Working Paper: NBER ID: w30784
Authors: Emmanuel Dhyne; Amil Petrin; Valerie Smeets; Frederic Warzynski
Abstract: We introduce a new methodology for estimating multi-product production functions. It embeds the seminal contributions of Diewert (1973) and Lau (1976) in our extended version of the semi-parametric econometric framework of Olley and Pakes (1996), where we address the simultaneity of inputs and outputs by allowing for the possibility of a possible vector of unobserved ”productivities,” all of which may be freely correlated with inputs and outputs. We show how to use the multi-product production function to recover estimates of firm-product marginal costs using the input and output elasticities by extending Hall’s (1988) single-product result to our multi-product setting using McFadden (1978). We focus on six 6-digit Belgian ”industries” that produce two products, finding all but five of the forty-eight input coefficients are positive and thirty eight are strongly significant. We find outputs are substitutes as the coefficients on ”other good output” is always negative and highly significant. 100% of marginal cost estimates are positive and close to 80% of markups are estimated to be greater than 1. We find very similar results when we move to 4-digit industries, when we use similar multi-product data from France, and when we use the trans-log approximation.
Keywords: No keywords provided
JEL Codes: L0
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| inputs (Y20) | production outputs (E23) |
| production structure (L23) | pricing behavior (D40) |
| outputs (Y10) | other good outputs (C67) |
| marginal costs (D40) | markups (D43) |