Third, we derive the real capital stock for each year between the firm’s birth year and 1998. We deflate the annual nominal investment in each year N into the real value using the investment deflator, which is in _China Statistical Yearbooks_ from 1990. For years 1986-1989, we ii ii RRNN use the investment deflator constructed by Perkins and Rawski (2008).

Fourth, we obtain the real capital stock in 1998 with the perpetual inventory method. Specifically, (A4) Where is the real capital stock in year ii _t_ , and is the depreciation rate as estimated by: ii−1 ii RRNN = (1 −δδ)RRNN + RRNN Finally, we obtain the annual real investment and the real capital stock after 1998. For years after 1998, we use the observed change in the firm's nominal capital stock at the original purchase prices as our estimate of the nominal annual investment, that is, the nominal annual investment N is still obtained from N N with the investment deflator in _China Statistical Yearbooks._ The real capital stock is ii ii<sup>−N</sup> ii−1<sup>. The real fixed investmentRRNN</sup> ii<sup>is obtained by deflating</sup> constructed using the perpetual inventory method, that is, ii r D (A6) r D is annual depreciation that is reported in ASIF, again deflated by the investment RRNNii = RRNNii−1 −DDrrDDr ccr ii + RRNNii deflators in _China Statistical Yearbooks_ . ii DDrrDDr ccr We estimate equation (A1) by ordinary least squares (OLS). We call this TFP-OLS. While this approach is commonly used in the literature, the existing research has argued that the OLS estimates suffer from two endogeneity issues: simultaneity of input choices and selection biases. These two issues will generate biased estimates of and , and therefore biased estimates of the TFP. A variety of techniques have been suggested to address these issues. We use the widely-used method kk ll ββ ββ proposed by Olley and Pakes (1996). We call this TFP-OP. As another key measure of TFP, we use a straightforward index number approach, which does not require estimating any parameters. To implement, the industry-specific wage share in the output is used to measure . One minus this share is used to measure . Here the assumption is that a cost-minimizing firm will make sure that the relative factor price ratio equals the local elasticity of ll kk ββ ββ substitution between the inputs of the production technology. To avoid potential bias from the cost shares using our own data—the cost shares in our data might reflect the ownership restructuring directly—we rely on the estimates of the factor shares at the two-digit industry level from SaintPaul and Bentolila (2003), as in Bloom, Sadun and Van Reenen (2012). We call this TFP-IN.

Overall, these three approaches yield quite similar results. The correlations of these productivity measures are fairly high (see Table C1 in this appendix): that between TFP-OLS and TFP-IN is 0.955; that between TFP-IN and TFP-OP is 0.937. Thus, it is not surprising that our results do not hinge on how we measure productivity.

Our index function approach relies on factor shares from Saint-Paul and Bentolila (2003). This has the virtue of not relying on the cost shares estimated from our own data. After all, the cost shares from the dataset itself might reflect the allocation effects of ownership restructuring itself, and thus bias the TFP measurements based on the cost shares from the data. However, it is also possible that the cost share based on our own data might better capture the underlying technologies and using them might result in more accurate measurements of TFP. We thus also experimented with the ``` 42 ```