In this endeavor, we are motivated by the policy implications that follow if practices are interrelated in adoption and productivity. For example, if a training subsidy affects the adoption of training programs, it will also have indirect effects on the adoption and productivity of complementary practices, such as a commitment to job security. Consequently, optimal subsidies need to account for both direct and indirect effects on organizational design. Similarly, complementarity between a set of practices implies that the adoption of one practice has externalities for adoption decisions about other practices; thus, to explain cross-sectional variation in one practice, it may be necessary to identify exogenous variation in the returns to complementary practices.
Interactions between elements of organizational design present several distinct empirical challenges that do not normally arise in the context of productivity analysis. First, in contrast to analyses of traditional factor inputs such as capital or labor, the econometrician does not typically observe the relevant “input prices” that each firm faces in adopting organizational practices. For this reason, the tools of duality, which are exploited throughout the productivity literature, are not applicable, and it is thus necessary to confront the difficulties associated with direct estimation of the production structure. In particular, we must allow for the possibility that the costs and benefits to employing practices might vary across firms, and yet be unobservable.
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A second challenge arises from the fact that some sets of practices are usually adopted in clusters (as theory would suggest, when practices are complements). The presence of clustering clearly implies that some combinations of practices will occur only infrequently, and so it may be difficult to precisely estimate the parameters describing the interactions between these parameters using a regression of productivity on practice combinations. We accommodate this potential difficulty by exploiting revealed preference: the fact that firms have chosen to adopt practices together is potentially informative about the joint returns to the practices. Formally, we can exploit a cross-equation restriction between the equations that describe practice adoption and the production function.
Our formal analysis begins by introducing a model of an “organizational design production function,” with parameters that specify the interactions between choices, as well as exogenous variables that determine the costs and benefits of each practice. The firm chooses a set of “organizational design practices” taking into account the relevant costs and benefits of adoption. We focus on a model of a cross-section of firms facing stable production parameters, and thus abstract away from issues of the diffusion of organizational design practices and the dynamics of adoption decisions.