The ‘proxy variable’ approach is often used to estimate production functions. This approach is not robust to measurement error, and it relies on some strong assumptions, including strict monotonicity, scalar productivity, and timing.
In this paper, I develop partial identification results that are robust to deviations from these assumptions and measurement errors in inputs. In particular, my model (i) allows for multi-dimensional unobserved heterogeneity, (ii) relaxes strict monotonicity to weak monotonicity, (iii) accommodates .
I show that under these assumptions production function parameters are partially identified by an ‘imperfect proxy’ variable via moment inequalities. Using these moment inequalities, I derive bounds on the parameters and propose an estimator. An empirical application is presented to quantify the informativeness of the identified set.
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