A key issue in the estimation of production functions is the correlation between unobservable productivity shocks and input levels. Profit-maximizing firms respond to positive productivity shocks by expanding output, which requires additional inputs. Negative shocks lead firms to pare back output, decreasing their input usage. Olley and Pakes (1996) develop an estimator that uses investment as a proxy for these unobservable shocks. More recently, Levinsohn and Petrin (2003a) introduce an estimator that uses intermediate inputs as proxies, arguing that intermediates may respond more smoothly to productivity shocks. This paper reviews Levinsohn and Petrin's approach and introduces a Stata command that implements it.

Previously, to fit an almost-ideal demand system in Stata, one would have to use the nlsur command and write a function evaluator program as described in [R] nlsur and Poi (2008, Stata Journal 8: 554-556). In this article, I introduce the command quaids, which obviates the need for any programming by the user. The command fits Deaton and Muellbauer's (1980b, American Economic Review 70: 312-326) original almost-ideal demand-system model as well as Banks, Blundell, and Lewbel's (1997, Review of Economics and Statistics 79: 527-539) quadratic variant. Demographic variables can also be included in the model. Postestimation tools calculate expenditure and price elasticities.

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.

We consider inference in the linear regression model with one endogenous variable and potentially weak instruments. We construct confidence sets for the coefficient on the endogenous variable by inverting the Anderson-Rubin, Lagrange multiplier, and conditional likelihood-ratio tests. Our confidence sets have correct coverage probabilities even when the instruments are weak. We propose a numerically simple algorithm for finding these confidence sets, and we present a Stata command that supersedes the one presented in Moreira and Poi (Stata Journal 3: 57-70).

In this paper, we propose a fix to the size distortions of tests for structural parameters in the simultaneous equations model by computing critical value functions based on the conditional distribution of test statistics. The conditional tests can then be used to construct informative confidence regions for the structural parameter with correct coverage probability. Commands to implement these tests in Stata are also introduced.