Industries’ Potential for Interdependency and Profitability: A Panel of 135 Industries, 1988–1996

Introduction

The interdependency among activities that comprise an industry’s production function has been advanced as an explanation for differences in profitability between firms and across industries.¹ As a source of interindustry heterogeneity, interdependencies are high when the value of conducting one or more activities in a particular manner depends on how other activities are conducted (Lenox et al. 2006). Activities may interfere or complement one another in complex ways that are only partially known (Cyert and March 1963, Levinthal 1997, Rivkin 2000, Simon 1957). For instance, the technologies used to perform activities along the value chain may be interdependent.² Interdependencies make it difficult to discover superior combinations of activities, even for managers who are not naïve, biased, or opportunistic (Rivkin 2000). While firms in the same industry may differ in their search for activity sets, industries vary in their potential for interdependency.³

Firm and industry average profitability are predicted to peak at moderate levels of such potential in industries where interdependencies are high enough that not all firms are efficient, but not so high that all firms are inefficient. The inverted-U-shaped relationship between profitability and interdependency is widely referenced and important for strategic management. The relationship is consistent with predictions made in Lenox et al. (2006), Lieberman (1987), Rivkin (2001) and Schoemaker (1990).

To date, there is only one empirical test of the concave relationship between profitability and industries’ potential for interdependency. Lenox et al. (2010, hereafter referred to as LRL) studied a panel of 109 industries and 3,452 firms from 1988 to 1996. They found that the effect of interdependency on firm profitability followed a concave relationship. However, they could not prove that the effect of interdependency on industry average profitability was concave at the standard statistical level of evidence. The lack of support for industry average profitability motivates us to solve the puzzle for such an important relationship in the field of strategy connecting industry characteristics and profitability.

We address this puzzle by replicating and extending the LRL study in two ways. First, we use a better measure to infer industries’ potential for interdependency. The measure used in LRL is created from survey responses; hence, it has two shortcomings: (1) range restriction and (2) time-invariance. Out of 218 total industries in the U.S. manufacturing sector, the LRL measure covers only 109.⁴ The LRL measure does not cover industries where no managerial perceptions of the complexity of their products and processes were available from the survey. And, since the survey was conducted only one time in 1994, the LRL measure is time-invariant (LRL: 125). In contrast, our measure addresses the two shortcomings of the survey-based one. Created from patent data, our measure has less range restriction because it covers all the industries in which technological patents are granted by the U.S. Patent and Trade Office (USPTO). It varies with time because patents continue to be granted. In addition, it encourages future replications and extensions because patent data are accessible to the general public.

More importantly, our time-varying measure enables us to analyze the panel data with fixed-effects estimations, while the LRL time-invariant measure allows only random-effects. If there are omitted variables, and these variables are correlated with the variables in the model, then fixed-effects estimations could provide a means for addressing omitted variable biases. So, in addition to replicating the random-effects estimations, we correct the biases that result from omitted industry effects and firm effects, by using fixed-effects estimations. Improving the model specification with our time-varying measure of interdependency is the second way in which our replication and extension address the puzzle.

Our study demonstrates empirical evidence that strongly supports the predicted concavity in the effect of industries’ potential for interdependency on industry average profitability. We also confirm the other concave relationship that is between industries’ potential for interdependency and firm profitability. Moreover, we show that both concave relationships remain robust after correcting omitted variable biases with improved model specification. Our results are also robust to using an alternate measure of industry average profitability, which allows us to examine LRL’s central notion in explaining industry average profitability about “a few large competitors who create and capture substantial value” (Lenox et al. 2006, p. 123). In summary, by using better measures and improved model specifications, we find strong support for an important relationship that is central to strategic management research.

Finally, we make conceptual contributions by explaining how profitability varies with temporal changes in the potential for interdependency within an industry. The potential for interdependency is an industry attribute exogenous to the actions of firms (Lenox et al. 2006, 2010). This underlying feature of an industry is largely determined by the fundamental human and physical factors at the time of industry birth, encapsulating a number of knowledge components with varying degrees of interdependency between the components. As scientific discovery achieves breakthroughs and the juxtaposition of disparate fields of thought or technology create new components and trigger new linkages between components, an industry’s potential for interdependency may possibly change over time. We illustrate how two mechanisms, namely, recombination and refinement, drive temporal changes in an industry’s potential for interdependency with a case of replacing aluminum with copper in semiconductor fabrication.

Focusing on the temporal change within an industry over time, we submit and find that the effect of an industry’s potential for interdependency on profitability follows a concave relationship. At a low level of interdependency, novel combinations can be found more easily, but competitors can also easily imitate, so no firm has any significant advantage. At a high level of interdependency, continuous efforts on refinement make the interdependency among existing components so severe that the search for a better solution becomes extremely difficult. Therefore, no firm has a significant advantage, either. Profitability peaks at a moderate level of interdependency because a balance between refinement and recombination provides the highest potential of finding solutions to the production decision problem.

Interdependency and Profitability

The inverted-U-shaped relationship between profitability and interdependency was studied by Lenox et al. (2006) with a formal model and computer simulations. As explained in LRL, the concave relationship occurs “because profits are highest when the production decision problem is difficult enough to generate heterogeneity among firms, but not so great as to dramatically reduce the average efficacy (efficiency or quality) of firms” (p. 123). At low levels of interdependency, “most competitions will be able to determine the most efficient way of operating. High efficiency creates value that could be captured, but competition among similar competitors eradicates profits. In other words, low variance in performance means that high average performance is not translated into high profits” (Lenox et al. 2010, p. 123). At high levels of interdependency, however, “it is rare for any firm to determine the most efficient ways of operating. Even though there is high variance in performance at high levels of interdependency […], poor average performance reduces the value available to be captured as profits.” Moderate levels of complexity, in comparison, “allow only a few firms to discover the most efficacious activity sets, leading to a few large competitors who create and capture substantial value” (ibid, 123). This is the logic behind the concave relationship between profitability and interdependency.

Industry Profitability

Despite the prediction, LRL’s empirical test does not show industry average profitability peaking at moderate levels of interdependency (Models 2 and 3, Table 3, LRL: 133). Model 2 shows that the effect of interdependency on industry average profitability is linear (the estimated coefficient is 0.421, p-value < 0.05). Model 3 shows that the estimated effect cannot be distinguished from a linear relationship at the normal standards of statistical proof (the estimated coefficient for the quadratic term is −0.633, p-value > 0.10). Therefore, LRL could not show that a concave relationship existed at the industry level. As such, the first hypothesis we examine is the predicted concave relationship between interdependency and industry average profitability.

Hypothesis 1

Industry average profitability rises then falls with rising potential for interdependency in activities.

Firm Profitability

In contrast, LRL’s empirical test shows that firm profitability peaks at moderate levels of interdependency (Models 4–6, Table 3, LRL: 133; Figure 1, ibid: 134). This supports a concave relationship between interdependency and firm profitability, as hypothesized in LRL (p. 123) about how mean firm profitability would differ among industries with different latent potential for interdependency among activities. The relationship is concave because moderate levels of interdependency allow only a few firms to discover the most efficacious activity sets. The production decision problem is difficult enough to generate heterogeneity among firms. By contrast, the problem is too easy at low levels of interdependency. Most firms can find the most efficacious activity sets. However, competition among firms with equally efficacious activity sets eradicates profits. On the contrary, the problem is too difficult at high levels of interdependency. Most firms cannot find the most efficacious activity sets. When all firms perform poorly, little value is created to be captured as profits.

Hypothesis 2

Mean firm profitability rises then falls with rising potential for interdependency in activities.

Methods and Measures

Omitted Variable Bias

In addition to replicating LRL, we extend their empirical test by considering the possibility of omitted variable bias. Their model of estimation is based on the random-effects specification. Omitted variables may produce biased estimates of the coefficients, although LRL finds the relationship between interdependency and firm profitability to follow an inverted-U shape. If there are omitted variables, and these variables are correlated with the observed explanatory variables, then the fixed-effects transformation can be applied to eliminate the unobserved firm-specific time-invariant effect, as explained in Wooldridge (2010, pp. 285–304, 328–334).

An example of omitted firm effect is a firm’s tendency to rely on heuristics, i.e., simplified and approximate rules of thumb (cf. Schoemaker 1990) that are a part of the firm’s decision-making routines. A firm’s tendency to rely on heuristics is likely to be correlated with an industry’s potential for interdependency. The use of heuristic solutions may be more prevalent in solving complex problems. Complex problems require managers to consider a wider range of alternative combinations of activities and examine how extensively the decisions about product configuration and process recipe are interconnected. In estimating firm profitability, the random-effects framework assumes zero correlation between the observed explanatory variables and the unobserved firm effect. Yet, a firm’s tendency to rely on heuristics could be a source of bias if it is omitted.

Similarly, in estimating industry average profitability, the random-effects framework assumes zero correlation between the observed explanatory variables and the unobserved industry effect. Yet, industry-specific time-invariant variables could be a source of bias, if they are omitted and correlated with the observed explanatory variables. An example of omitted industry effect is the geographical agglomeration of innovation and production activities by industry. The prevalence of Silicon Valley-style localizations of individual manufacturing industries in the United States as reported by Ellison and Glaeser (1997, 1999) raises a concern for omitted industry effect. As an example, the U.S. semiconductor industry has innovation and production activities localized in the Silicon Valley. The activities have high interdependency, i.e., parts of the product design and production process have rich interactions and technological components are linked together in a product’s architecture.⁵ In a given architecture, it is likely that activities with high interdependency tend to be geographically co-located, because co-location facilitates coordination and exchange of information. As such, an industry’s geographical localization is likely to be correlated with an industry’s potential for interdependency. If an industry’s geographical location is not specified in the random-effects model, the omitted variable may produce some bias in the estimates.

Measuring Interdependency

Measurement challenges have limited large-scale empirical tests. As noted in LRL, “[o]ne of the primary obstacles to large-scale empirical work has been the difficulty in measuring interdependency systematically across a wide number of industries…Measures of interdependency […] must reflect two basic premises that drive the theoretical results in the literature: interdependencies are industry-level characteristics; and (relevant) interdependencies are non-obvious to industry participants so that they present a barrier to optimization and imitation” (pp. 122, 124).

The measure used in LRL meets both premises by using responses to survey questions that elicit research & development (R&D) managers’ perceptions of the complexity of their products and processes.⁶ The survey-based measure is intended to assess the latent possibility of interdependencies at the product and process levels, among activities in the industry’s production function. At the product level, the survey item asked respondents to determine and report the percentage of their product innovations for which the “competitive advantage from those innovations” (Cohen et al. 2000, p. 5) had been protected by product complexity. At the process level, the same question and survey item was then repeated with respect to process innovations for which the competitive advantage from those innovations had been protected by process complexity (LRL: 125). The LRL measure was created from the product complexity and process complexity items, by averaging across all respondents in the same four-digit standard industrial classification (SIC) code.

A Better Measure of Interdependency Can Be Created with Patent Data

Following LRL, we create a measure that uses information associated with industrial R&D. Our measure also meets the two premises that pose stringent requirements on empirical work: interdependencies are industry-level characteristics; and (relevant) interdependencies are nonobvious to industry participants to present a barrier to optimization and imitation. Our measure is created from more than 1.93 million patents that have been approved by the USPTO since 1901, the earliest application year in the patents we use. Patterns of interdependency extracted from these many patents should be nonobvious to industry participants. These patents are accumulated over a long period of time, so the patterns we extract should be exogenous to the contemporaneous actions of firms. The patterns are aggregated at the industry level to represent industry-level characteristics, as we use a concordance that maps patent classifications to industry classifications.

The first step for constructing our measure of interdependency is to start with the level of interdependency in a technological patent. A measure of interdependency among the components of a technological patent has been developed and used by Fleming, Sorenson, and Rivkin (Fleming and Sorenson 2001, 2004; Sorenson et al. 2006; as a shorthand we refer to it as the FSR measure). The FSR measure of interdependency captures the historical difficulty of mixing and matching the components that constitute a technology. It draws from the intuition that “a technology whose components have, in the past, been mixed and matched readily with a wide variety of other components has exhibited few sensitive interdependencies” (Sorenson et al. 2006, p. 1002). As submitted by FSR, mixing and matching components that have sensitive interdependencies is more difficult than components that are relatively independent. “Suppose a patent embodies subclasses that have been combined with a variety of subclasses, even in a handful of previous patents. This indicates that the patent’s components do not have delicate interdependencies that prevent widespread recombination and the components can be mixed and matched independently…Suppose instead that a patent embodies subclasses that have been combined, again and again, with the same small set of other subclasses. We presume those subclasses to be highly interdependent; their repeated joint appearance in patents suggests that the presence of one requires the appearance of the others” (ibid, pp. 1002–1003).

Specifically, the FSR measure of interdependency for a patent is calculated in two stages (pp. 1002). The first stage measures the ease of recombination of subclass i. The measurement starts with identifying every use of the subclass i in a large sample of patents. The ease of recombination E_i, as shown in Equation (1), is the number of different subclasses that have been combined with subclass i, normalized by the number of patents in which subclass i has been used. That is, controlling for the total number of applications in which a particular knowledge component has been used, the ease of recombination increases as the focal component combines with a wider variety of components. The second stage measures the interdependence—the inverse of the ease of recombination—in patent j, as shown in Equation (2). To calculate the interdependence for an entire patent, FSR averaged the inverted ease of recombination scores for the subclasses in patent j.

Using the subclasses identified in a patent as proxies for technological components, the FSR measure not only has face validity, but also external validity. The external validity was reported in Fleming and Sorenson (2004) and Sorenson et al. (2006). A sample of patent holders were asked about their perceptions of how much change is required to make to the other module(s), when a change is made to one module in their invention. The patent holders’ responses were significantly correlated (the Pearson correlation coefficient is 0.30, p-value∼0.03) with the level of interdependence computed according to the FSR measure. The significant correlation suggests that the FSR measure is validated externally by patent holder perceptions.

An Industry-Level Interdependency

The second step for constructing our measure is to create an industry-level interdependency by taking the average of the FSR measure among the patents classified under the same four-digit SIC. We use Silverman’s concordance for the mapping between patent classifications and industry classifications.⁷ We assume that industries with technologies that exhibit higher interdependencies are likely to have higher potentials for interdependencies among the activities that are associated with making an industry’s output. While product configuration, process recipe, and organizational form may vary between firms, the industry-level interdependency captures a latent potential in the industry’s production function. The assumption about an industry’s potential for interdependency among activities is central to Lenox et al.’s conceptualization of the competitive environment (2006, 2010). The latent potential is “an industry attribute exogenous to the actions of [individual] firms” (LRL: 122). Building on Lenox et al.’s conceptualization, we submit that the FSR measure aggregated at the industry level can capture the potential interdependency in the technologies that are important to an industry’s production function. As a validation, the FSR patent-based measure that we aggregate at the industry level is correlated with the LRL survey-based measure of interdependency. As we will report in further detail, the Pearson correlation between the two is 0.26 (p-value = 0.04), across the 62 industries for which the LRL measure was reported (LRL: 129, Table 1, Column 4).

Table 1: Interdependency Measure for 109 Industries—A Comparison Between the LRL and Our Measure

Changes in Interdependency Potential Within an Industry Over Time

We submit that the changes in interdependency potential within an industry over time are driven by the relative accumulation rates between refinement—innovative efforts that focus on refining existing knowledge components—and recombination—innovative efforts that are dedicated to recombining existing knowledge components with new components. Refinement refers to the efforts that seek to better understand an existing knowledge component or combination of knowledge components. Successive patents that refine such understanding improve the solutions created with the existing components. As a result, the interdependency among the existing components deepens, reinforcing their linkages. Therefore, an industry’s potential for interdependency increases when refinement efforts accumulate.

However, increasing refinement makes recombination more difficult. Recombination refers to efforts that are dedicated to generating novel combinations by mixing and matching existing knowledge component(s) with other components. Through efforts dedicated to recombination, new linkages and new components including those that are recently invented or discovered are added to an existing component and combination. Severe interdependency among the existing components makes it difficult to add new linkages and components. Yet, as efforts dedicated to recombination accumulate, successive patents reveal novel solutions created with new linkages and new components. These patents show what constitutes the right combinations, thereby informing subsequent searches where potential solutions may locate in a high-dimensional combinatorial space.⁸ Successive patents that recombine existing components with new ones reduce an industry’s potential for interdependency. The potential is reduced because the new components used in creating novel solutions exhibit few sensitive interdependencies with the existing components. These new components function as modules that can be mixed and matched independently and used freely in creating novel combinations.

The mechanisms of recombination and refinement correspond to how the ease of recombination is measured, as shown in Equation (1). The numerator in Equation (1) is the number of components with which a focal component has jointly appeared, whereas the denominator is the cumulative amount of effort involving the focal component. Refinement efforts contribute to an increase in the denominator without changing the numerator. When the efforts focusing on refinement accumulate at a rate faster than the efforts dedicated to recombination, the ease of recombining the focal component with a wide variety of components decreases. Therefore, the interdependency of an industry changes with the relative accumulation rates of refinement and recombination. When more efforts focus on refinement (recombination), the interdependency increases (decreases) over time.

Profitability Measures

Following LRL, we measure profitability with Tobin’s q that controls for differences in the scale of investments needed across industries. Tobin’s q also has the advantage of reflecting market expectations of the discounted stream of future cash flows accruing to a firm and its industry. To calculate Tobin’s q, we assume that the market value (M) of firm (i) in time period (t) is a function of the scale of its tangible (Vp) and intangible (δVi) assets and of additional factors (α, X_it), such as an industry’s potential in interdependency among activities, that magnify or reduce the return that firms can generate with assets invested in the industries:

Next, we transform Equation (3) in the same way as LRL, by following Griliches (1981) to derive a profitability measure at the firm level:

where ɛ_it is a disturbance term, and Q_it is the ratio of the market valuation of the firm to the value of tangible assets (Q_it = M_it/Vp_it), commonly referred to as Tobin’s q. Also following LRL, Q_it is calculated as the sum of firm market value (share price multiplied by outstanding shares) and the book value of long-term debt, preferred stock, and net current liabilities all divided by the total asset value of the firm for each firm in each year of the sample.

Then we apply the same transformation and approximation as LRL for deriving an equation for the average Tobin’s q at the industry level, such that

where ${\overline{M}}_{it}$, ${\overline{Vp}}_{it}$, and ${\overline{Vi}}_{it}$ are the mean of firm values within an industry. To be consistent with LRL, we refer to the firm-level profitability ln(Q_it) as LogQ, and for the industry-level profitability, we use MeanQ as defined in LRL as $\text{log}{\overline{Q}}_{it}$, which is the natural log of the average Q_it within each four-digit SIC code industry. In addition, we propose an alternate measure of industry-level profitability based on an approach adopted in finance, which divides the sum of the market values of all firms in industry j by the sum of the firms’ replacement costs of their tangible assets (Durnev et al. 2004, pp. 73, 83).⁹

Control Variables

We control for the same variables and use the same procedures as those in the LRL: firm-level R&D and advertising intensities, industry-level R&D and advertising intensities, and industry growth (change in industry sales over the prior year sales). Following LRL, we also control for potential sources of unobserved heterogeneity by including year-effect dummy variables, and dummy variables for the two-digit industry classification.

Data

To replicate the sample used in the LRL study, we used the same data sources other than the CMS. We extracted firm-level data from Standard & Poor’s Compustat North America industrial annual data set for the period from 1988 to 1996. For industry growth, the data source is the U.S. Census of Manufactures input-output tables at the four-digit SIC level. For our measure of interdependency, the data source is the U.S. patent database from the National Bureau of Economic Research.

Analyses and Results

To ensure that our test is not driven by an artifact of patent accumulation, we start with a set of analyses using a time-invariant level of interdependency that is set in 1988. Then, we conduct a separate set of analyses with a time-varying measure of interdependency that is updated annually as the patents accumulate over time. Replicating LRL, we use random-effects specification. Extending LRL, in our model specification we take advantage of the within-industry variation over time by using fixed-effects estimations to address omitted variable biases.

Table 1 shows a comparison between the LRL measure of interdependency and ours for each of the 109 industries in the LRL sample. While the managerial perception was surveyed in 1994, the average of our measure covers years 1988–1996. The mean of the nine-year average is 54 (minimum = 34, maximum = 89) among the 109 industries. Table 1 also reports the standard deviation of our measure across the years 1988-1996 and the level in year 1988, which is the first year for which profitability is measured in LRL.¹⁰

Table 2 presents the 26 additional industries covered in our sample, but not LRL’s. These industries are in the U.S. manufacturing sector, but are excluded from the LRL sample. We have computed an interdependency measure for these industries with the patent data, increasing the industry sample from 109 to 135. Among the 135 industries, the mean of the nine-year average is 54 (minimum = 33, maximum = 106). Compared to the 109 industries in Table 1, the difference in the maximum (89 versus 106) suggests that the subsample of 109 is more restricted in range than the full sample of 135 industries.

Table 2: Interdependency Measure for an Additional 26 Industries

After comparing the measure of interdependency, we compare the descriptive statistics of the dependent and control variables between the LRL study and ours. Table 3 shows the sample size and descriptive statistics of the two studies. As shown in Table 3(a), our full sample covers 135 industries, including a total of 1,193 industry-year observations, 3,841 firms, and 17,955 firm-year observations in these industries. A subsample of 109 industries exactly matches with the ones examined in LRL. Although the match in industry is exact, we arrived at a total of 962 industry-year observations, 3,551 firms, and 16,579 firm-year observations, after following the methods documented in LRL (pp. 127–128) for computing the variables, interpolating missing values, and removing outliers.¹¹

Table 3: Comparison Between Our Sample and the LRL Sample

While the match is not exact, many variables show comparable descriptive statistics (see Table 3(b)). Advertising intensity has exactly the same distribution. Industry growth has the same mean. The standard deviation, the minimum, and the maximum between the two have a difference smaller than 50%. However, the maximum value of R&D intensity is very different between the two. The maximum value in our subsample is 3.84, whereas that in the LRL sample is 13.21. The minimum values of the two dependent variables, ${\overline{Q}}_{it}$ and LogQ, are also very different. The minimum values in our sample are 0.05 and −7.96, respectively, while LRL’s are 0.64 and −4.82. We made further comparisons by computing the second and third moments of firm profitability distribution. We found comparable distributions in higher moments. Both the variance in firm profitability within industries (VarQ) and the skew of firm profitability within industries (SkewQ) are comparable between the two samples, as shown in Table 3(b) (columns 5 and 6). Table 4 reports the descriptive statistics and pairwise correlations in our full sample, covering both industry and firm panel. Both panels are unbalanced.

Table 4: Descriptive Statistics and Pairwise Correlations—Our Full Sample

The Effect of Interdependency on MeanQ

Table 5 presents a comparison between the LRL regression results and ours in regard to the effect of interdependency on MeanQ. Models 5-1 through 5-3 are Models 1–3 reported in LRL’s Table 3 (pp. 133). Models 5-4 through 5-6 show our estimation with a time-invariant measure of interdependency set at its level in 1988. Models 5-7 through 5-9 extend the restricted sample of 109 industries to the full sample of 135 industries. In Tables 3–5, the numbers in bold are the key results.

Table 5: Regression Results: Interdependency and Industry Average Profitability—Using Time-Invariant Interdependency

As reported by LRL, the effect of interdependency on MeanQ is not concave (as shown in Models 5-2 and 5-3). In contrast, the effect of interdependency we find is concave (as shown in Model 5-9), supporting Hypothesis 1. However, the concavity is not supported with a sample that has range restriction (as shown in Model 5-6). A comparison between the restricted sample and the full sample is presented graphically in Figure 1, which shows the marginal effect of interdependency on MeanQ. While both samples display inverted-U-shaped relationships as predicted, only the full sample satisfies the normal standards of statistical proof.¹²

The effect of interdependency is substantial in size. We estimate that the difference between a minimal and moderate level of interdependency corresponds to a rise of 0.22 in ${\overline{Q}}_{it}$, from 0.84 to 1.06. And the difference between a moderate and maximal level of interdependency corresponds to a fall of 0.96 in ${\overline{Q}}_{it}$, from 1.06 to 0.10. These magnitudes in the rise and fall in ${\overline{Q}}_{it}$ are 29% and 128% of the full sample’s standard deviation, which is 0.75.

Using Model 5-9, we compare the relative importance of interdependency with R&D intensity, advertising intensity, and industry growth. We find that a one-standard-deviation increase in interdependency from the minimum corresponds to an increase of 0.19 in ${\overline{Q}}_{it}$ (a change of 23% higher than the ${\overline{Q}}_{it}$ estimated with sample mean values, rising from 0.84 to 1.03). The respective increase in ${\overline{Q}}_{it}$ associated with a one-standard-deviation increase in R&D intensity, advertising intensity, and industry growth is 0.06, 0.08, and 0.04, respectively. Therefore, interdependency represents an important characteristic of the industry environment that affects profitability, more than R&D intensity, advertising intensity, and industry growth.

The Effect of Interdependency on Q_jt

Table 6 shows the effects of interdependency on our alternate measure of industry average profitability, ln(Qjt). Models 6-1 through 6-6 are random-effects estimations with time invariant interdependency. Interdependency is found to have a concave relationship with ln(Qjt), but only for the full sample (Model 6-6). The relationship remains concave, as shown in Models 6-7 through 6-9, when interdependency changes over time. These findings suggest that, when industry sample has less range restriction, the concave relationship is confirmed with both measures of industry average profitability.

Table 6: Regression Results: Interdependency and Industry Average Profitability

Patent Effectiveness

Industries vary in the effectiveness of patents as a means of capturing and protecting the competitive advantages of new or improved processes and products. Patents are effective in only a few industries, as reported by Levin et al. (1987) with their survey data collected in 1983 from 650 R&D executives on the nature of appropriability in 130 industries defined at the Federal Trade Commission Line of Business level. The difference between industries on patent effectiveness persists over time, as reported by Cohen et al. (2000) with their survey data collected from 1,478 R&D labs in the U.S. manufacturing sector in 1994 covering 34 industries at the two- or three-digit ISIC level.¹³

We examine whether the effect of interdependency, which is informed with patent data, could be amplified in industries where patents are effective. We use the threshold established by Cohen et al. (2002, p. 9) to distinguish industries with greater patent effectiveness.¹⁴ Industries with effectiveness greater than 41% as shown in their Table 1 (ibid: 32) are coded as 1; 0 otherwise. The binary indicator of patent effectiveness is added to the model as a control variable. We find that patent effectiveness has a positive effect on industry profitability, consistent with previous research and LRL. Profitability is higher in industries in which patents can effectively protect the profits that are directly associated with the commercialization or sale (i.e., licensing) of patented inventions.

Table 7: Regression Results: Patent Effectiveness Added as a Control Variable and as a Moderating Variable

The concave relationship remains significant, after controlling for patent effectiveness (Models 7-3 and 7-8).¹⁵ Further, we test whether the concave relationship might be moderated by patent effectiveness, by adding interaction terms between interdependency and patent effectiveness. As shown in Models 7-4, 7-5, 7-9, and 7-10, the interactions between interdependency and patent effectiveness are not statistically significant. That is, patent effectiveness does not moderate the effect of interdependency on industry average profitability. The concave relationships we find, therefore, do not vary with patent effectiveness.

Within-Industry Variation Over Time

Further, we examine potential biases that may result from omitted industry effects. Models 8-1 through 8-3 use the fixed-effects specification. The Sargan-Hansen test (Sargan 1958, Hansen 1982), which accommodates robust standard errors regression in comparing model specifications, suggests that the fixed-effects estimator should be used, as does the Hausman test (Hausman 1978).¹⁶

A comparison between random- and fixed-effects estimations is presented graphically in Figure 2, which shows the marginal effect of interdependency on ln(Q_jt). Based on the fixed-effects estimation (black line with no markers), the marginal effect peaks at 0.75, corresponding to a moderate level of interdependency (78, which is equivalent to 0.58 as shown on the scale in Figure 2).¹⁷ The difference between the fixed-effects and the random-effects estimation (x markers) suggests that omitted industry-specific time-invariant variables shift the curve downward (21% off the peak marginal effects, reduced from 0.75 to 0.60).

Table 8: Regression Results: Fixed-Effects Estimations

The Effect of Interdependency on FirmQ

Table 9 presents a comparison between the LRL regression results and ours in regard to the effect of interdependency on firm profitability. Models 9-2 through 9-3 are Models 4–5 reported in LRL’s Table 3 (pp. 133).¹⁸ As shown in Models 9-2 and 9-3, LRL found the effect of interdependency on firm profitability to be concave. In comparison, Models 9-4 through 9-6 show our estimation with a time-invariant measure of interdependency set at its level in 1988. Following LRL, we estimate with the restricted sample using the random-effects specification and no industry dummies. Like LRL, we found the effect of interdependency on firm profitability to be concave. The concave relationship is also found with the full sample, as shown in Models 9-7 through 9-9.

Table 9: Regression Results: Interdependency and Firm Profitability—Using Time-Invariant Interdependency

Next, Table 10 shows estimates of models using a time-varying measure of interdependency. Models 10-1 through 10-3 use the restricted sample, while Models 10-4 through 10-6 use the full sample. These models suggest that the effect of interdependency on firm profitability also follows a concave relationship. Next, we examine potential biases that may result from omitted firm effects. Models 10-7 through 10-9 use the fixed-effects specification, and they also suggest a concave relationship, after correcting the omitted variable bias that results from firm effects. The Sargan-Hansen test (Sargan 1958, Hansen 1982) suggests that the fixed-effects estimator should be used, as does the Hausman test (Hausman 1978). Furthermore, we add industry fixed effects to Models 10-7 through 10-9 by using the technique of multilevel modeling that includes both firm and industry fixed effects in the same model. The results as reported in Supplemental Test A suggest a concave relationship.

Table 10: Regression Results: Interdependency and Firm Profitability—Using Time-Varying Interdependency

The concave relationships are presented graphically in Figure 3, which shows the marginal effect of interdependency on LogQ. With the firm fixed-effects estimation (black line with no markers), the marginal effect peaks at 0.29, corresponding to a moderate level of interdependency (66, which is equivalent to 0.44 as shown on the scale in Figure 3).¹⁹ The difference between the fixed-effects estimation and the random-effects estimation (x markers) suggests that omitted firm-specific time-invariant variables shift the curve upward (270% above the peak marginal effects, raised from 0.29 to 1.07).

As for the economic importance of interdependency, we estimate that the difference between a minimal and moderate level of interdependency corresponds to a rise of 0.24 in Q_it, increasing from 0.72 to 0.96. And the difference between a moderate and maximal level of interdependency corresponds to a drop of 0.39 in Q_it, decreasing from 0.96 to 0.57. These magnitudes in the rise and fall in firm profitability correspond respectively to 12% and 19% of the standard deviation in the full sample, which is 2.01. Compared to our finding on industry profitability, interdependency explains a narrower range for Q_it than for ${\overline{Q}}_{it}$.

The concavity we find implies that higher moments of firm profitability distribution would also be the highest at a moderate level of interdependency. As reported in Supplemental Test B, we show evidence in support of a concave relationship between industries’ potential for interdependency and the second moment of firm profitability distribution as well as a concave relationship between industries’ potential for interdependency and the third moment of firm profitability distribution.

Industries with Incremental vs. Significant Changes in Interdependency Over Time

Based on the levels of interdependency that correspond to peak profitability (78 and 66 for industry and firm profitability, respectively), we examine the changes in interdependency year by year from 1988 through 1996. Figure 4 presents the annual levels of interdependency for four industries, and compares them to moderate interdependency as benchmarks. The line on the very top of the figure shows a consistently high interdependency, way above the benchmark corresponding to peak industry profitability. By contrast, the line at the bottom of the figure shows consistently low interdependency, way below the benchmark corresponding to peak firm profitability. These two relatively flat lines suggest that the effort at refinement was too much (for the top line) or too little (for the bottom line) compared to the effort at recombination. The two lines in the middle have changing levels in interdependency that cover a broad range, including moderate levels of interdependency. These two lines with steep slopes suggest that the effort at refinement was increasing at a rate faster than the effort at recombination, but not exceedingly so.

Below Figure 4, we present two histograms comparing the number of industries by the amount of temporal change. Seventy-nine industries (59% of 135 industries) have a medium amount of change, where the difference between the maximal and minimal interdependency is between 21 and 26, and the standard deviation is between 6.99 and 8.88. In comparison, 48 industries (36%) have a smaller amount of change, whereas seven industries (5%) have a larger amount of change.

Robustness Checks

As robustness checks, we examine how sensitive our results are to changes in model specifications. The first set of robustness checks is to remove the singletons from the panel in fixed-effects estimations. Our results are robust to the removal of one industry singleton and 698 firm singletons. The second set of robustness checks is to use balanced panels, which allows us to compare the profitability of the same firms over the same time period. Robust with two balanced panels of 1,272 firms (1992–1996) and 1,104 firms (1991–1996), our results consistently show concave relationships between an industry’s potential for interdependency and firm profitability.

Discussions

A key finding that our analyses and results contribute is that a change in an industry’s potential for interdependency over time has significant effects on industry and firm profitability. The underlying potential for interdependency as an industry-level characteristic has been assumed to be constant. However, our study uncovers the importance of within-industry changes in such potential over time.

Changes in an Industry’s Potential for Interdependency Over Time

What is driving an industry’s potential for interdependency to change over time? We propose that the change is driven by the relative accumulation rates between efforts that focus on refining existing knowledge components and efforts that are dedicated to recombining existing knowledge components with new ones. The interdependency increases over time when more efforts focus on refinement, and decreases when more efforts are dedicated to recombination. The search for a useful combination of components is akin to finding a peak on a performance landscape (Fleming and Sorenson 2001). The search is more successful at a moderate level of interdependency, when the relative rates of accumulation suggest a balance between refinement and recombination. The landscape has a large number of tall peaks and some peaks are clustered in a mountain range, providing the highest probability of finding useful combinations.

At a low level of interdependency, the search for useful combinations is efficient. The landscape is smooth with few peaks and those that do rise are comparable in their height. The search can be achieved by altering one component at a time, replacing it with a different component or redesigning the arrangement of it relative to other components. Although the search can be achieved through incremental improvements, competitors can easily arrive at similarly performing peaks, as suggested by Rivkin’s (2000) research on complexity and imitation. Since the competitors are equally efficient in their search, no firm has any significant advantage.

At a high level of interdependency, the search for useful combinations is difficult. The landscape is rugged with many low peaks scattered apart and separated by valleys (Rivkin 2000, p. 835). With low height, there is no assurance that useful combinations can be found. Scattered peaks separated by valleys suggest that local search makes slow progress. Little information is available to predict where the peaks may locate, since their locations are not systematically correlated. Moreover, the sides of the peaks are rough. The roughness means that there is little basin of attraction to reveal monotonic and incremental paths to the peaks. Furthermore, continuous efforts on refinement using the same combination repeatedly exhaust what can be discovered from the limited combinatorial possibilities restricted to the same components. As more efforts focus on refinement, competition in the search becomes more intense, since it is confined to the increasingly exhausted combinatorial possibilities. As a result, the outcomes of the search are equally poor and no firm has any significant advantage.

Limitations

Both the LRL measure and ours use information associated with industrial R&D. While industrial R&D meets the two premises required for qualifying a measure as an industry-level characteristic, an industry’s potential for interdependency may come from sources that are not captured by patent data or perceptions of R&D managers. For instance, complementarity in a business ecosystem suggests that the potential for interdependency of a device-making industry is linked to the potential of a content-providing industry, with which the two industries jointly create value on the same platform. Although the mixing and matching of technology subclasses may reflect the link between industries in some patents, our measure is, by design, a general one so that it broadly covers industries without considering complementarity in a business ecosystem for value creation.

Our measure of interdependency is constructed with patent data, so we must ask ourselves how the data generating process would affect result interpretation and generalization.²⁰ Not all industries can use patents to codify their activities. Inventions that involve highly tacit, causally ambiguous and complex knowledge are likely to be under-represented. Consequently, our measure of interdependency is confined to industries where knowledge efforts are codified in the form of technological patents. For the knowledge that can be codified, inventors may restrict their patent applications to a subset of their discoveries, such as the most successful inventions. Less successful trial-and-error experimentations are less likely to be documented in the form of a patent. As a result, the topography of the underlying landscape are inferred from truncated data. Most importantly, inventors may choose to keep their discoveries secret.²¹ Knowledge efforts kept as secret are not reflected in patent data. Therefore, our measure of interdependency is only applicable to industries where knowledge efforts on refinement and recombination are disclosed in patents. Despite the data limitations, patents do offer a trail of innovative efforts for us to examine how frequently pieces of knowledge are used jointly in technological inventions. When aggregated over time, patents can inform the relative rates of knowledge accumulation between refinement and recombination, which are the mechanisms driving temporal changes in an industry’s potential for interdependency.

Another limitation is that we are not able to address omitted industry effects that vary with time. If some industry-specific time-varying variables are correlated with interdependency, our fixed-effects estimation is still biased. For instance, some industries have intensifying patent portfolio races, compared to other industries. Firms have felt increasingly compelled to apply for patents in the semiconductor (Hall and Ziedonis 2001) and electronics industry (Cohen et al. 2000).²² In the electronics industry, as an example, to become or remain a major competitor, firms use patents for blocking and negotiating with rivals. Patents are legal instruments for blocking rivals from imitation and forcing rivals to share their new technologies. Such use of patents ensures that firms can steadily improve and expand their product lines and processes, and appropriate a share of the oligopolistic rents accruing to the new technologies of all incumbents. Interindustry differences in how quickly patenting rates accelerate over time, however, are not time-invariant. We cannot rule out that the rates of refinement and recombination that we observe may reflect time-varying interindustry differences that are driven by patent portfolio races. Patent portfolio races generate a lot of knowledge accumulation, particularly efforts at refining the existing components in the portfolio. As such, an industry’s accelerating rate of patenting could be correlated with interdependency, resulting in an omitted variable bias in our fixed-effects estimations. Because of this limitation, our study provides only an intermediate piece of evidence about interdependency and profitability.

Conclusions

An industry’s potential for interdependency among productive activities is one of the central concepts in strategic management. It represents an important characteristic of the industry environment; we show that a change in an industry’s potential for interdependency has statistically significant and economically important effects on firm and industry profitability. While theoretical models have clarified how and why industry average profitability would peak at moderate levels of interdependency, the empirical evidence so far has not supported the inverted-U-shaped relationship.

By using a better measure of interdependency, we find empirical evidence that strongly supports the predicted relationship. We also confirm the other predicted concave relationship that is between interdependency and firm profitability. More importantly, we show that if industry-specific variables that correlate with interdependency are not addressed with fixed-effects estimations, the estimated curve would shift downward, reducing the peak marginal effect by 21%. Likewise, if firm-specific variables that correlate with interdependency are not addressed with fixed-effects estimations, the estimated curve would shift upward, raising the peak marginal effect by 270%.

An additional contribution we make is to facilitate a general implementation for quantifying an industry’s potential for interdependency. Our study is second to LRL in employing large-scale empirical analyses on interdependency, but the source of our data is in the public domain, so future studies can build on our measure of industries’ potential for interdependency.