The inter relationship between firm growth and profitability

The inter kindred mingled with squ atomic number 18 maturement and summationability crimpThere is a widespread presumption that thither is a close kin amidst true harvest and unfluctuating meshingability. However, most of the past studies on unbendable addition and pull inability piss been conducted without vulgar associations. Only a hardly a(prenominal) studies, thus far, thrust examined the inter- kinship between buckram gain and lollyability and the results control been inconsistent. The reason for the inconsistency is mainly due to the lock up structure of the models in to each one believe. To address the issue, this study conducted deco ramble unit of measurement-root studys on firm harvest-home and cabbageability sepa positionly and then made take over models apply propulsive instrument deco mark formation GMM estimators. Through the analyses of the models, this study found that in eating place firms the earlier long prison term servic eability had a positivist achievement on the proceeds target of the menstruum year, but the latest and preceding days branch evaluate had a negative impression on the topical years kalessability. This outcome implies that meshing creates appendage but the out ontogeny impedes gatherability in the restaurant industry. More implications be overly discussed in this paper.Keywords Firm gain Profitability Panel unit-root canvass Dynamic board administration GMM1. IntroductionThe changings of firm emergence and get aheadability (or earn enjoin) is an important issue for industrial practitioners as well as academic researchers (Goddard, McMillan and Wilson, 2006). Theoretically, if firm harvesting rate is unrelated to firm size and preliminary increment rate, then firm maturation follows random walk and the variance of firm size ignore increase indefinitely. This is known as the police of Proportionate Effect (LPE). This stochastic ripening process im plies untrammeled industry growth in the long run. However, if growth rate is contraryly 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 trustworthy level due to market competition, which is referred to as Persistence of Profit (POP). The POP literature argues that firm entry and exit be 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 non necessarily connected. Overall, the opposition and direction of this relationship remains ambiguous. The ambiguity is associated with mingled econometric issues. First, due to the endogeneity it is fractious to capture a clear causality and direction between them . Further, if firm growth and profitability sentence lags are corporal into the models the endogenous relationship becomes much complicated due to the unknown effects of different time lags.Recently, there have been a couple of attempts to analyse 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 rancid out to be inconsistent. In the precedent studies, two types of methodologies were utilise venire unit-root tryout and dynamic panel system GMM estimator. The panel unit-root test is appropriate for testing the convergence hypotheses of firm growth and profit place. It is as well uptakeful 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 can non directly examine the inter-relationship between firm grow th and profitability. Dynamic panel system GMM estimator can control for endogeneity and test the inter-relationship, but find out the number of lag terms remains ambiguous.Thus, in orderliness to address the analysis problems in the previous literature, we start 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 check up on 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 coif an appropriate model to investigate the inter-relationship between them by a vector auto simple reversal (VAR) model via dynamic panel system GMM estimator. We employ restaurant firms for the study sample and, thus, the results are useful for understanding the dyna mics of firm growth and profitability in the restaurant industry.In the following section, we summarize preceding LPE and POP literature and present the potential inter-relationships between firm growth and profitability. Next section preciss the details of the study methodology. The following section depicts 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 projections for go on studies.2. Literature Review2.1. Law of Proportionate Effect (LPE) and Persistence Of Profit (POP)The notion that firm growth rate is in strung-out 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, subgenus 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, art object the weakness of the test is its inability to include control variables that may affect firm growth (i.e., prior profitability, supplement, and market competition).Conversely, researchers on p ersistence 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) real 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 surmisal 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 grade are related to each other (Goddard et al., 2004). Some prior studies have suggested that profit rate has a affirmative impact on growth rate. Alchians (1950) theoretical study argued that fitter firms survive and grow, but less workable firms lose their market piece and exit through the evolutionary selection mechanism. Thus, if profit rate reflects the distributor point of fitness, it is possible to predict that profitable firms will grow. Further, according to the financing constraint hypothesis retained benefit 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 make of growth rate on profitability is inconsistent in theories and empirical studies. A Classical Ricardian perspective claims that if a firm shows senior hi gh schooler(prenominal) profit pass judgment it would grow to exploit superfluous growth opportunities that are less profitable but still create additional moolah. This notion implies ternion 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 envision a decrease in profit rates. even out 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 bee n supportive. Capon, Farley and Hoenig (1990) reported that firm growth is related to high financial performance, but it was authoritative only in some industries. Chandler and Jansen (1992) and Mendelson (2000) reported a significant positive correlativity between gross revenue 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 true-years growth rate, but a one-year lagged growth rate did not have a significant impact on the current-years profit rates. However, Coad (2007) showed that two- and three-years lagged profit rates have a positive significant influence on the current-years growth rate and that the current-years growth rate was positively significant in terms of the current-years profit rates. As noted, Goddard et al. (2004) and Coad (2007) reported opposing empirical results, which could be attributed to the difference in lag len gth. 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 methodologyThe data used in the analysis was compile 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 terminate income carve up by net sales and growth rate was gauged as the difference between the current and prior years net sales divided by the prior years 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-r oot 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 1 is equal to a unit in equation (1), the series is non-stationary. par (1) could be expressed as equation (2) by subtracting Yt-1 on two sides.Yt = 1Yt-1 + t (1)Yt = Yt-1 + t ( = 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 equals zero and the alternative hypothesis is pYt = Yt-1 + iYt-i + t ( = 1 1) (3)i=1However, the data structure of this study was an unbalanced panel. Thus, equation (3) could be expressed as a panel setting following equation (4)pYi,t = Y i,t-1 + iY i,t-i + i,t ( = 1 1) (4)i=1Equation (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 s etting, 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). establish on the p-values of individual unit root tests, Fishers test assumes that all series are non-stationary under the null hypothesis against the alternative that at least(prenominal) one series in the panel is stationary. Unlike other panel unit-root tests, Fishers test does not require a balanced panel. Thus, this study conducted Fishers test on the growth and profit rates and selected an appropriate lag length in ADF normal.After selecting the proper lag length in ADF formula, it was transformed as followspYi,t = Y i,t-1 + iY i,t-i + i,ti=1= Y i,t-1 + 1Y i,t-1 + 2Y i,t-2 + 3Y i,t-3 + + pY i,t-p + i,t= Y i,t-1 + 1(Y i,t-1 Y i,t-2) + 2(Y i,t-2 Y i,t-3) + + p(Y i,t-p Y i,t-(p+1)) + i,t= ( + 1) Y i,t-1 + (2 1) Y i,t-2 + (3 2) Y i,t-3 + + (p p-1)Y i,t-p pY i,t-(p+1) + i,t(5)Consequently, equation (5) could be express ed as followsYi,t = (1 + + 1) Y i,t-1 + (2 1) Y i,t-2 + (3 2) Y i,t-3 + + (p p-1)Y i,t-p pY i,t-(p+1) + 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+1SGi,t = 0 + iSGi,t-i + iPRi,t-i + 1Salei,t-i + 2LEVi,t-i + iDMAi,t-ii=1 i=1 i=0+ DYeart + i,tModel 1q+1 p+1PRi,t = 0 + iPRi,t-i + iGRi,t-i + 1Salei,t-i + 2LEVi,t-i + 3MarketSharei,t-ii=1 i=0+ DYeart + i,tModel 2SGi,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 include 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 years 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 thoroughgoing debt divided by entirety 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 sa les 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 come on 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 (MA) dummy variables from time t to t-(p+1) because MA execution abnormally increases growth rates. MA executions were identified from the SDC Platinum database. In the profitability equation (Model 2), we included a market luck 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 representation 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 s hare and profit rates is expected. Because the current years growth could affect the current years profit rate, following Coad (2007), we included the current years growth rate in Model 2.Statistically, mediocre least square (OLS) regression requires that the right-hand side variables should be independent of the fracture term. However, if there is a bi-directional causation between dependent (left-hand side) variables and informative (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 stick (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 sting (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 b etter 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 afterwards controlling for endogeneity and firm-specific effects even when the sample blockage 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 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. Results4.1. Panel unit-root test for firm growth and profit ratesAs indicated, we conducted the panel unit-root test developed by Maddala and Wu (1999) using Fishers 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 crock up bandages of growth and profit ratesTable 2 shows the descriptive statistics of the major variables of this study. The average sales of the sampled restaurant firms was 541.8 one thousand thousand 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 numerical 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 firs t plot, mind 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 years growth rates are positively correlated. However, Figure 1 represents all firms, including MA firms. Apparently, firms with MA can experience abnormally high growth rates compared with non-MA firms. Thus, we checked the same scatter plots after excluding MA firms, as presented in Figure 2. The relationship between current and prior years growth rate is all the way positive and growth rate at t-2 also looks positive on current years 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 years 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 GM M 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 mass 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 estimatorTables 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 years 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 vary 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 years (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 ti me 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 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 pursuit 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 years (time t-1) profit rate has a positively significant effect on current growth and the magnitude of the coefficient is large. Coads (2007) study showed that profit rates at time t-1 to t-3 were all positive but the prior years (time t-1) profit rate was not significant. Coad (2007) used an AR(3) m odel and thus a direct comparison of ours to Coads (2007) is not possible. Yet it is clear that the direction of the coefficients were really similar. Overall, our study results provide evidence that recently profitable firms may grow faster.In terms of the relationship between prior years 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 e ffect 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 years (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 years growth rate was posi