Parental Time Restrictions and the Cost of Children: Insights from a Survey Among Mothers

In this paper, we provide estimates of the subjectively perceived cost of children depending on the extent of parental time restrictions. Building on a study by Koulovatianos et al. (2009) that introduces a novel way of using subjective income evaluation data for such estimations, we conduct a refined version of the underlying survey, focusing on young women with children in Germany. Our study confirms that the monetary cost of children is substantial and increases with parental nonmarket time restrictions. The loss in the material living standard associated with supplying time to the labor market is sizeable for families with children.

"If we can agree that the economic problem of society is mainly one of rapid adaptation to changes in the particular circumstances of time and space, it would seem to follow that the ultimate decisions must be left to the people who are familiar with these circumstances, who know directly of the relevant changes and of the sources immediately available to meet them. We cannot expect that this problem will be solved by first communicating all this knowledge to a central board, which, after integrating all knowledge, issues its orders. We must solve it by some form of decentralization." ---Hayek (1945)

Introduction
One of the most important economic dramas in the last century was the emergence and then the decline of planned economy and state ownership. For more than half a century, it seemed that socialism could be as productive, if not more, than capitalist economy. In the 1973 edition of the economics textbook (Samuelson 1973), for instance, Samuelson predicted that the Soviet Union's income level would probably match that of the United States by 1990 and overtake it by 2010.
The debate of the merits of market socialism in the first half of the last century thus involved top economists such as Oscar Lange, Abba Lerner, Ludwig von Mises, and Frederick Hayek. The key arguments for why capitalism would be more efficient than socialism are perhaps two: the stronger individual incentives under the stronger protection of private property rights, and the efficiency of utilizing specific information dispersed among individuals and plants (Boettke, 2004). The second point is of course originated from Hayek (1945), one of the most influential papers of all time. 2 The key importance of incentives, ownership and property rights for explaining performance in socialist and transitional economies is perhaps one of the most active areas for research in the past few decades (Shleifer and Vishny, 1994;Megginson and Netter 2001;Djankov and Murrell 2002;Acemoglu, Johnson and Robinson 2001;Estrin et al., 2009). However, the importance of local information for efficiency in socialist or transitional economies or the state-owned sector is rarely systematically empirically explored.
In this paper we examine the causes of decentralizing state-owned enterprises (SOEs) in China, focusing on the role of local information. The data we use is the Annual Survey of Industrial Firms (ASIF) 1998-2007, which covers nonstate firms with sales exceeding 5 million yuan and all SOEs. Decentralization here is defined as the oversight government of an SOE shifting from a higher to a lower level of government-that is, from the central to provincial, or from provincial to municipality (alternatively called prefecture), or from municipality to county government. 3 The availability of local information is captured by the distance between an SOE and its oversight government. A larger distance between the oversight government and the SOE implies that the oversight government can have less direct observations on firm performance, managerial competence, and firm competitiveness. Indeed, there is a large literature providing evidence that distance has huge consequences for firms. For instance, distance (in terms of trust level and physical distance) helps explain decentralization decision between multinational headquarters and oversea subsidiaries (Bloom, Sadun and Van Reenen, 2012); distance helps explain a headquarters' investment allocation across plants in different locations (Giroud 2013); distance has been found to have profound implications for the lending relationship between banks and firms (Peterson andRajan 1994, 2002;Mian, 2006;Agarwal and Hauswalkd, 2010); and distance has been found to be a good proxy of information asymmetry in financial markets (Coval and Moskowitz 1999;Garmaise and Moskowitz, 2004;Grinblatt and Keloharju 2001;Hau, 2001).
Hayek (1945) implies that it would be more efficient for the oversight government with a larger distance to the SOE to delegate (or decentralize) the control rights to a lower level of government, which in general has a shorter distance to the SOE. Moreover, when firms' performance is harder to predict-and therefore local information figures more prominently-the same distance implies a stronger tendency to decentralize so as to better utilize local information. In addition, when communication costs are lower, the oversight government has less difficulty finding out what is going on in the SOE, and the same distance then implies a weaker tendency to decentralize. We should point out here that Hayek's point does not imply that SOEs should always be decentralized so that the distance between the SOE and the oversight government should be minimal. Tilting the balance toward centralizing include other considerations, such as internalizing externality of the SOE, pursuing goals of upper levels of government, and making top-notch experts who can specialize in complex and difficult problems to be in charge of some sophisticated SOEs (Garicano 2000).
We find support for these conjectures implied by Hayek (1945). In particular, the larger the distance between the oversight government and the SOE, the more likely the oversight government is to decentralize the SOE. Moreover, the positive decentralization-distance link is stronger when firm performance exhibits more uncertainty, and when communication costs are higher (as proxied by lower density of road, telecom or internet).
The relationship between decentralization and distance may be subject to other interpretations. To ensure that our interpretation is the right one, we conduct a number of checks. We mitigate omitted variable bias by including industry and year fixed effects, dummies indicating the same original oversight government, along with province-year-level macro controls (and in an alternative specification, fiscal conditions of the original oversight government and its lower level government). To guard against the possibility that the distance to the oversight governments may be simply a proxy for the distance to agglomeration centers, we construct a placebo distance to an alternative agglomeration city (at the same level as the oversight government), and this placebo distance measure is not significantly related to decentralization. Finally, we rely on exogenous source of variation of distance to identify its effect on decentralization. In particular, in the 1960s and 1970s, a large number of SOEs were relocated to inland provinces to confront the possibility of external wars with the Soviet Union and the U.S. As a result, their distance to their oversight governments was determined historically and likely had nothing to do with the decentralization decisions decades later. The instrumental variable results are qualitatively similar to our base specification.
To the best of our knowledge, this paper is the first paper that tests Hayek's idea of the fundamental importance of local information for understanding the workings of the economic system, in particular, the centralization or decentralization of state-owned enterprises. We test rich implications of Hayek's idea, such as how decentralization depends on the distance to the oversight distance government, and how this link depends on firm heterogeneity and communications costs.
Our paper is most closely related to the empirical literature examining decentralization within firms. In particular, Aghion et al. (2007) (2013), perhaps the only paper that examines how the within-firm distance between headquarters and their plants affects plant performance, find that proximity of the headquarters to a plant significantly increases the plant's investment and productivity. We differ from these papers in two ways. First, we focus on the role of distance between the oversight government and an SOE in the state sector for the decentralization decision of SOEs, and therefore directly address the original concern of Hayek in understanding the role of local information in determining efficiency of centralization versus decentralization. Second, the nature of our data set allows us to explore changes in organizational structure, thus we study decentralization in a dynamic setting. Our findings thus are complementary to the literature on decentralization within an organization-here we view the whole state economy of China as a gigantic organization with the state as the ultimate owner-that emphasizes the role of information in determining the control rights structure. We offer empirical support for the insight of the critical importance of local information in shaping the organization structure in the largest "organization" (i.e., the state economy of China) in the most populous country.
The paper is also related to a theoretical literature that sheds light on the benefits of decentralization. Bolton and Dewatripont (1994) suggest that decentralization has the benefits of allowing the agent to specialize in some information processing and therefore reducing information acquisition costs, freeing the principal from information-processing time constraint. Aghion and Tirole (1997) suggest that when information advantage of agents is severe, and conflict of interest is not large, it is efficient to formally delegate. Garicano (2000) suggests that in a hierarchy it makes sense to create a hierarchy of knowledge production, with bosses of higher layers of hierarchy focusing on more complex and difficult problems and employees of lower levels specializing in more basic and easier problems. Dessein (2002) suggests that when agents report information to their superiors strategically, it is often desirable for the uninformed principal to delegate the formal authority to the agent. Alonso, Dessein and Matouschek (2008) suggest that when local information is important and division managers communicate strategically, a higher need for coordination improves horizontal communication but worsens vertical communication, and decentralization can dominate centralization even when coordination is extremely important relative to adaptation. These theoretical papers provide further insights about why sometimes it makes sense to decentralize. These papers greatly enrich the insights of Hayek (1945), highlighting factors that Hayek considered, such as agent information advantage (Aghion and Tirole 1997), or did not consider, such as specialization in information acquisition (Bolton and Dewatripont 1994), hierarchy of knowledge production (Garicano 2000), and strategic reporting by agents (Dessein 2002;Alonso, Dessein and Matouschek 2008). Our evidence is consistent with some of the implications of these models, but our data do not allow us to test the more subtle implications of these new models. The key implications of Hayek (1945), however, are directly testable and receive strong support.
In the rest of the paper, Section 2 provides related institutional background and offers a simple conceptual framework to understand the causes of decentralizing SOEs in China. Section 3 provides empirical results on determinants of decentralization. Section 4 concludes.

Conceptual Framework
The top-down, lying largely in the hands of the incumbent oversight government. In general, the incumbent oversight government wants to control important assets in order to maintain some control of the state over the economy. Indeed, around the beginning of our sample period, in the second half of the 1990s, the Chinese government launched a major privatization and decentralization campaign. The slogan for the reform included "grab the big and let go the small" (Xu, Zhu and Lin 2005). With limited attention span, information processing ability (Bolton and Dewatripont, 1994), and comparative advantage in handling complex tasks (Garicano 2000), it makes sense for the upper government to focus its attention to important SOEs.
A second motive for the incumbent oversight government to decentralize SOEs is likely to unload fiscal burdens. Over time, due to incentive problems, many SOEs had experienced declining profitability, which partially motivated the government to decentralize. Since the cost of control is larger for ill-performing SOEs-with less rents to share and more subsidies to shoulder-we expect the incumbent oversight government to decentralize first ill-performing SOEs.
Prediction 1. The incumbent oversight government is more likely to decentralize less important and ill-performing SOEs.
A third likely motive for the government to decentralize is to revitalize SOEs to make them more efficient. Indeed, with many SOEs having difficulties in paying their employees and pension liabilities in the 1990s, some governments such The extent to which the oversight government can limit the information loss depends on its ability to directly acquire information and monitor the SOE. There are strong reasons that the ability to obtain direct information on the SOE depends on the distance between the oversight government and the SOE. 8 The oversight government officials are subject to time constraints. When the distance is shorter, the official is more likely to travel to the site to observe first-hand how the SOE is performing and whether the SOE manager is doing a good job. Anticipating better information by the oversight government, the SOE manager is also more likely to report honestly. Indeed, Giround (2013) find that when the distance between headquarters and the subordinate plant is reduced exogenously (due to the introduction of a direct flight), the plant tends to obtain more investment and perform better. We thus predict that the larger the distance between the oversight government and the SOE, the more likely the oversight government is to decentralize the SOE in order to improve the performance of the SOE.

Data and Sample
The data we use are from the Annual Survey of Industrial Firms (ASIF) of National The oversight government (for SOEs), from more centralized to more decentralized, can be the central, provincial, municipal (or prefecture), county, and township. We delete from our sample SOEs those observations that have missing or "others" values for the oversight variable (10,133 firms). We further restrict our sample in the following ways. First, we delete those SOEs which lie at the bottom of the hierarchy: those firms whose oversight government is at the county level or below (44,905 firms). These SOEs by definition could not be further decentralized.
Second, we drop those enterprises without at least three continuous years of data (22,115 firms). Finally, we delete those enterprises whose oversight relationship had changed more than twice (470 firms). 11 Our final sample consists of 14,420 SOEs.
Decentralization, our key variable, is defined as those firm-years that experience a change in oversight government to a lower level. In 1998, the initial year of our sample, firms under the oversight of the central, provincial, and municipal governments account for 15.2%, 27.4%, and 57.3%, respectively. In total, 1,116 firms, or 7.7% of the sample, experience decentralization. Of these decentralized firms, there are 318 (14.5%), 384 (9.7%), and 414 (5.0%) firms whose original oversight government were the central, provincial and municipal governments, respectively. The incidence of decentralization was spread out throughout our sample period: the numbers of SOEs being decentralized for each year from 1999 to 2007 was 168, 161,162,97,151,222,82,40, and 33, respectively.

Specification and Identification
To examine what determines the likelihood of decentralization, we estimate the following equation: Here, Decen * ijkt is the index function for the tendency to be decentralized, and Decenijkt is an indicator variable that equals one when the firm is decentralized.
The subscripts i, j, k, and t represent firm i in industry j under the initial oversight government with level k at year t. Distanceik measures the logarithm of (one plus) the physical distance (in km) between firm i and the city in which the initial oversight government is located. The constant is added to accommodate the fact that the distance could be zero. We obtain the distance based on GIS data. 12 In some robustness checks, we also discretize the variable into an indicator variable of whether the oversight government and the firm are at the same city. The vector X includes once-lagged firm characteristics including firm size as measured by firm assets, performance (i.e., returns to sales, or ROS), the importance of the firm to the oversight government (i.e., the ratio of the firm's value added to the total value added of all the firms in the same 2-digit industry and affiliated with the same oversight government), the dummy variable of full state ownership (i.e., 100 percent state ownership). The vector Zt measures province-level variables including GDP per capita, unemployment rate, and the share of SOEs in urban employment.
Importantly, we control for dummy variables indicating the initial oversight level of the SOE to hold constant oversight-specific tendency to decentralize. In our sample, the oversight government of an SOE could be the central government, or one of the 31 provincial governments, or one of the 331 municipal governments; there are 363 oversight government dummies in total. We also control for industry and year dummies. To allow for correlation of the error term both across time and space, we cluster our standard errors at the level of initial oversight government.
Since the decentralization decision is irreversible-at least in our sample period-we delete those observations after Decen has turned one. Our parameter of interest is the marginal effect of Distance. Its estimate is based on the comparison between SOEs with different distances to the original oversight government.
The probit or linear probability models assume that the distance is exogenous. However, the distance could be endogenous for decentralization decisions. For instance, unimportant or less profitable SOEs may be systematically located further. We try several ways to deal with this. First, we control for variables that capture key confounding factors, such as the SOE's importance and lagged firm performance. Second, for central SOEs, the distance to the oversight government means the distance to Beijing, a major metropolitan area and agglomeration center.
For SOEs under the oversight of other level of governments, the distance to the oversight government is also the distance to a local agglomeration center. Would this measure of the distance to political centers then merely capture economy of agglomeration rather than information and monitoring difficulties for the principal?
To check this, we replace the distance to the oversight government in the following way: for central SOEs, the distance to the oversight government is replaced by the distance to Shanghai, another metropolitan center as important as Beijing in terms of economic agglomeration; for provincial SOEs, to the largest city within the province other than the provincial capital; for municipal SOEs, to the largest county-level city within the prefecture other than the prefecture seat. 13 If the distance measure merely captures the agglomeration effect, we expect this placebo distance to be significant and of similar magnitude.
Third, we deal with the possibility that the distance is endogenous. Even after controlling for prominent determinants of decentralization, governments may still put better SOEs at nearby locations. Then the distance may represent something else rather than the quality of information or monitoring intensity. To deal with this concern, we rely on an instrumental variable that likely captures exogenous variations in the distance of an SOE to the oversight government. In particular, during the 1960s and 1970s, worried about potential wars (even nuclear ones) with Soviet Union and United States, China relocated many SOEs to the hinterland, which included relocating central SOEs in inland provinces, and relocating many province-and municipality-governed enterprises to more remote areas within the oversight jurisdiction. This migration of firms is called the Third Front Construction program (for details, see Appendix A). Third Front Construction covered a large area in China-with more than half of the provinces being covered.
The relocation sites were chosen to be far away from external threat, and it is implausible that it would affect SOE decentralization 30 to 40 years later when leadership had changed multiple times with the new leaders featuring distinct 13 Notice that we have used "prefecture" and "municipality" alternatively within this paper for the administrative level between province and county levels.
objectives. Because the Third Front Construction was a large program that covered 13 provinces, and 6.9% of firms in our sample were affiliated with this program, this instrument is likely a relevant one for the distance variable.
Finally, we try to shed light on the mechanisms of how distance affects decentralization. In particular, we allow the effect of distance on decentralization to differ by communication costs and information available to the oversight government on firms. These results would shed light on potential pathways for distance to affect decentralization.

Baseline Results
We first, in Table 3, compare how decentralized and non-decentralized SOEs differ in basic characteristics. 14 Relative to non-decentralized SOEs, the decentralized ones are much more likely to be in different cities from the oversight governments (59% vs. 30%), their logarithm of distance to the oversight government is much larger (4.4 vs. 3.0), their average asset size is slightly smaller, their performance is significantly worse in terms of labor productivity and profitability (but not TFP), their relative importance (i.e., the share of their value added in the oversight government's portfolio of SOEs) is lower, and the urban unemployment rates of their location tend to be slightly higher. The picture that emerges is that the oversight government tends to decentralize SOEs that are far away, smaller, less important, and worse-performing. The pattern is roughly consistent with our predictions in the conceptual framework.
In Table 4, we compare the incidence of SOE decentralization for central, provincial and municipal SOEs that are located in the same city as the oversight government with those that are located at different cities. The incidence is much higher when the firm is located in different cities from the oversight government 14 Tables 1 and 2 contain the definitions of the variables and the summary statistics.
than when it is in the same city: 15.6 vs. 5.5 percent for central SOEs,15.4 vs. 5.3 percent for provincial SOEs, and 11.4 vs. 4.2 percent for municipal SOEs. This pattern is consistent with our prediction that a larger distance to the oversight government leads to more decentralization. Based on the pooled sample, other determinants of decentralization behave similarly as we observed in the decentralization vs. non-decentralization samples comparisons. That is, decentralization is more likely for smaller firms.
Consistent with prediction 1, decentralization is more likely for worse-performing firms and for less important firms. However, these auxiliary controls do not behave consistently across oversight status. Thus, the effect of distance between SOEs and their oversight government seems to be more robust than other forces such as control benefits (i.e., firm importance) and fiscal burden (i.e., lagged firm performance).
It is useful to know that our results are robust to whether we include the privatized periods in our sample or not. In our baseline and the rest of paper (except in this paragraph), we delete the periods in which an SOE became privatized-for a firm that experienced privatization in the sample periods, the periods after the  Table 5. The result in Table 6 show that the distance between the firm and its original oversight government significantly increase the likelihood of decentralization, continuing to offer support to our conjecture; yet the same distance is not significantly related to the likelihood of privatization. Our key result thus remains intact whether or not we include the sample of "privatization years".

Omitted Variables, Agglomeration and Endogeneity
A potential concern is that the decentralization decisions may be affected by particular circumstances faced by both the original oversight government and, in the case of decentralization, the final oversight government at lower level. In such cases, the estimated effect of distance may only reflect the impact of omitted local economic environment. We thus, for all three subsamples of central, provincial, and municipal SOEs, include fiscal revenue per capita, GDP per capita, and fiscal autonomy (i.e., the ratio of fiscal revenue to fiscal expenditure in the firm's county)-for both the original oversight government and the government level immediately below it. 15 The results are shown in Table 7. 16 These additional oversight control variables barely matter in general, and the results on the distance are similar to those in Table 4. Omitted variables related to fiscal circumstances of the governments thus cannot explain the distance-decentralization link.
In China, political and economic centers tend to overlap. Beijing is not only the political center but also a top (economic) agglomeration center. Similarly, provincial capitals tend to be the largest cities in the provinces. Thus, a natural concern is that the distance to oversight government really measures the distance to major economic agglomeration. A priori there are no strong reasons why proximity to economic centers would matter for whether an SOE should be governed in a decentralized way. Still, this is a relevant concern that we should take seriously.
If this concern is valid, we should expect the distance of an SOE to other major agglomeration centers in the same oversight region to have positive effect on decentralization. To test the validity of this concern, we create a placebo distance measure (Placebo Distance) as follows. For central SOEs, Placebo Distance is the distance to Shanghai, another agglomeration center on par with the capital city of Beijing. For provincial SOEs, Placebo Distance is the distance to the largest city (other than the provincial capital) in the province. For municipal SOEs, Placebo Distance is the distance to the largest county-level city (other than the city seat) within the same prefecture. We re-run our baseline regressions using Placebo Distance to replace the real distance, and the results are in Table 8. For the pooled sample, Placebo Distance is completely insignificant. Thus, our key result on the positive effect of distance on decentralization of SOEs is not due to economic agglomeration.
Another relevant concern is that the distance of an SOE to its oversight government may be endogenous. For instance, far-away SOEs may be systematically less important. To examine this possibility, we now try to find exogenous source of variations for the distance. We exploit a large wave of SOE migration that took place in the 1960s and the 1970s due to the so-called Third Front Construction (TFC) program. TFC was implemented in response to the perceived threat from Soviet Union and U.S for major wars ( Figure 2 shows the number of firms established under this program during . This exogenously changed the distance of many SOEs to their oversight government. We thus construct a dummy variable Third Front, which is one if a firm was established during 1964-1966 or 1969-1972 in the TFC Region (Li and Long, 2013). Table 9 reports the IV regression results using various specifications. In general, our instrument seems to be valid and generates meaningful results. In the first stage regressions, we get significant positive effects of the TFC dummy on distance, suggesting that the politically-motivated TFC relocation did increase the distance between the firm and the oversight government. Distance gets the same positive and significant effect on the likelihood of decentralization in the second-stage regressions. When we only control for province dummies, the first-stage Fstatistics is 18.48 (column 1). When we put more controls and include all the 363 oversight government dummies, which likely takes away a significant portion of the variations in Distance, the F-statistics drops to 4.85 (columns 4 and 6). However, even in this case the IV regressions do pass the Anderson-Rubin test, suggesting that the variable Distance is significant even in the event of weak IV (see column 6). Nevertheless, we note that the qualitative results of a significant positive effect of Distance on decentralization remain intact. Since the results from the IV probit and the two-stage least square (2SLS) models are similar, we shall focus on the 2SLS results. As expected, being a Third-Front-Construction SOE would increase log distance by 0.19, and it is statistically significant at the 5% level. Once corrected for endogeneity, the distance remains exerting a positive influence on decentralization, and the coefficient increases to 0.03 (from 0.006). The results thus confirm the key importance of the distance between enterprises and their oversight government.

The Mechanisms of Distance on Decentralization
In the conceptual framework, we predict that the decentralization-distance link would be stronger for firms with higher communication costs or with higher performance uncertainty. To test this, we need measurements.
We proxy communication costs by three measures. The first is provincial road mileage (road mileage per capita): more convenient transportation significantly reduces the difficulty of on-site inspection, and thus makes information more accurate. The second is provincial telecom density, i.e., the share of people having either mobile or fixed phones. The third is the share of people using internet.
We proxy high uncertainty over a firm by several variables: the average share of intangible assets in total assets within the firm's industry, and several measures of the dispersion of firm performance within the firm's industry. A higher share of intangible assets for a firm in general implies higher uncertainty about the firm's technology and performance. Since we rely on three different ways to compute TFP-the OLS production function method, the Olley-Pakes method, and the index function method-we present three sets of results for the distance-TFPdispersion specification (see the data appendix for the details of the construction of TFP). In addition, we also present the dispersion in return-to-sales (ROS, that is, before-tax profit over sales), which is more transparent.
The results in Table 10

Figure 2. Number of New Firms in "Third Front Construction" Area during 1961-1985
Source: The data is from Annual Survey of Industrial Firms (ASIF).

Firm-level variables Decentralized
Dummy variable equals to one if a firm's affiliation-level is changed from a higher level government to a lower level government. Source: Annual Survey of Industrial Firms (ASIF). The default source for all variables is ASIF.

Different city
Dummy variable equals to one if located in a different city with the seat of the government with which it is affiliated, and zero otherwise. Distance The physical distance (log kilometers) between the firm and the seat of the government with which it is affiliated. Source: ASIF, and Geographic Information System. Placebo distance Distance from Shanghai for central SOEs, distance from the largest city within the province (except for the provincial capital) for province SOEs, distance from the largest county-level city within the same prefecture (except for the prefecture seat) for municipal SOEs. Source: ASIF, and Geographic Information System. Privatized Dummy variable equals to one if state share falls below 50% or exit from the database Firm asset Log of firm asset ROS Ratio of before-tax profit to sales TFP Total factor productivity, calculated as the residual from the regression of log value added on log fixed capital and log employment. Three methods are used, including OLS, Olley-Pakes and index number. Please see the Appendix E. Firm importance Ratio of the firm's valued added to the total value added of firms in the same 2-digit industry and affiliated with the same government Fully stateowned Dummy variable equals to one if state share in firm's equity equals 100%

Third front firm
Dummy variable equals to one if firm was established during 1964-1966 or 1969-1971 in the Third Frond Construction Area.  Cities, andCounties (1998-2005). County fiscal autonomy Ratio of fiscal revenue to fiscal expenditure in the firm's county. Source: Public Finance Statistical Materials of Prefectures, Cities, andCounties (1998-2005). TFP dispersion Standard deviation of firm TFP in the same 3-digit industry ROS dispersion Standard deviation of firm ROS in the same 3-digit industry Intangibility Average ratio of intangible assets to firm total assets in the same 3-digit industry Province telecom infrastructure Per capita number of mobile phone and fixed telephone users

Province internet infrastructure
Per capita number of internet users

Province road mileage
Per capita road mileage. Different levels of roads and railway are translated into the equivalent of second-level road according to transport capacity.   (3) shows the t-statistics of mean difference tests. An SOE is defined as decentralized if is affiliation level is changed from a higher-level government to a lower-level government. *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively.

Ratio of Decentralization
SOEs located in the SAME city with the seat of the government (967) This table compares ratio of decentralization of SOEs located in the same city with the seat of the government with which it is affiliated and SOEs that are located in a different city. Number of firms in each subsample is listed in brackets. A firm is decentralized if its affiliation level is lowered.  (t-1) 0.0063*** 0.0049** 0.0042*** 0.0055*** (0.0008) (0.0022) (0.0007) (0.0009) Different City (t-1) 0.0272*** 0.0187*** 0.0147*** 0.0444*** (0.0030) (0.0047) (0.0030) (0.0092) Firm asset (t-1) -0.0024*** -0.0036*** -0.0020*** -0.0020*** -0.0025*** -0.0037*** -0.0021*** -0.0018*** (0 Marginal effects on the probability of decentralization that are evaluated at the mean and their standard errors are listed. All these firm-specific and province-specific variables are lagged by one year. Standard errors are clustered at the level of the same oversight government. *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively. the multinomial logit model. Marginal effects evaluated at the mean and standard errors are listed. The baseline option is neither privatized nor decentralized. The second column reports the probability of being Privatized which takes on the value of 1 if a firm is privatized in year t, and 0 otherwise. The last column reports the probability of being Decentralized which takes on the value of 1 if a firm is decentralized in year t, and 0 otherwise. All these firm-specific and province-specific variables are lagged by one year. Standard errors are clustered at the level of the same oversight government. *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively.  Table 1 for definitions). Column 1-3 are the results for the regression on the subsample of central SOEs, province SOEs and mun We report marginal probabilities evaluated at the mean of the variables. Standard errors are clustered at the level of the same ove *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively. 39

Table8. Determinants of the Decentralization -Placebo Test
(1) Whole Sample Placebo distance (t-1) -0.0006 (0.0012) Firm asset (t-1) -0.0026*** (0.0008) ROS (t-1) -0.0031** (0.0012) Firm importance (t-1) -0.0053** (0.0024) Fully state-owned (t-1) -0.0059*** (0.0019) GDP per capita (t-1) 0.0009 (0.0056) State sector share (t-1) 0.0083 (0.0327) Unemployment rate (t-1) 0  Table 5 by replacing the distance variable with a new variable -Placebo distance which is defined as "distance from Shanghai for central SOEs, distance from the largest city within the province (except for the provincial capital) for province SOEs, distance from the largest county-level city within the same prefecture (except for the prefecture seat) for municipal SOEs". Marginal effects evaluated at the mean and standard errors are listed. The dependent variable, Decentralized, takes on the value of 1 if a firm is decentralized in year t, and 0 otherwise. All these firm-specific and province-specific variables are lagged by one year. Standard errors are clustered at the level of the same oversight government. *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively.  1964-1966 or 1969-1971 in the "Third Frond Construction Area." Marginal effects evaluated at the mean and standard errors are listed. The dependent variable Decentralized in the 2 nd stage takes on the value of 1 if a firm is decentralized in year t, and 0 otherwise. Columns 1-4 present the 2 nd and 1 st stage results from IV Probit model, which is estimated using conditional MLE (i.e., the first stage result is estimated jointly with the parameters of the Probit equation when implementing conditional MLE). Columns 1-2 control for province dummies. Columns 3-4 control for a full set of oversight government dummies. Columns 5-6 present results from a standard 2SLS model. Standard errors are clustered at the level of the same oversight government. *, ** and *** indicate statistical significance at 10%, 5% and 1% levels, respectively. This led to relief of security pressure and the Third Front Construction came to a halt afterwards.
During these two periods, 1964-1966 and 1969-1972, China relocated more than 1100 factories and about 4 million workers to mountainous areas in West China. The result was sudden increase in the number of SOEs in these areas during the two periods (see Figure 2).

Appendix B. Estimation of TFP
Here we describe in detail the approaches to estimate firm-level TFP.
We use a standard log-linear Cobb-Douglas production function to estimate firm-level TFP.
Specifically, TFP of firm i in year t is the estimated residual from the regression: where is the logarithm of value-added, and and are the logarithms of capital and labor, respectively. To allow for different factor intensities across industries, we estimate equation (A1) separately for each two-digit industry. 18 Accordingly, TFP can be interpreted as the relative productivity of a plant within its industry.
Real value added is constructed by subtracting deflated input from real output. We use the two-digit ex-factory price index from China Urban Living and Price Statistics to deflate output.
The input deflator is calculated based on available output deflators at 2-digit industry level and information from the National Input-Output (IO) tables in 1997, 2002, and 2007. From the IO table, we know how much inputs are needed to produce one unit of output. Then the average input price index will be the weighted average of the price index of those inputs. Thus, to obtain the input deflator for each industry, we calculate a weighted average of the input deflators, using as weights the coefficients in the IO table. 19 In the ASIF dataset, firms report total annual employment, but they do not report the real capital stock. Instead, firms report the value of their fixed capital stock at original purchase In our baseline analysis, we estimate equation (A1) by ordinary least squares (OLS). We call this TFP-OLS. While this approach is common in the literature, past research has argued that OLS estimates suffer from two endogeneity issues: simultaneity of input choice and selection biases.
These two issues will generate biased estimates of and , and therefore biased estimation of residual in equation (A1). A variety of techniques have been suggested to address the simultaneity and selection problems. We use the method proposed by Olley and Pakes (1996). We call this TFP-OP.
As a robustness check, we also use a straightforward index number approach, which does not require the estimation of any parameters. In particular, the industry-specific average wage share in output is used to measure , and one minus this share is used to measure . The intuition is that a cost-minimizing firm will make sure the relative factor price ratio equals the local elasticity of substitution between inputs of the production technology. Since we do not have good comparable data to compute factor shares based on our survey data, we rely on the estimates of factor shares in two-digit industry level from Bentolila and Saint-Paul (2003). Bloom, Sadun and Van Reenen (2012) use a similar treatment. We call this TFP-IN.
Overall, these three approaches yield similar qualitative results. The correlations of these productivity measures are quite high: that between TFP-OLS and TFP-IN is 0.92; between TFP-OLS and TFP-OP, 0.96. Thus, it is not surprising that our results in general do not hinge on how we measure productivity.