the armey curve : an empirical analysis of selected balkan countries and russia for the Period 2006 – 2019

the subject of the analysis is to check the validity of the Armey curve which is frequently used in the scientific literature and to establish the optimal level of the public sector. the aim of the present study is to analyze the impact of the public sector through public expenditure on the possibility of achieving economic growth. The estimation is based on annual data for the period 2006–2019 of selected Balkan countries and Russia. The authors apply the ordinary least squares (OLS) method for a nonlinear regression model. the conclusion is that the Armey curve is valid for some of the countries involved in the research among which Serbia, North Macedonia and Russia. The public expenditure to Gross Domestic Product ratio’s threshold value, which maximizes economic growth, ranges from 32.94 to 42.37%. The average share of public expenditure in the analyzed countries is approximately equal to the threshold values that are obtained which is indicative of achievement to some extent the desired economic performance. However, the results of the study show that the growth of the public sector and its impact on economic development should not be underestimated.

intrODUctiOn
There is no consensus in the scientific literature on the impact of public expenditure on a country's social and economic development. The topic of the degree of government intervention in the economic activity is discussed in many scientific debates between different schools of economic thought. The object of analysis in both theoretical and empirical research is the size of the public sector (measured by public expenditure as a percentage of Gross Domestic Product), on the one hand, and determining the optimal levels of this sector that would have a positive effect on the economy, on the other hand. For this reason, various models have been developed and tested, which present theoretically, empirically and graphically the relationship between expenditure and economic growth. In this regard, the Armey curve is used as an appropriate tool.
The present study focuses on empirical testing of the relationship between public expenditure and economic growth, using the Armey curve, for five selected countries in the Balkan region and Russia. Some of the Balkan countries are members of the European Union (Bulgaria and Greece). Serbia and North Macedonia are candidates for European Union membership. Kosovo and the European Union have already signed a Stabilisation and Association Agreement, which is the formal start of the accession negotiations. Russia is also included in the analysis, as a country that has strengthened foreign trade, socio-economic and partnership relations with the Balkan countries. The time period used for the purposes of the analysis is from 2006 to 2019.
The study is structured in four sections. The first section outlines the theoretical and empirical foundations of the relationship between public expenditure and economic growth in the light of the Armey curve. The second section presents the methodological framework of the analysis and descriptive statistics for the variables that are included in the model. The third section consists of applying the developed regression model, assessing the optimal level of the public sector and discussing the results. The last section includes conclusions.

literatUre reVieW
Public expenditure is an important tool in the conduct of any government financial, economic and social policy. The relationship between public expenditure and economic growth is modeled and presented in a large number of scientific studies. Some of them focus on establishing the direction of causality [1][2][3]. Meanwhile, other studies emphasize the impact of expenditure on growth, highlighting the structure of public expenditure and its effects on economic performance [4][5][6]. Moreover, in some of these researches, it is concluded that government activities have a stimulating role for the national economy. Other authors take the opposite side in this debate, arguing that rising public expenditure has a negative impact on economic growth. This provoked a group of authors, including R. J. Barro [7], G. Scully [8] and D. Armey [9], to find evidence to support the fact that the relationship is nonlinear. It is postulated that with the gradual increase in public expenditure, gross domestic product (GDP) also tends to grow, but this is valid until a certain point. The increase in expenditures, and hence the influence of the public sector above a certain threshold, is not accompanied by higher growth rates. D. Armey [9] argues that both low and very high levels of public expenditure can have adverse consequences in the pursuit of economic growth. This requires finding an optimal level (PubEXP*), at which the public sector will lead to an increase in GDP. The authors mentioned above derive and present the impact of public expenditure on economic growth in a similar way, using an inverted U-shaped curve (Fig. 1). The size of the public sector is shown on the horizontal axis (abscissa), represented by the public expenditure as a percentage of GDP, while the rate of economic growth is shown on the vertical axis (ordinate).
R. J. Barro [7] points out that improving a country's infrastructure through a public resource can be interpreted as a positive sign in terms of future investment activity, and hence for better economic performance. The subsequent expansion of the public sector (by increasing public expenditure) requires the provision of additional resources for its financing. This means that the public revenues have to be increased, which can create an additional tax burden for economic agents. The higher tax rates may lead to more adverse effects on private investors and their expected future rate of return, and this will also affect the incentives to invest in the economy [10]. The expansion of the public sector can be financed not only through taxes but also through the issuance of government debt. However, the participation of the government in the capital markets may lead to an increase in interest rates on borrowed funds and create a so-called crowding out effect on private investments [11]. C. N. García [12] derives two main characteristics of public expenditure. On the one hand, public expenditures contribute to tackling market failures, but on the other hand, their excessive growth and use in an ineffective way may lead to government failures. Thus, the Armey curve can be used as a tool for measuring the expenditure efficiency of the public sector.
In modern empirical studies, scholars have verified the validity of the theoretical foundations of the Armey curve, which describes the relationship between public expenditure and economic growth. Different groups of countries are subject to analysis. The basis of these studies is not only to establish the relationship between public expenditure and economic growth but also to determine the optimal level (threshold) of public expenditure that would promote a higher growth rate of the national economies. H. Mavrov [13] concludes that there is a nonlinear relationship between public expenditure and economic growth in Bulgaria, where the public expenditure to GDP ratio's threshold value is 28% for the period 1990-2004. In addition, the study investigates the impact of public expenditure categories (classified by function). The validity of the Armey curve is confirmed for some of them (for example education, healthcare services and social security), while for the categories of economic activities and services, general public services and other expenditures only the hypothesis of the linear relationship is established.
O. F. Altunc and C. Aydin [14] test the validity of the Armey curve for selected Balkan countries, including Turkey, Bulgaria and Romania. They find the presence of a nonlinear relationship based on available data for the period 1995-2012. The obtained results show that the threshold values of public expenditure vary between 22% and 25% of GDP, which does not correspond directly to the situation in the analyzed countries. It should be noted that the share of public expenditure to GDP significantly exceeds the calculated optimal levels in these countries. Therefore, governments need to focus on the opportunities to improve public sector efficiency. C. Yüksel [15] points out that the public expenditure and economic growth nexus are extremely dynamic, and differences can be observed not only for individual countries but also for different periods, including within the same economy.
De K. Witte and W. Moesen [16] also investigate and confirm the existence of the Armey curve using time series data for the member countries of the Organization for Economic Co-operation and Development (OECD). Through applying a DEA analysis, they find that the average value of the optimal level of public expenditure to GDP for 23 countries is equal to 41.22% in the long run. This result is significantly higher than the conclusions reached by H. Mavrov [13], O. F. Altunc and C. Aydin [14] for some of the Balkan economies. De K. Witte and W. Moesen [16] explain the higher expenditure to GDP ratio with the concept of the household size. According to this concept, the number of children in families is gradually declining in modern societies and this provokes parents to expect the government to take on more responsibilities. In other words, it strengthens the government's role in promoting social responsibility. Furthermore, P. V. Iyidogan and T. Turan [17] emphasize that the future challenge to the fiscal policy of the countries and the size of the public sector may be the growing ageing population and hence the rising social security expenditure. The differences in the obtained results may also be due to the specification of the empirical models and the explanatory variables included in the analysis. For example, some studies use V. N. Nikolova, A. G. Angelov government consumption expenditure (as part of the expenditure approach to calculating GDP) as a measure of the public sector, while other investigations use the value of public expenditure from the budget execution reports.
F. Forte and C. Magazzino [10] examine the relationship between the size of the public sector and the economic growth of the European Union Member States for the period 1970 to 2009. The countries under analysis are very heterogeneous. That is why, the authors divide them into groups, which they study separately. The differences between the groups arise from the labor market development, the structure of public expenditure and the level of welfare. The authors conclude that the optimal levels of public expenditure to GDP are as follows: for Eastern European countries -40%, for Western European countries -38.32%, for the Anglo-Saxon countries -40.77% and for the Mediterranean countries -42.06%. C. N. García [12] reaches similar estimates for the Spanish economy by calculating a threshold of 40% for the period 1980-2016.
There are scientific studies in which the theoretical foundations of the Armey curve are partly confirmed. For instance, D. Lupu and M. Asandului [18] conduct a study for eight Eastern European countries and conclude that only in three of them the validity of the curve is proved. G. Bozma, S. Basar and M. Eren [19] confirm the existence of the Armey curve only for some of the G7 countries (USA, France and Canada). This is not valid for Germany, United Kingdom, Japan and Italy.

Data anD MetHODOlOGY
In the present study, we use a nonlinear regression model to conduct econometric analysis. The dependent variable is economic growth (EGR) defined as the growth rate of real GDP. Economic growth is presented as a function of public expenditure (PubEXP) and other selected exogenous factors (ExVariables).
Therefore, public expenditure (presented as percentage of GDP) is included as an independent variable in the model. The square of the variable public expenditure as a percentage of GDP is also included in the regression model. This is frequently used when testing for the presence of the Armey curve and proving a nonlinear relationship between the dependent and the independent variable. This approach is applied in the studies of R. K. Vedder and L. E. Gallaway [20], H. Mavrov [13], F. Forte and C. Magazzino [10] and O. F. Altunc and C. Aydin [14]. In addition, an exogenous variable is added to the independent variables in the econometric model specification of the present study. In the empirical literature, this approach is commonly used in research on this topic. The following indicators are widely used as exogenous variables: unemployment rate [14,18], trade openness [21][22][23], investment and consumption expenditures [21,22], population and tax rates [24]. The public revenue as a percentage of GDP is chosen as an exogenous variable in the present analysis. In this way, the impact of both the expenditure and the revenue side of the budget on economic growth can be investigated. M. G. Attinasi and A. Klemm [25], F. T. Boldeanu, I. Tache and M. Ion [26] use a similar technique and thus aim to show the impact of fiscal policy on overall growth. Furthermore, in the literature review section of our study, it is emphasized that the expansion of the public sector requires additional resources in government budgets, which further affects economic development.
We use ordinary least squares (OLS) method as econometric technique of analysis. Following regression model is used to test the validity of the Armey curve: where: EGR -economic growth, presented as a growth rate of real GDP; PubEXP -public expenditure as a percentage of GDP; PubREV -public revenue as a percentage of GDP; ε -residual component; i = 1…6; t = 2006, … 2019.
To assume the validity of the Armey curve, the coefficient β 1 has to be positive (β 1 > 0), while the sign of the coefficient β 2 has to be negative (β 2 < 0). For countries where the Armey curve is valid, we can calculate the threshold value of the public expenditure to GDP, which promotes higher economic growth. F. Facchini and M. Melki [24], F. Forte and C. Magazzino [10], O. F. Altunc and C. Aydin [14], D. Lupu and M. Asandului [18] determine this optimum (threshold) using the value of the coefficients before the parameters of the model as follows: In the present study, we test the validity of the Armey curve for the economies of Bulgaria, Kosovo, Serbia, Greece, North Macedonia and Russia. The countries, which we include in the scope of our study, are positioned in Southeast Europe. Most of them are located in the Balkans. Russia is included in the analysis due to the

eMPirical resUlts
The results of the applied model are presented in Table  2, Table 3, Table 4 and Table 5. Based on the results shown in Table 2, we confirm the validity of the Armey curve for three of the analyzed countries -Serbia, North Macedonia and Russia. As can be seen from Table 2, all independent variables in the nonlinear regression model for these countries are statistically significant in levels at 1, 5 and 10%. Thus, the increase of the public sector in Serbia, North Macedonia and Russia contributes to a better economic performance, but this is valid up to a certain threshold value of the public expenditure to GDP ratio.
According to the results shown in Table 2, it can be concluded that the Armey curve is not valid for Bulgaria, Kosovo and Greece. As already mentioned above, the sign of the regression coefficient β 2 has to be negative while the regression coefficient β 1 has to be positive in order to confirm the existence of the curve.
The adequacy of the regression models is also checked ( Table 3). The obtained results verify that all nonlinear regression models are adequate at 5% significance level. The models are characterized by a relatively high explanatory power, measured by the coefficient of determination (R Square) and the adjusted coefficient of determination (Adjusted R Square). Taking into account the obtained values of the coefficients of determination, it is concluded that the differences in the economic growth can be to a large extent explained by the simultaneous influence of the expenditure and revenue of the public sector.
All regression models are additionally tested for heteroskedasticity (by the Breusch-Pagan test), autocorrelation (by the Breusch-Godfrey test) and normal distribution of the residuals (by the Chi-square test). The results in Table 4 highlight that the regression models for all countries included in the analysis can be accepted as accurate. The residuals are homoskedastic, normally distributed and lack of first-order autocorrelation.
In addition, we calculate the public expenditure to GDP ratio's threshold value (PubEXP*) for the countries where the Armey curve is valid. The results are published in Table 5 below.
The calculated threshold value of the public expenditure to GDP ratio in Serbia is 42.37% for the period 2006-2019. When we compare this value with the data from the descriptive statistics given in Table  1, it is established that the average value for the period in the scope of the analysis (42.87%) is approximate to the determined optimum. For instance, the public expenditure accounted for 45.16% of Serbia's gross domestic product in 2014. It is significantly higher than the calculated threshold. The period under review is characterized by volatility in the GDP growth rate, ranging from -2.7% to 6.4%. The obtained optimal values for the size of the public sector in North Macedonia and Russia are quite similar. The real growth rate of GDP would maximize when the public expenditure to GDP ratio is equal to 32.94% in North Macedonia, while in Russia the threshold is 33.97%. For both countries the annual average data shows that the economies are close to their optimum, which maximizes economic growth. However, it should be noted that while public expenditure varies between 31.62% and 36.03% of GDP for the period 2006-2019 in North Macedonia, in Russia this share varies more widely -from 31.12 to 41.35% of GDP. The dynamics in the ratio for Russia are observed primarily for the period up to 2011.
In Figure 2 we show a simulation model of the Armey curve in Serbia, North Macedonia and  Russia. The illustration of the curves is based on the results from the regression model developed and applied above, taking into account the effect of public expenditure and the calculated threshold in Table 5. The data shows that in Serbia the changes in the size of the public sector (with a change in public expenditure in the range of 10% to 60% of GDP) would significantly affect the rate of economic growth, especially when the government is not actively involved in economic processes. At the same time, the dynamics of the public expenditure to GDP ratio in North Macedonia can also have a substantial impact on economic development. This can be seen from the concave shape of the Armey curve for North Macedonia. When the share of public expenditure to GDP decreases (below the certain threshold), this would lead to a slowdown in the growth rate in North Macedonia, but this decline would be significantly less than the decline that would be observed in the economy of Serbia. On the other hand, the higher size of the public sector (above the set optimum) would have a significantly more negative effect on the economic growth of North Macedonia. The Armey curve for Russia is smoother than the curves for Serbia and North Macedonia. This suggests that more tangible changes in the public expenditure to GDP ratio would not lead to large variations in the level of Russia's real gross domestic product.

cOnclUsiOns
Empirical testing of the validity of the Armey curve allows us to conclude that the nonlinear model representing the relationship between public expenditure and economic growth is partly applicable. This permits us to further assess the optimal size of the public sector in countries where the Armey curve is valid. The results from this assessment show that in the period 2006-2019, countries such as Serbia, North Macedonia and Russia manage their public sector in a way that to some extent allows the desired economic performance to be achieved. The obtained thresholds are approximately equal to the average values of the analyzed fiscal indicators. However, in certain years of the analyzed period, these countries also show some changes in the ratio of public expenditure to GDP, which contributes to the stimulating or restraining effects on the national economies. This is a particularly actual problem in the current COVID-19 pandemic. Attempts by countries around the world (including Serbia, North Macedonia and Russia) to deal with the crisis lead to a sharp rise in the public expenditure in 2020. The uncontrolled increase in public expenditure during the pandemic, whether in the form of anti-crisis measures, can lead to fiscal imbalances if the effectiveness of these expenditures is not taken into account. That is why further research can focus on different types of public expenditure and analyze their optimal levels, which would maximize economic growth. This analysis could also be extended by prioritizing the importance of public expenditure to a national economy. In this way, it will be possible to analyze in more detail the policies pursued so far and to draw conclusions about whether the financial resources have been used in a sufficiently reliable manner.
In conclusion, it is necessary to find the necessary balance between the optimal size of the public sector, the structure of public expenditure and their efficiency in order to pursue higher rates of economic growth.


s2fieldsofstudy: Economics Business

text:
The Impact of State Ownership on the Productivity of China’s Agri-food Firms

This study examines the effects of state ownership on the productivity distribution of different quantiles of China’s agri-food firms based on data from the Chinese Industrial Enterprises Database between 1998 and 2013. Using panel quantile regression, this study finds that the contribution of state ownership to productivity varies across different quantiles of the productivity distribution. State ownership inhibits total factor productivity (TFP) of firms with low-level productivity but has no effect on TFP for firms with mediumand high-level productivity. Regions play a moderating role on the state ownership-productivity link. Regional economic development alleviates the inhibition of state-owned capital on the TFP of firms with lowand high-level productivity.

Introduction
The effect of ownership structures on firms' total factor productivity (TFP) has been debated for decades. Most studies of firm productivity or profitability indicate that private ownership is more efficient than state ownership (Bai et al., 2000;Barbetta et al., 2007;Boardman & Vining, 1989;Ehrlich et al., 1994;Le et al., 2021). Shleifer and Vishny (1997) present an explanation: state-owned enterprises (SOEs) are subject to bureaucratic control with extremely centralized management, and their cash liquidity is limited. On the other hand, Megginson and Netter (2001) argue that state ownership may be more efficient than private ownership in the presence of market failures. Some empirical studies on the public goods sector support this viewpoint (Bhattacharyya et al., 1995). However, previous studies ignore an important problem: the average value of TFP cannot be the representative of the entire distribution of TFP. Most of the previous literature study the effect of ownership structures on TFP through ordinary least squares (OLS) regressions or fixed effects (FE) models in which the dependent variables are represented in the form of average values, ignoring the possible quantile heterogeneity of dependent variables in the causal relationship. This study uses the panel quantile regression proposed by Koenker (2004) to examine the effect of state-owned capital on the TFP distribution of agri-food firms in China. In addition, considering the huge regional differences in the level of economic development in China, we also examine the role regions play in the state ownership-productivity link.
The literature related to the study focuses on the effect of ownership structures on firm productivity. Sappington and Stiglitz (1987) present a basic privatization theorem, stating that the government can achieve the same efficiency goals by contracting out production to private firms under ideal conditions. They also highlight several conditions under which state ownership is superior, such as the government is more risk tolerant than private firms, high contracting costs, limited information about government benefits. Conversely, private ownership is superior if the government's ability to commit to the private sector is stronger than to the state sector, or if the state sector faces hierarchical control. Le et al. (2021) examine the impact of Vietnamese state-owned capital on TFP and find that state ownership is negatively associated with TFP by using data adapted from enterprise surveys and Provincial Competitiveness Index (PCI) surveys 2011-2017. Parida and Madheswaran (2021) study the impact of ownership structures on TFP in four sectors: metallic, non-metallic, coal and petroleum in India and find that the superiority of private firms in three sectors-metallic, non-metallic, and coal-whereas the petroleum sector reports quite the opposite result. Brzić et al. (2021) study the relationship between the proportion of private ownership and productivity in 62 European telecom enterprises from 2012-2019 and find a positive relationship between the proportion of private ownership and TFP. Walheer and He (2020) use detailed firm-level data to examine how ownership structures affect technical efficiency and technological progress in the Chinese industrial sector, firm ownership is found to be important in explaining the technical efficiency and technological gap among Chinese firms. Foreign-invested firms are the technological leaders which set the standard for technical efficiency. Private ownership is found to dominate state and collective ownership in terms of technical efficiency and technological gaps. Over time, foreign-invested firms lead the way in efficiency, private firms contribute much to the technological progress. In addition, they find that China has successfully revitalized SOEs, although there is still room for improvement. Moreover, there are studies that further examine the role of foreign direct investment (FDI), such as Alka (2020)' study on the issue of foreign ownership in Africa, finding that the foreign ownership has a positive, but statistically insignificant, effect on TFP. Harris (2003) examines productivity differences between domestic and foreign-owned manufacturing plants using 1974-1995 Kingdom plant data and find that: foreign-owned plants are much more productive than domestically-owned plants. Ramondo's (2009) study for Chilean manufacturing indicates that TFP of foreign-owned plants is approximately 17 percent higher than that of domestic plants. The above literature ignores the issue of ownership structures' effect on the entire distribution of TFP. Teng et al. (2021) use the panel quantile regression and find that the foreign ownership's contribution to productivity is not linear and varies across different quantiles of the productivity distribution based on a sample of 428 small and medium-sized firms listed on the Growth Enterprise Market in the Shenzhen Stock Exchange between 2009 and 2016.
However, to the best of our knowledge, most studies on this topic have not accurately identified the causal effect of state ownership on the entire distribution of TFP. In this context, our study adds to the literature by attempting to determine the effect of state ownership on the distribution of TFP by using a large micro database containing extensive information of agri-food firms, the Chinese Industrial Enterprises Database (CIED), for 1998-2013. First, this study uses the Levinson and Petrin (LP) method for estimating the TFP of each firm; this is because the LP method can solve the simultaneity bias and selectivity bias which exist in the OLS estimation, and it can also avoid the problem of large sample loss due to negative investment value in the Olley and Pakes (OP) method (Olley & Pakes, 1996). Second, we use panel quantile regression to conduct our research. We examine the effect of the proportion of state-owned capital on the distribution of firm productivity by using the 10%, 25%, 50%, 75%, and 90% quantile of TFP as the dependent variables. In addition, we conduct robustness checks by using the TFP measured by the OP method. Finally, we examine the moderating role of regions on the state ownership-productivity link by constructing an interaction term between regional per capita Gross Domestic Product (GDP) and state-owned capital share. Our study has important implications for revealing the relationship between the proportion of state-owned capital and firm productivity in China. SOEs play a crucial role in Chinese manufacturing. Most of them are industry leaders. However, many studies present that the productivity of Chinese SOEs is lower than that of non-SOEs, which indicates that state-owned capital hurts the growth of firm productivity. Thus, we aim to deeply explore the impact of state-owned capital on firm productivity. Our conclusions indicate that there is a nonlinear relationship between the proportion of state-owned capital and firm productivity, and that the proportion of state-owned capital has different effects in firms with different productivity levels, which previous literature do not reveal.
The remainder of this study is organized as follows: the second section presents the methodology for measuring TFP and the panel quantile regression model used, the third section describes the data and descriptive statistics, the fourth section presents the regression results and discussion, and the last section presents conclusions and policy recommendations.

Empirical Framework
In this section, we present the theoretical development and TFP measurement method, followed by the panel quantile model in empirical analysis.

Theoretical Development
We hypothesize there is a nonlinear relationship between state ownership and firm TFP. Most previous studies argue that the state-owned system is a representative of low productivity. This is because firms with a large proportion of state-owned capital have the characteristics of low operating efficiency and high internal costs, which cannot give full play to the development potential of enterprises. However, in China, state banks tend to provide large preferential loans or "policy loans" to SOEs with high-level productivity for various reasons, such as political connections and social ties (Brandt & Li, 2003;Wang et al., 2008), thus the cash flow constraint problem may not exist in high-level productivity SOEs. Firms with high-level productivity may also have strong managerial capabilities and resource allocation efficiency. Therefore, state ownership may only suppress TFP for low-level productivity firms but has no effect on TFP for medium-and high-level productivity firms.

Measurement of TFP
Academics typically use OP (Olley & Pakes, 1996) or LP (Levinsohn & Petrin, 2003) methods when measuring TFP based on microdata. Both the OP and LP methods can solve the simultaneity problem and selection problem in OLS estimation, but they differ in the selection of variables that proxy for unobservable productivity shocks. The OP method uses the investment as a proxy, whereas the LP method selects intermediate inputs. In our sample, many investment values are negative, so a considerable number of observations will be lost if we use investment as the proxy variable. Thus, we select the LP method to measure TFP in this study.
First, we use the Cobb-Douglas (CD) function as the production function, taking the following logarithm: In Equation (1), y represents the logarithmic form of the firm's total output, l represents the logarithmic form of the number of employees in the firm, k represents the logarithmic form of capital stock, and i and t represent the individual firm and year, respectively. u it represents the logarithmic form of TFP. The level of TFP is calculated as follows: The gross industrial output value of firms is applied as the proxy variable of output (Y it ), capital stock as the proxy variable of capital (K it ), and the practitioners of firms as the proxy variables of labor (L it ). This study calculates the TFP of China's agri-food firms according to the LP method (Levinsohn & Petrin, 2003). There are two benefits to this approach: (a) The firm is affected by their observable efficiency in the process of deciding the input of production factors; that is, the observable part of the residual item is related to the input of production factors during the current period (simultaneity bias). The objective of using the LP method to solve the problem of simultaneity bias is to build an intermediate inputs function as a proxy for observable efficiency impact; that is, firms will make an intermediate inputs decision based on the current observable efficiency. (b) The other problem is selectivity bias. It tends to be easier for those with lager capital stock to face productivity shock and are therefore more likely to stay in the database. Consequently, the lack of data may be due to nonrandom factors; the capital stock will be associated with the residual term, resulting in bias. The LP method solves the problem of selection bias by constructing a survival probability function to estimate the exit and entry of firms. The above process mainly consists of three steps.
In the first step, Levinsohn and Petrin (2003) consider that part of u it in Equation (1) is observable by firms. This part is assumed to be g it . Then u it = g it + e it , where, e it is truly unobservable technical shocks, that is, the total factor productivity. The LP method assumes that firms decide the intermediate inputs situation according to the current productivity situation; that is, it uses the current intermediate inputs of the firm as the proxy variable of the unobservable technical shocks. Next, the LP method constructs the relationship between intermediate inputs and TFP that can be observed by the firm. If the firm is expected to have a higher productivity level in the future, it will choose to increase the intermediate inputs. The specific investment function is as follows: Then we present the inverse function of Equation (3) as follows: Substituting Equation (4) into Equation (1) produces the following: In the second step, α K ⋅k it + g t (m i,t , k i,t ) of Equation (5) can be defined as the contribution of capital to the output and uses ω it instead, followed by the specific form set. The LP method constructs a fourth order polynomial that contains the firm's capital stock and intermediate inputs, then estimates them to obtain unbiased estimates of labor input, which is a nonparametric estimation, and finally solves the problem of simultaneous deviations.
In the third step, the LP method uses a survival probability function to estimate the entry and exit of firms to solve the problem of sample selectivity bias. The specific approach uses the residuals obtained in the second step as dependent variables and capital stock and intermediate inputs as independent variables. The probit model is estimated as follows: jas.ccsenet.
The LP m Equation ( The regres and firm a variable (i (lnM it ). Th obtained b Figure 1 sh

Econom
We such as basic information of production and sales, financial indicators, etc. There are extensive studies using CIED to study Chinese issues (Aghion et al., 2015;Brandt et al., 2017;Hsieh & Klenow, 2009). We choose firms in agri-food industry which includes twelve sub-categories (Note 1) as research objects. It covers agriculture and industries closely related to agriculture, such as grain milling, feed processing, sugar processing, frozen processing of aquatic products, processing of vegetables, fruits, and nuts, and liquid milk, etc.
The next step is the processing of the data: First, we match the raw data year by year according to the firm code, the firm name and the legal representative name to get the 1998-2013 Chinese agri-food firms dataset (Brandt et al., 2012). Second, we fill in the missing values such as gross industrial output value according to the accounting standards. Third, we refer to Jefferson et al. (2008) and Cai and Liu (2009) to clean up the data using the following procedures: (a) Excluding the data if firm yield, capital stock, state capital or other key variables are missing, zero, or negative; (b) Excluding the data if the number of employees in a firm is less than 8; (c) Excluding the data if the firm is established before 1950; (d) Excluding the data if the capital stock is greater than the total assets; (e) Deflating the firm level continuous variables by 0.5% to eliminate the influence of outliers; (f) Deflating nominal variables using different price indices for different regions with the base period of 1998, such as using the producer price index for total industrial output value, the price indices of investment in fixed assets for capital stock, and the consumer price index for export values of firms. After processing, we get the data with 1 198 018 observations, containing 213 228 firms. Table 1 shows the description and basic statistics of main variables. In the China's agri-food industry, the average share of state-owned capital in firms is 6.3 percent. Note. The unit of Yield, Capital, M, Size, Exp, and RD is 1 000 RMB yuan.

Results
In this section, we first analyze the baseline results of the effect of state-owned capital share on TFP of agri-food firms based on the panel quantile model. Second, we perform a robustness check by using TFP measured by the OP method. Finally, we discuss whether differences in regional economic developments can explain the effect of state ownership. Table 2 reports the baseline result of state ownership's impact on the TFP over China's agri-food firms. We examine the impact of state ownership on TFP at the 10%, 25%, 50%, 75%, and 95% quantile, respectively. We additionally run two-way FE regressions as a reference. State-owned capital share is significantly negative at the 10% and 25% quantile of TFP, with values of -0.051 and -0.072, respectively, and is insignificant at the 50%, 75%, and 90% quantile of TFP. This indicates that for every 1% increase in the state-owned capital share, the TFP of firms in the 10% and 25% quantile decreases by 5.1% and 7.2%, respectively, and that the state-owned capital share has no significant effect on the TFP of firms in the 50%, 75%, and 90% quantile. The results of the FE regression indicate that, overall, the state-owned capital share has a significant negative effect on the TFP of firms, which is consistent with most previous literature. Our study further demonstrates that the state-owned capital share does not have a suppressive effect on the TFP of all agri-food firms. Instead, the suppressive effect of the state-owned capital share is mainly reflected in firms with relatively low-level TFP while having no significant effect on firms with medium-and high-level TFP. The regression results in Table 2 verify our  findings. Regarding the control variables, the coefficient of firm size is significantly positive at all quantiles of TFP, indicating that firm size promotes the TFP of agri-food firms. The coefficient of firm age is significantly negative at the 10%, 25% quantile of TFP, insignificant at the 50% and 75% quantile, and significantly positive at the 90% quantile, indicating that for firms with low TFP, younger firms are more productive compared to mature firms. Firm age has no effect on firms with medium-level TFP, and for firms with high-level TFP, mature firms have higher productivity compared to younger firms. The coefficients of firm exports and R&D investments are significantly positive at all quantiles, indicating that exports and R&D investments increase the TFP of agri-food firms. The coefficients of FDI are significantly negative at the 10%, 25%, and 90% quantile and insignificant at the 50% and 75% quantile, indicating that FDI reduces the TFP of low-and high-level productivity firms, whereas it has no significant effect on the TFP of medium-level productivity firms.  ,198,018 1,198,018 1,198,018 1,198,018 1,198,018 1,198,018 Note. Standard errors in parentheses. ***: p < 0.01; **: p < 0.05; *: p < 0.1. P # represents the "#" th percentile of TFP.

Robustness Check
In this section, we use the TFP measured by the OP method as a robustness check. The regression results are shown in Table 3. The coefficients of State are essentially consistent with the baseline results: the values are -0.080 and -0.043 at the 10% and 25% quantile, respectively. The coefficients are both insignificant at the 75% and 90% quantile. The only difference is the result for the 50% quantile, where the coefficient value for State is -0.027, whereas the coefficient for the baseline regression is not significant. Considering that the median value of TFP measured by either the LP or OP method is smaller than the mean value, the results in Table 3 still indicate that the increase in the state-owned capital share suppresses the TFP of low-level productivity firms and has no significant effect on the firms with medium-and high-level productivity firms.  ,198,018 1,198,018 1,198,018 1,198,018 1,198,018 Note. Standard errors in parentheses. ***: p < 0.01; **: p < 0.05; *: p < 0.1. P # represents the "#" th percentile of TFP.

The Effect of Regional Economic Development
The level of economic development varies significantly across different regions of China, with the eastern region having a huge economic advantage over the central and western regions. Thus, the effect of state ownership may vary across regions. First, we construct the PerGDP variable based on the GDP per capita of 31 provinces in China's mainland for each year from 1998 to 2013 based on the China Statistical Yearbook and deflate it by using the Consumer Price Index (CPI) for the base period of 1998. Second, we construct the interaction term of the state-owned capital share and the regional GDP per capita variable PerGDP to add to the panel quantile regression of Equation (8), the results of which are shown in Table 4.  Note. Standard errors in parentheses. ***: p < 0.01; **: p < 0.05; *: p < 0.1. P # represents the "#" th percentile of TFP.
The coefficients of the interaction term are significantly positive at the 10%, 25%, and 90% quantile, respectively, indicating that the higher the level of regional GDP, the less inhibitory the effect of state-owned capital share on the TFP of firms at these quantiles. The coefficient of PerGDP is significantly positive at all quantiles, indicating that the increase in regional GDP per capita has a boosting effect on TFP at all quantiles, which may be due to the regions with high-level economic development having advantages over regions with low economic levels in terms of policy support, market system, and regulation level. The difference in business operating environment affects firm productivity. The coefficient of State differs from the baseline results in two aspects: (a) The State coefficients are significantly negative at the 75% and 90% quantile, having values of -0.579 and -0.543, respectively, whereas the coefficients of the baseline regression are not significant at these two quantiles. (b) The absolute values of the State coefficients are higher than those of the baseline results at all quantiles.
Combining the results of the interaction term coefficients, leads us to the following conclusion: Among firms with high levels of TFP, the promotion effect of regional economic development on firms' TFP hedges the inhibiting effect of state-owned capital share. The inhibiting effect of state-owned capital share on TFP of firms with high-level productivity is offset when considering the effect of regional economic development. In the case of low-level TFP firms, although the effect of regional economic development dilutes the inhibitory effect of the state-owned capital share, the effect of regional economic development is not sufficient to completely offset the inhibitory effect of state-owned capital share. This is because the inhibitory effect on low-level productivity firms is stronger compared to that of high-level productivity firms, resulting in the state-owned capital share still having a significant suppressive effect on the TFP of low-level productivity firms, which is presented in the baseline results.

Conclusions and Policy Implications
What is the impact of state ownership on the TFP of Chinese agri-food firms? Unlike previous literature that focuses on changes of the average value of TFP, this study focuses on changes in the entire distribution of TFP.
We study this issue by using a panel quantile regression model with time and individual FE based on data from the Chinese Industrial Enterprise Database from 1998 to 2013 and drawing the following main conclusions: First, for every 1% increase in the state-owned capital share, the TFP of firms in the 10% and 25% quantile decreases by 5.1% and 7.2%, respectively, and that the state-owned capital share has no significant effect on the TFP of firms in the 50%, 75%, and 90% quantile. Second, the higher the level of regional economic development, the lower the depressive effect of state-owned capital share on the TFP of firms with low-and high-level productivity. In addition, we find that regional economic development has a significant enhancing effect on firms' TFP. Among firms with a high level of TFP, the promotion effect of regional economic development on firms' TFP hedges the inhibiting effect of state-owned capital share. The inhibiting effect of state-owned capital share on TFP of firms with high-level productivity is offset when considering the effect of regional economic development. In the case of low-level TFP firms, although the effect of regional economic development dilutes the inhibitory effect of the state-owned capital share, the effect of regional economic development is not sufficient to completely offset the inhibitory effect of state-owned capital share. This is because the inhibitory effect on low-level productivity firms is stronger compared to that of high-level productivity firms, resulting in the state-owned capital share still having a significant suppressive effect on the TFP of low-level productivity firms, which is presented in the baseline results.
Our findings have the following policy implications. First, the government should take measures to reduce the share of state-owned capital in low-productivity firms. The proportion of state-owned capital hinders the TFP growth of low-productivity firms, mainly because low-productivity firms cannot obtain the policy preferences of high-productivity firms, and state ownership limits firms' operating efficiency. The government should consider how to release the state-owned capital of low-productivity firms incrementally, such as transforming SOEs into mixed firms or private firms through state-owned reform. Second, the share of state-owned capital in regions with high levels of economic development can be appropriately increased in firms with high-level TFP. Our study shows that the regional economic development level and the share of state-owned capital have a synergistic effect in firms with high-level productivity. In the regions with a higher level of economic development, the policies supporting facilities are more complete, and firms do not need to pay a lot of money to maintain their relationship with the government and banks. Appropriately increasing the proportion of state-owned capital of enterprises can bring more policy benefits, such as in loan facilitation. These policies can help firms improve their competitiveness and stimulate increased R&D investment, thereby increasing productivity.