Essays on Estimating Production Functions

Abstract

In the first essay I estimate production functions of multiproduct firms when technologies are product-specific but inputs are observable only at the firm-level. I provide an estimation strategy that solves for the unobservable inputs while correcting for the well-known simultaneity, collinearity and omitted price problems in production function estimation. The key insights of the estimation strategy are, first, using output demand estimates in identifying the product-level input allocations and production functions, and second, using an inverse of the production function to control for endogeneity. The second essay describes the biases that arise when production functions are estimated under the standard assumption of a firm-level technology, while the true technologies are product-specific. The assumption of a firm-level technology implies that the technology parameters are identical across the various goods produced in the industry, and that a multiproduct firm produces all of its output with a single technology. To examine the implications of these simplifying assumptions, I estimate a firm-level production function on a dataset generated of an industry where two types of goods are produced with product-specific Cobb-Douglas production functions. I find that the biases in the estimated firm-level parameters are substantial even when the true product-specific technologies are very similar. The directions and the magnitudes of the biases are determined by intricate functions of the true product-specific technologies and the product scopes of the firms in the industry. The estimated productivity levels have a relatively low correlation with the true firm-level productivity levels when the firms' product scopes are heterogeneous, as they usually are. The third essay estimates the range of productivity gains achieved by information technology investments in the Finnish manufacturing sector. The contribution is to provide estimates of IT's productivity effects while accounting for some of the key characteristics of IT, i.e., that returns to IT depend on previous IT or complementary investments, come with lags, and, due to the aforementioned factors, are heterogeneous across firms and over time. I find that the productivity effects of IT range from negative to positive. For example, most firms obtain a negative productivity effect in the first year after the investment, which may be due to disruption in the production process caused by the implementation of the IT investment. Two years after the IT investment was made, most firms attain a positive productivity effect. In the third year after the investment, almost all firms gain a positive productivity effect. The estimation results suggest that the common practice of estimating a single output elasticity for an IT stock that is constructed as a linear function of the IT investments is unlikely to provide a truthful description of the productivity effects of IT.