The dynamics of company profits: A latent growth model

Abstract

Existing literature on profit dynamics focuses mainly on the erosion of profit differentials as a result of competitive pressures while largely ignoring the processes by which such differentials arise. Neoclassical models of competition and market equilibrium provide the theoretical base for such literature. We argue, on the contrary, for a view of competitive dynamics that encompasses both the emergence and the erosion of economic rents—a view rooted in strategic insights into how firms can create abnormal profits. Accordingly, we define a trend-based model explicitly acknowledging that firms differ in their ability to improve performance, which gives rise to heterogeneous profitability trends. We express the model as a multilevel latent growth curve, which allows us to address the significant challenges present in modeling profit dynamics. We employ such a model to analyze the dynamics of profitability in a sample of Spanish manufacturing firms from 1991 to 2008.

Keywords

Evolutionary economics latent growth curves multilevel models persistence profit dynamics trend-based models

Introduction

Strategic management builds on the notion that firms not only can, but should try to, consistently outperform their competitors. Not surprisingly, there is an overwhelming literature, both theoretical and empirical, that aims at explaining superior profitability. The widely accepted “resource-based view” (RBV), for example, deems enduring differences in performance to be the result of the heterogeneous distribution of resources across firms. The prescriptions of the literature on strategy largely rely on two assumptions regarding the empirical distribution of profits. First, from a cross-sectional perspective, profits must differ across firms. There is ample evidence supporting the existence of such cross-sectional differences at either the industry, corporate, or business-unit levels (e.g. Rumelt, 1991). Second, from a longitudinal perspective, at least some such differentials must persist over time (Rumelt et al., 1991). This second assumption is at odds with neoclassical models of competitive equilibrium, which imply that abnormal profits are an anomaly that should be rapidly eliminated by the force of competitive pressures.

This contradiction has motivated a well-established research stream that confronts the “strategic” and “competitive environment” hypotheses by analyzing whether, and under what conditions, abnormal profits persist over time (Mueller, 1986). We shall note three characteristics of such persistence-of-profits literature. First, it assumes that competition approaches a long-term equilibrium state. Second, it focuses exclusively on how rents erode, while overlooking how they emerge (Alfarano et al., 2011). From this perspective, profits appear merely as the result of unsystematic shocks, which are subsequently eroded by competition. The possibility of a firm systematically improving its long-term performance is not considered. Third, from a methodological standpoint, the overwhelming majority of the research builds on autoregressive econometric models.

Meanwhile, strategy scholars are paying increasing attention not only to the question of if and why profits persist but also to how they emerge (Cockburn et al., 2000; Jacobides et al., 2012; Zott, 2003). Firms can build superior endowments of resources by consistently outsmarting competitors in the factor markets (Makadok and Barney, 2001). Aggressive challengers can eventually dethrone industry leaders (Ferrier et al., 1999). Firms enjoying better dynamic capabilities reconfigure their resource endowments and adapt to environmental change better than competitors (Eisenhardt and Martin, 2000; Teece et al., 1997). Changes in performance arise systematically from the firms’ capabilities and strategies. Recent empirical research has been consistent with this view in showing that the dynamics of company profits are shaped by the interplay of two complementary processes, namely, profit-seeking undertakings by firms and profit-eroding competitive pressures (Alfarano et al., 2011; Cable and Jackson, 2008; Cable and Mueller, 2008). Moreover, some works have provided evidence, either qualitative (Baaij et al., 2011), descriptive (McGahan and Porter, 2003), or simulated (Zott, 2003), on how systematic changes in performance may occur.

In this study, we build on such evidence and approach the study of profit dynamics from rather different assumptions than those of the ubiquitous persistence literature. First, we do not assume that any long-run steady state is to be approached. Second, we allow for systematic changes in company returns, and following Cable and Jackson (2008), we assume that firms differ in terms of their performance trends.

From a methodological standpoint, we applied latent growth modeling (LGM) techniques to the analysis of profit dynamics. The LGM is a powerful and flexible tool for the analysis of change, according to which observed patterns of profits are deemed to stem from latent firm-specific longitudinal trajectories (Bollen and Curran, 2006). Heterogeneity in latent trajectories captures the emergence and evolution of performance differentials, allowing us to disentangle variance-in-levels and variance-in-trends as two separate constituents of the dynamics of interfirm profit heterogeneity.

We tested our research model on an unbalanced panel of 2,764 firms classified in 20 different manufacturing industries between 1991 and 2008, estimating firm-specific linear growth curves and examining the distribution of the parameters of interest across the sample. The total number of data points is 27,763 with an average of slightly over 10 observations per firm. The size, scope, and time span of the sample are in line with previous literature and respond adequately to our research objectives.

This article extends previous studies on performance dynamics in two ways. First, by explicitly modeling variation in trends as a source of performance heterogeneity, we push the study of performance dynamics beyond the analysis of persistence. This has some relevant theoretical implications, since we explicitly acknowledge that firms engage in idiosyncratic efforts to improve their competitiveness. The relative success of such efforts in the form of innovations, new resources, competitive moves, and the like will determine profitability trends. Previous works in the persistence-of-profits tradition allowed testing the effects of alternative microeconomic models on the erosion of abnormal profits (Geroski, 1990); by defining a trend-based growth curve, we aim to provide further insights into the dynamics of competition and strategy. Second, we also contribute to a more comprehensive analysis of profit persistence. Unlike the literature based on autoregressive models (McGahan and Porter, 2003), we are not restricted to analyzing the rate of persistence of the incremental component to profitability (McGahan and Porter, 1999). By testing whether latent performance trends converge, we can explore the mean-reverting properties of total returns.

Background: the persistence-of-profits literature

The dynamics of company profits have received substantial scholarly attention in recent decades, resulting in what we could label as the persistence-of-profits literature. Empirical evidence shows that profit rates differ significantly across firms and industries at any given point in time and that at least some companies earn abnormal profits. Neoclassical microeconomics suggests that unless there are significant barriers to competition, market forces should rapidly erode abnormal profits and drive returns back to competitive levels, or to the level of return just sufficient to maintain capital investment (Jacobsen, 1988). Long-term equilibrium should approach a zero-profit solution (Mueller, 1977), in which any remaining differences in profit rates would account for interfirm differences in relative risk.

The field of strategic management, in contrast, generally builds on the idea that companies not only can, but also should try to, outperform their competitors in the long run; they should seek to attain sustainable competitive advantage. In this view, profits above the norm may persist for long periods of time, and no zero-profit solution is to be approached.

Empirical research on profit dynamics has confronted the strategic notion of sustained advantage vis-à-vis the so-called competitive environment hypothesis (Mueller, 1986) by analyzing the rate of convergence in profit rates. Research questions are often posed along the lines of “can we expect high profits to fall to competitive levels, and how long will we have to wait?” (Mueller, 1977: 369) or “does superior economic performance persist in a manner consistent with sustained competitive advantage?” (Wiggins and Ruefli, 2002: 83).

The AR(1) autoregressive model of profit dynamics

From a methodological standpoint, the vast majority of works, following Mueller (1986), draw on Anderson and Hsiao’s (1982) dynamic state dependence model and adopt a first-order autoregressive process as its standard workhorse (Alfarano et al., 2011). The model runs as follows

Y_{it} = A_{i} + S_{it} + U_{it}

(1)

S_{it} = λ_{i} S_{it-1} + E_{it}

(2)

where subscripts i and t denote firm and time, respectively. The dependent variable Y_it represents firm’s i profits at time t, measured as deviations from average profitability. It is partitioned in terms of a fixed component that varies across firms but is constant for the entire period in the dataset (A_i) and an incremental component (S_it), representing the additional effect (above or below the fixed component) that arises in firm i and time t. U_it and E_it are independent disturbance terms and are assumed to satisfy standard assumptions.

As equation (2) shows, the incremental component is assumed to follow an AR(1) process. The autoregressive parameter λ_i determines the behavior of the profit time series. Provided that λ_i ∈ (−1, 1), there is evidence of a stationary series and a meaning-reverting process, so that profits converge toward a long-run equilibrium level (Y_it = Y_it−1) given by the unconditional mean of the stochastic process, A_i/(1 − λ_i). The rate of convergence is inversely related to the size of the AR(1) parameter; the bigger the absolute value of λ_i, the slower the short-run rents erode and the longer it takes for profit rates to revert to long-run equilibrium levels.

Estimates of λ_i are consequently taken as indicators of profit persistence or, in strategic terms, sustainability of competitive advantage (Villalonga, 2004). However, as McGahan and Porter (1999, 2003) note, this involves some serious interpretive caveats, as the autoregressive parameter refers exclusively to the persistence of the incremental component A_it. A high persistence rate may in fact be paired with a small incremental component, making it largely irrelevant to the actual tendency of profits to last between periods. We should thus distinguish two types of persistence (Cable and Mueller, 2008): long-run deviations from the norm (A_i) and the rate at which incremental profits converge toward long-run equilibrium (λ_i). Bou and Satorra (2010) also derive an additional persistence index from equation (1), which they define by [Var(A) + λVar(S)]/[Var(A) + Var(S)]. Empirical research has produced a vast array of evidence that rather consistently confirms the existence of persistent differences that extend across a number of industries, countries, and time periods (e.g. Geroski and Jacquemin, 1988; Gschwandtner, 2005; McGahan and Porter, 1999; Mueller, 1990). While some degree of mean reversion does seem to exist, in most cases, it is neither immediate (λ_i ≠ 0) nor complete (A_i ≠ 0). We conclude that although competition does cause some erosion of abnormal profits, we cannot accept the competitive environment hypothesis, since some interfirm performance differentials remain in the long run.

The autoregressive process of first order has proved a fruitful methodological instrument. It has produced a remarkable body of empirical evidence that helps to trace the dynamics of competition. Not only has it shown that long-run profit differentials do exist—thus validating a fundamental underlying assumption of strategy research—but it has also explored what factors, either industry- or firm-related, influence profit persistence, since Jacobsen (1988) argued that persistence should not be assumed to be the same for all firms. Many variables have been considered, including, among others, market share (Jacobsen, 1988; Martin, 2002), concentration (Gschwandtner and Hirsch, 2011; Yurtoglu, 2004), industry size and growth (Gschwandtner, 2005; Kessides, 1990), technological intensity (Vaaler and McNamara, 2010), marketing expenditures (Jacobsen, 1988), innovation (Roberts, 1999, 2001), corporate reputation (Roberts and Dowling, 2002), intangible resources (Villalonga, 2004), and top management effectiveness (Acquahh, 2003). Gschwandtner (2005) extended previous works by comparing persistence of surviving firms and exiters for a 50-year period. Meanwhile, Mueller (1990) and Bou and Satorra (2010) explored how persistence parameters varied across countries.

Extensions of the model have also allowed scholars to revisit traditional studies on the partitioning of profits (Rumelt, 1991; Schmalensee, 1985) by analyzing the persistence of returns at industry and firm levels (Bou and Satorra, 2007; McGahan and Porter, 1999, 2003). Other authors have studied how the persistence parameters have evolved over the years searching for changes in the nature and intensity of competition (Crespo Cuaresma and Gschwandtner, 2008; Gschwandtner, 2012; McNamara et al., 2003).

The importance and variety of the empirical findings can hardly be overstated. Reviewing them, even superficially, is well beyond the scope of this article. There is, however, one common aspect worth noting. The theoretical foundations of the persistence-of-profits literature root into the microeconomic model of competition posed by Geroski (1990). Equations (1) and (2) result from the reduction of a system of two equations in which, first, high profits trigger the entry of new competitors, and second, increased competition subsequently reduces profits in the following periods. This model depicts competition as a negative feedback mechanism leading to profit equalization. Consequently, virtually all the cited works are concerned with the erosion of abnormal returns, but not with their appearance, and with how long profit differentials persist, but not with how they emerge (for an exploratory exception, see McGahan and Porter, 2003). This is equally true for a minority of works that while adopting alternative methodological approaches, share the same focus on profit persistence (Powell and Reinhardt, 2010; Wiggins and Ruefli, 2002, 2003, 2005).

The emergence of new rents and the interpretation of profit dynamics

From a dynamic perspective, competition is a process of rent creation as much as it is one of the rent erosion (Jacobson, 1992; Kirzner, 1997); it is a mechanism by which profit-seeking firms discover and seize upon hitherto unexploited business opportunities. The emergence and the convergence of abnormal returns are both outputs of the competitive interaction and can be considered two sides of the same coin.

Nonetheless, most previous research on profit dynamics—and particularly that based on the AR(1) model—overlooks this double-faceted nature of competition and omits discussion about how rents are generated (Alfarano et al., 2011; Cable and Jackson, 2008). This has some substantial and not always sufficiently understood theoretical implications. The implicit assumption is that new profits appear as the result of unsystematic year-specific shocks, they are captured by the error term of the model, and they erode in subsequent years. Since residuals are assumed to be independent, there is no provision for a firm consistently generating new profits. This perspective is consistent with a neoclassical view of competition, in which the interaction of profit-maximizing firms exhausts all the profitable business opportunities available at every period. The strategic management literature, on the other hand, holds a different opinion on how profits emerge and evolve.

There are several strategic theories as to how superior performance appears. The RBV highlights the role that the acquisition, combination, and leveraging of resources play in building competitive advantages (Sirmon et al., 2007). The so-called Austrian School of Strategy (Jacobson, 1992), meanwhile, emphasizes the importance of entrepreneurial discovery and innovation (Foss and Ishikawa, 2007; Young et al., 1996). The competitive dynamics perspective shows how firms can profit from specific actions than disrupt the competitive status quo (Chen and Miller, 2012).

Different research streams focus on different antecedents of performance, but they converge in the assumption that firms vary in their ability to generate new profits. Some companies have better access to the factor markets or more accurate expectations on the value of resources, thus making superior acquisition decisions (Makadok and Barney, 2001). Dynamic capabilities improve the firm’s ability to anticipate, evaluate, and recombine resources to generate a competitive advantage (Danneels, 2012; Teece et al., 1997). Entrepreneurial discovery depends on the subjective knowledge and judgment of managers and employees, so that some firms are more entrepreneurial—and more successfully so—than others (Foss et al., 2008). Some companies but not others manage to introduce a regular flow of (profitable) innovations (Roberts, 1999). Firm characteristics such as size, information-processing capacity, and the top management team, among others, shape the company’s strategic competitive behavior, which, in turn, has a differential effect on performance change (Chen and Miller, 2012).

The standard interpretation of the arguments above leads strategy scholars to conclude that some firms can enjoy a persistent performance advantage over others. This interpretation, however, is incomplete in that it fails to recognize that the dynamic force that actually drives observed persistence is the creation of new profits. Alternatively, we can conclude that some firms are more likely than others to generate positive profitability shocks and thus show a favorable trajectory in terms of performance.

The arguments presented thus far pose some serious challenges to the literature that builds on autoregressive models. First, we can no longer interpret the persistence parameter λ_i as a measure of competitive pressures eroding abnormal returns, but as the net effect of two opposing forces: rent-creating innovation and rent-eroding imitation (Cable and Mueller, 2008). Both forces are difficult, if not impossible, to disentangle in the autoregressive framework; higher persistence may be the consequence of either lower competitive pressures or new innovations creating abnormal profits as previous ones erode (Roberts, 1999, 2001). Second, it calls for a more comprehensive view of competition and profit dynamics, in which mean-reverting competitive pressures are just one side of the coin.

Particularly troublesome is the partitioning of profits into a fixed and an incremental component as in equation (1). If fixed effects are nonzero (A_i ≠ 0), it is legitimate to question when and how such effects appeared. Treating them as truly constant assumes that the origins of any enduring differences in profitability can be traced back to the founding of the firm. The firms’ fate would be somehow engraved in its DNA, and it could not be modified by subsequent events or managerial choices. Or, at minimum, it assumes that any events with a permanent effect on profitability occurred prior to, not during, the sample period.

Such assumptions are not only counterintuitive but also contradict conventional wisdom in the field of strategy. Moreover, recent empirical research has provided evidence suggesting that constant effects are indeed less constant than the persistence-of-profits literature seems to imply. Cable and Mueller (2008) conducted an in-depth analysis of the profit time series for eight US and UK companies, using between 32 and 50 years of data. They applied the AR(1) model to the eight firms and tested for structural breaks and underlying trends in the profit series using structural time series (STS) methods. They found evidence of significant breaks in at least five out of the eight cases, breaks that they related to relevant events in the history of the companies. Cable and Jackson (2008) also made use of STS to analyze the profit series of 53 UK companies. They found that companies exhibited different and significant performance trends, suggesting a variety of evolutionary structures extending well beyond the standard mean-reverting process in autoregressive models. Silvia and Iqbal (2011) also found evidence of a growth trend and structural breaks in the aggregate profit series of US companies. They argued that in a Schumpeterian world, deviations from equilibrium create rents that, once dissipated, do not bring the market back to the previous equilibrium but rather to a new one. Thus, what they observed is not mean reversion, but profit growth trends and persistent deviations from competitive levels. Alfarano et al. (2011), meanwhile, followed a rather different methodological route. They defined a statistical equilibrium model of competitive firms and analyzed the properties of the empirical distribution of return rates, along with the dynamic stochastic processes that generate such a distribution. They concluded that the distribution of profits—which they found to correspond to a Subbotin distribution in which the shape parameter is not significantly different to a Laplacian—was not coherent with an AR(1) process and that it results from the interplay of both centrifugal and centripetal competitive forces. Finally, Furman and McGahan (2002) studied business turnarounds—an evolutionary pattern that does not fit with a mean-reverting logic.

Altogether, the aforementioned works not only call for new interpretations of standard models but also should motivate search for alternative approaches (Cable and Jackson, 2008).

The model: a linear latent growth curve

The arguments we have presented thus far suggest that a comprehensive model for the evolution of profits would encompass both rent-eroding and rent-generating competitive dynamics. Mean-reverting processes would be complemented by new profit-seeking efforts by competitive firms. Companies permanently engage in processes, actions, and decisions that may influence their competitive position and that consequently may have an effect on the company’s expected profitability that goes beyond the idea of unsystematic shocks. Such an effect may be captured in a trend-based model (Cable and Jackson, 2008; Silvia and Iqbal, 2011)

Y_{it} = A_{it} + U_{it}

(3)

A_{it} = A_{0i} + B_{i} (T)

(4)

U_{it} = {λ U}_{it - 1} + e_{it}

(5)

where the so-called permanent effect A_it is no longer treated as fixed; instead, it is time dependent, as shown in equation (4): B_i is a vector of parameters and T a vector of time variables. The error term U_it is assumed to follow an AR(1) autoregressive structure; the process, however, can no longer be described as mean-reverting, but rather as trend-reverting. Trend-based estimation is not totally novel to the persistence literature. Mueller (1986) reported a number of polynomial time trends along with AR(1) estimates. However, consistently with the dominant focus on profit persistence, he estimated trends for the incremental, rather than the fixed component, the latter remaining constant over time.¹

In its simplest form, the model in equations (3) to (5) can be defined by a linear growth trend

Y_{i} t = A_{0i} + β_{i} t + {λ U}_{i} t_{- 1} + e_{i} t

(6)

Firm-specific slopes β_i represent average (yearly) profit growth rates, which capture whether—and by how much—companies have been able to improve performance in a systematic fashion during the estimation period; they can also be interpreted as the average net effect of all structural breaks in the profitability series along such period. Should Var(β_i) > 0, this leaves room for new profit differentials arising as a result of companies engaging in rent-seeking initiatives.

Time trends have been criticized because they impose a restrictive structure on the evolution of the profit series. The linear trend defined in equation (6) does not emerge freely from the data, but is imposed by design. There are no theoretical reasons to assume that firm returns actually follow a deterministic linear trend. Moreover, the model cannot be extrapolated in the long run, and if it were, no equilibrium would be reached: for any β_i ≠ 0, equation (6) implies that abnormal profits would tend toward infinitely large positive and negative values as t increases, which is obviously implausible; in general, simple trend-based models perform poorly in out-of-the sample projections.

There are, however, four reasons that support opting for a linear trend. First, it is the most parsimonious model that allows for the systematic generation of new rents. Second, it allows for a straightforward interpretation of the model parameters, and particularly of the linear slope, as described above. Third, there are no sound theoretical reasons to prefer any other—more complex—functional forms. Fourth, Cable and Jackson (2008), after allowing for a variety of evolutionary structures, including exponential patterns of the AR(1) form, find that “the largest single category in our sample exhibited exact or approximately linear trends (38 cases, or 72% of the sample as a whole)” (p. 235). Therefore, we can conclude that equation (6) provides, if not a model of long-run equilibrium, a parsimonious, meaningful, and acceptably realistic depiction of the evolution of firm performance in a given finite time period.

Trend-based models have also been criticized for giving undue weight to early observations, consequently being heavily influenced by the arbitrary choice of the starting point. Growth models, as described in Duncan et al. (2006), can contribute to overcoming this problem. Model parameters describing the trend in equation (6) can be estimated as realizations of two random variables

A_{0 i} = A_{0} + U_{0 i}, U_{0 i} \sim N (0, σ_{0 i}^{2})

(7)

β_{i} = β + U_{1 i}, U_{1 i} \sim N (0, σ_{1 i}^{2})

(8)

Intercepts and slopes are normally and identically distributed across firms. All the observations in the dataset are employed in order to identify the properties of the distributions (Skrondal and Rabe-Hesketh, 2004), greatly reducing the weight of random disturbance and outliers at the time of the first observation.

Growth modeling is common in the study of evolutionary processes in a number of fields from biometrics to education. They are also not entirely novel in the field of management; see, for example, the work by Deadrick et al. (1997), who used this technique to analyze the dynamics of individual job performance. Some excellent discussions of growth modeling can be found in the organizational literature (e.g. Chan, 1998; Bliese and Ployhart, 2002; for a discussion in the context of different approaches to the longitudinal analysis of change, see Ployhart and Vandenberg, 2010).

Because our main interest lies in analyzing the appearance and evolution of interfirm performance heterogeneity, we will focus primarily on the variances of the model parameters, namely, $σ_{0 i}^{2}$ and $σ_{1 i}^{2}$ . Variance in firm-specific intercepts ( $σ_{0 i}^{2}$ ) accounts for a constant component of profitability. As A_0i is the expected value of Y_it when time = 0, we can interpret $σ_{0 i}^{2}$ as the component of firm profitability that explains interfirm profit differentials as the enduring effects of distinctive competitive positions held by firms at some point in the past, given by the first year in the sampling period. Meanwhile, the relative interfirm dispersion of slopes $σ_{1 i}^{2}$ represents interfirm heterogeneity in what we can refer to as a trend component. The error of the model is the incremental component, defined as deviations from the firm’s profitability trend; its dispersion is given by σ²(e_it) . Comparing $σ_{0 i}^{2}$ , $σ_{1 i}^{2}$ , and σ²(e_it) can provide useful information on the importance of the different components in explaining the evolution of the company results and thereby on the nature of competitive dynamics.

As stated in equation (5), short-run profitability shocks are assumed to follow an AR(1) process. If λ∈(–1,1), the process will be stationary and trend-reverting, thus providing evidence of competitive pressures eroding abnormal incremental returns. This is analogous, mutatis mutandis (incremental returns are measured as deviations from profitability trends, rather than as deviations from average profitability), to the analyses commonly found in the persistence-of-profits literature (McGahan and Porter, 1999, 2003). However, the erosion of the incremental component does not imply convergence in actual profits, since linear trends might actually be diverging. In order to conclude that there is convergence, we should also find cov(U_0i, U_1i) < 0. A negative and significant covariance would provide evidence of some profit erosion, as it shows that firm- specific trends are negatively correlated with profitability at t = 0. In order to analyze the rate of such convergence, if it actually exists, we need to define a new equation that supplements equation (6). Hierarchical linear models (HLM), also known as multilevel models, treat random parameters such as U_0i and U_1i as latent variables that can be explained in terms of other variables, either observed or latent (Skrondal and Rabe-Hesketh, 2004). We can thus define a supplementary regression taking firm-specific slopes (U_1i) as the dependent variable and firm-specific intercepts (U_0i) as the only covariate

U_{1 i} = α_{1} + β_{1} (U_{0 i}) + ε_{i}

(9)

Equation (9) is a model of the relationship between the initial status of company i at t = 0, proxied by U_0i, and how it evolves over time (Choi and Seltzer, 2005). The coefficient β₁ provides an estimate of the rate of convergence—if negative—of firm performance. The greater the size of β₁, the more rapid the erosion of superior returns. A remarkable feature of equation (9) is that the explanatory variable U_0i is not the actual profitability at the time of the first observation, but a latent variable obtained from the whole sample as per equation (9). This has important implications for the interpretation of empirical evidence.

The issue of regression toward the mean has been well known in econometrics literature since the classic discussion between Hotelling (1933) and Secrist (1933). Actual company profitability is determined not only by the company’s true competitive position but also by some phenomena that occur at random. If that is the case, companies showing superior performance in any one year will, on average, perform worse in subsequent years, not because their competitive positions have eroded, but simply because they are more likely to have been lucky than unlucky.

The same issue can be posed in terms of measurement theory. We can observe actual company profits, but not true profitability. Convergence in observed profits may stem from changes in measurement error and does not provide evidence of converge in true company performance. This is the well-known regression fallacy, where regression toward the mean is a statistical artifact, but it is interpreted in substantive terms. However, as we have already noted, equation (9) does not regress profitability trends on actual profits at t = 0. Given a large enough number of observations, the independent latent variable U_0i is largely free of year-specific measurement error. In other words, U_0i is a much more consistent indicator of true initial performance than Y_i0.

Even though the latent growth curves can alleviate the aforementioned problem, we cannot rest fully assured that the regression fallacy does not bias our results unless we conduct the appropriate empirical tests. Accordingly, we checked our empirical model on a simulated dataset in order to ascertain whether our methodological approach might or might not induce spurious regression toward the mean. Further details and evidence are discussed in the “Results” section below.

One final property of our model is worth noting. By defining both an AR(1) for the error term and an equation analyzing convergence-in-trends, we are able to explore the relative persistence of the different components of company returns, and not only of the abnormal shocks to profitability noted by McGahan and Porter (1999). Our approach is thus more comprehensive than most previous literature as well as being better suited for analyzing the sustainability of competitive advantages, defined as the ability of a company to consistently outperform its rivals. Table 1 summarizes the model and its main parameters and compares them to those in the much more common AR(1) autoregressive model.

Table 1.

Comparison of AR(1) and linear latent growth curve approaches.

	AR(1) autoregressive model	Linear latent growth curve
Model	Y_it = A_i + S_it + U_it	Y_it = A_0i + β_it + λU_it−1 + e_it
	S_it = λ_iS_it−1 + E_it	A_0i = A₀ + U_0i, U_0i ~ N(0, $σ_{0 i}^{2}$ )
		β_i = β + U_1i, U_1i ~ N(0, $σ_{1 i}^{2}$ )
		U_1i = α_1; + β₁(U_0i)+ ϵ_i
Main results (firm level)	A_i: permanent component of profitability λ_i: persistence of the incremental component of profitability (S_it)	A_i0: time-unvarying component of profitability; expected returns at time t = 0
Main results (firm level)	A_i/(1 − λ_i): long-run equilibrium profitability	B_i: profitability linear trend; annual change in expected returns
Main results (aggregate)	Distribution of firm-level parameters: average λ_i, percentage of 0 < λ_i <1, percentage of A_i significantly ≠ 0, variance of long-run equilibrium levels A_i/(1 − λ_i)	$σ_{0 i}^{2}$ : interfirm variance in profit levels
		$σ_{1 i}^{2}$ : interfirm variance in profit trends
		$σ_{0 i}^{2}$ / $σ_{1 i}^{2}$ : ratio of variance in levels over variance in trends
		λ: average persistence of short-term deviations from profitability trends
		β₁: expected relation between initial status and linear trend; average rate of convergence in profit trends (if β₁ < 0)

Sample and variables

We applied our model of analysis to a sample of manufacturing companies in Spain drawn from the Encuesta sobre Estrategias Empresariales (Business Strategies Survey (BSS)), an annual rotating panel survey conducted by the Spanish Ministry of Industry and Fundación SEPI, a state-owned Spanish foundation. The survey collects a wide range of data on a large sample of Spanish manufacturing companies, classified into 20 different industries classified at the two-digit level. The sampling frame of the BSS includes companies with 10 or more employees, and the sample is obtained using two complementary methods: complete enumeration is used for firms with over 200 employees and stratified random sampling for companies with employees between 10 and 200. When interpreting empirical results, it should be considered that some degree of overrepresentation of large firms is to be expected in our data.

We used an unbalanced panel from 1991 to 2008, yielding a maximum of 18 observations per firm. In order to obtain meaningful company-specific trends and to maintain enough degrees of freedom, we removed companies with less than three observations from the sample. In addition, we identified and analyzed some extreme outlier values in the profitability variable. In most cases, such outliers can be attributed to apparent measurement error—for example, total assets (TA) abnormally high or low compared to previous and subsequent years for the same company, with no apparent explanation for the difference. Therefore, we also removed them from the sample. The final dataset comprises 27,763 observations for a total of 2,764 companies, with an average number of 10.04 observations per firm. We report some descriptive statistics for the sample, classified by industry, as given in Table 2.

Table 2.

Descriptive statistics.

Industry	NACE codes	Observations	Industry averages
			Employees	Sales	EBITDA	Total assets	EBITDA/total assets (%)
1	101	746	242	21,630,101	1,381,513	10,670,550	12.9
2	102–109, 120	2739	268	28,097,492	3,458,806	22,992,221	15.0
3	110	582	362	42,365,788	8,486,155	41,144,575	20.6
4	131–133, 139, 141–143	2600	156	4,785,292	344,158	3,971,608	8.7
5	151–152	777	45	1,515,762	127,685	982,622	13.0
6	161–162	757	94	7,708,096	844,216	7,344,427	11.5
7	171–172	827	249	25,447,222	2,619,871	28,270,182	9.3
8	181–182	1407	156	13,261,821	2,027,690	11,230,936	18.1
9	201–206, 211–212	2007	327	42,422,982	4,589,362	34,344,049	13.4
10	221–222	1493	207	18,944,005	1,859,142	18,563,808	10.0
11	231–237, 239	1958	234	20,011,456	3,604,527	62,704,443	5.7
12	241–245	960	555	77,800,299	9,085,145	70,193,040	12.9
13	251–257, 259	2733	128	8,970,171	987,738	7,960,053	12.4
14	281–284, 289	2065	244	13,945,508	1,142,882	11,177,226	10.2
15	261–268	426	446	31,412,193	3,437,968	22,830,354	15.1
16	271–275, 279	1842	319	24,026,712	2,058,721	14,625,603	14.1
17	291–293	1327	1038	152,017,035	8,088,675	63,461,376	12.7
18	301–304, 309	593	655	32,449,884	1,342,213	41,921,233	3.2
19	310	1339	111	5,705,289	535,691	5,410,415	9.9
20	321–325, 329	585	129	6,304,040	560,108	3,986,339	14.1
Total		27,763	275	26,878,253	2,619,636	22,923,134	11.4

EBITDA: earnings before interest, taxes, depreciation, and amortization; NACE: statistical classification of economic activities in the European community. Sales, EBITDA, total assets are given in Euros (€).

We measured performance as return on assets (ROA), defined as the ratio of earnings before interest, taxes, depreciation, and amortization (EBITDA)—operating income minus operating expenses, excluding amortization—over average TA, given by (TA_t + TA_t−1)/2, where TA_t accounts for the book value of TA at the end of year t. This variable is neutral to the financial structure of the company and excludes extraordinary items, which are by definition year-specific.

This article focuses on the firm-specific component of business performance as a function of the competitive position of the firm. We are interested in intercompany (i.e. within-industry heterogeneity) rather than interindustry heterogeneity. Consequently, we standardized profitability measures relative to their industry averages and standard deviations

Y_{ijt} = \frac{[{ROA}_{ijt} - avg ({ROA}_{jt})]}{stddev ({ROA}_{jt})}

(10)

where the subindices i, j, and t account for company, industry, and year, respectively. Industries were defined according to the classification provided by the BSS, which is roughly equivalent to the two-digit statistical classification of economic activities in the European community (NACE) Rev. 1 system (see Table 2).

Provided that the distribution of firm profits varies between years and sectors, profitability data, even when measured as deviations from industry means, may not be directly comparable across time periods and industries, (Powell and Reinhardt, 2010). By using year- and industry-specific standard deviations to standardize data, we account for differences in the dispersion of return rates, we enhance the homogeneity and comparability of our dependent variable and we allow identically scaled comparisons across different periods and industry settings. Standardized profits also contribute to account for interindustry differences in risk. Standardized measures of performance have been reported in a number of previous studies (e.g. Dubofsky and Varadarajan, 1987; Geringer et al., 1989; Morse et al., 2011).

Accounting measures of profitability have a distinct advantage for analyzing profit dynamics vis-à-vis measures based on market value data: they do not incorporate market expectations of future performance (Dubofsky and Varadarajan, 1987), which could render the analysis tautological. Two major shortcomings of accounting data, though, must be considered. First, book values are based on historical information and can be influenced by the age of assets; second, accounting data do not consider intercompany differences in risk-taking. Risky strategies imply a higher cost of capital so that higher profits may not actually imply superior performance.

In order to test for potential biases arising from these two spurious effects, we regressed ROA on the weighted average age of assets and the average cost of long-term debt, as a proxy for financial risk. The results suggest that both variables have a very limited impact on rates of return, the R² for the multivariate regression being as low as 0.004.

A potential problem of panel data that is seldom considered in longitudinal studies of company profitability is selection bias arising from nonrandom attrition. If lower performance is systematically linked to market exit, attrition will affect mainly those companies with weaker initial status; only the initial low performers that manage to significantly improve performance would remain in the sample. This might induce spurious convergence in profit rates. The use of an unbalanced panel design significantly alleviates this potential problem, since unbalanced panels consider all the available observations, even if the company does not remain in the sample for the whole sampling period. In addition, we conducted some tests based on the work by Fitzgerald et al. (1998) and Hausman and Wise (1979) to check for attrition bias and to assure the validity of our conclusions. First, we ran a logistic regression analyzing the impact of company results measured as standardized ROA in t − 1 on the probability of attrition in t. Next, we estimated two regressions in order to analyze whether profits at t = 0 would affect either the number of years a company remains in the sample or the probability of it still being in the sample by 2008. In both cases, the coefficients were small and nonsignificant, suggesting that nonrandom attrition is unlikely to have a significant effect on the validity of our results.

Empirical results

Figure 1 graphically represents the evolution of profits for 12 firms, chosen among those in our sample for which data are available from 1991 to 2008. We also report AR(1) estimates, obtained as per equation (1). The graphs reveal a variety of dynamics. In some cases, abnormal profits seem to converge relatively quickly toward long-term stable values that do not differ much from industry averages (e.g. firms 689 and 2326). Other firms show higher persistence, but the series still appear to converge toward some long-term level (e.g. firms 451 and 1566). On the other hand, there are a number of firms whose dynamics can hardly be described as approaching a steady state. Some companies display either consistent positive or negative performance trends (e.g. firms 1450, 1593, 1796, and 2009) or substantial breaks in the series (e.g. firm 417). The estimates displayed reveal that the AR(1) model captures just part of the complexity in profit dynamics. It is worth noting in this regard that the model may produce similar estimates for pairs of companies that exhibit different, even opposite, dynamics (e.g. firms 451/1796, 689/1010, and 1604/2009). Overall, the exploratory evidence presented in Figure 1, despite not being representative of the whole sample, motivates further analyses exploring interfirm heterogeneity in profit dynamics.

Figure 1.

Plots of selected examples of profit dynamics.

Table 3 presents the results for the different specifications of the empirical model described in section “The model: a linear latent growth curve.” We focus not on the average value of the coefficients, as the dependent variable is centered around 0 by design, but on the error structure in the random part of the model. This structure can be interpreted in terms of variance components—both static or time invariant and dynamic or time varying—that explain heterogeneous firm performance.

Table 3.

Results from linear latent growth curve estimation.

	Linear regression		Random intercepts		Random slopes		Random slopes with AR(1) errors
	Mean	Standard deviation	Mean	Standard deviation	Mean	Standard deviation	Mean	Standard deviation
Intercept	0.0239	0.0113	0.0603	0.0147	0.0544	0.0170	0.0499	0.0166
Time	−0.0025	0.0011	−0.0069	0.0012	−0.0069	0.0016	−0.0062	0.0015
stddev(U_0i)			0.4861		0.6101		0.4913
stddev(U_1i)					0.0489		0.0335
corr (U_0i, U_1i)					−0.6430		−0.5110
stddev(e_i)			0.8592		0.8338		0.8687
Phi							0.1974
ICC			0.2420

ICC: intraclass correlation coefficient.

The random intercepts model shows the results of what multilevel literature refers to as an empty model (Goldstein, 2003), and it is also known as one-way random effects analysis of variance (ANOVA). This model provides information on the intraclass correlation coefficient (ICC), which can be calculated as $σ_{0 i}^{2}$ /( $σ_{0 i}^{2}$ +σ²(e_it))=0.242. The ICC has two complementary interpretations (Snijders and Bosker, 1999). First, it represents the correlation between two randomly drawn observations in the same randomly drawn company. Second, and perhaps more interestingly, it also represents the proportion of total variance that is accounted for by the group, that is, company, level. Within the time span we considered, nearly 24% of variance in business profits is explained by between-company differences in average profitability, whereas 76% corresponds to intracompany variability.

The random slopes model extends this empty model by introducing company-specific linear time trends (column 4). Finally, the random slopes model with AR(1) residuals (column 5) also addresses nonindependency of the error term. Likelihood ratio tests show that both of these additions significantly improve the fit of the model; thus, evidence calls for selecting the fuller model, which corresponds with the one we presented in equation (6).

The ratio σ_0i/σ_1i provides important information on the evolution of firm profits. It compares two sources of heterogeneous performance: on the one hand, constant differences representing the permanent effects of the firms’ initial conditions; and on the other hand, variance-in-trends, resulting from idiosyncratic profit-seeking efforts. The larger the ratio, the greater the salience of initial conditions in determining differences in company performance and vice versa. The estimated values for this ratio range from 12.5 in the model assuming independent errors to 14.7 in the model with AR(1) residuals.

Figure 2 portrays how variance in both initial conditions and trends interacts in shaping the expected evolution of company profits. A consideration of two of the hypothetical companies in Figure 2 may help to illustrate the implications of these results. Let us define company C, which has a fairly good starting position, so that its expected profit for t = 0 is one standard deviation over the mean (A_0C = 0.0499 + 0.4913 = 0.5412, according to the results from the random slopes model with AR(1) residuals presented in Table 3), but its expected performance weakens with time by a comparable amount in standardized terms, so that β_C = −0.0062 − 0.0335 = −0.0397, according to the results from the same model. We then define company G as representing the opposite case (A_0G = −0.4414, β_G = 0.0273). In both cases, we assume no year-specific incremental component, so that e_Ct = e_Gt = 0. The parameter estimates suggest that the expected profit differential will diminish by 50% after 7 years, and that on average, G will outperform C within 15 years.

Figure 2.

Heterogeneity in profit growth curves. Hypothetical firms based on estimates from the model with random slopes and AR(1) residuals.

The previous paragraph presents just two hypothetical firms. In order to see whether profit differentials actually erode over time, we need to consider the empirical relationship between firm-specific intercepts and slopes. Results in Table 3 consistently show a negative, strong, and significant correlation between U_0i and U_1i. Companies with weaker initial competitive positions, that is, lower U_0i, exhibit, on average, better profit trends, that is, higher U_1i, gradually narrowing the profitability gap with superior performers. In order to analyze the rate of such convergence processes, we estimated the latent-variable regression specified in equation (9). Table 4 presents the results from the latent-variable models, which confirm a negative and significant effect of intercepts on linear trends. The coefficient shows that on average, initial differences in expected profitability erode at a yearly rate of between 3.4% and 5.2%, depending on whether or not the model considers the AR(1) structure of residuals.

Table 4.

Results of latent-variable regressions.

	Random slopes			Random slopes with AR(1) errors
	Mean	Standard deviation	Significance	Mean	Standard deviation	Significance
Intercept	−0.0041	0.0011	0.0000	−0.0046	0.0012	0.0000
U_0i	−0.0515	0.0026	0.0000	−0.0341	0.0045	0.0000
Original coefficient	−0.0069			−0.0063
Adjusted coefficient	−0.0041			−0.0046
Difference	−0.0028	0.0023		−0.0017	0.0020
stddev(U_1i)	0.0374			0.0281

As Mueller (1986), among others, shows, a mean-reverting process can produce heterogeneous profit trends. Let us consider, for example, the case of two firms converging to the same equilibrium level; should one experience positive abnormal profits (S_it in equation (1)) and the other negative ones, their growth curves will show opposite-sign slopes. Therefore, it is legitimate to question whether heterogeneous performance trends do indeed capture idiosyncratic profit-seeking initiatives, as we argue, or are just an artifact produced by the erosion of abnormal profits. Results in Table 4 confirm that all mean-reverting forces considered, that is, AR(1) errors and converging slopes, there still remains significant heterogeneity in profit trends (σ_1i = 0.0281). Comparing results in Tables 3 and 4, we conclude that U_0i explains (0.0335² − 0.0281²)/0.0335² = 29.6% of the variance in profit trends, while the remaining 70% stays unexplained and can be attributed to other firm-specific variables. This result reinforces our previous arguments suggesting that the evolution of firm profits is shaped by dynamics that go beyond mean-reverting competitive pressures.

The likelihood ratio tests show that the error term follows a first-order autoregressive process, as expected. The coefficient λ_i = 0.197 implies that the persistence of short-term profitability shocks generating deviations from long-term trends is rather low, so that only a negligible effect remains after 2 or 3 years.

We conducted a number of additional analyses in order to evaluate the validity and robustness of our results. First, we tested whether the observed convergence in profits might be a mere statistical artifact. Second, we checked for significant differences in our findings when we altered the period under analysis.

Regarding the first issue, Kelly and Price (2005) suggest two alternatives to address the bias that can be generated by the regression toward the mean artifact: first, calculating the bias, whenever possible, and subsequently correcting the results; and second, setting up an experimental or quasi-experimental design and comparing the results with those of a control group. We followed this second route and created an artificial pseudo-control group. To do so, we generated a simulated dataset that shares the properties of our real data, with one exception: by design, the simulated sample is generated from a population in which profit levels and trends are independent, so that cov(U_0i, U_1i) = 0. Table 5 presents the characteristics of the data and the main findings.

Table 5.

Results from simulated data.

	Random slopes			Random slopes with AR1 errors
	mean	stddev	p-value	mean	stddev	p-value
Intercept	0,0478	0,0164	0,0036	0,0478	0,0163	0,0022
time	−0,0034	0,0016	0,0297	−0,0037	0,0016	0,0172
stddev(u_0i)	0,5621			0,4617
stddev(u_1i)	0,0451			0,0309
corr(U_0i, U_1i)	−0,2230			0,2130
stddev(e_i)	0,8601			0,8923
Phi				0,2028
Results from latent-variable regression
Intercept	−0,0026	−0,0026	0,0700	−0,0004	0,0018	0,0130
U_0i	−0,0179	0,0039	0,0000	0,0138	0,0039	0,0660
Original coef	−0,0034			−0,0037
Adj. Coef.	−0,0026			−0,0044
Difference	−0,0009	0,0018		0,0007	0,0015
Var U_1i	0,0019			0,0009

We argued in section “The model: a linear latent growth curve” that we can avoid falling into the regression fallacy, or at least reduce the risk of doing so, by using all the available observations to estimate the companies’ starting positions. The results we obtained from the simulated data support this argument. Once we accounted for serial dependence of the AR(1) form in the residuals, we did not find any significant relationship between initial intercepts and slopes, suggesting that the estimation technique does not induce spurious convergence in the terms discussed by Hotelling (1933) and Friedman (1992), among others.

Regarding the time period spanned by our data (1991–2008), it was chosen on the basis of information availability. Consequently, the idea of initial conditions, similar to Cockburn et al.’s (2000), refers to the position of the company at some given time in the past—in our case, 1991—and is conditioned by arbitrary left-censoring of the data. Such initial conditions, except in the case of new ventures, are the result of prior dynamics that escape our analysis. This demands serious caution when interpreting individual growth curves, as the starting point has no substantive meaning. However, our interest lies not in individual firms but in aggregate dynamics, and those are not substantially affected by changes in the period of analysis.

Table 6 shows that our main conclusions hold when we modify the first year of the estimation, progressively reducing the period under analysis. It also shows that as shorter periods are considered, variability-in-trends becomes ever more relevant; hence, σ_1i increases and the ratio σ_0i/σ_1i decreases. This was to be expected: as we increase the number of years, performance trends tend to flatten out. In addition, when we consider the 2003–2008 period, both the standard deviation σ(e_i) and the autoregressive parameter (λ) of the error term decrease. This suggests a better fit of the model. All the models in Table 6 confirm the results from the latent regression in which company-specific intercepts have a negative and significant effect on the company-specific linear trends.

Table 6.

Results for different estimation time periods.

	1994–2008			1997–2008			2000–2008			2003–2008
	Mean	Standard deviation	Significance	Mean	Standard deviation	Significance	Mean	Standard deviation	Significance	Mean	Standard deviation	Significance
Random slopes with AR(1) errors
Intercept	0.046	0.019	0.016	0.027	0.018	0.134	0.055	0.021	0.009	0.058	0.025	0.020
Time	−0.007	0.002	0.000	−0.007	0.003	0.003	−0.013	0.004	0.001	−0.020	0.007	0.003
stddev(U_0i)	0.578			0.516			0.486			0.606
stddev(U_1i)	0.050			0.051			0.060			0.112
corr(U_0i, U_1i)	−0.655			−0.513			−0.415			−0.582
stddev(e_i)	0.851			0.854			0.849			0.815
Phi	0.196			0.183			0.187			0.137
Latent-variable regression results for U_1i
Intercept	0.005	0.001	0.001	−0.006	0.002	0.002	−0.010	0.003	0.002	−0.014	0.005	0.007
U_0i	−0.055	0.004	0.000	−0.047	0.008	0.000	−0.048	0.014	0.001	−0.105	0.016	0.000
Original coefficient	−0.007			−0.008			−0.013			−0.020
Adjusted coefficient	−0.005			−0.006			−0.010			−0.014
Difference	−0.002	0.003		−0.001	0.003		−0.003	0.005		−0.006	0.009
stddev(U_1i)	0.037			0.042			0.052			0.090
Null model (one-way ANOVA)
stddev(U_0i)	0.4933			0.4949			0.4941			0.5300
stddev(e_i)	0.850			0.8464			0.8368			0.8153
ICC	0.252			0.255			0.259			0.297
Firms	2456			2374			1812			1565
Observations	22,676			18,332			12,648			8212
Observations per firm	9.233			7.722			6.980			5.247

ICC: intraclass correlation coefficient; ANOVA: analysis of variance.

We can conclude that even if some noteworthy peculiarities show up when reducing the analysis to only 6 years (2003–2008)—greater variance of firm slopes, a more marked convergence in profit trends, and less persistent residuals—the results are fairly consistent to changes in the time period. Overall, while the individual curves may vary, aggregate dynamics appear quite stable, at least for periods greater than 9 years.

We also checked for consistency of the results when expanding the period of analysis beyond the average of 10 years available in our original sample. In order to do so, we reran the model with AR(1) errors on a subsample of firms for which data were available for the whole 1991–2008 period (6,786 observations). As expected, results show that variance of fixed differences decreases and that profit trends tend to flatten out as the time period increases (σ_0i = 0.303, σ_1i = 0.023). A likelihood ratio test, still, demonstrates that allowing linear trends to vary across firms significantly improve model fit (p value < 0.001), showing that variance-in-trends remains as a relevant determinant of profit dynamics. Deviations from trends become slightly more persistent (λ = 0.269), and the association between initial status and subsequent profit trends remains negative and significant, if somewhat weaker—corr(U_0i, U_1i) = −0.296. This last result was to be expected, since, as longer periods are considered, more factors other than initial status are likely to shape the evolution of firm returns. Overall, these findings are consistent with the evidence presented thus far.

Discussion

The evidence presented in the previous section provides empirical support for a profound intuition underlying management literature: companies are heterogeneous not only in terms of profitability levels but also in terms of the profitability trends. Even when considering time period as long as 18 years, the average rates of yearly profit change vary considerably among companies; results from column 4 in Table 3 show that those rates vary between +0.061 and −0.073 measured in terms of industry-specific standard deviations within a range of ±2 standard deviation. This highlights the importance of what we can label as variance-in-trends in explaining the outcomes from competition in a given time. We find that firms can experience substantial changes in their competitive positions in the midterm.

The vast majority of literature on strategic management, both theoretical and empirical, focuses on the idea of sustainable competitive advantage and the conditions that should exist for superior results to persist over time. The strategic factors and the conditions of market equilibrium that underlie superior performance have received a great deal of scholarly attention. We show that the nature of competition is probably better represented by a state of disequilibrium, in which competitive positions are rather unstable. Unlike in the works based on autoregressive models, no long-run equilibrium is to be reached. Our results suggest that the longitudinal dimension of strategy (Porter, 1991) is indeed highly relevant and that the dynamic processes that give rise to performance change merit attention from empirical researchers.

Some authors have approached the dynamics of competition from neoclassical dynamic equilibrium models. Jovanovic (1982) considers a model of passive learning in which companies adopt optimizing decisions with imperfect information. Each period, market outcomes provide companies with new information that they feed into their optimization process, resulting in new decisions, new market outcomes, and so forth, giving rise to heterogeneous paths. This type of model is rather restrictive in its conception of competitive dynamics and it is not always consistent with the available empirical evidence (Hodgson, 1994; Nelson and Winter, 2002; Pakes and Ericson, 1998). Accordingly, other authors hold that the study of change in markets and organizations requires renouncing neoclassical assumptions and replacing them with evolutionary frameworks (Nelson and Winter, 2002). From this perspective, companies are guided not by optimizing criteria but by goal-seeking search routines that modify their rules of behavior in a systematic and intentional fashion (Nelson and Winter, 1974, 1982). The relative success of these routines and change processes for each competitor will determine the changes in their performance. In this regard, management scholars often highlight the role of strategic choice (Child, 1972) and managerial action in shaping the firm’s fate. If managerial choice could not influence firm competitiveness, there would be no point in strategizing (Rond and Thietart, 2007).

Whatever specific factors may underlie the evolution of company outcomes, our results suggest that the explanation for superior profitability typically lies in successful strategic orientation in the organization’s recent past (Slater et al., 2006), rather than in the enduring effect of some unique past conditions. Moreover, the intensity of the dynamics we observe seems to point toward evolutionary arguments, rather than to neoclassical dynamic equilibrium models. This conclusion, however, will need to be further explored in subsequent research.

This work also extends and complements previous evidence from the persistence-of-profits literature. The latent-variable models presented in Table 4 analyze convergence-in-trends. Our results show that beyond the erosion of unsystematic profitability shocks, systematic profitability trends also converge. This process, although gradual—the differences prove to be substantially more persistent than the incremental component—is by no means negligible. The erosion of short-term shocks is captured by the AR(1) parameter λ. Unlike in previous works, such shocks are defined as deviations not from average profitability levels but from linear profitability trends. This would explain why the rate of persistence is measurably lower than that usually found in the literature.

The findings from growth models complement, rather than substitute for, those from the AR(1) model that dominates the persistence-of-profits literature. Autoregressive models are parsimonious, produce easily interpretable parameters, and are soundly based on an elegant microeconomic model (Geroski, 1990). However, our findings reinforce existing evidence challenging the assumptions of the AR(1) model, since they suggest that changes in performance emerge in a systematic manner and that profit dynamics are shaped by the interaction of rent-creating and rent-eroding forces.

The results are also rather complementary to those of trend-based models based on STS (Cable and Jackson, 2008; Cable and Mueller, 2008). STS are more flexible than growth curves because they do not need any a priori assumptions regarding the functional form of the series. The components of the time series can vary between periods so that they capture structural breaks, and since the model is estimated separately for each firm, the parameters can vary among companies. The cost of such flexibility is that they do not provide information on the aggregate dynamics of profitability, as LGM do. In this regard, the linear model that we have presented here is the most parsimonious model that produces systematic evidence on the emergence of performance differentials.

Conclusion

The academic interest on the dynamics of strategy and their implications for the origins of competitive advantage has been clearly on the rise for decades. However, previous research on the dynamics of firm performance has been, by and large, confined to analyzing the progressive erosion of abnormal profits. Much less is still known about how such profits emerge (Cockburn et al., 2000).

In this article, we suggest that the autoregressive model that dominates the literature does not adequately capture how the process of competition not only erodes previous profits but also originates new ones. Consequently, following Cable and Jackson (2008), we define and test a linear latent growth model that allows for the generation as well as the erosion of economic rents. From this perspective, abnormal returns appear not only as the result of unsystematic shocks but also in a systematic way, so that firm profitability follows different latent trajectories.

We operationalized our model employing the LGM techniques, a well-established approach to the analysis of change. We obtained empirical evidence suggesting that firms are heterogeneous not only in terms of profitability levels but also in terms of systematic profitability trends.

We must note some relevant limitations of this study, the most salient being that while we assess changes in performance, we provide no explanation as to the causes of such changes. We argue that strategic management provides some theories as that can explain heterogeneous profitability trends, and the evidence we have obtained delivers relevant information about the dynamics of strategy. However, as McGahan and Porter (2005) note, it is impossible to infer the causes of the changes in firm performance from the mere observation of such changes. Further research can build on this work and can contribute to provide causal explanations for the effects we have found. In this regard, it may be worth considering applying techniques for classifying latent trajectories, such as latent growth class analysis (LGCA).

Further research may also extend this work by analyzing longer time spans. Much like an Impressionist painting, the images we obtain of longitudinal processes may change with the distance from which we observe them. In this article, we have tracked the evolution of profits for a maximum of 18 years per firm, a period of undeniable strategic relevance. It would be interesting, however, to extend the analysis to the very long run, as some authors have made with autoregressive models (Cable and Gschwandtner, 2008; Gschwandtner, 2005).

It should also be noted that our dataset was confined to manufacturing industries; new evidence would be required in order to extend our conclusions to the primary and service sectors, which account for a substantial fraction of output in most national economies. Finally, it would also be of interest to make use of alternative measures of firm performance—particularly nonaccounting measures—as they may be of help in developing a richer understanding of the evolution of competitive positions.

Despite its limitations, this study can provide both scholars and practitioners with some relevant insights. If we assume a context in which competition is stable and firms do not change routinely, “a strategic theory that addresses the cross sectional problem of explaining superior performance at a given point in time is helpful in addressing the more important longitudinal problem of explaining how firms achieve superior performance over time” (Eisenhardt and Santos, 2002: 142). However, we provide empirical evidence suggesting that this is not the case; on the contrary, our results should motivate research that contributes to the development of new theoretical frameworks and empirical evidence explicitly addressing the so-called longitudinal problem of strategy (Porter, 1991).

As for practitioners, strategists have traditionally been urged to defend their sources of competitive advantage from the competition. Firms enjoying superior performance should focus on maintaining the competitive status quo—in other terms, market equilibrium—rather than on creating new sources of advantage. Our results suggest on the contrary that competition is largely a disequilibrium process that challenges competitive positions; on average, substantial room seems to exist for weaker competitors to catch up via better trend effects. Under such conditions, long-term competitive success will depend on how firms navigate disequilibrium and on their ability to consistently generate new sources of profits.

Footnotes

Funding

This study received financial support from the Spanish Ministry of Science and Innovation (project ECO 2008-01513).

Notes

Author biographies

Antonio J Revilla is Assistant Professor of Business Organization at Carlos III University of Madrid. He received his PhD from Carlos III University of Madrid and an MSc in Social Research Methods from the London School of Economics and Political Science. His current research interests focus on the origins and dynamics of competitive advantage and on the role of technological and organizational innovation in creating superior firm performance. He has recently published his research in Technovation, among other journals.

Zulima Fernández is Professor of Strategy at Carlos III University of Madrid, where she is also Chair of the Institute for Entrepreneurship and Family Firms. She is President of the Spanish Scientific Association of Business Economics and Management (ACEDE). Her research interests include internationalization strategies, innovation, and family firms. Her works have been published in journals such as Journal of International Business Studies, Family Business Review, Technovation, and Journal of World Business, among others.

References

Acquahh

(2003) “Corporate Management, Industry Competition and the Sustainability of Firm Abnormal Profitability,” Journal of Management & Governance 7(1): 57–85.

Alfarano

Milakovic

Irle

Kauschke

(2011) “A Statistical Equilibrium Model of Competitive Firms,” Journal of Economic Dynamics & Control 36(1): 136–49.

Anderson

T. W.

Hsiao

(1982) “Formulation and Estimation of Dynamic Models Using Panel Data,” Journal of Econometrics 18(1): 47–82.

Baaij

De Jong

Van Dalen

(2011) “The Dynamics of Superior Performance among the Largest Firms in the Global Oil Industry, 1954-2008,” Industrial and Corporate Change 20(3): 789–824.

Bliese

P. D.

Ployhart

R. E.

(2002) “Growth Modelling Using Random Coefficient Models: Model Building, Testing, and Illustrations,” Organizational Research Methods 5(4): 362–87.

Bollen

K. A.

Curran

P. J.

(2006) “Latent Growth Models: A Structural Equation Approach. Hoboken,” NJ: Wiley.

Bou

J. C.

Satorra

(2007) “The Persistence of Abnormal Returns at Industry and Firm Levels: Evidence from Spain,” Strategic Management Journal 28(7): 707–22.

Bou

J. C.

Satorra

(2010) “A Multigroup Structural Equation Approach: A Demonstration by Testing Variation of Firm Profitability across EU Samples,” Organizational Research Methods 13(4): 738–66.

Cable

J. R.

Gschwandtner

(2008) “On Modelling the Persistence of Profits in the Long Run: A Test of the Standard Model for 156 US Companies, 1950-99,” International Journal of the Economics of Business 15(2): 245–63.

10.

Cable

J. R.

Jackson

R. H. G.

(2008) “The Persistence of Profits in the Long Run: A New Approach,” International Journal of the Economics of Business 15(2): 229–44.

11.

Cable

J. R.

Mueller

D. C.

(2008) “Testing for Persistence of Profits’ Differences across Firms,” International Journal of the Economics of Business 15(2): 201–28.

12.

Chan

(1998) “The Conceptualization and Analysis of Change over Time: An Integrative Approach Incorporating Longitudinal Means and Covariance Structures Analysis (LMACS) and Multiple Indicator Latent Growth Modeling (MLGM),” Organizational Research Methods 1: 421–83.

13.

Chen

M.-J.

Miller

(2012) “Competitive Dynamics: Themes, Trends, and a Prospective Research Platform,” Academy of Management Annals 6: 1–89.

14.

Child

(1972) “Organizational Structure, Environment and Performance: The Role of Strategic Choice,” Sociology 6(1): 1–22.

15.

Choi

Seltzer

(2005) “Modeling Heterogeneity in Relationships between Initial Status and Rates of Change: Latent Variable Regression in a Three-Level Hierarchical Model,” CSE Report. 647. March, 2005 Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing.

16.

Cockburn

I. M.

Henderson

R. M.

Stern

(2000) “Untangling the Origins of Competitive Advantage,” Strategic Management Journal 21(10–11): 1123–45.

17.

Crespo Cuaresma

Gschwandtner

(2008) “Tracing the Dynamics of Competition: Evidence from Company Profits,” Economic Inquiry 46(2): 208–13.

18.

Danneels

(2012) “Second-Order Competences and Schumpeterian Rents,” Strategic Entrepreneurship Journal 6: 42–58.

19.

Deadrick

D. L.

Bennett

Russell

C. J.

(1997) “Using Hierarchical Linear Modeling to Examine Dynamic Performance Criteria over Time,” Journal of Management 23(6): 745–57.

20.

Dubofsky

Varadarajan

P. R.

(1987) “Diversification and Measures of Performance: Additional Empirical Evidence,” Academy of Management Journal 30(3): 597–608.

21.

Duncan

T. E.

Duncan

S. C.

Strycker

L. A.

(2006) An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues and Applications. Mahwah, NJ: Lawrence Erlbaum.

22.

Eisenhardt

K. M.

Martin

J. A.

(2000) “Dynamic Capabilities. What Are They?,” Strategic Management Journal 21(10–11): 1105–21.

23.

Eisenhardt

K. M.

Santos

F. M.

(2002) “Knowledge-Based View: A New Theory of Strategy?” in Pettigrew

Thomas

Whittington

(eds) Handbook of Strategy and Management, 1st edn, pp. 139–64. London: Sage.

24.

Ferrier

W. J.

Smith

K. G.

Grimm

C. M.

(1999) “The Role of Competitive Action in Market Share Erosion and Industry Dethronement: A Study of Industry Leaders and Challengers,” Academy of Management Journal 34: 372–88.

25.

Fitzgerald

Gottschalk

Moffit

(1998) “An Analysis of Sample Attrition in Panel Data. The Michigan Panel Study of Income Dynamics,” Journal of Human Resources 33(2): 251–99.

26.

Foss

N. J.

Ishikawa

(2007) “Towards a Dynamic Resource-Based View: Insights from Austrian Capital and Entrepreneurship Theory,” Organization Studies 28(5): 749–72.

27.

Foss

N. J.

Klein

P. G.

Kor

Y. Y.

Mahoney

J. T.

(2008) “Entrepreneurship, Subjectivism, and the Resource-Based View: Toward a New Synthesis,” Strategic Entrepreneurship Journal 2(1): 73–94.

28.

Friedman

(1992) “Do Old Fallacies Ever Die?,” Journal of Economic Literature 30: 2129–32.

29.

Furman

J. L.

McGahan

A. M.

(2002) “Turnarounds,” Managerial and Decision Economics 23(4/5): 283–300.

30.

Geringer

J. M.

Beamish

P. W.

DaCosta

R. C.

(1989) “Diversification Strategy and Internationalization: Implications for MNE Performance,” Strategic Management Journal 10(2): 109–20.

31.

Geroski

P. A.

(1990) “Modelling Persistent Profitability,” in Mueller

D. C.

(ed.) The Dynamics of Company Profits: An International Comparison, pp. 15–34. Cambridge: Cambridge University.

32.

Geroski

P. A.

Jacquemin

(1988) “The Persistence of Profits: A European Comparison,” Economic Journal 98(391): 375–89.

33.

Goldstein

(2003) Multilevel Statistical Models, 3rd edn. London: Edward Arnold.

34.

Gschwandtner

(2005) “Profit Persistence in the ‘Very’ Long Run: Evidence from Survivors and Exiters,” Applied Economics 37(7): 793–806.

35.

Gschwandtner

(2012) “Evolution of Profit Persistence in the USA: Evidence from Three Periods,” Manchester School 80(2): 172–209.

36.

Gschwandtner

Hirsch

(2011) “Profit Persistence in the Food Industry: Evidence from Five European Countries.” In: Paper presented at the EAAE Congress, Zurich, Switzerland, August 30 to September 2, 2011.

37.

Hausman

J. A.

Wise

D. A.

(1979) “Attrition Bias in Experimental and Panel Data: The Gary Income Maintenance Experiment,” Econometrica 47(2): 455–74.

38.

Hodgson

G. M.

(1994) “Optimisation and Evolution: Winter’s Critique of Friedman Revisited,” Cambridge Journal of Economics 18(4): 413–30.

39.

Hotelling

(1933) “Review of the Triumph of Mediocrity in Business by Horace Secrist,” Journal of the American Statistical Association 28: 463–5.

40.

Jacobides

M. G.

Winter

S. G.

Kassberger

S. M.

(2012) “The Dynamics of Wealth, Profit, and Sustainable Advantage,” Strategic Management Journal 33(12): 1384–410.

41.

Jacobsen

R. T.

(1988) “The Persistence of Abnormal Returns,” Strategic Management Journal 9(5): 415–30.

42.

Jacobson

(1992) “The Austrian School of Strategy,” Academy of Management Review 17(4): 782–807.

43.

Jovanovic

(1982) “Selection and the Evolution of the Industry,” Econometrica 50(3): 649–70.

44.

Kelly

Price

T. D.

(2005) “Correcting for Regression to the Mean in Behaviour and Ecology,” American Naturalist 166: 700–7.

45.

Kessides

I. N.

(1990) “The Persistence of Profits in US Manufacturing Industries,” in Mueller

D. C.

(ed.) The Dynamics of Company Profits, pp. 59–76. Cambridge: Cambridge University Press.

46.

Kirzner

I. M.

(1997) “Entrepreneurial Discovery and the Competitive Market Process: An Austrian Approach,” Journal of Economic Literature 35: 60–85.

47.

McGahan

A. M.

Porter

M. E.

(1999) “The Persistence of Shocks to Profitability,” Review of Economics and Statistics 81(1): 143–53.

48.

McGahan

A. M.

Porter

M. E.

(2003) “The Emergence and Sustainability of Abnormal Profits,” Strategic Organization 1(1): 79–108.

49.

McGahan

A. M.

Porter

M. E.

(2005) “Comment on ‘Industry, Corporate and Business-Segment Effects and Business Performance: a Non-Parametric Approach,” Strategic Management Journal 26(9): 873–880.

50.

McNamara

Vaaler

P. M.

Devers

(2003) “Same as It Ever Was: The Search for Evidence of Increasing Hypercompetition,” Strategic Management Journal 24(3): 261–78.

51.

Makadok

Barney

J. B.

(2001) “Strategic Factor Market Intelligence: An Application of Information Economics to Strategy Formulation and Competitor Intelligence,” Management Science 47: 1621–38.

52.

Martin

(2002) Advanced Industrial Economics. Cambridge, MA: Blackwell Publishers.

53.

Morse

Nanda

Seru

(2011) “Are Incentive Contracts Rigged by Powerful CEOs?,” Journal of Finance 66(5): 1779–821.

54.

Mueller

D. C.

(1977) “The Persistence of Profits above the Norm,” Economica 44(176): 369–80.

55.

Mueller

D. C.

(1986) Profits in the Long-Run. Cambridge: Cambridge University Press.

56.

Mueller

D. C.

(ed.) (1990) The Dynamics of Company Profits: An International Comparison. Cambridge: Cambridge University Press.

57.

Nelson

R. R.

Winter

S. G.

(1974) “Neoclassical vs. Evolutionary Theories of Economic Change: Critique and Prospectus,” Economic Journal 84(226): 886–905.

58.

Nelson

R. R.

Winter

S. G.

(1982) An Evolutionary Theory of Economic Change. Cambridge, MA: Harvard University Press.

59.

Nelson

R. R.

Winter

S. G.

(2002) “Evolutionary Theorizing in Economics,” Journal of Economic Perspectives 16(2): 23–46.

60.

Pakes

Ericson

(1998) “Empirical Implications of Alternative Models of Firm Dynamics,” Journal of Economic Theory 79(1): 1–45.

61.

Ployhart

R. E.

Vandenberg

R. J.

(2010) “Longitudinal Research: The Theory, Design, and Analysis of Change,” Journal of Management 36(1): 94–120.

62.

Porter

M. E.

(1991) “Towards a Dynamic Theory of Strategy,” Strategic Management Journal 12(Special issue): 95–117.

63.

Powell

T. C.

Reinhardt

(2010) “Rank Friction: An Ordinal Approach to Persistent Profitability,” Strategic Management Journal 31(11): 1244–55.

64.

Roberts

P. W.

(1999) “Product Innovation, Product-Market Competition and Persistent Profitability in the US Pharmaceutical Industry,” Strategic Management Journal 22(7): 655–70.

65.

Roberts

P. W.

(2001) “Innovation and Firm-Level Persistent Profitability: A Schumpeterian Framework,” Managerial and Decision Economics 22(4–5): 239–50.

66.

Roberts

P. W.

Dowling

G. R.

(2002) “Corporate Reputation and Sustained Superior Financial Performance,” Strategic Management Journal 23(12): 1077–93.

67.

Rond

Thietart

(2007) “Choice, Chance, and Inevitability in Strategy,” Strategic Management Journal 28(5): 535–51.

68.

Rumelt

R. P.

(1991) “How Much Does Industry Matter?,” Strategic Management Journal 12(3): 167–85.

69.

Rumelt

R. P.

Schendel

Teece

D. J.

(1991) “Strategic Management and Economics,” Strategic Management Journal 12: 5–29.

70.

Schmalensee

(1985) “Do Markets Differ Much?,” American Economic Review 75(3): 341–51.

71.

Secrist

(1933) The Triumph of Mediocrity in Business. Bureau of Business Research, Northwestern University. Chicago, IL.

72.

Silvia

Iqbal

(2011) “Profits: Mean Diverting with High Volatility,” International Journal of Economics and Finance 3(2): 200–11.

73.

Sirmon

D. J.

Hitt

M. A.

Ireland

(2007) “Managing Firm Resources in Dynamic Environments to Create Value: Looking Inside the Black Box,” Academy of Management Review 32(1): 273–92.

74.

Skrondal

Rabe-Hesketh

(2004) Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Boca Raton, FL: CRC Press.

75.

Slater

S. F.

Olson

E. M.

Hult

T. M.

(2006) “The Moderating Influence of Strategic Orientation on the Strategy Formation Capability-Performance Relationship,” Strategic Management Journal 27(12): 1221–31.

76.

Snijders

Bosker

(1999) Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modelling. London: Sage.

77.

Teece

D. J.

Pisano

Shuen

(1997) “Dynamic Capabilities and Strategic Management,” Strategic Management Journal 18: 509–33.

78.

Vaaler

P. M.

McNamara

(2010) “Are Technologically-Intensive Industries More Dynamically Competitive? No and Yes,” Organization Science 21(1): 271–89.

79.

Villalonga

(2004) “Intangible Resources, Tobin’s Q, and Sustainability of Performance Differences,” Journal of Economic Behavior & Organization 54(2): 205–31.

80.

Wiggins

R. R.

Ruefli

T. H.

(2002) “Competitive Advantage: Temporal Dynamics and the Incidence and Persistence of Superior Economic Performance,” Organization Science 13(1): 82–105.

81.

Wiggins

R. R.

Ruefli

T. H.

(2003) “Industry, Corporate, and Segment Effects and Business Performance: A Non-Parametric Approach,” Strategic Management Journal 24(9): 861–79.

82.

Wiggins

R. R.

Ruefli

T. H.

(2005) “Schumpeter’s Ghost: Is Hypercompetition Making the Best of Times Shorter?,” Strategic Management Journal 26(10): 887–911.

83.

Young

Smith

K. G.

Grimm

C. M.

(1996) “‘Austrian’ and Industrial Organization Perspectives on Firm-Level Competitive Advantage and Performance,” Organization Science 7: 243–54.

84.

Yurtoglu

B. B.

(2004) “Persistence of Firm-Level Profitability in Turkey,” Applied Economics 36(6): 615–25.

85.

Zott

(2003) “Dynamic Capabilities and the Emergence of Intraindustry Differential Firm Performance: Insights from a Simulation Study,” Strategic Management Journal 24(2): 97–125.