The Measurement of Capital: Retrieving Initial Values from Panel Data

Abstract

A common problem with micro‐level analysis is that capital stock data is missing. Typically, a feasible measure of capital is calculated by accumulating investment flows from an initial value of the capital stock. As the time dimension of most disaggregated data is rather short, the choice of this initial value can have significant effects on the resulting capital estimates. Most empirical studies impute the initial value using a single arbitrary proxy. In this paper, we propose a panel data framework that assigns weighting coefficients to multiple proxy variables. We conduct a series of Monte Carlo experiments to test the performance of the proposed method and apply the method to a U.S. manufacturing dataset. The results suggest that our method improves the approximation of the capital stock and thus in turn reduces the bias in the production function estimation.

Estimating Firm‐Level Capital Stock: The Evidence From Turkey

“…Chen and Plotnikova (2017) emphasize the advantage of using multiple proxies rather than using only one proxy with the help of Monte Carlo simulations. By the simulations, they show that the generalized approach introduced by themselves produces capital stock series that are highly correlated with the true capital stock, in comparison to the single proxy approach.…”

“…After calculating the initial capital stock for the sector (), we allocate it among the firms by their share of electricity consumption and value added in the sectoral aggregate using the methodology of Chen and Plotnikova (2017). The equation for the initial capital stock is as follows: where Y i is the value added of firm i , E i is the electricity demand of firm i , and Y j and E j are their sectoral aggregates, respectively.…”

“…For this study, we also applied this sort of allocation procedure as well as other methods. In doing so we benefited from Chen and Plotnikova (2017), who developed an allocation method that the authors call the generalized approach and suggested a data-driven method of choosing proxy weights. Although it is called data-driven, it still uses proxies to allocate the aggregate initial capital stock to each firm.…”

“…After calculating the initial capital stock for the sector (K A 0 ), we allocate it among the firms by their share of electricity consumption and value added in the sectoral aggregate using the methodology of Chen and Plotnikova (2017). The equation for the initial capital stock is as follows:…”

“…While the allocation of aggregate capital stock to firms is a widely used approach to obtain initial capital stock, the choice of allocation method makes significant differences, especially in short panels. Chen and Plotnikova (2017) propose an approach-which the authors call the generalized approach-to be used for the firm-level micro data. This method uses multiple variables as proxies to allocate the aggregate capital stock to firms and proposes a method for finding the optimal weights for these proxies.…”