As discussed above, a central component of our analysis is the presence of exogenous variables that are observed by the firm but not the econometrician. These variables are the source of variation in firm practices that cannot be explained by observables but affect the marginal returns or costs of adoption.2 Building on recent advances in the econometrics literature,3 this paper establishes conditions under which the parameters of the production function and the joint distribution of unobservables are identified.4 In the most general model, each combination of practices, or “system,” (for example, the joint use of training programs, job security, and incentive pay) is subject to a random shock.
We call this a Random Systems Model (RSM). The RSM model is a specific application of the general “switching regressions” model (Heckman and MaCurdy, 1986) of an agent choosing between several discrete choices; in our context, the discrete choices are systems of organizational design practices. In such a model, only the distribution of interactions among practices is identified; practices may be complements for some firms, and substitutes for others. Further, without additional assumptions, it is impossible to test whether the adoption of practices is consistent with static optimization on the part of the firm.
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We then identify a testable restriction on the Random Systems Model, which we call the Random Practice Model (RPM), which allows for sharper empirical tests and policy predictions.
The RPM essentially assumes that there is no unobserved variation in the interactions between practices. This is analogous to assuming a constant elasticity of substitution between inputs. Thus, the RPM incorporates an unobserved return to each individual practice, but that unobserved return does not depend on the adoption of other practices.
We use this formal structure in several ways. We first focus on the conditions under which a set of empirical procedures used in the existing literature provides a consistent test for complementarity between a given pair of practices. To do so, we distinguish between the two conditions: (TC) the practices are complements in the organizational design production function, and (TI) the practices are technologically independent. Previous empirical studies have attempted to distinguish between (TC) and (TI) in two main ways: first, by testing whether the practices are positively correlated, conditional on observables; and second, by using OLS or instrumental variables approaches to estimate the parameters of a productivity equation and test whether the interaction effects are positive.