Production Function Estimation in Stata Using the Olley and Pakes Method

Abstract

Productivity is often computed by approximating the weighted sum of the inputs from the estimation of the Cobb-Douglas production function. Such estimates, however, may suffer from simultaneity and selection biases. Olley and Pakes (1996, Econometrica 64: 1263-1297) introduced a semiparametric method that allows us to estimate the production function parameters consistently and thus obtain reliable productivity measures by controlling for such biases. This study first reviews this method and then introduces a Stata command to implement it. We show that when simultaneity and selection biases are not controlled for, the coefficients for the variable inputs are biased upward and the coefficients for the fixed inputs are biased downward.

Factor content of bilateral trade: the role of firm heterogeneity and transaction costs

“…In order to estimate the TFP using a panel of firm‐level data several issues need to be addressed. In particular, simultaneity and selection bias need to be addressed (Yasar et al, 2008). Given that the productivity is known to the profit maximizing firms (but not to the econometrician) when they choose their input levels, the problem of simultaneity may arise.…”

“…Second, selection bias needs to be addressed when estimating production function parameters. Selection bias results from the relationship between the productivity shocks and the probability of exit from the market (Yasar et al, 2008). If a firm's profitability is positively related to its capital stock, then a firm with a larger capital stock is more likely to stay in the market despite a low productivity shock than a firm with a smaller capital stock because the firm with more capital can be expected to produce greater future profits.…”

“…19 19 Other methods, including instrumental variables approaches, have also been proposed to control for this bias when estimating the parameters of production functions (Yasar et al, 2008). …”

Export behaviour and firm productivity in China

“…In order to address this problem, early researchers used a two-way fixed-effects model. Although it is effective in controlling some effects of implicit productivity shocks, Yasar, Raciborski, and Poi (2008) argued that a fixed-effect estimator would solve the simultaneity problem only if we assumed that unobserved firm-specific productivity is time-invariant.…”

“…If a firm with more capital can be expected to produce greater future profits, then a firm with larger capital stock is more likely to survive in the market given a negative productivity shock than a firm with smaller capital stock. The negative correlation between capital stock and probability of exit for a given productivity shock will cause the coefficient of the capital variable to be biased downward unless we control for this effect (Yasar, Raciborski, and Poi 2008). Olley and Pakes (1996) proposed a novel semi-parametric approach to address simultaneity and selection problems while estimating production function parameters.…”