Tracing the dynamics of competition: evidence from company profits.

Cuaresma, Jesus Crespo ; Gschwandtner, Adelina

I. INTRODUCTION

Since the seminal contributions of Mueller (1977, 1986), there is a fruitful and steadily growing literature aimed at investigating empirically the persistence of company profits. While the competitive environment hypothesis predicts that profit differentials across firms should disappear in the long run, the empirical evidence tends to give little support to this theory. Several studies analyze the question of competition within the frame of profit persistence across different economies, industries, and time periods.

Mueller (1990) presented a comprehensive international comparison of profit dynamics. In his study, the dynamics of company profits were analyzed and compared for seven developed economies--United States, United Kingdom, Japan, France, Germany, Sweden, and Canada--during the 1960s-1980s. The main finding of this study was that in all these seven developed economies, a high degree of profit persistence was found. The percentage of companies with persistent long-run profit rates was much higher than one would expect to be in a competitive environment. Kambahampati (1995) analyzed and compared the profits differentials in 42 Indian industries over the period 1970-1985 and showed that competition is less intense in fast-growing, concentrated industries. Glen, Lee, and Singh (2001) analyzed and compared the dynamics of competitive forces in seven emerging markets--India, Malaysia, South Korea, Brazil, Mexico, Jordan, and Zimbabwe--during the 1980s and early 1990s and concluded that the intensity of competition is, if anything, greater in emerging countries than in advanced countries. Odagiri and Maruyama (2002) analyzed the intensity of competition in Japan during the period 1964--1997 and still found a considerable degree of profit persistence. Yurtoglu (2004) analyzed the persistence of firm-level profitability for the largest 172 manufacturing firms in Turkey during the period 1985--1998 and concluded that the intensity of competition in Turkey is no less than in developed countries. Gschwandtner (2005) analyzed the differences in profit persistence between surviving and exiting firms in the United States for the second half of the twentieth century.

The empirical literature on profit persistence uses two different but interrelated definitions of persistence of profits. The persistence measure related to long-run deviations from normal profits is given by the unconditional expectation of the stochastic process that profit rates are assumed to follow (usually an autoregressive process). Short-run persistence (which corresponds to the context in which "persistence" is usually used in time series analysis), on the other hand, is given by the size of the autoregressive parameter in the dynamic representation of the profit rate. If the time series span a long period of time, considering persistence (whichever its definition) constant might be very restrictive since the degree of overall competition in the economy or the sector under study may be expected to change over time. There is evidence, for example, that competition increased in the United States after the opening to international competition in the 1960s, and structural breaks of this kind could have taken place also afterward. Recently, Gschwandtner (2004), using data for U.S. companies in the period 1950--1999, found evidence of significantly different profit dynamics when dividing the sample into different subperiods.

According to the Chamberlinian hypothesis (see, e.g., Scherer [1980] and Kessides [1990]), in an industry of small size, firms are bound to accept their mutual strategic interdependence and therefore maintain oligopolistic discipline. Fluctuations in industry size, therefore, would lead to changing profit persistence in time. The empirical literature dealing with profit persistence has also found other variables to be robust determinants of differences in profit persistence across firms and in the time dimension. Mueller (1986), Ravenscraft (1983), and Martin (2002), just to name a few, studied the impact of market share on profit persistence. Kessides (1990) and Gschwandtner (2005) found effects of industry size and growth on profitability. Mueller (1986), Ben-Zion and Shalit (1975), Bothwell and Keeler (1976), Bowman (1980, 1982), and Harris (1986) found significant effects of risk proxies on profit persistence. To the extent that these variables (and other potential determinants of profitability) are time varying, the assumption of a constant persistence parameter may not be adequate for the study of profit persistence during long spans of time.

In this article, we study the dynamics of profit rates making use of an unobserved components model with a time-varying persistence parameter. This allows us to trace the dynamics of competition for any given company and thus assess the validity of the competitive environment hypothesis without constraining the persistence parameter to be constant. The advantages of this methodology are exemplified by analyzing profit data from 156 U.S. companies. Similar models have also been used by Stavins (2001) and Busse and Rysman (2005), bringing empirical evidence for a counterintuitive result: price differentiation increases with competition. While the first article analyzes the U.S. Airline Market, the second brings evidence from the U.S. Yellow Pages Advertising Market.

The structure of the article is as follows. The time series model used in the study is discussed in Section II and the results of the estimation of the model for the profit data are reported and commented in Section III. Section IV concludes and indicates potential future paths of research using the methodology put forward in this article.

II. MODELING TIME-VARYING PERSISTENCE

Since Mueller (1986) and Odagiri and Yamawaki (1986), the autoregressive process of first order (AR(1)) has been the most widely used representation of the dynamics of profits and has become the modeling workhorse for evaluating the adequacy of the competitive environment hypothesis empirically. Let [[pi].sub.i,t] be the profit rate of firm i in period t, eventually normalized by taking the difference to the sample average profit rate in period t. The dynamic behavior of [[pi].sub.i,t] is assumed to be given by

(1) [[pi].sub.i,t] = [[alpha].sub.i] + [[lambda].sub.i][[pi].sub.i,t-1] + [[epsilon].sub.i,t],

where [[lambda].sub.i] [member of] (-1, 1) and [[epsilon].sub.i,t] is white noise with constant variance [[sigma].sup.2.sub.[epsilon],i]. Notice that the specification given by Equation (1) can be justified theoretically (see, e.g., Geroski 1990) as a reduced form of a two-equation system, where profits are assumed to depend on the threat of entry in the market and the threat is itself assumed to depend on the profits observed in the last period.

The unconditional expectation of [[pi].sub.i,t] in Equation (1) is given by [[alpha].sub.i]/(1 - [[lambda].sub.i]). The empirical literature on profit persistence usually compares the estimates of the unconditional expectations from Equation (1) (or alternative AR(p) generalizations) and tests the equality of unconditional expectations--long-run projections of the series--across companies. However, this procedure is appropriate only for stationary AR processes, as [[alpha].sub.i]/(1 - [[lambda].sub.i]) is not defined for unit root processes, where [[lambda].sub.i] = 1.

Evidence of nonstationary (unit root) behavior in company profits is often reported in the empirical literature dealing with the competitive environment hypothesis. Kambahampati (1995), using the Dickey-Fuller (DF) test, could reject nonstationarity of profits in only 13 out of 42 cases for Indian industry-level data. Goddard and Wilson (1999) employing data for 335 UK firms over the period 1972-1991 likewise reported nonstationarity in 76%-81% of firms in the sample. Gschwandtner (2003) failed to reject the unit root hypothesis in 69 out of 187 cases (36.9%) for U.S. companies.

We aim at modeling profits in a framework of time-varying persistence (thus leading to a constant long-run-projected profit rate only if the dynamics of the persistence parameter converge to a constant value). The model specification we propose and implement is nested in the following model:

(2) [[pi].sub.i,t] = [[alpha].sub.i] + [[lambda].sub.i,t][[pi].sub.i,t-1] + [[epsilon].sub.i,t], [[lambda].sub.i,t] = [[PHI].sub.i,0] + [[PHI].sub.i,1][[lambda].sub.i,t-1] + [v.sub,i,t],

that is, in the model, the persistence parameter [[lambda].sub.i,t] is specified as general AR(1) process itself and [v.sub.i,t] is assumed to be a white noise process with constant variance [[sigma].sup.2.sub.v,i], uncorrelated with [[epsilon].sub.i,t]. Since, in principle, the persistence of profits may have increased or decreased in certain sectors (or firms) continuously for the sample available, a random walk specification (with or without drift) for the autoregressive parameter might as well fit the development of persistence better for certain firms in the sample. The model with random walk dynamics in the persistence parameter is nested in Equation (2) for [[PHI].sub.i,1] = 1 (with or without a drift depending on whether [[PHI].sub.i,0] equals 0 or not). The characteristics of an AR(1) where the autoregressive parameter follows an AR(1) process itself have been studied in Weiss (1985). The autoregressive process with parameter dynamics such as Equation (2) is a conditionally Gaussian model, which can thus be estimated using maximum likelihood methods (see, e.g., Harvey 1989).

This is the specification used in our application with profit data from our sample of U.S. firms in the period 1950-1999. This method allows us to draw conclusions on the development of competitive pressures in the period considered.

III. THE DYNAMICS OF PROFIT PERSISTENCE: EVIDENCE OF U.S. FIRMS

This section presents the results obtained from the estimation of the AR(1) model with time-varying autoregressive parameter using profit data ranging from 1950 to 1999 for our sample of U.S. firms.

The relevant variable used for the analysis ([[pi].sub.i,t]) will be defined as the percent deviation from company i's profit rate from the average profit rate in a sample of 156 firms for which data are available in the period 1950-1999 (Crespo Cuaresma and Gschwandtner 2005). (1) This normalization is aimed at removing business cycle fluctuations and common shocks. Furthermore, the literature tends to interpret the average profit as a measure of the competitive profit and thus [[pi].sub.i, t] as deviations from the competitive norm. The profit rate is given by a firm's profits after taxes (Compustat's Income Before Extraordinary Items, which represents the income of a company after all expenses, including special items, income taxes, and minority interests--but before provisions for common and/or preferred dividends) divided by total assets (Compustat's Assets-Total). The main source for the profit data is Compustat, while for the most recent years (1977-1999), Global Vantage was employed as a data source. The data set was completed using "Moody's Industrial Manual" (Messner, 1950-1999) for those years for which Compustat and/or Global Vantage did not provide data. (2)

Using Augmented DF tests, we reduced the sample to those firms for which there is evidence of stationarity in the profit data. The stationary sample is formed by 105 firms that reject the null hypothesis of unit root nonstationarity at the 10% significance level. For these firms, the modeling strategy is the following. A simple AR(1) model with a constant persistence parameter is estimated for the sample available. Initiating the maximum likelihood algorithm by setting the long-run average of the time-varying [lambda] parameter ([[PHI].sub.i,0]/ (1 - [[PHI].sub.i,1]) equal to the estimate in the model with constant persistence, estimates for the model with a time-varying coefficient are obtained. For each firm, we perform a likelihood ratio test between the model with constant persistence parameter given by Equation (1) and the proposed model with time-varying parameters given by Equation (2).

Our results are summarized in Table 1, where we present the most relevant statistics of the estimation. The results of the likelihood ratio tests indicate that approximately a third of the firms under study present significant evidence for the model with time-varying parameters. The estimated models with time-varying parameters are, however, very heterogeneous. The average point estimate of the unconditional expected value of [[lambda].sub.1,t] across models is 0.723, with a relatively tight standard deviation of 0.187, indicating a significant estimate of the average persistence parameter across models. However, the short-run dynamics of the persistence parameter appear very different across firms, with a negative average point estimate of the autoregressive parameter attached to [[lambda].sub.i,t] in Equation (2) but with a large standard deviation, which indicates that while the dynamics of the short-run persistence parameters resemble white noise for certain firms, others present strong persistence in the dynamics of [[lambda].sub.i,t]. In order to exemplify the differences in the dynamics of [[lambda].sub.i,t] emerging from different estimates, Figure 1 presents the smoothed estimates of [[lambda].sub.i, t]) for three representative firms of the sample. The figure presents the smoothed estimate together with a confidence interval of twice the conditional standard deviation. The differences in interpretation of the results presented in Figure 1 compared to those which would emerge from estimating models with constant persistence parameters are very relevant. For instance, while the constant parameter model given by Equation (1) would conclude that the profit rate in Air Products and Chemicals Inc. presents significant short-run persistence (the corresponding estimate of [[lambda].sub.i] in Equation (1) is 0.58, with a SD of 0.12), the results shown in Figure 1 indicate that the persistence parameter was high and significant for the first half of the sample and has since become low and insignificant. Similar contradictory results emerging from neglecting the dynamic nature of [[lambda].sub.i,t] can be inferred from the dynamics of profit persistence for Northop Grumman Corp. and Burlington Inds. Inc., which are also plotted in the figure.

IV. CONCLUSIONS

This article presents a simple time series model with a time-varying persistence parameter aimed at modeling the dynamics of profit rates. Until now, the empirical literature on profit persistence has relied on single measures of persistence for the whole sample of profits available, thus abstracting away from the dynamic nature of competition. We propose a simple way of modeling changes in the persistence of company profits by generalizing the autoregressive process used in the literature to an autoregressive process where the dynamics of the autoregressive parameter itself follow an autoregressive process. We exemplify the method using profit data from more than a hundred U.S. companies and show that there is evidence that roughly a third of the profit rates under study have evidence of time-varying profit persistence. The simple time series model proposed can furthermore give interesting insights to the dynamics of profits.

[FIGURE 1 OMITTED]

The issue of time variation in the persistence parameter is of particular relevance for policy. In this piece of research, we give examples of firms where estimating a constant profit persistence parameter would lead to wrong conclusions concerning the current degree of imperfection in the fulfillment of the competitive environment hypothesis. This, in turn, could lead to wrong conclusions based on statistical measures assuming constant persistence for cases of antitrust violation and dominant firm abuses.

The model put forward in this piece of research can be easily expanded to include explanatory variables of the persistence parameter (see Crespo Cuaresma and Gschwandtner [2006] for a first step in this direction) and to account for asymmetric profit rate (and profit persistence) dynamics or regimen shifts in the autoregressive parameter governing the auto-correlation in profit rates.

ABBREVIATION

DF: Dickey-Fuller

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JESUS CRESPO CUARESMA and ADELINA GSCHWANDTNER *

* The authors are indebted to an anonymous referee and Dennis C. Mueller for very helpful comments and suggestions on earlier drafts of this article.

Crespo Cuaresma: Professor of Economics, Department of Economics, University of Innsbruck, Universitatstrasse 15, 6020 Innsbruck, Austria. Phone +43 (0) 512 507 7357, Fax +43 (0) 512 507 2980. E-mail jesus.crespo-cuaresma@uibk.ac.at

Gschwandtner: Assistant Professor, Department of Economics, University of Vienna, Bruennerstrasse 72, 1210 Vienna, Austria. Phone +43 (1) 4277 374 80, Fax +43 (1) 4277 374 98, E-mail adelina.gschwandmer@univie.ac.at

(1.) The companies in the sample belonged to the largest 500 (in terms of sales) in 1950 and managed to survive until 1999. We therefore choose the largest available data set covering the period 1950-1999 in order to approximate the level of normal profits.

(2.) Standard & Poor's Compustat (United States) and Global Vantage (international) databases contain fundamental financial and price data for both active and inactive publicly traded companies. Compustat goes back annually to 1950 and Global Vantage to 1993. The two databases are provided by the same company and are perfectly compatible. Moody's Manuals are essentially an encyclopedic history of American business since 1909. They provide company profiles and financial information for thousands of U.S. public corporations and are therefore very well suited to provide historical data. The two variables used in the present article are identical in all three data sources.

TABLE 1
Estimation Results

 Constant
 Full Sample Parameters

Average [[??].sub.i]/(1 - [[??].sub.i]) -0.014 -0.011
SE [[??].sub.i]/(1 - [[??].sub.i]) 0.028 0.03
Average [[??].sub.i] 0.474 0.457
SE [[??].sub.i] 0.189 0.2
Number of firms 105 71
Number of likehood ratio 34 (32.38)
 test rejections, n (%)

 Time-Varying
 Parameters

Average [[??].sub.0, i]/1 - [[??].sub.0, i] 0.723
SE [[??].sub.0, i]/(1 - [[??].sub.0, i]) 0.187
Average [[??].sub.0, i] -0.127
SE [[??].sub.0, i] 0.459
Number of firms 34
Number of likehood ratio
 test rejections, n (%)

Notes: See Equations (1) and (2) for definition of parameters. "Number
of LR-test rejections" refers to the number of models that reject the
null hypothesis of constant parameters at the 10% significance level
using a likelihood ratio test of Model (1) against Model (2).