Production Functions and Price-Cost Markups

This course will cover two major empirical topics which play a central role in studying the productivity and market power of firms: the estimation of production functions, and the estimation of price-cost markups. There have been important developments in both areas in recent years, which will be outlined and discussed in the course. Our focus will be on the use of micro datasets which are widely available, either from company accounts for individual firms, or from census of production surveys for individual business establishments. 

For the tutorials, please bring your own laptop with Stata installed to all the sessions.

Estimation of Production Functions: 

Production functions relate measures of output to measures of inputs. Variation in output not explained by variation in inputs is known as total factor productivity (TFP). A key challenge is that firms choose input levels knowing more about their productivity than we can observe. That generates correlation between observed explanatory variables and the error term in the production function, which makes ordinary least squares estimation inconsistent. Approaches that have been used to develop consistent estimators in this context include: (a) assuming a simple dynamic process for unobserved productivity, which may allow lagged input levels to be used as instrumental variables for current inputs, after appropriately transforming the original model (the ‘dynamic panel data’ approach); and (b) exploiting properties of the firm’s optimal demand for particular inputs, under certain assumptions, to suggest proxies for unobserved productivity (the ‘proxy variable’ or ‘control function’ approach). These two approaches are combined in a number of ‘two stage’ methods, which can allow for non-linear TFP dynamics. An older idea, which estimates some parameters of the production function directly from the demand equations for particular inputs, has recently been revived and given a non-parametric interpretation. 

Some key papers which will be covered in this module include: 

• Blundell, R. and Bond, S. (2000) “GMM estimation with persistent panel data: an application to production functions”, Econometric Reviews. 

• Olley, G.S. and Pakes, A. (1996) “The dynamics of productivity in the telecommunications equipment industry”, Econometrica. 

• Levinsohn, J. and Petrin, A. (2003) “Estimating production functions using inputs to control for unobservables”, Review of Economic Studies. 

• Ackerberg, D., Caves, K. and Frazer, G. (2015) “Identification properties of recent production function estimators”, Econometrica. 

• Gandhi, A., Navarro, S. and Rivers, D. (2020) “On the identification of gross output production functions”, Journal of Political Economy 

Estimation of Price-Cost Markups: 

The markup is the ratio of a firm’s output price to its marginal cost of production, neither of which is measured directly in widely available datasets. This module will briefly review the ‘accounting’ approach, which infers markups from the ratio of revenue to total costs, under the assumption of constant marginal = average cost. The main focus will be on the ‘production’ approach, which requires at least one input to be ‘flexible’ in the sense of being optimally chosen after the firm has observed its productivity and demand for the current period, and in the absence of any adjustment costs or frictions. The ‘ratio estimator’ then infers markups from the ratio of the output elasticity for that flexible input to its revenue share (i.e. expenditure on that input as a share of revenue). The output elasticity would ideally be estimated from a production function specification which relates output to inputs. The challenge in applying this approach is that we generally observe revenue, or the value of production, but lack data on output quantities. The methods covered in the first module will estimate output elasticities only if we have a quantity measure of output, or a sample of perfectly competitive firms. Otherwise they will at best estimate revenue elasticities, and unfortunately the ratio of the true revenue elasticity to the revenue share for a flexible input should be one for any profit-maximising firm, and hence provides no information about the markup. Moreover, with unobserved heterogeneity in markups, these methods will not estimate revenue elasticities consistently, which may account for the finding of estimated markups above one in most applications of this approach. Recent attempts to extend ‘control function’ methods to estimate output elasticities using revenue data for imperfectly competitive firms will be outlined, and several problems will be discussed. The module will conclude by outlining assumptions under which we can infer bounds for an average measure of price-cost markups using only data on revenue shares. 

Some key papers which will be covered in this module include: 

• De Loecker, J. and Warzynski, F. (2012) “Mark-ups and firm-level export status”, American Economic Review. 

• De Loecker, J., Eeckhout, J. and Unger, G. (2020) “The rise of market power and the macroeconomic implications”, Quarterly Journal of Economics. 

• Bond, S., Hashemi, A., Kaplan, G. and Zoch, P. (2021) “Some unpleasant markup arithmetic: production function elasticities and their estimation from production data”, Journal of Monetary Economics. 

• Doraszelski, U. and Jaumandreu, J. (2023) “Re-examining the De Loecker and Warzynski (2012) method for estimating markups”, Discussion Paper, Wharton School, University of Pennsylvania.  

Estimation of Production Functions: 

Estimation of Price-Cost Markups: