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08.12.2023

Is output growth of Chinese manufacturing firms input or productivity driven? A flexible production function approach with endogenous inputs

verfasst von: Subal C. Kumbhakar, Mingyang Li

Erschienen in: Empirical Economics | Ausgabe 4/2024

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Abstract

In this paper, we focus on estimating output growth and its components attributed to quasi-fixed inputs, variable inputs, and productivity change, while treating variable inputs as endogenous. We consider two approaches. In the classical approach the time trend variable proxies for technical (productivity) change, while in the productivity (proxy variable) approach, we add a “productivity” term which is correlated with the variable inputs. Therefore, estimation strategies in the two models are different. Instead of using a Cobb–Douglas production function, we employ a translog production function to add flexibility. We showcase our theoretical results with Chinese manufacturing as an empirical exercise.

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Fußnoten
1
Endogeneity is addressed while using either the cost and profit functions. It can also be addressed in a system consisting of the production function and the first-order conditions of cost minimization/profit maximization. Note that we are not referring to production models with inefficiency which is not included here. This is because we are considering a modeling approach that includes productivity (instead of inefficiency).
 
2
This is often attributed as total factor productivity, the calculation of which uses factor shares in the total cost. Note that the TFP computed this way does not require any econometric estimation.
 
3
It is possible to treat all the inputs as variable in this formulation.
 
4
To make things comparable across the two models, we treat M as endogenous although the reason for their endogeneity is different.
 
5
The parameter \(\theta \) is not identifiable or separable from \(\varepsilon _{M, it}\) which contains an intercept term. For example, if the production function is Cobb–Douglas, \(\varepsilon _{M, it} = \beta _M\) which is a constant and it cannot be separated from the other constant \(\theta \) either in level or in log.
 
6
Note that we added subsidy, s, in the Markov process because we use it in our application. However, in principle any variable can be used in the \(g(\cdot )\) function. For example, R &D, FDI, etc., are policy variables that can be used in \(g(\cdot )\). We used s instead of R &D and FDI because these variables were either not available or mostly missing in our data set.
 
7
One can argue that treating \(h(\cdot )\) as a fully non-parametric function ignores the parametric relation (\(R(t-1)-TL(t-1,\beta _2)\)) inside the non-parametric function \(h(\cdot )\). However, this is not the case. Since \(R(t-1)-TL(t-1,\beta _2)\) has unknown parameters (\(\beta _2\)) in it, we cannot include it directly in the \(g(\cdot )\) function as a variable. That is, if we denote, \(q_{it-1} = R(t-1)-TL(t-1,\beta _2)\), and write \(g(\cdot )\) as \(g(q_{it-1}, s_{it})\) we cannot use it in estimation because \(q_{it-1}\) cannot be treated as a known variable (like \(s_{it}\)) which is necessary to consider \(g(q_{it-1}, s_{it})\) as a non-parametric function.
 
8
This is also called the power series. For instance, \(\text {poly}_2(m_{it-1}, k_{it-1}, l_{it-1}, s_{it})\) is \( \text {poly}_2(m_{it-1},\) \(k_{it-1},\) \(l_{it-1},\) \(s_{it}) =\) \((1, m_{it-1}, k_{it-1},\) \(l_{it-1}, s_{it},\) \(m_{it-1}^2, k_{it-1}^2,\) \(l_{it-1}^2, s_{it}^2,\) \(m_{it-1}k_{it-1}, m_{it-1}l_{it-1},\) \(m_{it-1}s_{it},\) \(k_{it-1}l_{it-1}, \) \(k_{it-1}s_{it},\) \(l_{it-1}s_{it}).\)
 
9
We choose k separately for each of the industries in our empirical application.
 
10
Output and inputs are frequently measured in monetary units instead of physical units and we do the same here. Following the literature (e.g., Levinsohn and Petrin 2003; Doraszelski and Jaumandreu 2013; Ackerberg et al. 2015), we assume perfect competition and homogeneous prices in the input and output markets, which allows using the deflators to convert the monetary units into physical units for all the inputs and output.
 
11
Note that we aggregate the values for all firms, all years, for each industry. To give some information about the variations, we report the quartile values. The boxplots of the components for each industry give more information. We report these results only for 4 industries to save space. Results for other industries are provided in “Appendix B”.
 
12
Balk (2014, 2016) discusses several decomposition methods, including the Olley-Pakes method discussed here, to get an aggregate productivity measure using a bottom-up approach. His decompositions distinguish between continuing, exiting, and entering firms. He also discussed the effect of using industry-level deflators instead of firm-level deflators on the estimation of production functions and productivity change. However, he does not talk about econometric estimation of production functions.
 
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Metadaten
Titel
Is output growth of Chinese manufacturing firms input or productivity driven? A flexible production function approach with endogenous inputs
verfasst von
Subal C. Kumbhakar
Mingyang Li
Publikationsdatum
08.12.2023
Verlag
Springer Berlin Heidelberg
Erschienen in
Empirical Economics / Ausgabe 4/2024
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-023-02505-8

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