equation (1) could be expressed as equation (2) by subtracting Yt-1 on both sides.

Yt = Ï†1Yt-1 + Îµt (1)

Î”Yt = Î³Yt-1 + Îµt (Î³ = Ï†1 - 1) (2)

Equation (2) above is a simplified Dickey-Fuller unit-root test (DF test). The null hypothesis of a DF test is that Î³ equals zero and the alternative hypothesis is Î³ < 0. Under the null hypothesis the series is non-stationarity. By including lags of order p this formulation allows for higher-order autoregressive processes, which is referred to as an Augmented Dickey-Fuller unit-root test (ADF test). Equation (3) shows the ADF test formula.

p

Î”Yt = Î³Yt-1 + âˆ‘Ï†iÎ”Yt-i + Îµt (Î³ = Ï†1 - 1) (3)

i=1

However, the data structure of this study was an unbalanced panel. Thus, equation (3) could be expressed as a panel setting following equation (4):

p

Î”Yi,t = Î³Y i,t-1 + âˆ‘Ï†iÎ”Y i,t-i + Îµ i,t (Î³ = Ï†1 - 1) (4)

i=1

Equation (4) is the testable model for the panel unit-root test in this study. A few studies have developed panel unit-root tests (Im, Pesaran and Shin, 2003; Levin, Lin and Chu, 2002; Maddala and Wu, 1999). However, in the case of an unbalanced panel setting, the Fisher test is the only one available. It combines the p-values from N independent unit root tests, as developed by Maddala and Wu (1999). Based on the p-values of individual unit root tests, Fisher's test assumes that all series are non-stationary under the null hypothesis against the alternative that at least one series in the panel is stationary. Unlike other panel unit-root tests, Fisher's test does not require a balanced panel. Thus, this study conducted Fisher's test on the growth and profit rates and selected an appropriate lag length in ADF formula.

After selecting the proper lag length in ADF formula, it was transformed as follows:

p

Î”Yi,t = Î³Y i,t-1 + âˆ‘Ï†iÎ”Y i,t-i + Îµ i,t

i=1

= Î³Y i,t-1 + Ï†1Î”Y i,t-1 + Ï†2Î”Y i,t-2 + Ï†3Î”Y i,t-3 + â€¦ + Ï†pÎ”Y i,t-p + Îµ i,t

= Î³Y i,t-1 + Ï†1(Y i,t-1 - Y i,t-2) + Ï†2(Y i,t-2 - Y i,t-3) + â€¦ + Ï†p(Y i,t-p - Y i,t-(p+1)) + Îµ i,t

= (Î³ + Ï†1) Y i,t-1 + (Ï†2 - Ï†1) Y i,t-2 + (Ï†3 - Ï†2) Y i,t-3 + â€¦ + (Ï†p - Ï†p-1)Y i,t-p

- Ï†pY i,t-(p+1) + Îµ i,t

(5)

Consequently, equation (5) could be expressed as follows:

Yi,t = (1 + Î³ + Ï†1) Y i,t-1 + (Ï†2 - Ï†1) Y i,t-2 + (Ï†3 - Ï†2) Y i,t-3 + â€¦ + (Ï†p - Ï†p-1)Y i,t-p

- Ï†pY i,t-(p+1) + Îµ i,t (6)

Thus, if the panel unit-root test chooses p lags in ADF formula, it could be transformed to AR(p+1) model. This AR(p+1) model was then used for the dynamic panel system GMM estimator. Also, since the purpose of this study was to investigate the inter-relationship between firm growth and profitability, this study adopted the vector autoregression (VAR) model to find the reciprocal relationship between growth rates and profit rates.

p+1 q+1 p+1

SGi,t = Î²0 + âˆ‘Î·iSGi,t-i + âˆ‘Ï€iPRi,t-i + Î²1Salei,t-i + Î²2LEVi,t-i + âˆ‘Î¶iÎ”DM&Ai,t-i

i=1 i=1 i=0

+ DYeart + Îµi,t

Model 1

q+1 p+1

PRi,t = Î²0 + âˆ‘Ï€iPRi,t-i + âˆ‘Î·iGRi,t-i + Î²1Salei,t-i + Î²2LEVi,t-i + Î²3MarketSharei,t-i

i=1 i=0

+ DYeart + Îµi,t

Model 2

SGi,t is the sales growth rate and PRi,t is the profit rate at time t for firm i. Salei,t is the net sales at time t for firm i. We also included control variables in both models. In the LPE literature, recent studies showed that prior firm size is inversely related with current growth rate (Evans, 1987; Hall, 1987; Geroski and Gugler, 2004). On the other hand, Baumol (1959) provided evidence that firm profitability increases with firm size, while Amato and Wilder (Kwangmin!!, Year and reference?) showed that no relationship exists between firm size and profit rate. Finally, Samuels and Smyth (1968) stated that profit rate and firm size are inversely related. Thus, we included the prior year's net sales as a firm size variable in both models to control for size effect.

Debt leverage (LEVi,t) was also incorporated in both models as a control variable, which was calculated as total debt divided by total assets. Theories of optimal capital structure based on the agency costs of managerial discretion suggest that the adverse impact of leverage on growth increases firm value by preventing managers from taking on poor projects (Jensen,1986; Stulz, 1990). Opler and Titman (1994) empirically found that sales growth is lower in firms with higher leverage. Thus, the influence of debt leverage on growth could be negative. However, the prior literature on the relationship between debt leverage and profit rate, has shown mixed results. Debt affects profitability positively according to Hurdle (1974), but negatively according to Hall and Weiss (1967) and Gale (1972). Debt could also yield a disciplinary effect under the free cash flow hypothesis (Jensen, 1986; Stulz, 1990). Firms with high debt leverage can reduce wasteful investment opportunities and increase firm performance, suggesting a positive relationship between debt leverage and profit rates. However, using debt can increase conflicts between debt and equity holders. Equity holders encourage managers to undertake risky projects because the benefits are transferred only to equity holders (Stiglitz and Weiss, 1981). Thus equity holders tend to support the use of debt. However, high uses of debt could deteriorate firm profitability by taking on overly risky projects. The effect of leverage on profit rate may not be uni-directional. Consequently, we incorporated leverage as a control variable due to its important potential effects on profitability.

In the growth rate equation (Model 1), we incorporated mergers and acquisitions (M&A) dummy variables from time t to t-(p+1) because M&A execution abnormally increases growth rates. M&A executions were identified from the SDC Platinum database. In the profitability equation (Model 2), we included a market share variable, which was calculated as the net sales of firm i at time t divided by the sum of net sales at time t. According to Buzzell, Gale and Sultan (1975), market share had a positive impact on firm profitability. Because a larger market share means stronger market power, firms with large market shares could have the power to control market prices and be in a better position to negotiate with their suppliers. Thus, a positive relationship between market share and profit rates is expected. Because the current year's growth could affect the current year's profit rate, following Coad (2007), we included the current year's growth rate in Model 2.

Statistically, ordinary least square (OLS) regression requires that the right-hand side variables should be independent of the error term. However, if there is a bi-directional causation between dependent (left-hand side) variables and explanatory (right-hand side) variables, this condition is not satisfied and thus OLS regression produces biased and inconsistent estimates. This endogeneity problem could be solved by choosing appropriate instrumental variables, which are correlated with the explanatory variables but not the error term. This means that the instrumental variables should be exogenous but if they are endogenous, the equation would be over-identified. However, if the instrumental variables are weakly correlated with the explanatory variables, which is called a weak instrument, the estimates are biased and inconsistent.

Arellano and Bond (1991) proposed the GMM estimator for panel data, which could control the potential endogenous explanatory variables. This method uses the first difference model, which eliminates the time-invariant firm-specific effect, and instrumental variables for the endogenous variables were generated by lags of their own level. However, if the lagged level instruments are weakly correlated with the endogenous explanatory variables, there could be a finite sample bias in estimators. In particular, if the variable series tends to show a highly persistent profit rate series (Mueller, 1977), this weak correlation between lagged level instruments and endogenous explanatory variables is problematic. Arellano and Bover (1995) and Brundell and Bond (1998) developed a dynamic panel GMM estimator that estimated with level-equation and difference equation, which is called a 'system GMM'. Consequently, the dynamic panel system GMM estimator has better asymptotic and finite sample properties than the one used by Arellano and Bond (1991).

Thus, this study analyzed the proposed models using the dynamic panel system GMM estimator, which produces unbiased and consistent estimates after controlling for endogeneity and firm-specific effects even when the sample period is short. Even though the full sample period of this study is 30 years, the panel structure is not balanced due to the entry and exit of firms. Bludell and Bond (1998) suggested the minimum requirement for panel length as T â‰¥ 3. Thus, we excluded firms which did not exist at least three years in the sample period. Another requirement was that there is no serial correlation of the second order error terms. We conducted the serial correlation test for panel GMM estimators developed by Arellano and Bond (1991). In order to test the exogeneity of instrumental variables, we used the Hansen test instead of the Sargan test because the Sargan test is not robust enough to detect heteroskedasticity and autocorrelation (Roodman, 2006). Finally, as Roodman (2006) suggested, we included year dummies in the models and estimated the system GMM by two-step estimator because the two-step estimator is robust enough to detect the heteroskedasticity. For comparisons with the dynamic panel system GMM estimator, we conducted ordinary least square (OLS) and fixed-effect regression.

## 4. Results

4.1. Panel unit-root test for firm growth and profit rates

As indicated, we conducted the panel unit-root test developed by Maddala and Wu (1999) using Fisher's test, which assumes that all series are non-stationary under the null hypothesis. Equation (4) was tested on both growth and profit rates. The results are presented in Table 1. For the series of sales growth and profit rates, lag(4) was justified. Thus, the law of proportionate effect hypothesis was rejected but the persistence of profit hypothesis was validated. The results indicate that the growth rates are serially correlated and the profit rates are convergent. The purpose of the panel unit-root tests on growth and profit rates was to examine the stationarity of the two series and to make an appropriate model for the dynamic panel system GMM estimator. As shown earlier, if the panel unit-root test justifies p lags, the ADF formula could be transformed to AR(p+1) model. Consequently, the testable model is AR(5) for both growth and profit rates. Based on the lag length from the panel unit-root test, we excluded any firm that existed less than five years in testing the dynamic panel system GMM estimator. Then, we tested the proposed models using AR(5) in order to identify the inter-relationship between firm growth and profit rates in various time lag structures.

(Insert Table 1 Here)

4.2. Descriptive statistics and scatter plots of growth and profit rates

Table 2 shows the descriptive statistics of the major variables of this study. The average sales of the sampled restaurant firms was 541.8 million dollars and the average growth rate in sales was 16.3%. The average profit rate (return on sales) was - 1.3% and total debt rate (debt leverage) was 61.3%. Thus, the figures show that the restaurant industry has a high growth rate, but its profitability is not positive and it uses more debt than equity.

(Insert Table 2 Here)

Before conducting the dynamic panel system GMM estimator, we checked the scatter plots between growth and profit rates using various time lags. As Coad (2007) indicated, the non-parametric scatter plots of growth and profit rates gave us a visual appreciation of the underlying phenomenon. Thus, before testing the quantitative relationship, we can obtain useful information via scatter plots. Figure 1 shows the scatter plots of growth at time t (Y-axis) and growth rates at time t-1 to t-5 (X-axis) for all samples. Except for the first plot (growth rate time t versus t-1), all other plots seem to show no relationship. The plots, excluding the first plot, look like a cloud shape but are a bit scattered horizontally. Based on the plot for growth rate time t and t-1, the current and prior year's growth rates are positively correlated. However, Figure 1 represents all firms, including M&A firms. Apparently, firms with M&A can experience abnormally high growth rates compared with non-M&A firms. Thus, we checked the same scatter plots after excluding M&A firms, as presented in Figure 2. The relationship between current and prior year's growth rate is clearly positive and growth rate at t-2 also looks positive on current year's growth rate. However, the earlier years' growth rates (i.e., t-3, t-4 and t-5) appear to have no relationship with the current year's growth rate. Figure 3 shows scatter plots of profit rate at time t (Y-axis) and profit rates at time t-1 to t-5 (X-axis). Interestingly, clear heteroskedasticity is detected in the relationship between them. Thus, the usage of the two-step estimator in the dynamic panel system GMM estimator is justified by Figure 3. In all of the scatter plots there is a tendency toward a positive relationship between current and prior profit rates.

(Insert Figures 1, 2, and 3 Here)

Figure 4 shows scatter plots of profit rate at time t (Y-axis) and growth rates at time t-1 to t-5 (X-axis). In all plots, points were spread horizontally. It seems that there is no effect of growth rate on profit rate. Surprisingly, the scatter plot of current growth rates appears to have no relationship with current profit rate. On the other hand, Figure 5 shows that profit rates clearly have a positive influence on the current growth rate. The majority of the points were spread vertically. The scatter plots show that prior profit rates seems to have a positive influence on current growth rates, but the influence of prior growth rates on current profit rates was not found.

(Insert Figures 4 and 5 Here)

4.3. Results from Dynamic panel system GMM estimator

Tables 3 and 4 show the results of the proposed models explained in the methodology section. Even though yearly dummies were not reported in Tables 3 and 4, they were included in the models. As shown in Table 3, the prior year's growth rate at time t-1 was found to be positively significant on current growth rates in all three regressions (OLS, fixed-effect and system GMM). However, the directions and significances of the coefficients of the other prior growth rate terms varied across the three models. As explained earlier, however, the system GMM is the most appropriate model for this study due to the endogeneity and time invariant firm-specific effect and the results of the OLS and fixed-effect regression models were used simply for the purpose of comparison.

Goddard et al. (2004) reported that the prior year's (time t-1) growth rate was positive but not significant. It is difficult to directly compare their results with ours due to the difference in the lag length structure. Interestingly, our study showed that growth rates at time t-1 and t-5 were positively significant on current growth rates, but growth rates at time t-2 and t-4 were negatively significant. These results suggest that short-term and long-term prior growth rates have a positive impact, but mid-term prior growth rates have a negative influence on current growth rates.

Our primary interest in Model 1 was the effect of the prior years' profit rates on current growth rates. The system GMM results show that profit rates at time t-1 and t-5 were positively significant. The magnitude of the coefficient of profit rate at time t-5 was small, meaning that the positive impact of long-term prior profit rates on current growth rates is small. However, the prior year's (time t-1) profit rate has a positively significant effect on current growth and the magnitude of the coefficient is large. Coad's (2007) study showed that profit rates at time t-1 to t-3 were all positive but the prior year's (time t-1) profit rate was not significant. Coad (2007) used an AR(3) model and thus a direct comparison of ours to Coad's (2007) is not possible. Yet it is clear that the direction of the coefficients were very similar. Overall, our study results provide evidence that recently profitable firms may grow faster.

In terms of the relationship between prior year's firm size and current growth rate, all three results show a negative coefficient but the negative effect was significant only in OLS. Also, debt leverage had a negative effect on current growth rates but the system GMM result was not significant. Additionally, all serial correlation tests were not significant, showing that there was no serial correlation problem. Also, the over-identification tests were not significant, meaning that our instruments were not endogenous and the estimates were reliable.

(Insert Table 3 Here)

Table 4 shows the results of the profitability equation (Model 2). The results of the system GMM shows that profit rates at time t-1, t-2 and t-5 were had positively significant effect on current profit rates. However, profit rates at time t-3 and t-4 were negatively significant. The results suggest that short-term and long-term prior profit rates have a positive impact on current profit rates, but mid-term prior profit rates have a negative influence on current profit rates. Similarly, Goddard et al.'s (2004) results showed that the prior year's (time t-1) profit rate was positive and significant in its AR(1) model. Table 4 also presents the effect of the prior years' growth rates on current profit rates were negatively significant in time t and t-1. Unlike our results, Goddard et al. (2004) found that the prior year's growth rate was positive, but not significant, in terms of current profit rates. Conversely, Coad (2007) reported that the current growth rate was positively significant on current profit rates. That is, our results were different from those of the two prior studies. However, as pointed out earlier, a direct comparison with the prior studies is not possible due to the differences in the lag structure of the models. Basically, Goddard et al. (2004) used AR(1) model and Coad (2007) used growth rates of time t, t-1 and t-2 in the profit equation.

The results of this study revealed that high growth rates in the current and prior years impede current profit rates, which is consistent with a classical Ricardian view and the managerial growth-maximization hypothesis. Moreover, our results suggest that restaurant firms are growing by victimizing their profits. Thus, the notion that growth draws the profit cart should be rejected in the restaurant industry.

(Insert Table 4 Here)

## 5. Conclusions

This study investigated the inter-relationship between firm growth and profit rates (profitability) using Dynamic panel system GMM estimator models. This study showed that prior profit rates had a positive impact on current growth rate, but current and prior growth rates had a negative effect on current profit rates in the restaurant industry. Hence, a key message in relation to firm growth and profitability is that profits could create growth, but growth impedes the profitability of restaurant firms.

Academically, this study contributes to the LPE and POP literature and shows that the inter-relationship between growth and profit rates could differ depending on the lag structure of the tested models. As explained earlier, this study made a unique contribution in addressing the analysis issues embedded in the LPE and POP studies by using panel unit-root tests and then a subsequent Dynamic panel system GMM estimator. The difference in results could also be derived from the samples used. The sample used in Goddard et al. (2004) was European banking companies and Coad (2007) analyzed datasets from French firms. Thus, this study also contributed to better understanding how growth and profitability mechanisms work in the restaurant industry.

The results of this study provide managerial implications for the restaurant industry. The results indicated that profitable restaurant firms could grow but growing restaurant firms might suffer from low profits. In other words, if restaurant firms focus only on growth, their long-term performance could be jeopardized. According to other studies claiming the positive effect of growth on profit, however, cost reduction via growth could enhance profit rates (Gupta, 1981). Therefore, growth in restaurant firms might not be associated with cost reductions. Consequently, growth-focused strategies are not desirable for a restaurant firm's long-term performance. Instead, restaurateurs should understand the importance of maintaining an appropriate level of profits, because profits can lead to firm growth.

This study is not free from limitations. The results of this study can not be generalized to other industries due to the limitation of the sample. Thus, future studies can investigate the inter-relationship between firm growth and profit rates in other hospitality and tourism industries. It is also necessary to further examine the relationships among growth, cost reduction, efficiency gain and profits in the hospitality industry due to its difference from the manufacturing industry.

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