Posted by Connie R. Aponte on March 21, 2015 in ORGANIZATIONAL DESIGN |

Our analysis highlights how particular forms of unobserved heterogeneity bias the test statistic from these procedures in specific directions. Consider the following two alternative assumptions about the unobserved returns to practices: (a) the unobserved returns among practices are affiliated (a strong form of positive correlation) and (b) the unobserved returns are independent. Even when the choices do not interact in determining productivity (TI), the presence of positive correlation between the unobserved returns to the two different practices yields (i) positive correlation in adoption among practices and (ii) a positive estimate of the interaction effect in an OLS or 2SLS productivity regression. More generally, positive correlation in the unobservables results in a force for a positive bias in the estimate of interaction effects in a productivity regression.

In contrast, complementarity between practices (TC) results in a competing effect for the direction of the bias: (TC) creates a force towards understating interaction effects. Under (TC), adopting a given practice (such as a training program) leads to a less favorable selection of firms adopting complementary practices (such as higher skill requirements). If the unobserved returns to practices are independent and (TC) holds, the bias on the interaction effect will always be negative. While each of these biases are specific examples of selection biases (as analyzed by Heckman (1974) or Heckman and MaCurdy (1986)), the nature of selection biases which arise from statistical and technological interactions between choices has not received attention in the existing literature.
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Our second use of the formal model is to analyze the properties of a structural estimator of the parameters with two main features: (i) it explicitly models the distribution of the unobserved heterogeneity, and (ii) it includes a system of equations, including an equation describing productivity and a set of equations describing the practice adoption decisions.

There are several advantages to using such a structural approach in the context of this problem. First, by accounting for the unobserved heterogeneity, it is possible to obtain consistent estimates of the parameters of the organizational design production function as well as the covariance between the unobserved returns to different organizational design practices. Second, our model nests all prior models we are aware of, and so direct comparisons can be made between the implicit assumptions associated with previous approaches. Third, by specifying an internally consistent simultaneous equations system, we can impose the cross-equation restrictions on the interaction effects; as suggested above, since organizational design practices are often positively correlated in applications, the use of revealed preference can yield substantial efficiency gains. Finally, (if the Random Practice Model is appropriate) we can perform tests about the process that leads to the adoption of practices, including whether or not practice adoption appears to be consistent with optimal behavior.

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