Back Matter
Author: Hui He, Ms. Nan Li, and
• 1 https://isni.org/isni/0000000404811396, International Monetary Fund

### Appendix A. Constructing Firm-Specific Markups

Our construction of firm-specific markups closely follows De Loecker and Warzynski (2012). A firm i at time t produces output using the following production technology:

$\begin{array}{cc}{Q}_{it}={Q}_{it}\left({K}_{it},{L}_{it},{\omega }_{it}\right)& \left(18\right)\end{array}$

The only restriction we impose on Qit to derive an expression of markup is that Qit is continuous and twice differentiable with respect to its arguments.

Cost-minimizing producers consider the following Lagrangian function:

$\begin{array}{cc}Lag\left({K}_{it},{L}_{it},{\lambda }_{it}\right)={r}_{it}{K}_{it}+{w}_{it}{L}_{it}+{\lambda }_{it}\left({Q}_{it}-{Q}_{it}\left(.\right)\right)& \left(19\right)\end{array}$

where wit and rit denote a firm’s input cost for labor and capital, respectively. The first-order condition with respect to labor input is

$\begin{array}{cc}\frac{\partial La{g}_{it}}{\partial {L}_{it}}={w}_{it}-{\lambda }_{it}\frac{\partial {Q}_{it}\left(.\right)}{\partial {L}_{it}}=0& \left(20\right)\end{array}$

where the marginal cost of production at a given level of output is λit as $\frac{\partial La{g}_{it}}{\partial {Q}_{it}}={\lambda }_{it}$. Rearranging terms and multiplying both sides by $\frac{{L}_{it}}{{Q}_{it}}$, we can express the labor elasticity, θi as:

$\begin{array}{cc}{\theta }_{i}=\frac{\partial {Q}_{it}\left(.\right)}{\partial {L}_{it}}\frac{{L}_{it}}{{Q}_{it}}=\frac{1}{{\lambda }_{it}}\frac{{w}_{it}{L}_{it}}{{Q}_{it}}& \left(21\right)\end{array}$

Define markup μ as the ratio of price over marginal cost, $\mu =\frac{{P}_{it}}{{\lambda }_{it}}$. Using this definition, we can rewrite equation (21) as

$\begin{array}{cc}{\theta }_{i}={\mu }_{it}\frac{{w}_{it}{L}_{it}}{{P}_{it}{Q}_{it}}& \left(22\right)\end{array}$

Based on equation (22), once the labor elasticity, θi, is obtained from the production function estimation and the share of labor costs in total sales, $\frac{{w}_{it}{L}_{it}}{{P}_{it}{Q}_{it}}$, is measured from data, firm’s markup can be constructed as follows:

$\begin{array}{cc}{\mu }_{it}={\theta }_{it}\frac{{P}_{it}{Q}_{it}}{{w}_{it}{L}_{it}}.& \left(23\right)\end{array}$

### Appendix B. The Analysis of Propensity-Score Matching

Our difference-in-difference analysis hinges crucially on the compariability between patenting and nonpatenting firms. To guarantee the comparison is meaningful, we have to make sure the treatment group (patenting firms) and control group (nonpatenting firms) are similar in terms of the major firm characteristics. Propensity-Score Matching (PSM) method serves this propose. Here we lay out the PSM procedure as follows.

For each firm i, define the treatment Di = 1 if the firm applies for at least one patent, and zero otherwise. We run the following logit model to estimate the propensity score:

$\mathrm{Pr}\left({D}_{i}=1|X\right)=G\left(\text{size, age, industry dummy, year dummy}\right)$

where X = {size, age} and G(z) = exp(z)/(1 + exp(z)).

For firm i in the treatment group, we define pi(x) = Pr(Di = 1 | X = x). Under the common support condition, we have 0 < pi(x) < 1. We then take the nearest matching approach to pick the “matched” non-treated firm j for a treated firm i, based on the following criteria:

$||{p}_{i}-{p}_{j}||=\underset{k\in \left\{D=0\right\}}{\mathrm{min}}||{p}_{i}-{p}_{k}||.$

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We thank Luis Cubeddu, Daniel Garcia-Macia, Zheng Liu, Jianhuan Xu, Xiaodong Zhu, and participants from China Economics Annual 2015 and seminar in Wuhan University for helpful discussions and comments. We are grateful for Hanya Li for excellent research assistance. Hui He thanks research support by Shanghai Pujiang Program, and the Program for Professor of Special Appointment (Eastern Scholar) funded by Shanghai City Government.

Using the number of patents granted as a ratio of the number of patents applied and the foreign citations of Chinese patents, Wei, Xie and Zhang (2016) argues that this explosion of Chinese patents is not simply an outcome of easy approval or low-quality of patents in China,

Many have argued that part of China’s TFP gorwth may not reflect technical progress but rather an outcome of resource reallocation across sectors and across ownership forms (Borensztein and Ostry (1996)).

Novelty, in particular means that, before the date of filing, no identical invention or utility model has been publicly disclosed in publications or has been publicly used or made known to the public anywhere in the world. Furthermore, there should be no other earlier-filed Chinese applications, which describe the identical invention or utility model even if the publication date thereof is after the date of filing of the present case.

About 95% of firms from 1998 to 2007 are identified by the registration IDs, while the remainders are matched based on other information.

If a firm in SIE was established after 1998, the initial nominal capital stock is the book value of capital stock that the firm reports first time in SIE data. If a firm was established before 1998, initial capital stock is calculated by using information from the 1993 annual enterprise survey to construct estimates of the average rate of growth of the nominal capital stock between 1993 and the year that this firm appears in SIE first time. The real initial capital stock is then obtained by deflating with the investment de ator in that year.

The variance of the Negative Binomial is $\mathrm{exp}\left({x}^{\prime }\beta \right)+\alpha \mathrm{exp}\left(2{x}_{it}^{\prime }\beta \right)$, allowing for the variance to be larger than the mean (α is the over-dispersion measure). This relaxes the restrictions imposed by Poisson regression (i.e. α = 0). Given that the unconditional mean of patent count is much lower than its variance, Negative Binomial Model is more appropriate than the Poisson Model. In addition, we find that estimations based on a Poisson model yield qualitatively similar results and thus do not report them here.

As discussed in Blundell et al (1999), this method relaxes the strict exogeneity assumption required by the approach of Hausman, Hall and Griliches (1984).

Note that firm patenting is endogenous. Factors that contribute to more patents can simultaneously drive up firm size and productivity. Unfortunately, valid instruments are not available due to data limitation. Observations such as R&D tax subsidies or regulation concerning R&D only are not available at the firm or industry level.

The results are largely unchanged when more than one nonpatenting firms are matched with a given patenting firm as control groups

To test the robustness of the results of equations (11) and (12) to different quality of innovation, we run the regressions for the three different types of patent: invention, utility model and design. The coeffcients of all five TFP measures are positive and significant for invention and utility patent. The coeffcients of labor productivity and Solow residual of equation (12) are not significant for design patent.

Among the 142,717 firms in our merged patent-SIE sample, 20,737 of them have changed ownership, which account for 14.5% of the firms in the benchmark sample.

Also noted in Aghion et al. (2015) is a similar pattern in terms of the percentage of SOEs and POEs that received positive subsidies. It rose from 14% in 1998 to 25% in 2007 by SOEs, compared to 8% in 1998 to 12% in 2007 by POEs.

China’s Rising IQ (Innovation Quotient) and Growth: Firm-level Evidence
Author: Hui He, Ms. Nan Li, and Jing Fang