Profit Persistence An Application of a Dynamic Panel Method Term paper for the course “Econometric Methods for Panel Data” Vienna, June 30, 2005 Gürkan Birer Matr.nr.: 0254010 Michael Weichselbaumer Matr.nr.: 9640369 2UK 300632 Ökonometrische Methoden für Paneldaten Lehrveranstaltungsleiter: O. Univ.-Prof. Dr. Robert Kunst Contents 1 Introduction 1 2 Method 2.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 3 Models 3.1 Time Dummies . . . . . . . . . . . . . . . . . . . . . 3.2 Dynamic Panel . . . . . . . . . . . . . . . . . . . . . 3 4 4 4 Results 4.1 Time Dummies . . . . . . . . . . . . . . . . . . . . . 4.2 Dynamic Panel . . . . . . . . . . . . . . . . . . . . . 7 7 8 5 Conclusion 10 1 Introduction In a competitive economy firm profits above the average should diminish over time. Hence, the empirical question of interest is if this can be observed and thus confirmed for a given set of data or if profits tend to persist. The problem is normally analysed as a time-series problem, since in the structural model profit persistence is dominated by the influence of past profits (Goddard & Wilson 1999). This means that for every individual firm a particular ARparameter is estimated from the corresponding individual time series of profits. In our work we want to investigate this question using panel data methods. Our approach differs from the time-series approach in two important ways: first, we hypothesise that persistent profits do not exist and hence exclude the intercept; second, we model a single coefficient of disappearance of profit deviations from the average, meaning that the speed of convergence is the same for all firms – and thus over all industries. In terms of model specification this implies the formulation with a single parameter for the influence of lagged profits. The next section gives a bit more of the underlying method to provide the reader with some understanding of the time-series approach and the arising differences from our approach. Additionally, it defines the variables included and describes the data. Section 3 describes the estimated models: a time-dummy model and a dynamic panel. This splitting is retained in section 4, where the results are presented. We conclude with section 5. 2 Method First we describe the dependent variable in a bit more detail. Then, a summary for the explanatory variables is given for those that are usually associated with the possibility of profits above the average and we were able to construct from our database. Afterwards, two different models are presented for estimation of persistence of profits above average over time: a model with time dummies hoping that one can observe the effect of competition in decreasing time dummies; a dynamic model with the alternative and dominantly used modelling strategy of persistence shown in a positive autoregressive coefficient. Both models are used in a random effects version, since we assume that the firms that are in our database and remain in the sample after the construction process of our explanatory vari1 ables is like a sample obtained from random draws of all firms in the economy. In both estimations we apply the same set of explanatory variables. 2.1 Variables First, the dependent variable: The profit of a firm that we use is defined as the ratio of profit after taxes and before interest to total assets. Taxes are excluded since effective tax-rates may differ and firms should then base their decision on entry or exit on the after-tax profit. Interest paid is included since total assets in the denominator do also encompass those assets financed by debt (argumentation follows Maruyama & Odagiri 2002). Profit of firm i at time t is denoted πit . The variable of interest, denoted ρit , is the deviation of firm i’s profit at time t from the average profit of all firms in year t. It is calculated as follows: ρit = where π̄t = πit − π̄t π̄t N 1 X πit N n=1 Next, a description of the calculation of the explanatory variables that we used and the basic intuition. Industry Dummy Our data is classified into four-digit codes following the Standard Industrial Classification (SIC) of the United States Government. It classifies every firm for every year according to their main field of production and is thus called ”Primary SIC-Code”1 . We use the industries classified in the large groups 2 and 3, the classes of manufacturing and construction, and reduce them to the three-digit-level, since only this level is specified accurately for all usable observations. Market Share This is calculated as share in sales of aggregate sales in the three-digit-level industry where a firm is classified. Though all firms with availability of sales are used to compute aggregate sales and not only those firms which are used in the very final data set for computation (i.e. where all variables are available), it remains an approximation. There 1 Though this classification system was replaced by the North American Industry Classification System (NAICS), we use the old SIC-Codes, since our data is originally classified in SIC and the last year we use is 1996. 2 are different causes that support the inclusion of market share as an explanatory variable, for example higher market power, higher efficiency due to economies of scale. We expect it to be positively related to profitability. Risk As a proxy for risk we calculate the standard deviation of industry profits, again at the three-digit-level. This variable is also expected to have a positive relationship. Growth of Industry It is calculated as the percentage growth in aggregate sales per three-digit-industry-level. We adopt the usual expectation that the relationship is positive, since more rapid growth relieves competitive pressure due to supposedly higher demand. Growth in the Number of Competitors Calculated as the percentage change in the absolute number of competitors in the industry. If it is high, competition should also increase and higher profits are expected to vanish. Entry/Exit Profits, in turn, depend on both actual and threatened entry. Since one has at most data about actual entry, entry’s impact on profits must always be understated. Thus, in timeseries models of profit persistence entry is dropped as an explanatory variable and is treated as a latent variable (Goddard & Wilson 1999). 2.2 Data The data stems from the Standard & Poors database Compustat. After adaptations necessary due to missing data for some variables and after the construction process that is as usual subject to the trade-off between number of years and number of observable individuals, we obtain a balanced sample of 900 U.S.-American firms for the time period of 1985 to 1996. The operations of the firms are spread over 98 three-digit-classes of SIC. 3 Models Now we will describe the two different models that we want to use for measuring the effect of competition over time: a simple random effects model with time dummies and a dynamic panel with random effects. 3 3.1 Time Dummies In a first trial, we model the persistence with time dummies and hope that the increase in competition will be reflected in diminishing time effects. As described above, we chose some other explanatory variables to control for important influences on profits. The estimation equation is: πit = Constant + MSit β1 + RiskIndustry,t β2 + ∆CompetitorsIndustry,t β3 +∆OutputIndustry,t β4 + Zλ,it λt + uit with 3.2 uit = µi + νit µi ∼ i.i.d.(0, σµ2 ) νit ∼ i.i.d.(0, σν2 ) µi , νi independent Dynamic Panel As mentioned above, from the economic point of view the inclusion of a lag of the dependent variable as an explanatory variable is legitimate. The model then takes the form (Baltagi 1995, pp.125): 0 yit = γyi(t−1) + xit β + uit , i = 1, . . . , N t = 1, . . . , T where uit = µi + νit – a one way error component model. For the estimation of the dynamic panel, it is well documented in the literature that the OLS estimation will lead to biased and inconsistent parameter estimates, even if the νit are not serially correlated, because yit and yi(t−1) are both a function of µi and hence yi(t−1) is correlated with the error term. For the fixed effects estimator the within transformation – the multiplication with the mean-adjusting matrix – wipes out the µi , but still the estimators will be biased, since νi(t−1) is contained in ν̄i , which is thus correlated with yi(t−1) . The same holds for random effects models. Only if T tends to infinity, the fixed effects estimator of γ and β will be consistent for the dynamic error component model. Since our data has the shape of a cross section panel with N large and T small, we do not rely on this property. A possibility to avoid the bias is the first-difference transformation of the data, because it wipes out the individual effects but does not create the problem of correlation. Among the alternative methods that use first-differencing, we choose for our dynamic panel regressions the method developed by Arellano & Bond (1991). First 4 we describe the method and than we discuss some of the advantages of using this method than the other methods like the well known method of Anderson & Hsiao (1981). In their paper, Arellano & Bond start with the simplest autoregressive specification with random effects in the form: yit = γyi(t−1) + ηi + νit , |γ| < 1 They assume lack of serial correlation in the error terms but not necessarily independence over time, i.e. they assume that E(νit ) = E(νit νis ) = 0. The model works as follows. First they take the first differences to get rid of the individual effects that leads to an equation of the form yit − yi(t−1) = γ(yi(t−1) − yi(t−2) ) + vit − vi(t−1) So for the first period (t=3) we have yi3 − yi2 = γ(yi2 − yi1 ) + vi3 − vi2 and for the second period (t=4) we have yi4 − yi3 = γ(yi3 − yi2 ) + vi4 − vi3 and if we continue in this iterative way we get for the last period (t=T): yiT − yi(T −1) = γ(yi(T −1) − yi(T −2) ) + viT − vi(T −1) They use the GMM (Generalized Method of Moments) for obtaining an optimal estimator of γ. The advantage of using GMM is that it will still work even if we have no information about the initial conditions and the distributions of vit and µi – hence it is preferred to other estimation methods like Maximum likelihood or OLS. The GMM estimator γ̂ is based on sample moments, defined as N −1 N X 0 0 Zi ν̄i = N −1 Z ν̄ i=1 0 0 0 0 where ν̄ = (ν̄1 , . . . , ν̄N ) – the column vector of all ν̄i , which, in turn is the column vector of the first differences of the νit for all t. Thus, 0 ν̄i has length T − 2 (since it is reduced by one observation due to first differencing and another one by formulation of a model with lagorder one) and ν̄ has length T − 2 times the number of individuals, 5 0 0 N . Z is a N (T − 2) × m matrix consisting of (Z1 , . . . , ZN ), which are used as instruments. The estimator γ̂ is given by: 0 0 γ̂ = argminγ (ν̄ Z)AN (Z ν̄) where AN is the so-called weighting matrix. Any such matrix would lead to unbiased estimates of γ, provided that the instruments are orthogonal to the errors. The choice of the instruments is an important factor because they should be highly correlated with the dependent variables and uncorrelated with the errors. Under these assumptions for the simplest AR(1) specification Arellano & Bond provide a set of instruments for the GMM estimation. The instrument matrix will be of the form: [yi1 ] 0 [yi1 , yi2 ] Zi = ... 0 [yi1 , . . . , yi,T −2 ] These instruments are different from the ones that suggested by Anderson & Hsiao (1981). From their Monte-Carlo study, Arellano & Bond provide evidence that the AH-estimates are either biased due to reasons of singularity or, in the best case, are more inefficient. That is why we have chosen to use the Arrelano-Bond method explained so far. What now remains among the central issues that have to be considered in the chosen estimation method are two tests that we want to describe shortly: first, a test procedure that can be used for testing if the errors vit are serially uncorrelated or not. This test is very important because the GMM estimators are only consistent if these errors are serially uncorrelated; second, since for T > 3 it will be an over-identified system – in other words, there will be more equations than unknowns – we need an over-identifying restrictions test. They suggest the test that has been developed by Sargan. Now, a few more words about the extended model with exogenous variables, which has the following form: Model with exogenous variables 0 yit = γyi(t−1) + β xit + ηi + νit , |γ| < 1 where νit are not serially correlated. The GMM estimator of the 6 coefficient vector will be 0 0 0 0 0 0 (γ̂, β̂) = (X̄ ZAN Z X̄ )−1 X̄ ZAN Z ȳ where the matrix of instruments Z will include the same instruments ˆ This as before for γ̂ plus an additional set of instruments for beta. additional set can be formed in two ways: if xit are strictly exogenous, in other words, E(xit , νis ) = 0 for all t, s, then all the x are valid instruments for all the equations; if the xit are predetermined in the sense that E(xit , νis ) 6= 0 for s < t and zero otherwise, then only xi1 , . . . , xi(s−1) are valid instruments. 4 Results Now we want to present the results of the two models introduced above: 4.1 Time Dummies For the first panel regression where we had four explanatory variables and time dummies the results are quite fuzzy (see table 1). Out of the four explanatory variables only two of them – market share and risk – turn out to be significant at the five percent level with risk unexpectedly having a negative coefficient. The only significant explanatory variable with the correct sign turns out to be the market share (2.04 with z=5.48). The two variables that were not significant at any meaningful level – ∆competitors and ∆sales – had the correct sign. Only four out of 12 time dummies were significant at the five percent level and they had different signs. The industry dummies were not significant. Thus the estimations below did not include them. Theoretically, the time dummies should all be insignificant, because we subtracted yearly averages from our dependent variable. Hence, the time-dummies can not explain differences between the years by construction. But since we calculated the deviations from the yearly means before dropping observations where not all necessary data was available, though the data to calculate profits was available, positive or negative average yearly deviations can still remain. What we can conclude now is that the data that remains after dropping some observations due to data limitations is representative with respect to the sample from which we calculated the yearly profit averages for most years at least. Besides that, the overall model can explain only up to five percent of the change in the dependent variable. The first explanation for 7 Table 1: Results from the time-dummy-estimation on profits above the mean (1985-1996) Explanat. variable Market Share Risk ∆Competitors ∆Sales Year86 Year87 Year88 Year89 Year90 Year91 Year92 Year93 Year94 Year95 Year96 constant συ σ² ρ Observations Coefficient 2.040 -.211 -.814 -.0528 0.097 0.601 -0.753 -0.371 -0.001 -0.448 -0.094 -0.020 0.071 -0.306 -0.289 -0.549 (Std. Err.) (0.373) (0.072) (1.458) (0.123) (0.204) (0.201) (0.213) (0.205) (0.200) (0.198) (0.199) (0.208) (0.200) (0.201) (0.201) (0.153) z 5.48 -2.93 -0.56 -0.43 0.48 2.99 -3.53 -1.81 0.00 -2.26 -0.47 -0.10 0.35 -1.52 -1.44 -3.58 P > |z| 0.000 0.003 0.577 0.668 0.633 0.003 0.000 0.070 0.997 0.024 0.637 0.922 0.723 0.128 0.150 0.000 0.996 4.002 0.058 (fraction of variance due to ui ) 900 groups 12 obs./group the results is that the model was not correctly specified. When we check the correlation structure of the explanatory variables we can say that they are not highly correlated. Another reason can be that the data suffers heavily from outliers. As a result we find that this simple method could not capture the effect of competition over time and continue with the results of the dynamic panels. 4.2 Dynamic Panel The performance of the dynamic panels with or without the set of explanatory variables from above – we assume that all are strictly exogenous – is slightly better than the models from above. At least we see (in tables 2 and 3) a positive (rather small) and highly significant autoregressive parameter γ. In the dynamic setting risk has the correct sign but now it turns out to be insignificant and unexpectedly the market share now turns out to have a big negative and highly significant coefficient which is totally contradicting economic theory. As we mentioned before Stata gives two test results which 8 may be interpreted as follows: the Sargan test which is used to test the validity of the over-identifying restrictions (or the validity of the instruments) has been rejected. The results of the serial autocorrelation tests are quite good. In both panels the null hypothesis that there is no second order serial autocorrelation in the error term could not be rejected. Table 2: Results from the dynamic-panel-estimation (1985-1996) Explanat. variable ρt−1 Coefficient 0.168 (Std. Err.) (0.013) z 13.06 P > |z| 0.000 χ2(54) =321.76 Prob≥ χ2 =0.000 average autocovariance in residuals of order 1 is 0: z = -50.54 Prob>z = 0.000 average autocovariance in residuals of order 2 is 0: z = -0.89 Prob>z = 0.375 900 groups 10 obs./group Sargan test of over-identifying restrictions: Arellano-Bond test that H0 : no autocorrelation Arellano-Bond test that H0 : no autocorrelation Observations Table 3: Results from the dynamic-panel-estimation with exogenous variables (1985-1996) Explanat. variable ρt−1 Market Share Risk ∆Competitors ∆Sales Coefficient 0.168 -5.374 0.011 -1.861 0.140 (Std. Err.) (0.013) (1.878) (0.096) (2.043) (0.164) z 13.05 -2.86 0.12 -0.91 0.86 P > |z| 0.000 0.004 0.904 0.363 0.392 χ2(54) =317.94 Prob≥ χ2 =0.000 average autocovariance in residuals of order 1 is 0: z = -50.57 Prob>z = 0.000 average autocovariance in residuals of order 2 is 0: z = -0.89 Prob>z = 0.375 900 groups 10 obs./group Sargan test of over-identifying restrictions: Arellano-Bond test that H0 : no autocorrelation Arellano-Bond test that H0 : no autocorrelation Observations The coefficients of the lagged dependent variables are the same in both estimations. The cases of the wrong sign of market share and non-significant parameters for all of the exogenous variables made us suspicious for the reliability of our database. The rela- Discussion 9 tionships seem to be reasonable and a lot of empirical evidence could be found for them. Additionally, a persistence of profit-deviations from the mean by only 16.8 percent from one year to the next seems too low and is also too low in light of estimates from the dominantly used method of estimating the autoregressive parameters from every time-series individually (as done, e.g. in Goddard & Wilson 1999, Maruyama & Odagiri 2002; see also the references there.). 5 Conclusion We conclude that our method is not useful to model the persistence of profits. Probably one could try to model a different data set, hoping that the expected relationships with the exogenous variables will hold then and be significant. Additionally, the estimation of individual coefficients of persistence, γi , could be necessary and thus yield better results. This is suggested by the argument that the internal structure and functioning of firms is likely to differ as well as that different firms face different entry and mobility barriers – though there is no strong evidence that the convergence process differs between above- and below-mean profit firms (Mueller 1990, p.194-196). Still, the doubt that our method should be preferred over the time-series approach mentioned remains strong. 10 References Anderson & Hsiao (1981), ‘Estimation of dynamic models with error components’, Journal of the American Statistical Association 76, 598–606. Arellano, M. & Bond, S. (1991), ‘Some tests of specification for panel data: Monte carlo evidence and an application to employment equations’, Review of Economic Studies 58, 277–297. Baltagi, B. H. (1995), Econometric analysis of panel data, John Wiley and Sons, New York. Goddard, J. & Wilson, J. (1999), ‘The persistence of profit: a new empirical interpretation’, International Journal of Industrial Organization 17, 663–687. Maruyama, N. & Odagiri, H. (2002), ‘Does the ’persistence of profits’ persist?: a study of company profits in japan, 1964-97’, International Journal of Industrial Organization 20, 1513–1533. Mueller, D. C. (1990), The dynamics of company profits. An international comparison, Campridge University Press. 11