# A System Approach to Structural Identification of Production Functions with Multi-Dimensional Productivity

## TL;DR

This paper develops a new system-based method for identifying multi-dimensional production functions, accounting for firm heterogeneity and non-neutral productivity, with weaker data requirements than existing approaches.

## Contribution

It extends existing proxy variable frameworks to handle multi-dimensional productivity, enabling identification without relying on cross-sectional input price variation.

## Key findings

- Achieves point identification under perfect competition using static optimality conditions.
- Provides partial identification of non-neutral production technology with market power.
- Reduces data requirements compared to traditional methods.

## Abstract

There is growing empirical evidence that firm heterogeneity is technologically non-neutral. This paper extends Gandhi et al.'s (2020) proxy variable framework for structurally identifying production functions to a more general case when latent firm productivity is multi-dimensional, with both factor-neutral and (biased) factor-augmenting components. Unlike alternative methodologies, our model can be identified under weaker data requirements, notably, without relying on the typically unavailable cross-sectional variation in input prices for instrumentation. When markets are perfectly competitive, we achieve point identification by leveraging the information contained in static optimality conditions, effectively adopting a system-of-equations approach. We also show how one can partially identify the non-neutral production technology in the traditional proxy variable framework when firms have market power.