Essays on nonseparable models
This dissertation consists of three chapters in econometrics with a focus on nonseparable models. Nonseparable models has a wide application in many areas of economics such as industrial organization and labor economics.
The first chapter of this dissertation studies a partially separable panel data model with multiple shocks, emphasizing an application to estimation of production functions. The model is partially separable in the sense that the marginal effects of the explanatory variables depend on the unobservables, but not on some of the other explanatory variables. Identification and estimation results are provided for the unspecified functions and error-disturbance distributions in the model. Identification requires assumptions on the existence of valid instruments (used in a control function approach), conditional independence among shocks, and shape restrictions on the unknown functions. Under additional regularity conditions, a consistent estimator is provided and its non-standard rate of convergence is established.
In the second chapter, the model studied in the first chapter is applied to estimation of a partially separable production function with a Hicksian productivity shock, a labor productivity shock, and a capital productivity shock to investigate the roles of both Hicksian and non-Hicksian shocks of Spanish firms from 1990 to 2006, controlling for the endogeneity of inputs. The estimation results show that all types of productivity shocks are heterogenous across firms and over years, and greatly affect the levels of output. The model also generates plausible estimates of the effects of capital on output and labor on output.
The third chapter studies studies a fully nonseparable production function. It extends the standard Cobb-Douglas production function by relaxing the additive functional form assumption. Besides this major difference, this paper also relaxes the assumptions that the productivity shock follows an M-th Markov process and the functional form is constant over years, both of which are widely imposed in production function literature. Some standard assumptions in production function literature are imposed to identify the unspecified time-varying production function, the unobserved productivity shock and the unobserved random shock. The productivity shock is identified from the investment equation by using the capital and investment in previous period as control variables. The identified productivity shock is then used to identify the production function and the random shock. An easy to implement kernel estimator is proposed. These estimator is shown to be consistent. A Monte-Carlo study indicates the estimator performs very well in finite samples. The model is applied to study Spanish firms behaviors from 2004 to 2006. The estimation results show the productivity shocks are widely distributed and greatly affect the levels of output. The estimation results also show oscillating capital productivity and labor productivity as capital and labor change.