## Appendix A. Detailed Calculation of the Degree of Resource Misallocation at the Provincial Level in China

At present, the academia usually adopts the indirect method represented by Hsieh and Klenow (2009) to measure the resource misallocation [

41], which is to add all the potential distortion factors to a “tax wedge” generated by the first-order condition of the enterprise optimization problem. The “tax wedge” reflects the loss of TFP caused by all input factors affected by distortion factors. However, the theoretical framework of Hsieh and Klenow (2009) is based on micro-enterprises, and is not precisely applicable to the resource misallocation measurement at the regional level. Therefore, this paper, drawing on the method in Aoki (2012), enriched the theoretical model for resource misallocation measurement from the meso-industrial level to the macro-regional level [

42]. Actually, it is to simplify the three-layer theoretical framework of Hsieh and Klenow (2009), namely, modify “enterprise-industry-country” to a two-layer analytical framework of “region (province)—country.” The basic theoretical logic is as follows:

The total national output is assumed to be the CES aggregation of 31 provinces’ output, i.e.,

where

${Y}_{t}$ represents the national industrial added value during the

$t$ period;

${Y}_{it}$ is the industrial added value of various provinces during the same period;

${\rho}_{it}$ refers to the share of industrial added value of each province out of the national total;

$\sigma $ measures the elasticity of industrial output substitution between provinces. This paper took

$\sigma =\frac{1}{3}$ by following Brandt et al. (2013) [

60].

${Y}_{it}$, the industrial added value of each province, is defined as the capital, labor, and TFP in the form of Cobb-Douglas function, and the scale return is assumed variable, namely,

In Equation (A2), ${K}_{it}$ and ${L}_{it}$ respectively represent the industrial fixed capital stock and the total number of industrial practitioners in each province during the $t$ period; $\alpha $ and $\beta $ respectively demonstrate the capital and labor production elasticity of each province in the same period; ${A}_{it}$ is the actual industrial TFP of each province.

Based on the capital factor input

${K}_{it}$ and the labor factor input

${L}_{it}$ of each province, the overall capital input and labor input of the whole country were expressed as

${K}_{t}={{\displaystyle \sum}}^{\text{}}{K}_{it}$ and

${L}_{t}={{\displaystyle \sum}}^{\text{}}{L}_{it}$, respectively, and the corresponding capital share and labor share of each province are

${k}_{it}=\frac{{K}_{it}}{{K}_{t}}$ and

${l}_{it}=\frac{{L}_{it}}{{L}_{t}}$ respectively. Similarly, if the overall industrial added value of the country is the capital, labor, and TFP is in the form of Cobb-Douglas function, the national industrial TFP is:

In economic activities, the actual industrial TFP in a country is lower than the effective industrial TFP, due to the different degrees of capital and labor misallocation between provinces. Assuming that the capital and labor misallocation is reflected by the factor price distortion and the unit capital cost

$r$ and the unit labor cost

$w$ of each province are subject to the distortion of

${\tau}_{it}^{K}$ and

${\tau}_{it}^{L}$ [

41,

42,

58], then the shares of industrial capital input

${k}_{it}$ and labor input

${l}_{it}$ of each province under the resource misallocation must be calculated to obtain the national actual (distorted) industrial TFP shown in Equation (A3). It requires resolution of the following maximization objective function:

According to the first-order conditions of profit maximization in Equations (A4) and (A5), the allocation distortion coefficients of the industrial capital input

${\tau}_{it}^{K}$ and labor input

${\tau}_{it}^{L}$ of each province can be obtained, as well as the shares of the capital input

${k}_{it}$ and labor input

${l}_{it}$ of each province under the resource misallocation, as can be seen below:

where

${Y}_{it}^{norm}$ represents the industrial added value (current market price) of each province during the

$t$ period, with

${\tilde{A}}_{it}={\left({\tau}_{it}^{K}\right)}^{-\alpha}{\left({\tau}_{it}^{L}\right)}^{-\beta}$.

In the absence of resource misallocation, the allocation distortion coefficients of the capital and labor factors of each province show

${\tau}_{it}^{K}={\tau}_{it}^{L}=1$. In this context, the shares of the industrial capital input and labor input of each province under optimal resource allocation can be obtained by Equation (A7), namely,

Referring to the study by Jin (2018), the degree of resource misallocation in each province can be measured by the ratio of the factor input share with misallocation to that without misallocation calculated by Equations (A7) and (A8) [

53]. Therefore,

$Mis{K}_{it}$ and

$Mis{L}_{it}$ respectively indicate the degrees of capital misallocation and labor misallocation of each province in different periods, i.e.,

In Equation (A9), $Mis{K}_{it}$ and $Mis{L}_{it}$ reflect the share of capital and labor allocated to provinces and the necessity of the capital and labor inflow and outflow for provinces. By definition, $Mis{K}_{it}$ or $Mis{L}_{it}$ equal to 1 indicates no misallocation between capital and labor factors in corresponding province; $Mis{K}_{it}$ or $Mis{L}_{it}$ greater than 1 means that the province’s capital or labor factors are over-allocated, squeezing the capital and labor factor supply for other provinces; $Mis{K}_{it}$ or $Mis{L}_{it}$ less than 1 implies that the capital or labor factor of the province is insufficiently allocated, and should be increased accordingly.