An Empirical Framework for Testing Theories About Complementarity in Organizational Design

This paper studies alternative empirical strategies for estimating the effects of organizational design practices on performance, as well as the factors which determine organizational design, in a cross-section of firms. Our economic model is based on a firm where multiple organizational design practices are endogenously determined, and these organizational design practices affect output through an “organizational design production function.” The econometric model includes unobserved exogenous variation in the costs and returns to each of the individual practices. The model is used to evaluate how different econometric strategies for testing theories about complementarity can be interpreted under alternative assumptions about the economic and statistical environment. We identify plausible hypotheses about the joint distribution of the unobservables under which several different approaches from the existing literature will yield biased and inconsistent estimates. We show that the sign of the bias depends on two factors: whether the organizational design practices are complements, and the correlation between the unobserved returns to each practice. We find several sets of conditions under which the sign of the bias can be determined, and we provide economic interpretations. Our analysis shows that for a particular set of hypotheses, a variety of different procedures may all yield qualitatively similar biases, presenting a challenge for the identification of complementarity. We then propose a structural approach, which is based on a system of simultaneous equations describing productivity and the demand for organizational design practices. As long as exogenous variables are observed which are uncorrelated with the unobserved returns to practices, the structural parameters are identified, yielding consistent tests for complementarity as well as the cross-equation restrictions implied by static optimization of the organization’s profit function. *MIT Department of Economics and NBER (Athey); MIT Sloan School of Management and NBER (Stern). For useful comments, we would like to thank seminar participants at the 1997 AEA Winter Meetings, the 1997 Academy of Management Meetings, Haas School of Business (UC-Berkeley), Harvard, Harvard Business School, NBER, Rochester, Rutgers, Stanford Institute of Theoretical Economics, MIT, the Sloan Industry Studies Program, as well as Ashish Arora, George Baker, Erik Brynolfsson, Jody Hoffer Gittell, Shane Greenstein, Jerry Hausman, Jim Heckman, Rebecca Henderson, Bengt Holmstrom, Margaret Hwang, Casey Ichniowski, Tom MaCurdy, Paul Milgrom, Whitney Newey, Nancy Rose, John Rust, Kathryn Shaw, and Frank Wolak. We are grateful to the MIT Sloan School of Management as well as the National Science Foundation (Grant No. SBR9631760) for financial support.