Non-Neutral Technology, Firm Heterogeneity, and Labor Demand

Transcription

1 Non-Neutral Technology, Firm Heterogeneity, and Labor Demand Hongsong Zhang, The University of Hong Kong (First Draft: 211) June 11, 216 Abstract The neutrality (non-neutrality) nature of technology is the key to understanding of many firm activities. This paper investigates the non-neutrality nature of technology heterogeneity across firms and over time. I develop a method to estimate the production function with nonneutral technology heterogeneity at the firm level, which is captured by a multidimensional productivity measure allowing for a capital-augmenting efficiency, a labor-augmenting efficiency, and a material-augmenting efficiency. The empirical results from Chinese steel industry show that: (1) the non-neutral technology heterogeneity across firms is large, both in efficiency levels and technological non-neutrality; (2) technology change over time is non-neutral towards saving labor and the trend is stronger for large firms; (3) while capital and labor efficiencies converge slowly in levels during the sample period, I found no obvious converging trend for the technological non-neutrality; (4) the non-neutral technology explains a large portion of the cross-firm variation in labor demand. Counterfactual experiments show that if the technological non-neutrality is completely removed starting 21, the labor demand in 27 would have been about 115% higher than that observed in the data in order to produce the same output. Keywords: non-neutral technology dispersion; non-neutral technology change; firm heterogeneity; labor demand JEL classification: D24, O33 The author would like to thank participants in the 12th International Industrial Organization Conference (IIOC), the 214 European Economic Association & Econometric Society Parallel Meeting, the 41st Annual Conference of the European Association for Research in Industrial Economics (EARIE), the 8th Biennial Conference of Hong Kong Economic Association, the 213 AAEA & CAES Joint Annual Meeting, and the IO workshop at the Pennsylvania State University for very helpful comments. The author is grateful to Mark Roberts, James Tybout, Paul Grieco, Saroj Bhattarai, Jorge Balat, Johnathan Eaton, Edward Green, Jordi Jaumandreu, Francis Kramarz, Joris Pinkse, Larry Qiu, Spiro Stefanou, Wing Suen, and Neil Wallace for many insightful suggestions. The author also acknowledges the financial support from the Seed Funding Programme for Basic Research at The University of Hong Kong (project code: ). All errors are the author s own responsibility. Correspondence: Faculty of Business and Economics, The University of Hong Kong. hszhang@hku.hk.

2 1 Introduction The neutrality (non-neutrality) nature of technology is the key to understanding individual firm activities and aggregate economic growth. Intrinsically, technology change could be non-neutral towards saving some specific inputs. For example, earlier literature has shown that aggregate technology changes towards saving labor in developed countries (Gollop and Jorgenson, 198; Jorgenson et al., 1985; Gollop et al., 1987; Gollop and Roberts, 1981; David and Van de Klundert, 1965; Kalt, 1978; Diamond et al., 1978; Sato, 197). Acemoglu (1998, 22) has also shown the possibility of non-neutral technology change 1 in a dynamic balanced economic growth model. Hanlon (forthcoming) provides empirical evidence on directed technology change at the product level by showing that supply shocks to high-quality cotton from U.S. due to U.S. Civil War stimulated firms in Britain to develop more technologies that use low-quality cotton from India more efficiently, lending support to the key predictions in Acemoglu (22). In the same vein, technology differences across firms could also be non-neutral even within very narrowly defined industries, in the sense that some firms manage capital more efficiently, while others excel at managing labor or material. Virtually, however, all of the empirical literature on production function and productivity estimation at the firm level assumes that technology differences, both across firms and over time, are Hick s neutral in economics fields such as industrial organization and international trade (Olley and Pakes, 1996; Ackerberg et al., 26; Eaton and Kortum, 22). In this framework, technology differences and technology changes affect the marginal products of different inputs symmetrically. It is very hard, in this case, to explain the observed large variations in factor shares across production observations using only input price dispersion and other observed firm characteristics even within narrowly defined industries. Likewise, it is also unlikely to explain the large increases of material and capital per worker using input price changes, because the input price ratios are relatively stable or only increases slightly, as we will show in the data section. This paper investigates the non-neutrality nature of technology heterogeneity across firms, and that of technology change over time. I develop a new method to estimate a gross production function with constant elasticity of substitution (CES) and non-neutral technology differences across firms and over time. The non-neutral technology is characterized by a multidimensional productivity measure, which allows for a capital-augmenting efficiency, a labor-augmenting efficiency, and a material-augmenting efficiency. If a firm adopts a technology with high labor-augmenting efficiency, for example, it will increase the marginal output of labor more than that of other inputs, other things being equal. This technology is labor-saving (labor-using) if inputs are gross complements (substitutes). This productivity measure in its nature is very flexible for at least three reasons. 1 Acemoglu (1998, 22) uses the term directed technology change instead. 1

3 First, it allows technologies to differ not only in their levels, but also in their components (technological non-neutrality). Second, all the three factor-augmenting efficiencies are firm-time specific, so we can study the technology differences both across firms and over time. Moreover, the full set of factor-augmenting efficiencies capture all possible technology patterns, including both neutral and non-neutral technologies. In fact, it accommodates all the three conventional concepts of neutral (non-neutral) technology in the literature, namely Hicks-neutral technology (Hicks, 1932), Harold-neutral technology (Harrod, 1939), and Solow-neutral technology (Solow, 196; Jorgenson, 1966), which are very important in the growth literature. This nice feature allows the possibility to directly test the technological non-neutrality assumption against different notions of neutral technologies after estimation. The estimation method relies on the conventional assumption that firms choose labor and material statically to maximize period profit and choose investment dynamically to maximize expected long-term payoff. One challenge in the production estimation is the transmission bias caused by unobserved productivity, which is correlated with firms labor and material choices. The estimation method incorporates both the parametric and non-parametric approaches to recovering the unobserved multidimensional productivity measure in order to solve the transmission bias. First, given the parametric production function we can recover the capital-material efficiency ratio and labor-material efficiency ratio from the (parametric) first order conditions associated with optimal labor and material decisions. The idea of exploiting the parametric first order conditions of profit maximization in the production function estimation is also used in many other papers, such as Van Biesebroeck (23), Gandhi et al. (29), Doraszelski and Jaumandreu (213), and Grieco et al. (215), to name a few. 2 An innovation in my application is that, instead of using the original form of first order conditions, I use the first order condition in the form of factor revenue shares, in which the demand shifters are absorbed in the shares. This treatment largely simplifies the estimation. Second, the nonparametric dynamic investment decision provides a third restriction to control for the (scaled) material efficiency under a conditional invertibility condition. The idea of using the nonparametric investment function to control for unobserved productivity at the firm level was first developed by Olley and Pakes (1996) and has been widely applied in many other following works such as Ackerberg et al. (26), Aw et al. (211), and Zhang (214). The recovered unobserved efficiencies based on the parametric and nonparametric inversion are then inserted in the production function and the Markov productivity evolution equations to form the estimation equations, which can be estimated using generalized method of moment (GMM). In the extension I show that this approach has the potential to apply in more general production functions. To construct the GMM estimator, I jointly use the production function, demand function, and 2 More papers uses similar first order conditions of labor and material in other scenarios. For example, Epple et al. (21) develop a procedure to estimate the housing supply function using the first order condition of the indirect profit function maximization; De Loecker (211), De Loecker and Warzynski (212), and De Loecker et al. (212) use the first order condition of labor and/or material choice of profit maximization to estimate firm-level markup. 2

4 (part) of Markov productivity evolution process to construct moment conditions. The approach here differs from León-Ledesma et al. (21) in two aspects. First, I assume that capital stock is a dynamic fixed variable and use the non-parametric dynamic investment function as a restriction, instead of using the first order condition implied by flexibly chosen capital in each period. Second, instead of assuming a time trend of biased technology change, following Doraszelski and Jaumandreu (213) and Aw et al. (211) I assume that efficiencies follow Markov process and use it together with the first order conditions to construct the moment conditions. This allows the factor-augmenting efficiencies to change flexibly over time with unobserved random shocks, further adding to differences of non-neutral technology across firms. The Chinese steel industry provides a good background to investigate the potential non-neutral technological differences both across firms and over time, due to the large geographical and technological differences across firms and rapid technological progress over time. I apply the approach developed in this paper to study the feature of technology at the firm level in this industry. There are four basic findings. First, there is large heterogeneity of non-neutral technology across firms, both in efficiency levels and technological non-neutrality. Second, technology change over time is fast and non-neutral labor efficiency (17.81%) grows much faster than capital efficiency (3.85%), while the growth of material efficiency is even slower (.83%). As a result, technology change is labor-saving given that the estimated elasticity of substitution is smaller than one (.455). Third, firm size matters. I find that the evolution of non-neutral technology, both in levels and technological non-neutrality, differs substantially across firms of different size. The largest 2% of firms enjoy a faster growth of labor-augmenting efficiency, while the smallest group of firms have a faster growth of capital-augmenting efficiency. As a result, although technology changes for all firms of all sizes are labor-augmenting in general, that for large firms are more so. Finally, although capital and labor efficiency levels are converging slowly during the sample period, I found no obvious converging trend of the technological non-neutrality over time in the dataset, as measured by the three input efficiency ratios. Moreover, restricting technology to be Hicks-neutral will substantially overestimate the elasticity of substitution and underestimate the effect of wage rate on labor demand, which is consistent with Antràs (24). I apply the recovered non-neutral productivity measures to analyse the firm-level labor demand in Chinese steel industry. It is shown that non-neutral technology can explain around 14% of the variation in labor demand across firms. More sharply, the non-neutral technology explains roughly 7% of the variation in labor-material ratios across firms. In the counterfactual experiments, I evaluate the contribution of non-neutral technology to labor demand, by comparing the labor demand in the data with that in the counterfactual world when the technology non-neutrality is removed. Because we allow Hick s neutral productivity to grow, this exercise isolates the effect of non-neutral technology. I found that the labor demand in 27 would have been about 115% 3

5 higher than that observed in the data in order to produce the same amount of output, should there be no non-neutral technology differences both across firms and over time starting 21. This paper relates to and extends a series of seminal work on aggregate biased technology change at the country- or industry-level dating back to 196s. Some earlier studies, such as David and Van de Klundert (1965), Sato (197, 198), Panik (1976), Binswanger (1974a), Gollop and Jorgenson (198), Jorgenson et al. (1985), and Gollop et al. (1987), use aggregate data to study the biased technology change in developed countries 3. A common feature of these works is that the rate of biased technology change is assumed to be a constant time trend, which is common across firms. Following this literature, Klump et al. (27) and León-Ledesma et al. (21) estimate the direction of biased technology change to be labor-saving for U.S. economy, utilizing the first order conditions implied by static optimal choice of labor and capital. Gollop and Roberts (1981), in contrast, use micro data to investigate the direction of biased technology change in the electric power industry in U.S. The rate of biased technology change, however, is maintained as constant and common to all firms. Jin and Jorgenson (21) relaxes the constant time trend assumption and construct empirical measures of both the rate and biases of technical change as latent variables, while maintaining flexibility in modeling elasticity of substitution in terms of observables in a flexible translog function. While all these studies focus on the evolution of biased technology over time, similar idea can be applied to study the biased technology differences across firms which could be an important source of firm heterogeneity. My paper builds on this idea and investigates the non-neutrality nature of technology both across firms and over time. The setup of the non-neutral technology in my paper is more flexible because I allow a full set of factor-augmenting efficiencies which are firm-time specific. This paper also relates to several recent papers on estimating production function using micro data while partly allowing for factor-augmenting efficiencies at the firm level. Raval (214) estimates a value-added CES production function with both capital and labor augmenting efficiencies and constant return to scale (CRS). He was able to recover the capital and labor efficiencies, as well as the elasticity of substitution, under a crucial assumption that firms can adjust both capital and labor flexibly. While this assumption makes the estimation more tractable, as in Klump et al. (27) and León-Ledesma et al. (21), in practice it is unlikely that capital is flexibly adjusted. My paper relaxes this assumption by allowing capital to be a dynamic fixed variable, while keeping the assumption that labor and material can be flexibly adjusted in a gross CES production function without assuming constant return to scale. Van Biesebroeck (23), based on parametric inversion to recover unobserved productivity, also 3 More studies following this line include, but not limited to, Brown and De Cani (1963), Wilkinson (1968), Binswanger (1974b), Stevenson (198), Kalt (1978), Jorgenson and Fraumeni (1983), and Cowing and Stevenson (1981). Refer to Binswanger et al. (1978), Jorgenson (1986), Ruttan (21), and Jin and Jorgenson (21) for a review of the approaches used to estimate the technological bias following this line. 4

6 estimates a production function with a firm-time specific labor-saving efficiency and a fixed effect Hicks-neutral efficiency. Doraszelski and Jaumandreu (214) extend this work by further allowing the Hicks-neutral efficiency term to be firm-time-specific and estimate a gross CES production function with a labor-augmenting efficiency in addition to a Hicks-neutral efficiency, both of which are firm-time specific. Their approach also relies on the first order conditions implied by flexible adjustment of labor and material by profit-maximizing firms and that both Hicks Neutral and labor-augmenting efficiencies follow Markov process. This setup implicitly assumes that capital efficiency and material efficiency always grow at the same rate, which is a testable empirical question. 4 My paper differentiates from Doraszelski and Jaumandreu (214) by relaxing this restrictive assumption and considering a full set of factor-augmenting efficiencies for capital, labor, and material. This extension naturally motivates my new approach based on a combination of parametric and non-parametric inversion to recover the unobserved productivity measures. Balat and Sasaki (214), in contrast, identify and estimate a Cobb-Douglas production function with firm-time specific random coefficients on labor share, while restricting capital and material efficiencies to be time varying only. The Cobb-Douglas production with varying output elasticity has a taste of non-neutral technology change because, for example, an increase of output elasticity of labor will increase labor share accordingly, ceteris paribus. His approach is also based on first order conditions implied by profit maximization, but allowing some frictions in labor adjustment (but not in material choice) which is an attractive advantage. While Cobb-Douglas function is very useful and handy in many applications, as is well known, however, it limits the elasticity of substitution to be one, which might not be practical in many scenarios. 5 My paper distinguishes from Balat and Sasaki (214) in that I consider a more flexible setup of technology and in that I use a more general CES production function with the potential to extend to more general function forms. This paper also relates to the literature on estimation of elasticity of substitution among different inputs in production. For instance, Antràs (24) and Klump et al. (27) estimate the elasticity of substitution between capital and labor at the aggregate level, using aggregate data in U.S. for five decades in the second half of 2th century. It is also related to a wide range of literature whose results largely depends on the value of the underline elasticity of substitution, such as Acemoglu (22) for balanced growth path, Mankiw (1995) for differences in international factor returns, and Blanchard (1997) for change of income shares. Refer to León-Ledesma et al. (21) for a complete 4 In a recent version of this paper, Doraszelski and Jaumandreu (214) also added a discussion the possibility to introduce the third-dimension of productivity in the extension, similar to what I discuss in this paper. They suggest a solution based on the first order condition of static capital choice when capital is flexibly adjustable, or simply assuming a time trend of capital efficiency in the appearance of capital adjustment friction. 5 Many studies in the literature has documented that the elasticity of substitution is significantly different from one, such as Arrow et al. (1961) and Bodkin and Klein (1967) under Hicks Neutral technology, and David and Van de Klundert (1965), Kalt (1978), Antràs (24), and Klump et al. (27) under factor-augmenting technology. See León-Ledesma et al. (21) for a review. 5

7 review of these two lines of literature. My paper distinguishes from these papers in a combination of two features. First, I use micro data to estimate the elasticity of substitution at the firm level. Second, it is estimated together with a full set of factor-augmenting efficiencies which are firm-time specific. I found that the estimated elasticity of substitution is substantially lower after controlling for non-neutral technology at the firm level. The next section introduces the data and background of this study. Section 3 develops the approach to estimate production function with non-neutral technology. Section 4 reports the estimation results and investigates the heterogeneity of non-neutral technology both across firms and over time. In Section 5, I examine the effect of non-neutral technology on labor demand. Section 6 shows that the estimation approach developed in this paper can be applied to more general production functions and Section 7 concludes. 2 The Background and Data 2.1 The Chinese Steel Industry The Chinese steel industry provides rich soil to investigate the differences of non-neutral technology both across firms and over time. First of all, the large dispersion of geographic and other economic characteristics of Chinese firms allow us to investigate the non-neutral technological heterogeneity across firms. Even within narrowly defined industries, the large size of Chinese economy guarantee that there are enough observations with widely-dispersed variations in firm characteristics to perform statistically reliable inference. Secondly, unlike other slow-growing economies, the rapid economic growth in China including steel industry provides us with a nice background to investigate the evolution of non-neutral technology over time, if any. We can identify the change of technological level and non-neutrality even with relatively short panels. China adopted a series of policies to encourage technological change after 1997, which also applied to steel industry. The initial purpose of these policies was to prepare Chinese firms for international competition after entering the World Trade Organization (WTO) in 21, and to maintain a sustainable aggregate economic growth as well. Two of the most important policy documents are The guide to High-Tech Areas for Industrial Development with Priority and The list of Out-dated Productivity, Production Process and Products to be Eliminated, both issued in These policies encourage firms to update their technology, production processes, and products. The former document lists the technology, production process and products that are encouraged to develop, which require up-to-date technology; the latter lists the ones that firms should eliminate, which use outdated technology. The government, on one hand, encouraged firms to update 6

8 their technology through strong economic incentives such as tax credits, loan appraisals and land rationing, and on the other hand implements a strict appraisal procedure for firms to invest in new projects. New projects using the encouraged technologies would be easily approved by the Censoring Bureau, while otherwise very hard. The Guide for Industrial Structure Change, issued in 25, more clearly lists the encouraged, restricted, and forbidden projects. To accompany these policies, the Ministry of Land and Resources issued two land-use restrictions, Projects Restricted from Using Land and Projects Forbidden from Using Land, to help implement technology-promoting policies. These policies together provided strong incentives for existing firms to update their technology, and for new firms to use new technology. This paper examines the pattern of technological change of Chinese firms in this background and evaluate its effect on labor demand. 2.2 The Data Two panel data sets are combined and used in the empirical application. The main data source is a rich, firm-level panel data set from Chinese manufacturing industries, which was collected through annual surveys of manufacturing enterprises and maintained by the China National Bureau of Statistics. The panel is unbalanced. The surveys cover two types of manufacturing firms: (1) all state-owned enterprises (SOEs), and (2) all non-soes whose annual sales are more than five million RMB (approximately 65, US dollar). The data set contains information on firm-level annual revenue, input expenditures, wage rate, detailed firm characteristics (e.g. age, ownership, location etc.), and many other financial variables. For a detailed description of the data set, refer to Feenstra et al. (211). I use data from steel industry partly because there was rapid technology change in this industry and large dispersion of technology used by different firms, and partly because there is another dataset with input and output prices for steel industry to supplement the main dataset. Here the steel industry broadly contains four four-digit SIC industries: iron smelting, steel making, Steel rolling processing, and ferroalloy smelting industries. I pool all these four industries together in the study because the classification of firms in these four industries is not so clear in China. After dropping unusual observations, I construct a sample of 33,133 observations from 2 to 27. In the estimation, I also construct capital investment using perpetual inventory method. Dropping all observations without investment data leaves a sample of 22,434 observations from 21 to 27. All variables used in the empirical application, except for output and material input prices, are drawn from this dataset. See Appendix A for detail about the sample construction and Appendix B for variable definitions. Table 1 provides summary statistics for main variables used in the estimation. 7

9 The second dataset is from China Economic Information Network (CEIN), which provides provincelevel price indices for both input and output for steel industry. Because steel industry in China has very organized local markets for inputs and output, firms in the same area share very close prices of input and output for the same products. So province-level prices represent firm price well. The summary statistics of input and output prices are also included in Table Technological Non-neutrality: A First Glimpse The idea to investigate the technological non-neutrality, both across firms and over time, is directly motivated by two facts observed in the data. The first fact is that there is a large dispersion of labor-revenue share across firms and over time. In Table 2, the sample observations are divided into five groups of equal number of observations according to their sales size, year by year. I compute the simple average of labor-revenue share for each year-size group. The first observation is that, large firms have a much lower labor share. Taking 2 for example, while the mean labor share for the largest 2% of firms is 5.23%, this number is almost 5% higher (7.66%) for the smallest 2% of firms. This gap has been widening in subsequent years. The second fact in Table 2 is that the average labor-revenue share is almost monotonically decreasing over time in the sample period, for all size groups. For the whole sample, the average labor share drops from 5.71% in 2 to 4.7% in 27, representing a drop of 28.72% in seven years. The second panel of Table 2 shows similar pattern for labor-material ratio it has large variation across firms with large firms having much lower labor-material ratio, and it has been decreasing sharply from 2 to 27. It is unlikely that these large dispersion (sharp decrease) of labor share can be explained by the heterogeneity of input prices across firms (over time). In Figure 1 and Table 3, I examine the relationship between input ratio and input price ratio, and show that input prices are not enough to explain the heterogeneity and movement of input ratios. Figure 1 plots the movements of mean labor-material price ratio and labor-material ratio from 2 to 27. The wage rate to material price ratio increases slightly during this period, by 9% in total from.9 to.981 in the seven years. In contrast, the mean labor-material ratio decreases sharply by almost 4%, from to.6527 during the same period. It is unlikely to explain such a sharp drop of labor-material ratio by the small change of input price ratio, given that the estimated elasticity of substitution is mostly smaller than or close to one (Antràs, 24; Klump et al., 27; León-Ledesma et al., 21). Figure 1 further plots the simulated average labor-material ratio for 21-27, choosing 2 as the base year. I compute the simulated labor-material ratio based on the observed price changes and the largest estimate of elasticity of substitution,.7743, estimated 8

10 in Table 3 when Hicks-neutral technology is assumed 6. It is shown that the predicted change of labor-material ratio is much smaller than that observed in the data, leaving a large gap which cannot be explained by input price changes. This gap is consistent with a labor-saving non-neutral technology change over time. Table 3 provides further evidence on that input price ratio can only explain a small portion of the variation in input ratio. To illustrate the idea, take the CES production function as an example. If technology is Hicks-neutral and labor and material are flexibly chosen to maximize period profits, the input ratio and input price ratio has a simple relationship, ln labor quantity material quantity Here σ is the elasticity of substitution. = σ ln wage rate material price + constant. Based on this equation, I use the logarithm of labormaterial ratio as the dependent variable and run a series of linear least square regressions (OLS) with logarithm of labor-material price ratios as the major independent variable. The results are reported in the first four columns of Table 3. These regressions differ from each other in what additional covariates are controlled for in each regression. The R-square, as reported in the last row, is our major interest. It is shown that even after controlling for firm characteristics such as ownership, age, and year dummy, input prices can only explain less than 3% of the variation in input ratio. Similar results are found in fixed effect and random effect models, as shown in the last two columns of Table 3. These results suggest that some other factors are responsible for the large variation in labor-material ratio. Non-neutral technology provides an alternative explanation to these observed facts. With nonneutral technology, firms differ not only in the absolute level of efficiency, but also in the relative efficiency ratios. The former determines the absolute level of inputs used, or the size of factor demand; the latter determines the relative amount of the input used, or the composition of factor demand. More specifically, the relative factor efficiency differentials among firms imply a different marginal products of factors among firms, which leads to different input ratios among firms even when their input prices are the same. This paper estimates the effect of non-neutral technology on input ratios based on a structural model which allows for a flexible non-neutral technological heterogeneity, both across firms and over time. 6 The simulated average labor-material ratio for years 24, for example, are computed as: ( ) ( ) [ ( )] L L = 1 σ PL / PL, M 24 M 2 P M P M where σ is the elasticity of substitution and P L P M / P L P M is the percentage change of labor-material price ratio from 2 to 24. The simulated labor-material ratios for other years all similarly computed. 9

11 3 The Econometric Model This section introduces a new method to estimate the production function which allows for nonneutral technology differences both across firms and over time. I develop a model of firms optimal choice of both static and dynamic inputs to help identify the non-neutral technology, which is characterized by a multi-dimensional productivity measure at the firm level. The basic idea is that the optimal choice of inputs contains information about the unobserved non-neutral technology. As a result, we can recover the multidimensional productivity from the observed input choices to solve for the transmission bias. The first order conditions of firms optimal input choices also establish a link between the elasticity of substitution and the efficiency ratio, which helps identify both non-neutral technology and elasticity of substitution. I will focus on constant elasticity of substitution (CES) production function in this paper, with a discussion about how to apply the method to more general production functions in Section Production Function with Non-Neutral Technology I extend the Hicks neutral production function to allow for a full set of factor-augmenting efficiencies for all inputs, namely labor, capital, and material. In this case, improvement of factor efficiencies changes the marginal products of different factors asymmetrically, allowing for non-neutral technology heterogeneity both across firms and over time. Specifically, the CES production function for firm j at time t is characterized by Q jt = { [exp(ω jt)k jt ] γ + [exp(ν jt)l jt ] γ + [exp(µ jt)m jt ] γ} κ γ, (1) where Q jt denotes the output and K jt, L jt and M jt denote capital, labor, and material inputs, 1 respectively. The parameter γ captures the elasticity of substitution, which equals 1 γ. The production function may have non-constant return to scale, as captured by the parameter κ. ωjt, ν jt and µ jt, respectively, represent the capital-augmenting efficiency, labor-augmenting efficiency, and material-augmenting efficiency. They are the focus of this paper. The firm-time-specific productivity measure allows us to study both the cross-sectional non-neutral technology heterogeneity across firms and the evolution of non-neutral technology over time. In particular, when the efficiency ratio (ωjt : ν jt : µ jt ) differs across firms for a given date t, the ratio of marginal products of capital, labor, and material will be asymmetric across firms. So there is non-neutral technology heterogeneity across firms. Similarly, when the efficiency ratio (ωjt : ν jt : µ jt ) changes over time t, technology change will affect the marginal product of different inputs asymmetrically, leading to a non-neutral technology change over time. terminologies for easy reference. Following this idea, I define the following two 1

12 Definition 1 (Non-neutral Technology Heterogeneity (NNTH)) A production function displays non-neutral technology heterogeneity across firms at given time t if and only if at least one of the following three cases holds: (1) ωjt ν jt constant(t), (2) ω jt µ jt constant(t), and (3) µ jt ν jt constant(t). Definition 2 (Non-neutral Technology Change (NNTC)) A production function displays non-neutral technology change over time for given firm j if and only if at least one of the following three cases holds: (1) ωjt ν jt constant(j), (2) ωjt µ jt constant(j), and (3) µ jt ν jt constant(j). The production function with non-neutral technology in Eq. (1) accommodates several traditional concepts of neutral technology as its special cases. When ωjt ν jt and ω jt µ jt are both constant for all j and t, the production function displays a Hicks Neutral Technology. When both ωjt and µ jt are constant for all j and t but ν jt is not, the technology is Harold Neutral (labor-augmenting). Similarly, when both νjt and µ jt are constant for j and t but ω jt is not, the technology is Solow Neutral (capital-augmenting). As a result, the three traditional concepts of Neutral technology are all special cases of, and are nested in, Eq. (1). Further note that Eq. (1) allows the technology to differ in a very flexible way. The production function needs not to be neoclassical 7, as it is allowed to have retrogressive technological change. In fact, It is not even necessarily classical as it allows non-constant returns to scale. I further assume that the productivity vector (ωjt, ν jt, µ jt ) satisfies a vector auto regression process VAR(1),8 ω jt = ρ ω + ρ ωω ω jt 1 + ρ ων ν jt 1 + ρ ωµ µ jt 1 + ξ ω jt, ν jt = ρ ν + ρ νω ω jt 1 + ρ νν ν jt 1 + ρ νµ µ jt 1 + ξ ν jt, (2) µ jt = ρ µ + ρ µω ω jt 1 + ρ µν ν jt 1 + ρ µµ µ jt 1 + ξ µ jt. Here all ρ s are parameters and (ξjt ω, ξν jt, ξµ jt ) are the productivity shocks, which are iid across firms and over time, to corresponding efficiencies. Note that I also allow the efficiencies to have an impact on each other in next period. 7 A production function with constant returns to scale is said to be classical if it is continuous and has positive marginal products and diminishing marginal rates of substitution. The production function is said to be neoclassical if it further satisfies the non-retrogression condition, which says technological change is always positive. 8 It is straightforward to extend the VAR process to Markov process. Also, due to the short panel we have in the empirical analysis (seven years), I assume first order VAR process. In the case of longer panel data, it is also possible to extend this assumption further to allow for more general Markov process with higher order. 11

13 For expositional purpose, I reformulate the production function in Eq. (1) a little bit, by defining ω jt = ω jt µ jt, ν jt = ν jt µ jt, (3) µ jt = κµ jt. Then Eq. (1) can be equivalently rewritten as { } Q jt = exp(µ jt ) [exp(ω jt )K jt ] γ + [exp(ν jt )L jt ] γ + M γ κ γ jt. (4) The new term ω jt, which is named as capital-material efficiency ratio, is the capital efficiency normalized by material efficiency. It measures the non-neutrality of capital efficiency relative to material efficiency. Similarly, the labor-material efficiency ratio, ν jt, measures the non-neutrality of labor efficiency relative to material efficiency. The difference, ω jt ν jt, measures the nonneutrality of capital efficiency relative to labor efficiency and I call it capital-labor efficiency ratio. µ jt is the material efficiency augmented by returns to scale. In the following sections in this paper, I will focus on estimating the production function given by Eq. (4). The original productivity (ωjt, ν jt, µ jt ) can be recovered afterwards. 3.2 Identification Issue Suppose that the data contains output quantity (Q jt ), output price (P jt ), expenditures on capital, labor and material, wage rate, and material price. We want to identify the unobserved multidimensional productivity measure (ωjt, ν jt, µ jt ), or equivalently (ω jt, ν jt, µ jt ), and the production parameter (γ, κ) from the observed data. One of the challenges is to overcome the transmission bias caused by the correlation between the three dimensional unobserved productivity and input choice, because firms observe their productivity before choosing labor and material inputs. The nonparametric control function approach (Olley and Pakes, 1996) cannot be applied directly here, because it is subject to the controversial invertibility problem even in their single unobservable case as discussed in Ackerberg et al. (26). This problem becomes even more serious in the case of multidimensional unobservables. Moreover, even when the invertibility condition is established and the unobservables are recovered from observed variables, we still cannot identify the model in the case of multidimensional unobservables because we have multiple nonparametric functions to be estimated in a single equation, after replacing (ω jt, ν jt, µ jt ) by three nonparametric functions. The second challenge is the difficulty associated with identifying both the capital-labor efficiency ratio and the elasticity of substitution simultaneously. The reason is that both the capital-labor 12

14 efficiency ratio and elasticity of substitution are free to change, and both affect the optimal choice of inputs. The effect of a change in the elasticity of substitution on input ratio offsets the effect of a change of technology ratio, and vice versa. As a result, more than one combination of elasticity of substitution and the technology ratio are consistent with the observed data. Therefore, the model is not identified. In this paper I make use of the structure implied by firms optimal choice of labor and material as additional constraints to help achieve identification, besides using the nonparametric constraints implied by capital investment as in Olley and Pakes (1996). The basic idea is that these additional constraints establish a link between the efficiency ratio and the elasticity of substitution. As a result, when there is a change in the efficiency ratio we cannot change the elasticity of substitution arbitrarily to generate the observed data. This additional structure helps identify both the nonneutral technology and elasticity of substitution. One obvious advantage of this method is that the additional structure has a solid theoretical ground and is naturally implied by the microeconomic theory on firms objectives. 3.3 A Model of Optimal Inputs Choice Following the tradition, I assume that firms face monopolistic competition in the output market, and they are price takers in labor and material inputs market 9. I also assume that the firms choose labor and material statically to maximize period profits. The assumption of static labor choices, besides material decisions, is quite plausible in China compared with other countries. There are several practical reasons for this. First, the labor market in China is very competitive due to the high volume of labor supply in the market, which favors firms. Second, generally there is a lack of effectively-enforced laws and regulations to protect workers in China. Third, the labor union in China is very weak, and most of the cases they are controlled by firms. These factors together result in much lower hiring and firing costs in China, compared with developed countries, where the labor policies and unions generally favor workers. I further assume that capital is a dynamic fixed variable, which is fixed at the beginning of each period but can be adjusted through investment with one-period lag. The demand function for firm j s output is assumed to be the simple Dixit-Stiglitz type Q jt = Φ jt P η jt, where P jt is the output price endogenously chosen by the firm itself. constant demand elasticity. The parameter η is the Φ jt is a time-specific demand shifter observed by the firm before choosing labor and material at each period, which is further decomposed to be a time dummy Φ t common to all firms, a iid shock ξjt D, and effects of other observed firm characteristics, such as firm 9 The price-taker assumption in the labor and material inputs market does not preclude that firms may still have different wage rate and material price due to factors such as transportation costs, as discussed in Grieco et al. (215). 13

15 size, age, and ownership. Assume that Φ jt can be written in the following form ln Φ jt = Φ t + α size firm size + α age firm age + α own firm ownership + ξ D jt. At the beginning of each period, firms observe their own non-neutral productivity, capital stock, input prices, and demand shifter Φ jt, and then choose labor and material to maximize their own period profit. The output price for firm j, P jt, is endogenously determined by the market clearing condition for the differentiated product produced by this firm. After that, firms choose investment dynamically to maximize the accumulated expected future profit of their own. Denote W jt and P Mjt, respectively, as the wage rate and material price for firm j at time t. Firm j s optimal static decision at time t is to choose labor and material to maximize its period profit, max L jt,m jt {P jt Q jt W jt L jt P Mjt M jt } s.t. Q jt = exp(µ jt ) { [exp(ω jt )K jt ] γ + [exp(ν jt )L jt ] γ + M γ jt Q jt = Φ jt P η jt. } κ γ, The optimal labor and material demand is determined by the associated first order conditions, κ 1 + η η 1 η Φ 1 jt Q η jt κ 1 + η η { } [exp(ω jt )K jt ] γ + [exp(ν jt )L jt ] γ + M γ κ γ 1 jt exp(µ jt ) exp(γν jt )L γ 1 jt = W jt, (5) 1 1 { } η Φjt η jt [exp(ω jt )K jt ] γ + [exp(ν jt )L jt ] γ + M γ κ γ 1 jt exp(µ jt )M γ 1 jt = P Mjt. (6) Endogenous variables are L jt and M jt and exogenous variables are ω jt, ν jt, µ jt, W jt, P Mjt, and K jt. To simplify the analysis, I further assume that production function and demand function satisfy conditions such that there is a unique interior solution to Eq. (5) and (6). Investment, I jt, is chosen dynamically to maximize the expected firm value, given current state (ω jt, ν jt, µ jt, K jt ). So the optimal investment function can be written as a nonparametric function I jt = I(ω jt, ν jt, µ jt, K jt ). 3.4 Estimation Equation The parameters of interest include the production parameters (κ, γ), the demand elasticity η, the parameters in the productivity evolution process (ρ, ρ ω, ρ ν, ρ µ ), and the firm-time-specific nonneutral productivity measure (ωjt, ν jt, µ jt ). We have data on output quantity and price, material quantity and price, wage rate, number of workers, book value of capital stock, and investment. As mentioned above, the basic idea of the estimation is to utilize the first order conditions of labor and material choice to recover two efficiency ratios first and then use the nonparametric investment 14

16 function to control for the (scaled) material efficiency. Recover Efficiency Ratios ω jt and ν jt First we recover the two efficiency ratios, ω jt and ν jt, from the first order conditions associated with labor and material. Define the labor and material shares as S Ljt = W jtl jt P jt Q jt and S Mjt = P MjtM jt P jt Q jt. Multiplying both sides of the first order conditions in Eq. (5) and (6) by L jt and M jt, respectively, and dividing both sides by P jt Q jt yield the first order conditions in share form κ 1+η η exp(γν jt )L γ jt { [exp(ω jt )K jt ] γ + [exp(ν jt )L jt ] γ + M γ jt } = S Ljt, (7) κ 1+η η M γ jt { } = S Mjt. (8) [exp(ω jt )K jt ] γ + [exp(ν jt )L jt ] γ + M γ jt The advantage of the share-form first order condition is that the demand shifter, Φ jt, and the scaled material efficiency, µ jt, are absorbed in labor share and material share, which are both observed. So, we can solve out both of the two efficiency ratios, ω jt and ν jt, directly from the two first order conditions in share form if γ 1. In contrast, the original first order conditions do not have this nice feature. Dividing Eq. (7) by (8) and rearranging the yielded equation, we can solve out the labor-material efficiency ratio as a function of observables up to unknown parameters exp(γν jt ) = S Ljt S Mjt ( M jt L jt ) γ. (9) Plugging it into Eq. (8), we can solve out the capital-material efficiency ratio as a function of observables up to unknown parameters exp(γω jt ) = κ 1+η η S Ljt S Mjt S Mjt ( Mjt Replacing ω jt and ν jt in the production function by Eq. (9) and (1) yields K jt lnq jt = µ jt + κ ( γ ln κ 1 + η ) + κlnm jt κ η γ lns Mjt. ) γ. (1) As usual, we allow for an iid error in the above equation which may be caused by optimization error, specification error, or other statistical errors. By assumption, these errors are independent of firm choices. Then the above equation generates the following empirical estimation equation, lnq jt = µ jt + κ ( γ ln κ 1 + η ) + κlnm jt κ η γ lns Mjt + ε jt. (11) 1 This condition naturally excludes Cobb-Douglas production function, which is well known not to accommodate factor-augmenting efficiencies. 15

17 Solve the Transmission Bias Caused by µ jt The scaled material efficiency, µ jt, is correlated with labor and material choice and it is the only source of transmission bias remaining in Eq. (11) that prevents us from consistently estimate production parameters. We can use the structure implied by the dynamic optimal choice of capital investment, i jt = i(ω jt, ν jt, µ jt, k jt ), to control for µ jt, following the insights of Olley and Pakes (1996) and Ackerberg et al. (26). Assume investment is strictly monotonic in its third argument µ jt conditional on (ω jt, ν jt, K jt ), 11 so we can invert the investment function to solve for the scaled material efficiency, µ jt = µ(i jt, ω jt, ν jt, k jt ). On the right hand side, the efficiency ratios ω jt and ν jt are already parametrically recovered in Eq. (9) and (1). Plugging them into the µ( ) function, the unobserved scaled material efficiency µ jt is recovered as a nonparametric function of observed variables, µ jt = µ(i jt, ω jt, ν jt, k jt ) ( = µ i jt, ω jt (m jt, k jt, S Ljt, S Mjt ), ν jt (m jt, l jt, S ) Ljt ), k jt S Mjt S Mjt ( = µ i jt, l jt, m jt, S ) Ljt, S Mjt, k jt. (12) S Mjt Replacing µ jt in Eq. (11) by the above equation leads to the first stage estimation equation ln Y jt = φ(i jt, l jt, m jt, k jt, S Ljt, S Mjt ) S Mjt }{{} φ jt µ jt + κ γ 1+η ln(κ η ) κ γ ln S Mjt+κ ln M jt +ε jt (13) In the empirical exercise, I parameterize the function φ( ) as a polynomial function up to third order, φ( ; α), where α is the set of parameters in the polynomial function. Because by assumption, ε jt is independent of input choices as well as the input shares, we can estimate this equation directly using non-linear least square. 12 Then I can compute an estimate of φ jt, by φ jt = φ(i jt, l jt, m jt, k jt, S Ljt S Mjt, S Mjt ; ˆα). This actually allows us to separate the iid statistical error, ε jt, from the structural terms, with the statistical error being recovered as ε jt = ln Y jt φ jt. 11 The invertibility condition is generally satisfied. Basically we want to show that the investment function is strictly increasing in µ jt, conditional on (ω jt, ν jt, k jt). Consider an increase in µ jt by µ jt. It is equivalent to an increase in µ jt by 1 κ µjt because µjt = κµ jt. Note that ω jt = ω jt µ jt and ν jt = ν jt µ jt. Conditioning on (ω jt, ν jt, k jt) requires that both ω jt and ν jt also increase by the same amount, 1 κ µjt, as µ jt. So the invertibility condition here is equivalent to the condition that when capital, labor, and material efficiencies all increase by the same amount (looks like a Hicks-neutral technology change), investment increases strictly, which is the same condition as in Olley and Pakes (1996). 12 In the case when there might be correlation between ε jt and the shares of labor and material, we can use non-linear IV regression by choosing the corresponding lagged variables and prices as instrument variables. The estimation results are very similar to that from non-linear least square. These results are available upon request, and will be included in the online appendix. 16

18 Accordingly, the scaled material efficiency can be recovered as a function of observables up to unknown parameters, µ jt = φ jt + κ γ ln S Mjt κ ln M jt κ ( γ ln κ 1 + η ). (14) η Notice that µ jt = κµ jt and we can recover the original material-augmenting efficiency as µ jt = 1 κ µ jt = 1 κ φ jt + 1 γ ln S Mjt ln M jt 1 ( γ ln κ 1 + η ). (15) η Also, using the relationship between original efficiency levels (ω jt, ν jt ) and efficiency ratios (ω jt, ν jt ) in Eq. (3), and the recovered (ω jt, ν jt ) in Eq. (9), and (1), we can recover the unobserved capitaland labor-augmenting efficiencies, (ωjt, ν jt ), as follows ω jt = ω jt + µ jt = µ jt + 1 γ 1+η κ η ln S Ljt S Mjt S Mjt + ln M jt K jt, (16) where µ jt ν jt = ν jt + µ jt = µ jt + 1 γ ln S Ljt S Mjt + ln M jt L jt, (17) is defined in Eq. (15). Using the VAR(1) assumption on the factor-augmenting efficiencies defined in equation (2), we can recover the iid productivity shocks to each of the three efficiencies. They can then be used to construct moment conditions for estimating parameters. In addition, the demand shock can be recovered as follows from the demand function, ξjt D = ln Q jt (η ln P jt + Φ t + α size firm size + α age firm age + α own firm ownership). (18) This equation provides another group of moment condition to identify demand elasticity and other demand parameters, based on the iid feature of the demand shock ξjt D. Generalized method of moment (GMM) estimator The parameters to be estimated include the production parameters, (κ, γ), the demand parameters, (η, α size, α age, α own ) plus year effect, and the parameters in the VAR(1) productivity evolution process, all ρ s. The unobserved factor-augmenting efficiencies can be recovered from Eq. (15), (16), and (17) after estimating these parameters. In total we have fourteen parameters of interest plus year effects to be estimated. We can construct the moment conditions using the restrictions from the demand function and VAR(1) process of factor-augmenting efficiencies. As we have more moments than necessary if we use all three VAR(1) process for capital, labor, and material efficiencies, in the estimation I use the evolution process of (νjt, µ jt ) and the restriction from demand function to estimate the parameters. The additional restriction from the evolution of capital-augmenting efficiency ωjt is used to validate the property of the recovered efficiencies after estimation. 17

19 Using the VAR(1) assumption on labor- and material-augmenting efficiencies and the empirical demand function, we can compute the error terms for constructing GMM moment conditions as ξ jt = ξ µ jt ξ ν jt = κµ jt (ρ µ + ρ µω ω jt 1 + ρ µνν jt 1 + ρ µµµ jt 1 ) (ν jt µ jt ) (ρ ν + ρ νω ω jt 1 + ρ ννν jt 1 + ρ νµµ jt 1 ), (19) ξ D jt ξ D jt where ε D jt is defined in Eq 18 and (ω jt 1, ν jt 1, µ jt 1 ) are the lagged version defined in Eq. (15), (16) and (17). The associated moment conditions are written as Z jt = Z µ jt Z ν jt Z D jt, (2) where (Z µ jt, Zν jt, ZD jt ) are instrument variables associated with the evolution process for labor and material efficiencies and demand function, respectively. The resulting moment conditions are E(Z jtξ jt ) =. The parameters governing the evolution process of labor and material efficiencies, all ρ s, are naturally identified by their corresponding lag terms (ωjt 1, ν jt 1, µ jt 1 ), given other parameters. In order to make use of this idea and to improve efficiency, I concentrate out all ρ s in the GM- M estimation. Specifically, the optimizer in GMM will only iterate on (κ, γ, η, α size, α age, α own ) plus year effects. Given all these parameters, ρ s are estimated within each iteration using linear least square. By doing this, ρ s are identified with corresponding lagged efficiency terms automatically, so we just need to find instrument variables in Z jt to identify the other parameters: (κ, γ, η, α size, α age, α own ) plus year effect. In the empirical application, based on the functional form of the three moment conditions, I define (Z µ jt, Zν jt, ZD jt ) as follows Z µ jt = (φ jt 1, S Mjt 1, 1), ( Zjt ν = φ jt 1, S Mjt 1, ln( P ) Mjt ), 1, P Ljt Z D jt = (ln(p Ljt ), ln(p Mjt ), k jt, firm age, firm ownership, year effect). The parameter estimates are reasonably robust enough to different choice of instrument variables. Note that the concentrated-out parameters, ρ s, are also estimated in this estimation automatically using linear least square with other parameters in the GMM. I collect all model parameters in θ, including both the concentrated-out ones and all others. θ can then be estimated by minimizing 18

20 a sample version of the above moment conditions using generalized method of moment, ˆθ = min θ 1 N j,t Z jtε jt W 1 N j,t Z jtε jt. (21) Because we have over identification constraints, I add a positive definite weighting matrix W to improve efficiency. All parameters are estimated using iterated general method of moments. This is achieved by using the variance-covariance matrix of the moments estimated from the previous iteration to approximate the optimal weighting matrix in each iteration. Equipped with the estimated parameters, the efficiency ratios and the scaled material efficiency level, (ω jt, ν jt, µ jt ), can be recovered from Eq. (9), (1), and (14). The original level of factoraugmenting efficiencies, (ωjt, ν jt, µ jt ), can then be recovered accordingly from Eq. (3). 4 Empirical Results 4.1 Parameter Estimates I estimate the model using an unbalanced panel from the Chinese steel industry from The estimates of production parameters and evolution process of labor efficiency and material efficiency are reported in Table 4. The return to scale is close to one (κ =.9929), indicating that technology in this industry has almost constant return to scale. The estimated elasticity of 1 substitution, which is defined as 1 γ, equals.455. This is lower than that estimated in Klump et al. (27) (.51) under factor-augmenting efficiency using aggregate US data from It is much lower than that in Antràs (24) (.8 under factor-augmenting efficiency and under Hicks-neutral efficiency assumption) which also uses aggregate US data from The difference of the elasticity value may arise from the fact that I am estimating the elasticity of substitution at the firm level using micro data, while they are estimating the aggregate elasticity using aggregate data. The smaller-than-one elasticity of substitution suggests that inputs are gross complements to each other, which is the key to predict many firm behaviors. For example, it implies that labor-augmenting technology change is labor-saving and that firms using a technology with higher labor-augmenting efficiencies will use relatively less labor. A comparison with Table 3 also shows that omitting the non-neutrality feature of technology will substantially bias up the estimates of elasticity of substitution. While technology is assumed to be neutral in Table 3, OLS estimates of elasticity of substitution range from , which is more than 75% higher than that estimated in the full model when non-neutral technology is allowed. Random and fixed effect models partially correct for the omitted variable bias because they partially control for the unobserved labor-material efficiency ratio, which are quite persistent 19

21 over time as we will show later, by adding a random or fixed effect in the regression. In the random effect model, the elasticity of substitution is.6345, which is 46% higher than that estimated in the full model. In the fixed effect model, the estimated elasticity (.57) is closest to that derived in the full model, which still represents an upward bias of about 3%. This result is consistent with Antràs (24) who also estimates a lower elasticity of substitution after controlling for factoraugmenting efficiency using aggregate data from United States. The labor-augmenting efficiency is very persistent. It is estimated that about 82% of the labor efficiency can be carried over to next period (ρ vv =.8193), advocating that it could be an important firm characteristics which potentially influence firm activities persistently. In contrast, the material-augmenting efficiency, although still persistent, is less so. Slightly more than one third of the material-augmenting efficiency can be carried over to next period (ρ µµ =.3416). The cross efficiency effects in the labor and material efficiency evolution process are slightly negative according to the estimation. The demand parameters are reported in Table 5, which are jointly estimated with the production parameters. The estimated demand elasticity is η = in steel industry. It means that a 1% increase in output price ceteris paribus will reduce the firm demand significantly by about 5.6%. It also implies a gross markup of about 24% for the steel firms, which is close to that estimated in other studies. In the regression I also control for firm size, firm age, year effect, and ownership. It is shown that larger and older firms have a higher demand. relatively lower demand, other things being equal. State-owned firms (SOE) have After estimating all these parameters, I recover the capital-material efficiency ratio, labor material efficiency ratio, and the scaled material efficiency, (ω jt, ν jt, µ jt ), from Eq. (9), (1), and (14). Then by inserting them into Eq. (3), we can recover the original factor-augmenting efficiencies, (ωjt, ν jt, µ jt ), for each firm in each year. This firm-time specific multidimensional productivity measure completely describes the differences of technology used by firms in both levels and technological non-neutrality, both across firms and over time. Table 6 summarizes the basic correlations among the three efficiencies. Capital and labor efficiencies, which are the most important firm heterogeneity in technology as we will show later, are positively correlated. However, material efficiency is negatively correlated with the other two, indicating that technology non-neutrality does exist. Moreover, the last row of Table 6 shows a negative correlation between input ratios and corresponding efficiency ratios. This is consistent with the fact that the elasticity of substitution is smaller than one a labor-augmenting technology change actually reduces labor demand when inputs are gross complement. I will investigate the dispersion and evolution of the recovered non-neutral technology in detail in Subsection 4.2 and 4.3. Before moving on, let s take a look at the persistence of capital-augmenting efficiency. Recall that 2

22 we did not use the evolution process of capital-augmenting efficiency in the parameter estimation stage. Instead, after recovering (ωjt, ν jt, µ jt ) and their lags post estimation, I run a simple OLS regression of ωjt on all lagged efficiencies to check the property of ω jt predicted by the model, as a validation of the model performance. Table 7 reports the evolution process of capital-augmenting efficiency, ω jt. It turns out that the firm level capital-augmenting efficiency is quite persistent (ρ ωω =.5193), although not assumed in the model. 4.2 Non-neutral Technology Heterogeneity One focus of this paper is to investigate the heterogeneity of non-neutral technology across firms, both in levels and technological non-neutrality. This is the theme of this section. In addition, I also check their correlation with firm size, providing more visualized results to the non-neutral technology differences across firms Heterogeneity of efficiency levels I plot the kernel density of the recovered factor-augmenting efficiencies, (ωjt, ν jt, µ jt ), derived from Eq. (2) by pooling data from all years together in Figure 2. The within-year distributions, as will be reported in Figure 7, are very similar. There are two points to take away from this figure. First, there is substantial heterogeneity of factor-augmenting efficiency levels across firms, especially for capital- and labor-augmenting efficiencies. The interquartile range is 1.84 for capital-augmenting efficiency and 2.2 for labor-augmenting efficiency. For material efficiency, the interquartile range is.33. Note that although (ωjt, ν jt, µ jt ) are called factor-augmenting efficiencies in this paper for simplicity, they are actually the logarithm of factor-augmenting efficiencies. So an interquartile range of.33 in µ jt means that the original material-augmenting efficiency, as defined by exp(µ jt ), at the 75th percentile is roughly 33% higher than that at the 25th percentile, still showing substantial dispersion across firms. The second key point is that the technology heterogeneity across firms is mainly due to differences in capital- and labor-augmenting efficiencies. Their dispersion, as shown by interquartile range in the last paragraph, is much larger than that of material-augmenting efficiency. The standard deviation also shows the same results the value is 1.48 for capital-augmenting efficiency, 1.53 for labor-augmenting efficiency, and a much lower.4 for material-augmenting efficiency. All of these evidence points to the conclusion that technology heterogeneity in all efficiency levels is large across firms, and that capital- and labor-augmenting efficiencies are the relatively more important sources of differences in technology levels across firms. 21

23 4.2.2 Heterogeneity of technological non-neutrality Figure 3 plots the kernel density of the recovered capital-material efficiency ratio ω jt, labor-material efficiency ratio ν jt, and capital-labor efficiency ratio ω jt ν jt, by pooling data from all years together. The within-year distributions are very similar, as will be reported in Figure 8. These three ratios, from different angles, measure the technological non-neutrality across firms. The results suggest a large dispersion of technological non-neutrality across firms. The standard deviations of the three ratios are 1.63, 1.62, and 1.72, respectively, showing large dispersion of efficiency ratios across firms. Similarly, the interquartile range of the three ratios are 1.94, 2.11, and 2.2, again showing consistent large dispersion of efficiency ratios across firms. The large dispersion of efficiency ratios implies that technological non-neutrality, besides efficiency levels, is an important source of firm technology heterogeneity. Both of them deserve equally important attention when analyzing firm behaviors such as inputs demand, growth/shrinking, entry/exit, and trade decisions Firm size and non-neutral technology heterogeneity To further understand the heterogeneity of non-neutral technology across firms, I examine the relationship between firm size and non-neutral technology as an example to visualize the result. The first three graphs in Figure 4 plots the three efficiency levels versus firm size measured by logarithm of output quantity. The trends are fitted to polynomial curves for each graph. We see that the labor efficiency is almost monotonically increasing in firm size, suggesting that large firms organize workers more efficiently than small firms. The correlation between labor efficiency and logarithm of output quantity is.472. As a comparison, the material efficiency does not vary much for firms of different sizes. For the same size of firms, the dispersion of material efficiency is smaller too. The capital efficiency, in contrast, may be the most interesting one. It increases in firm size at the beginning and then decreases, showing a slight inversed-u shape relationship between firm size and capital-augmenting efficiency. In general, both capital- and labor-augmenting efficiencies contribute significantly to the technology heterogeneity across firms of different size, though in different patterns. The last graph in Figure 4 plots the capital-labor efficiency ratio against firm size, pooling data of all years together. There is an obvious negative correlation between firm size and capital-labor efficiency ratio. This suggests that large firms are better at organizing workers relative to managing capital. Because inputs are gross complements (elasticity of substitution is.455), technology with lower capital-labor efficiency ratio is more labor-saving and capital-using. This implies that large firms have a higher capital-labor ratio, which is well documented in the literature. 22

24 I further investigate the relationship between firm size and non-neutral technology in Table 8. In this table, I classify the sample within each year into five groups of equal observations and increasing firm size, as we did in Table 2. Then I compute the mean factor-augmenting efficiencies for each of size-year-specific group. Again, it is shown that larger firms have a much higher labor-augmenting efficiency on average within each year. In contrast, their material-augmenting efficiency is slightly lower. For capital efficiency, we also find that it is a slight inverse-u shape as found in Figure 4. Generally, Table 8 shows that there is large dispersion of factor-augmenting efficiency levels across firms, even within one year. Moreover, the differential correlation between firm size and efficiencies suggests that technology dispersion across firms, even within a year, is non-neutral. Large firms use technologies which relatively save labor more. 4.3 Non-neutral technology change A second focus of this paper is to understand how the heterogeneity of non-neutral technology evolves over time, both in levels and technological non-neutrality Growth of factor-augmenting efficiencies The yearly mean of capital-augmenting efficiency (ωjt ), labor-augmenting efficiency (ν jt ), and material-augmenting efficiency (µ jt ) are computed separately to illustrate the evolution of nonneutral technology level over time. All means are weighted by output quantity. Figure 5 plots the mean efficiencies for each year from 21 to 27. We can see generally the levels of capital- and labor-augmenting efficiencies are growing during this period, with some variations in some years. As shown in Table 9, labor-augmenting efficiency grows the fastest during the data period, at a annual rate of 17.81% on average. Capital-augmenting efficiency also grows substantially, at a rate of about 3.85% per year on average. In contrast, the growth of material-augmenting efficiency is much smaller, at a annual rate of.83% for weighted average, and.78% for simple average. 13 These results suggest that capital and labor efficiencies are the major driving forces of productivity growth in Chinese steel industry from This again is in line with the findings in the last subsection both suggest capital- and labor- efficiencies are the more important sources of technology differences relative to material-augmenting efficiency, both across firms and over time. However, although the material-augmenting efficiency only contributes marginally in the technology evolution over time, its sizable dispersion across firms identifies itself as a non-negligible components of a valid productivity measure especially when we are interested in understanding firm heterogeneities. 13 This implies a total productivity growth rate of around 2% per year, if we approximate it by the weighted average of the three growth rates using inputs share as the corresponding weights. 23

25 4.3.2 Non-neutral technology change In addition to the evolution of efficiency levels, we further explore the evolution of technological non-neutrality over time in this subsection, as captured by the relative efficiency ratios. Figure 6 plots the yearly mean of capital-labor efficiency ratio (ω jt ν jt ), capital-material efficiency ratio (ω jt ), and labor-material efficiency ratio (ν jt ) for years between 21 to 27. All means, again, are weighted by output quantity. These three ratios are either increasing or decreasing significantly, lending support to non-neutral technology change over time. In particular, the labor-material efficiency ratio (ν jt ) grows very quickly, supporting the idea that technology change is non-neutral towards saving labor relative to material (note that the elasticity of substitution is less than one). The capital-material efficiency ratio grows but at a much lower speed, suggesting that technology progress saves capital only slightly relative to material in the data period. Finally, the capital-labor efficiency ratio decreases sharply in the data period, providing further evidence that technology progress in Chinese steel industry from is non-neutral. It saves labor more than saving capital Firm size and non-neutral technology change Table 8 also investigates the differential evolution pattern of non-neutral technology for firms of different size. The yearly mean of factor-augmenting efficiencies are reported for each of the five groups of different firm size within each year. It is shown that labor efficiency is on average increasing over these years, both for the whole sample and for each size group. However, the growth rate differs significantly across firm groups. For the smallest 2% of firms, the annual growth rate of labor efficiency is 13.1% on average in these years. In contrast, the largest 2% of firms have a growth rate of 25.49%. The average growth rates of labor efficiency for the other three medium groups are very close ranging between 15.1%-16.6%. In general, labor efficiency grows faster in large firms, especially the top 2% firms in output size. For material efficiency, the growth rate also differs in firm size and shares similar growth pattern as labor efficiency large firms grow faster on average. While the four groups of smaller firms have a lower growth rate between.34%-.81%, the largest 2% of firms enjoy an faster growth at 1.33% annually. Capital efficiency, in contrast, shows a very different growth pattern across firms of different size. The smallest group and the largest group enjoy a relatively higher growth rate than medium-size firms 7.82% for the smallest group and 6.89% for the largest group. In contrast, the other three groups representing the medium 6% of firms have annual average growth rates below 2.2%. In sum, these results suggest that the growth of factor-augmenting efficiency levels are heterogenous 24

26 across firms of different size. In addition, the differential growth rates of the three efficiencies also indicate that technology change over time is non-neutral. It is basically biased towards saving labor for all groups of firms. However, the change of the bias rate is different. While for the smallest 2% of firms, the labor-capital efficiency ratio increases by about 5.19% (=13.1%-7.82%), the increase for the largest 2% of firms is 18.6% (=25.49%-6.89%). This result suggests that evolution of technological non-neutrality is uneven across firms of different size. In general on average, larger firms are becoming relatively more and more labor-saving, compared with smaller firms. 4.4 Convergence/Divergence of Non-neutral Technology The persistence of factor-augmenting efficiencies, as shown in Table 4 and 7, already implies that the non-neutral technology is a persistent feature for individual firms. A related question we want to clarify is: will the heterogeneity of technology across firms, both in levels and non-neutrality, converge over time? The short answer is: yes for technology levels, but no for technology nonneutrality. Figure 7 plots the estimated kernel density of factor-augmenting efficiency levels, year by year, from 21 to 27. As in the pooled data, again we see a large dispersion of efficiency levels across firms for all three factor-augmenting efficiencies. The within-year standard deviation (interquartile range) ranges from ( ) for capital-augmenting efficiency, ( ) for labor-augmenting efficiencies, and ( ) for material-augmenting efficiency. They are very close to that calculated from the pooled data reported in 4.2. The standard deviation and interquartile range for all efficiencies are overall decreasing in the data period. This suggests that the technology levels used by different firms in this industry is converging over time, although only slightly. Taking capital-augmenting efficiency as a example, the standard deviation and interquartile range are 1.54 and 1.9 in 21, respectively. These numbers reduce to 1.42 and 1.77 in 27, respectively, representing an about 12% decrease in dispersion. The estimated kernel densities of the three technological non-neutrality measures the capitalmaterial efficiency ratio, labor-material efficiency ratio, and capital-labor efficiency ratio are plotted in Figure 8. Again we see that there is large within-year dispersion in all three ratios across firms, as found in the pooled data. The range of stand deviation and interquartile range are close to that in the pooled data. The shifts of the distribution over year shows that technology change is non-neutral towards saving labor and capital relative to material. The evolution of these distributions displays a interesting pattern. Relative to material-augmenting efficiency, the capital- and labor-augmenting efficiencies are both converging during the data pe- 25

27 riod, as captured by capital-material efficiency ratio and labor-material efficiency ratio reported in the first two columns of Figure 8. These convergence trends, however, are mainly driven by the convergence of capital- and labor-augmenting efficiencies, because the evolution of material efficiency is small. In contrast, the capital-labor efficiency ratio actually diverges significantly in the data period. While its standard deviation (interquartile range) is 1.66 (2.8) in 21, these number increases to 1.72 (2.22) in 27. This finding is stark. It suggests that although the level of capital and labor efficiencies are both converging over time, the technological non-neutrality (measured by the capital-labor efficiency ratio) is actually diverging. This result further supports the idea that technological non-neutrality, as an important technology aspect besides technology level, should not be ignored in order to understand firms technology difference and predict firm behavior based on that. 5 Labor Demand under Non-neutral Technology While technology level in general determines the absolute level of input demand, the technological non-neutrality contributes to the relative usage of different types of inputs. In this section, I investigate how firms labor demand responds to their estimated non-neutral technology measures. In particular, I will focus on how the technological non-neutrality across firms contributes to the observed differences in labor-material ratios and labor demand across firms. 5.1 Labor Demand The structural analysis of firms optimal choice of labor and material described in Section 3 implies that labor demand is a complicated function of capital stock, wage rate, material price, all three factor-augmenting efficiencies, as well as a yearly demand shifter common to all firms. In this section, to simplify the analysis we run a linear reduced-form version of the structural model to analyze labor demand, which already performs reasonably well in explaining the variation of labor demand. Table 1 reports the results. The first four columns report the labor demand function, when technology is allowed to be non-neutral. Column 1 is the basic model, while columns 2-4 are extensions by controlling for different covariates year dummy, firm age, and ownership. The results are very robust. The first observation is that the three factor-augmenting efficiencies, which capture the non-neutral technology, contribute to the labor demand in very different ways, both quantitatively and qualitatively. Labor-augmenting efficiency is negatively correlated with labor demand. This is sensible given that the elasticity of substitution is smaller than one (.455) firms with higher labor-augmenting efficiency will employ less workers because inputs are gross complements. The estimated coefficients implies that a 1% increase in labor-augmenting efficiency reduces labor de- 26

28 mand by about.34%. This is the net effect of two offsetting forces. On one hand, the increased labor-augmenting efficiency reduces the total cost of production, calling for higher demand for all inputs generally. On the other hand, the increased labor-augmenting efficiency tends to reduce labor demand. Because the elasticity of substitution is smaller than one, the latter force dominates and the labor demand decreases in labor-augmenting efficiency. In contrast, capital- and -material efficiencies are positively correlated with labor demand. When captial- and/or materia-efficiency is higher, the marginal output of labor will increase, which leads to an increase in labor demand. The estimates show that a 1% increase of capital-augmenting efficiency increases labor demand by about.36%. This effect is much smaller for material efficiency at only about.6%. These different effects of factor-augmenting efficiencies on labor demand suggest that non-neutral technology is of vital importance in analysing labor demand at least at the firm level. It is also shown that higher inputs prices reduce labor demand. The estimates show that when wage rate increases by 1%, the labor demand will be reduced by about.24% because of both substitution effect and reduced output due to higher production costs. Not surprisingly, higher material price also reduces labor demand, but at a much smaller magnitude. An increase of material price by 1% reduces the labor demand by about.7% after controlling for year dummy, age, and ownership. This result is driven by the fact that the labor and material are gross complement. When material price increases, the substitution effect increases labor demand and the increasing cost due to the higher material price reduces labor demand. Because inputs are gross complements, the substitution effect is small. The total effect of an increase in material price on labor demand is dominated by the cost-increasing effect, which reduces labor demand. In comparison, I report the demand function estimates under Hicks-neutral technology in the last three columns of Table 1, using OLS, random effect, and fixed effect model, respectively. It is shown that price effects are significantly biased in this case. The own price effect effect of wage rate on labor demand is estimated in the range of -.19 to -.21, substantially biased downwards compared with the case when non-neutral technology is allowed. The cross price effect effect of material price on labor demand is estimated at -.1 in OLS, -.3 in random effect model, and a positive.7 in fixed effect model. Due to the omitted variable problem when nonneutral technology is not allowed, the estimates are not robust when using different estimation methods. If we compare the R square in these regressions, we find that after considering nonneutral technology, the R square is reasonably high (>.82) in all these regressions. In contrast, the R square is much lower (<.7) in the regressions when technology is restricted to Hicksneutral. This simple comparison implies that technology non-neutrality alone can explain about 14% more of the variation in labor demand. 27

29 5.2 Input Ratio Labor demand is a concept of levels, which largely depends on level variables such as gross productivity level and capital stock. In contrast, input ratio is a concept of relative input usage, which in principle would be more seriously affected by technological non-neutrality. In the this subsection, I will show how well the technological non-neutrality explains input ratios at the firm level. Allowing for factor-augmenting efficiencies in CES production function, the first order condition of flexible labor and material choices imply the following labor-material ratio ln L jt M jt = σ ln P Ljt P Mjt + (σ 1)ν jt, where σ = 1 1 γ is the elasticity of substitution. In the special case of Hicks-neutral technology, the labor-material efficiency term ν jt is assumed to be constant across firms and over time. Table 3 has shown that, under Hicks-neutral technology, the variation in input prices together with other controlling variables, can explain only a small portion of the variation in labor-material observed in the data. In Table 11, I examine how well the recovered non-neutral technology measure performs in explaining the the labor-material ratio, by conducting a reduced-form regression of ln L jt M jt on the input price ratio, ln P Ljt P Mjt, and the recovered labor-material efficiency ratio, ν jt. The regression shows that the R square is close to one, suggesting that adding the technological non-neutrality together with the price ratio explains the variation in labor-material ratios almost perfectly. The good fitness of this equation is not surprising, because this equation plus the Markov process of ν jt is used as a moment condition in the structural estimation in Section 4. However, the almost perfect fitness in this regression does indicate that the estimated elasticity of substitution and labormaterial efficiency ratio do a good job in matching the model with the data. A comparison of Table 11 with Table 3 indicates that the recovered technological non-neutrality alone explains roughly 7% of the variation in labor-material ratio, while input prices and other controlled variables together account for less than 3%. The estimated coefficient on the labor-material price ratio is.455, which implies almost exactly the same elasticity of substitution derived in the structural model estimation. Similarly, the coefficient on ν jt is.5495, implying the same value of elasticity of substitution too. This result suggests that introducing technological non-neutrality does correct the upward bias in the estimate of the estimated elasticity of substitution, which is usually identified and estimated in the labormaterial equation based on input price ratios. Moreover, recall that Table 2 shows that labor-material ratio is negatively correlated with firm size, and decreases significantly over time from The negative effect of ν jt on labor-material ratio, together with the observation that labor-material efficiency is increasing in firm size and 28

30 over time as shown in Table 8, contributes to the observed decreasing labor-material ratio both in firm size and over time shown in Table Counterfactuals: Contribution of Non-Neutral Technology to Labor Demand in Chinese steel industry This section examines the contribution of Non-Neutral Technology Change to labor demand in Chinese steel industry from 21-27, based on two counterfactual experiments. The idea is to evaluate by how much the labor demand will be changed if there is no heterogeneity in technology non-neutrality across firms and/or over time, in order to produce the same amount of output as observed in the data for each firm. Because we allow the Hicks neutral productivity to be changed in the counterfactual in such a way that the firm still produce the same amount of output as observed in the data after removing technology non-neutrality, this exercise isolates the effect of non-neutral technology. Throughout the counterfactual experiments, I assume that the input prices, demand shifters, and parameters (κ, γ, η) remain the same as those generated the data. This assumption relieves us from considering the input markets equilibrium, while still sheds light on the effect of non-neutral technology on labor demand. 14 The detail of the two counterfactual experiments is summarized in Appendix C. In the first counterfactual experiment, I evaluate the influence of removing non-neutral technology completely, both across firms and over time. To achieve this goal, I assume that all firms have the same factor-augmenting efficiency ratios, (ω : ν : µ ), which are chosen as the median of the factoraugmenting efficiencies in the year 21. Then I construct a counterfactual Hicks-Neutral productivity measure, ω jt, in such a way that given ω jt, demand shifter, and input prices, each firm s profit maximizing output equals the ones observed in the data. The predicted labor demand for each firm in the counterfactual is L jt = L( ω jt ) and the industry-level mean labor demand is L t = j L( ω jt)/(number of firms). The predicted demand in the counterfactual differs from that observed in the data. The difference represents the contribution of non-neutral technology to labor demand. In the second counterfactual experiment, I quantify the effect of non-neutral technology dispersion to labor demand. To do so, I do a similar experiment as above, except that only non-neutral technology dispersion across firms is removed within each year but the non-neutral technology 14 The cost, of course, is the difference between the results from the general equilibrium analysis and partial equilibrium analysis. Considering the price adjustment in input market equilibrium, the actual effect on labor demand of non-neutral technology will be smaller than what we predict here, because price adjustment will partly offset this effect. In a similar manner, if we allow firms to adjust their investment in the counterfactual, the estimated effect of non-neutral technology on labor demand will also be smaller. Because the main focus of this paper is to examine the nature of technology, I abstract myself from the temptation of developing a full general equilibrium model with inputs markets clearing condition, in order to simplify the analysis. 29

31 change over time is kept. More specifically, within each year t, I assume that all firms have the same factor-augmenting efficiency ratios, (ω t : ν t : µ t ), which are chosen as the median of the factor efficiency ratios of all firms in year t. Then I similarly compute the optimal labor demand L jt = L( ω jt ) for all firms in year t, by choosing their Hicks-neutral efficiency in such a way that the generated optimal output in the counterfactual equals the one observed in the data for each firm. The industry level mean labor demand in year t, after removing non-neutral technology dispersion across firms, is L t = j L( ω jt)/(number of firms). I do the same for all years, year by year. Within each year, there is no non-neutral technology dispersion across firms. But over time, there is still non-neutral technology change. The difference between the predicted labor demand in the counterfactual and that in the data represents the contribution of non-neutral technology dispersion across firms. For more detail about how to construct these measures, please refer to Appendix C. The counterfactual results are reported in Table 12. The counterfactual (1) reports the mean labor demand at the industry level for each year predicted by the first counterfactual experiment, which removes both the dispersion and evolution of non-neutral technology. It shows that removing nonneutral technology completely will substantially increases labor demand. Fixing the technological non-neutrality at the level of 21, the labor demand in 27 would have been about 115% higher than that observed in the data as reported in the second column of Table 12. This difference is mainly driven by the labor-biased technology change over these years. The counterfactual (2) reports the predicted labor demand when only non-neutral technology dispersion across firms is removed (but keep the non-neutral technology change over time). Its effect is mixed. In 21-22, removing the non-neutral technology dispersion reduces the industry labor demand slightly. In the latter 5 years, removing the non-neutral technology actually increases industry labor demand, meaning that non-neutral technology dispersion across firms serves to reduce labor demand after 23. For example, from 24-27, removing non-neutral technology dispersion across firms alone within each year will increase labor demand by about 2% on average, in order to produce the same amount of output. Of course, we need to admit that the counterfactual results are based on fixed input prices and output level. If we allow adjustment of input prices and output level, the predicted effect of nonneutral technology on labor demand will be smaller. However, the growth rate of wage rate will be even higher if there is no non-neutral technology change and dispersion. In general, the counterfactual results indicate that non-neutral technology has a significant impact on labor market, by saving labor and moderating the growth of wage rate. 3

32 6 Extension: more general production function This section shows that the method developed in this paper can be applied to more general production function forms. I will focus on showing the conditions under which the capital-material efficiency ratio and labor-material efficiency ratio, (ω jt, ν jt ), can be recovered from observed variables up to parameters. 15 Suppose the production function is in the flexible form Y jt = F [ exp(ω jt)k jt, exp(ν jt)l jt, exp(µ jt)m jt ], which is homogeneous of degree κ. Then it can be rewritten into the transformed form similar to Eq. (4), Y jt = exp(µ jt )F [exp(ω jt )K jt, exp(ν jt )L jt, exp(m jt ]. Here the triple (ω jt, ν jt, µ jt ) are defined exactly the same as that in Eq. (3). Assuming firms choose material and labor optimally to maximize period profit, we can derive two first order conditions in share forms, F 2 (exp(ω jt )K jt, exp(ν jt )L jt, M jt ) exp(υ jt )L jt F (exp(ω jt )K jt, exp(ν jt )L jt, M jt ) F 3 (exp(ω jt )K jt, exp(ν jt )L jt, M jt ) M jt F (exp(ω jt )K jt, exp(ν jt )L jt, M jt ) = S Ljt, (22) = S Mjt. (23) There are two unknowns, (ω jt, ν jt ), in this two-equation system. In principle we can solve for them uniquely if this two-equation system is not degenerated. This can be guaranteed if the following two conditions are satisfied: (1) F ( ) is strictly increasing in all its arguments and is strictly concave and, (2) El jtω Ejtω m El jtν Ejtν m, where Ejt i is the output elasticity of input i {l, m} and Ei jtx = Ei jt x is the derivative of output elasticity Ejt i with respect to efficiency x. The first condition is quite standard in the literature. The second condition basically ensures that the capital- and laboraugmenting efficiencies affect the output elasticity of inputs differently. In the special case of CES, this condition is just that the elasticity of substitution does not equal one. Given this condition, the idea to solve for ω jt and ν jt from the above share-form first order conditions is clear. Because ω jt and ν jt affect the output elasticity differently and the output elasticity determines the revenue share of inputs, we can infer ω jt and ν jt from the relative revenue share of labor and material, which are observed in the data. Given these conditions, the labor-material efficiency ratio ν jt can be solved out directly by dividing Eq. (22) by (23). ω jt can be solved out by inserting ν jt back into either one of the two first order conditions. 15 The subsequent steps, namely inserting (ω jt, ν jt) into the production function to get a similar equation of 11 and estimating the parameters based on the resulted equations, are quite straightforward following a similar procedure developed in Olley and Pakes (1996) and applied in Section 3 in this paper. These subsequent steps are omitted here to save space. 31

33 7 Conclusion In this paper I investigate the non-neutrality nature of technology difference both across firms and over time. I develop an approach to estimating the production function with non-neutral technology heterogeneity at the firm level. This approach relies on both parametric and nonparametric methods to control for the unobserved multidimensional productivity measures, based on firms optimal static choices of material and labor, as well as the dynamic choice of capital investment. This approach allows us to recover the multidimensional factor-augmenting efficiencies which capture the non-neutral technology differences at the firm level for each date, besides estimating all the model parameters. The empirical evidence from Chinese steel industry between first confirms that there is large heterogeneity of non-neutral technology across firms, both in efficiency levels and technological non-neutrality. Second, technology change over time is non-neutral labor efficiency grows much faster than capital efficiency. The change of material efficiency is minimal. As a result, technology change is labor-saving given that the estimated elasticity of substitution is smaller than one. I also find that the evolution of non-neutral technology, both in efficiency levels and technological non-neutrality, differs substantially across firms of different size. More importantly, while capital and labor efficiency levels are converging slowly during the sample period, I found no obvious converging trend of the technological non-neutrality over time in the data period. This suggests that heterogeneity in technological non-neutrality is quite a pervasive and persistent feature at the firm level, which should be paid enough attention when analyzing firm productivity and other applications based on it. Moreover, restricting technology to be Hicks-neutral will substantially overestimate the elasticity of substitution and underestimate the wage rate effect on labor demand. I apply the recovered non-neutral productivity measures to analyze labor demand at the firm level in the data sample. It is shown that non-neutral technology alone explains around 14% of the variation in labor demand across firms. More importantly, the non-neutral technology explains over 7% of the variation in labor-material ratios. The counterfactual experiments show that the labor demand in 27 would have been about 115% higher than that observed in the data in order to produce the same amount of output, should there be no non-neutral technology differences both across firms and over time starting 21 if we do not consider the price adjustment in the inputs market. 32

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37 Appendices A Sample Construction The basic data used in the empirical exercise is the firm-level survey data in Chinese steel industry from 2 to 27. I refine this dataset by the following treatment: Missing and negative values: drop any observation with missing or non-positive value for any of the following variables: number of workers, capital stock, revenue, wage expenditure, intermediate inputs expenditure. Firm size: drop any observation when revenue is smaller than 1,, or number of workers is smaller than 5. Factor-revenue share: drop any observation when labor share in revenue is higher than 99%, or material share is higher than 99%, or the sum of labor and material shares is less than 1%, or any of them is less than.5%, or capital share is less than.5%. After this treatment, we have a sample of 33,133 from 2 to 27. This is the basic dataset we use in this paper. I summarize the data facts using this basic data, in order to give a more complete description of the technology pattern for the whole industry. In the estimation, however, investment data is used to help control for part of the unobserved multidimensional non-neutral technology measure. So I construct the investment data at the firm level using perpetual inventory method. Specifically, I compute the investment for firm j at year t, I jt, using the following formula I jt = (year end capital) jt (year end capital) jt 1 + (capital depreciation) jt. Then I drop those observations with missing investment information. This eventually leaves me with a sample of 22,434 observations from 21 to 27. The parameter estimations are based on this refined dataset. Also, because the formula to recover the non-neutral technology requires knowledge of investment, we eventually can recover the multidimensional measure of non-neutral technology at the firm level from 21 to 27 in this refined sample. B Variable Definition The major variables used in this paper is defined as follows: Revenue (R jt ): total sales within year t for firm j. Capital stock (K jt ): year-end depreciated book value of capital stock in year t for firm j. Labor employment (L jt ): number of workers employed in year t for firm j. Total wage expenditure (T W jt ): total expenditure on wages and benefits to workers in year t for firm j. Wage rate (W jt ): average wage rate for firm j in year t. It is computed by dividing the wage expenditure by labor employment. Material expenditure (MV jt ): includes all expenditure on intermediate inputs, but not capital 36

38 equipments or other fixed/long-term investment. Capital investment (I jt ): constructed using perpetual inventory method from capital stock. It is computed as the difference between the year-end capital stock in year t and t-1, plus yearly depreciation in year t. Labor share (shl jt ): the ratio of total wage expenditure to revenue. Material share (shm jt ): the ratio of material expenditure to revenue. Material price (P Mjt ): proxied by the province-level material price index where the firm locates. Because the market for Chinese steel industry is very organized locally, the provincelevel material price should be very close to firm-level price. The same for output prices. Material quantity (M jt ): the ratio of material expenditure to material price. Output price(p jt ): proxied by the province-level output price index where the firm locates. Output price (Q jt ): the ratio of revenue to output price. Firm age (age jt ): defined as the difference between the data year and the year in which the firm started up. Firm ownership-state owned enterprise (own soe jt ): a dummy equals 1 if more than 1% of the stock share is owned by the state. Firm ownership-foreign direct investment (own fdi jt ): a dummy equals 1 if more than 1% of the stock share is owned by foreign firms or other foreign agencies. C Construction of counterfactual Hicks-neutral productivity and labor demand The idea is to eliminate non-neutral technology change over time and/or non-neutral technology dispersion across firms, and evaluate its effect on labor demand. I use two counterfactual experiments to illustrate this effect. In the first one, I remove the non-neutral technology completely, both across firms and over time. In the second, I remove the non-neutral technology dispersion across firms, but keep the non-neutral technology change over time. Counterfactual (1): remove non-neutral technology completely In the first step, I choose the first year (21) as the base year and assume that all firms share the same factor-augmenting efficiencies, (ω, ν, µ ). (ω, ν, µ ) is chosen as the median of (ω jt, ν jt, µ jt ) in year 21 (t = 21) estimated in the full model. So the production function in the counterfactual world is Q jt = exp( ω jt ) {[exp(ω )K jt ] γ + [exp(ν )L jt ] γ + [exp(µ )M jt ] γ } κ γ, where ω jt is the counterfactual Hicks-neutral productivity. Given the production function, demand shifter, and input prices, I solve firms profit maximization problem in the counterfactual world as 37

39 follows max {P jt Q jt W jt L jt P Mjt M jt } L jt,m jt s.t. Q jt = exp( ω jt ) {[exp(ω )K jt ] γ + [exp(ν )L jt ] γ + [exp(µ )M jt ] γ } κ γ, Q jt = Φ jt P η jt. The optimal labor and material demand is determined by the associated first order conditions, κ 1 + η ηφ κ 1 + η ηφ 1 η jt 1 η jt 1 η Qjt {[exp(ω )K jt ] γ + [exp(ν )L jt ] γ + [exp(µ )M jt ] γ } κ γ 1 exp( ω jt + γν )L γ 1 jt = W jt (C.1) 1 η Qjt {[exp(ω )K jt ] γ + [exp(ν )L jt ] γ + [exp(µ )M jt ] γ } κ γ 1 exp( ω jt + γµ )M γ 1 jt = P Mjt (C.2) These two equations determine the optimal demand of labor and material as functions of ω jt, given that (P jt, P Mjt, W jt, K jt, Φ jt ) and all model parameters are known. The only variable that we have not constructed is the demand shifter Φ jt. It can be constructed from the demand function in the full model, after estimating all parameters and the unobserved factor-augmenting efficiencies, Φ jt = Q jt P η. With a little abuse of notation, I denote the optimal demand of labor and material jt as L jt = L( ω jt ) and M jt = M( ω jt ), by suppressing other state variables. Similarly the optimal output level is denoted as Q jt = Q( ω jt ). By letting the counterfactual output equal the output observed in the data for each firm, we have Q( ω jt ) = Q jt. The counterfactual Hicks-neutral productivity can be solved out from this equation. Note that the counterfactual Hicks-neutral productivity eliminates non-neutral technology dispersion across firms, and at the same time ensure the same output for each firm as in the data. Labor demand at the individual firm level L jt = L( ω jt ) and that at the aggregate level L t = j L( ω jt), however, differ from those observed in the data. To speed up the computation, I use the following practical procedure to recover ω jt and compute the counterfactual labor demand, which is equivalent to the above model. In the two first order conditions, replace Φ jt = Q jt P η and replace the big term in the braces jt by Q jt using the production function. The two first order conditions become Or equivalently, κ 1 + η η κ 1 + η η P jt { P jt { } γ Qjt κ ( κ γ 1) exp( ω jt + γν )L γ 1 jt exp( ω jt ) = W jt } γ Qjt κ ( κ γ 1) exp( ω jt + γµ )M γ 1 jt exp( ω jt ) = P Mjt κ 1 + η P jt Q 1 γ κ jt exp( γ η κ ω jt) exp(γν )L γ 1 jt = W jt κ 1 + η P jt Q 1 γ κ jt exp( γ η κ ω jt) exp(γµ )M γ 1 jt = P Mjt 38

40 Then we can solve out labor demand and material demand accordingly, L jt = M jt = [ κ 1 + η η [ κ 1 + η η P jt γ κ Q 1 jt exp( γ W jt κ ω jt) exp(γν ) P jt γ κ Q 1 jt exp( γ P Mjt κ ω jt) exp(γµ ) ] 1 1 γ ] 1 1 γ (C.3) (C.4) Replacing L jt and M jt in the production function by Eq. (C.3) and (C.4) leads to an equation with ω jt. From this equation, we can solve out ω jt. Then the individual labor demand can be recovered from Eq. (C.3). The industry labor demand for each year can be computed accordingly. Counterfactual (2): remove only the non-neutral technology dispersion The solution procedure is very similar to that in counterfactual (1), except that we do the above computation year by year. In each year, we fix the factor-augmenting efficiency ratios at (ω t, ν t, µ t ), which is the median of corresponding efficiencies in year t. Then we do the above solution procedure for observations in year t only. We repeat this for each year and compute the labor demand for each year when there is no non-neutral technology dispersion across firms within each year, while keeping non-neutral technology change over time. The counterfactual results are reported in Table 12. Table 1: Summary statistics of major variables variable notation num.obs mean std p25 p5 p75 revenue R jt ,192 2,221,867 13,63 32, 91,34 capital K jt ,739 1,272,984 1,682 4,738 16,37 employee L jt , investment I jt , , labor share shl jt material share shm jt wage rate W jt material price P mjt output price P jt output quantity Q jt , , material quantity M jt ,71.4 1, All variables are defined in Appendix B. 2 All means are simple average. std refers to standard deviation. p25 refers to the 25th percentile. Others similarly defined. 39

41 Table 2: Heterogeneity in labor share and labor-material ratio: cross firms and over time year mean labor share for each group all groups labor share all years labor-material ratio all years Firms are divided into five groups by firm size defined by sales, with each group having 2% of firms in the sample. 2 Labor share is defined as the ratio of labor expenditure to revenue. 3 All means are simple average for each year-size group. Table 3: Input prices and input ratio: reduced-form regression 1 variable OLS (1) (2) (3) (4) random effect fixed effect σ (.74) (.74) (.74) (.74) (.65) (.75) constant (.189) (.262) (.262) (.272) (.228) (.246) year dummy Yes Yes Yes Yes Yes age Yes Yes Yes Yes ownership Yes Yes Yes sigma-u sigma-e rho R-square Dependent variable: labor-material ratio; independent variable: labor-material price ratio and other control variables. Standard deviations are reported in parenthesis. 2 sigma-u: the between group variance in fixed and random coefficient model; sigma-e: the within group variance. rho: fraction of variance due to between group variance. 3 Overall R-square in fixed and random coefficient models. 4

42 Table 4: Estimates of the production function and productivity evolution process parameter estimates standard deviation κ γ labor efficiency: νjt ρ νω ρ νν ρ νµ ρ ν material efficiency: µ jt ρ µω ρ µν ρ µµ ρ µ The implied elasticity of substitution is 1 1 γ. Table 5: Estimates of the demand function parameter estimates standard deviation η size effect age SOE year effect Yes - constant Yes - 1 Here firm size is measured by the logarithm of capital stock, log(k). Table 6: Correlation: efficiencies and input ratio correlation type correlation among efficiencies (ωjt, ν jt ) (ω jt, µ jt ) (ν jt, µ jt ) efficiency ratio and input ratio (ω jt, K M ) (ν jt, L M ) (ω jt ν jt, K L ) Table 7: Post estimation check: evolution of capital-augmenting efficiency parameter estimates standard deviation ρ ωω ρ ων ρ ωµ ρ ω Note the restriction from evolution of ω jt is not used in the original estimation. These parameters are estimated post estimation, after computing all the efficiencies using estimates in Table 4. 41

43 Table 8: Firm size and non-neutral technology: dispersion and growth year mean efficiencies for each group all groups labor efficiency: νjt total growth rate 13.1% 16.25% 16.6% 15.1% 25.49% 17.22% material efficiency: µ jt total growth rate.76%.67%.81%.34% 1.33%.78% capital efficiency: ωjt Total growth rate 7.82% 1.95%.86% 2.19% 6.89% 3.91% 1 Firms are divided into five groups by firm size defined by sales, with each group having 2% of firms in the sample. 2 All means are simple average for each year-size group. Table 9: Average annual growth rate of productivity level: capital efficiency labor efficiency material efficiency growth rate (simple average) 3.91% 17.22%.78% growth rate (revenue-weighted average) 3.85% 17.81%.83% 1 The average annual growth rate of capital efficiency from 21 to 27, x, is obtained by solving the equation (1 + x) 6 exp(ω jt=21) = exp(ω jt=27). Growth rates for labor and material efficiencies are similarly defined. 42

44 Table 1: Non-neutral technology and labor demand: reduced-form analysis 1 variable non-neutral technology neutral technology (1) (2) (3) (4) OLS random effect fixed effect ωjt (.32) (.32) (.32) (.32) νjt (.27) (.28) (.28) (.28) µ jt (.93) (.94) (.94) (.94) ln(p L ) (.62) (.63) (.63) (.63) (.83) (.61) (.63) ln(p m ) (.122) (.171) (.171) (.171) (.229) (.124) (.128) ln(k) (.23) (.23) (.23) (.24) (.26) (.35) (.5) constant (.62) (.821) (.821) (.824) (.184) (.679) (.727) year dummy Yes Yes Yes Yes - - age Yes Yes Yes Yes Yes ownership Yes Yes Yes Yes sigma-u sigma-e rho R-square Dependent variable: logarithm of labor. Standard deviations are reported in parenthesis. 2 sigma-u: the between group variance in fixed and random coefficient model; sigma-e: the within group variance. rho: fraction of variance due to between group variance. 3 Overall R-square in fixed and random coefficient models. Table 11: Non-neutral technology and labor-material ratio parameter estimates standard deviation labor-material price ratio (σ) e-9 labor-material efficiency ratio (σ 1) e-1 constant 1.19e e-9 R square Dependent variable is the logarithm of labor-material ratio. 43

45 Table 12: Counterfactual: non-neutral technology and labor demand year data counterfactual result (1) (2) In counterfactual (1), both NNTD and NNTC are removed by choosing the efficiency ratio in 21 as the base point for the whole sample. We then solve for firms optimal labor demand, conditional on that each firm reaches their level as observed in the data. In counterfactual (2), only NNTD are removed, by using the median efficiency ratio within each year as the base point. Appendix C. Figure 1: Evolution of labor-material ratio and relative price in Chinese steel industry: labor material ratio simulated labor material ratio: σ=.7743 labor material price ratio L/M or PL/PM 1.5 unexplained area year 44

46 Figure 2: Heterogeneity of input-specific efficiencies capital efficiency ω jt labor efficiency ν jt material efficiency c jt density capital/labor/material efficiency Figure 3: Heterogeneity of technological non-neutrality K M efficiency ratio (ω jt ) L M efficiency ratio (ν jt ) K L efficiency ratio (ω jt ν jt ).25 density technology non neutrality (efficiency ratio) 45

47 Figure 4: Firm size and non-neutral technology Figure 5: Growth of factor-augmenting efficiencies ω jt, νjt, cjt 2 1 capital efficiency: ω jt labor efficiency: ν jt material efficiency: c jt year 46