# **Appendix C. Estimating TFP**

Here we describe how we estimate the firm-level TFP in three ways.

We use a standard log-linear Cobb-Douglas production function to estimate the firm-level TFP. Specifically, the TFP of firm _i_ in year _t_ is the estimated residual from the regression: i 0 i i i (A1) where i is the logarithm of value-added, and kk i and ll i are the logarithms of capital and labor, yy = ββ + ββ kk + ββ ll + DD respectively. To allow for different factor intensities across industries, we estimate equation (A1) yy kk ll separately for each two-digit industry. TFP can be interpreted as the relative productivity of a firm within its industry.

Real value added is obtained by subtracting the real input from the real output. We use the twodigit ex-factory price index from _China Urban Living and Price Statistics_ to deflate the output. The input deflator is calculated based on the available output deflators at the two-digit industry level and information from the National Input-Output (IO) tables in 1997, 2002, and 2007. From the IO tables, we know how much inputs are needed to produce a unit of output. Then the average input price index is the weighted average of the price indices of those inputs. Thus, to obtain the input deflator for each industry, we calculate a weighted average of the input deflators, using as weights the coefficients in the IO table.<sup>23</sup> In the ASIF dataset, firms report the total annual employment, but they do not report the real capital stock. Instead, the firms report the value of their fixed capital stock at the original purchase prices. As these book values are the sum of the nominal values for different years, they are not equal to the real capital stock and are not comparable across time and across firms. Since we do not have all past investments of a firm to construct the real capital stock, we follow Brandt, Van Biesebroeck and Zhang (2012) and make several assumptions to convert the value of their capital stock at the original purchase prices into the real values using the following procedures.

First, we estimate the nominal value of the capital stock for each year between a firm’s birth year and the first year in which the firm appears in our data set. We assume that it is 1998, the first year of our panel. We assume that the growth rate of the nominal capital stock of each firm equals to the growth rate of the nominal capital stock in the corresponding two-digit industry as reported in the _China Statistical Yearbooks_ .<sup>24</sup> We then calculate the nominal capital stock in 1998 as follows: N 1998<sup>= N</sup> 1998 ) (A2) Where N 1998<sup>is the nominal captial stock in 1998 reported in the ASIF data,</sup> ss<sup>∏</sup> ττ=ss (1 + rrττ<sup>_s_indicates the firm’s</sup> first year of operation, N growth rate of the nominal capital stock in the two-digit industry in year _t_ , as reported by the _China_ ss<sup>is the nominal captial stock of the firm in its birth year, andrr</sup> ττ<sup>is the</sup> _Statistical Yearbooks_ . From equation (A2), we calculate the nominal stock in each year between the firm’s birth year and 1998. Second, the annual nominal investment N is the change in the nominal capital stock between two consecutive years, that is, ii N = N ii ii<sup>−N</sup> ii−1<sup>(A3)</sup>

> 23 The 1997 IO table is used to construct the input deflators of 1998-2000, the 2002 IO table is used to construct the input deflators of 2001-2005, and the 2007 IO table is used to construct the input deflators in 2006-2007.

> 24 Since _China Statistical Yearbooks_ report the growth rate of nominal capital stock in the two-digit industry from 1986, we assume that firms established before 1986 are established in 1986.

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