Silviase/jgov_v1.4_full_ann huggingface dataset:
The superscripts stand for affiliates, that is, 1 is for private and 0 for public centers. For the above equations for truncated mean $ \lambda_{i} $ , $ \phi $ , and $ \Phi $ indicate the standard normal probability density and the standard normal cumulative density functions, respectively. $ \theta^{1} $ and $ \theta^{2} $ measure the relation between wage rates and the unobservable characteristics that influence the sector allocation. $ \theta^{1} > 0 $ implies a positive selection bias among workers in the private sector, such that $ E[W_{i}^{1} \mid Z_{i}^{*} \geq 0] > E(W_{i}^{1}) $ , or those who earn greater than predicted wages derived from observed factors of workers in private homes are more likely to be working in the private sector than the predicted probability. In contrast, $ \theta^{2} < 0 $ indicates a negative selection bias among public workers, such that $ E[W_{i}^{2} \mid Z_{i}^{*} < 0] > E(W_{i}^{2}) $ , or those who earn greater than the observed predicted wages in the public sector, are less likely to be allocated to the private sector than the expected prospect (Willis and Rosen (1979), Holtmann and Idson (1993)).

Suppose that a worker in the child care labor market chooses to work in the sector that rewards higher his or her personal characteristics, such as ability, talent, education, and experience. This argument suggests the condition such that $ \theta^{1}>0 $ and $ \theta^{2}<0 $ , which means that the employee with the highest earnings who is able to provide the best quality of services in the private sector would also give the best performance with the greatest wages in the private sector, along with a strictly hierarchical self-allocation pattern based on ability $ ^{4} $ .
### 4. Data

The empirical analysis of this study is based on two different surveys on the child care centers: non-licensed and licensed. Both surveys were conducted by the Price Policy division of the Cabinet Office, Japanese government, in the summer of 2002. These two data sets are, to our knowledge, the largest and most comprehensive ones on non-licensed and private licensed child care centers currently available in Japan. We were able to perform the survey with special cooperation and deep understanding by local governments. Before the survey, we explained the purpose of our research and consulted with officials in charge of child care policies at local governments. We presented them with our detailed questionnaire, considering the feasibility of the survey and preciseness of response. Surprisingly, micro-level wage data on child care workers had not been previously available. Thus, those were the first surveys on child care workers in Japan. They were also unique.

The sample of the survey on non-licensed child care facilities comprises those operating in Tokyo Prefecture, facilities that had the unfortunate experience of having the largest number of children on a waiting list of all the child care centers in our survey. The data in Tokyo were randomly collected by the local government, and were regarded as being for-profit. $ ^{5} $ However, due to the lack of necessary indicators for examining sectoral wage differences, note that only child care workers from non-licensed facilities subsidized by local governments are included in our study. Therefore, in this study, for-profit facilities represent proprietary centers financially supported by local governments. To adjust for the wage differences owing to the amounts of government subsidies between not-for-profit and subsidized for-profit sectors, we include area and facility dummies into our regression analysis.

We have a rich set of information on both employees and employers as described below, which enables us to control the characteristics of facilities to investigate the
nonprofit wage premiums.

Obviously, we also need a data set on workers and their wages in nonprofit counterparts to evaluate the nonprofit wage premiums. The second data set we use in this paper is that of workers in private and licensed nonprofit facilities collected in Tokyo Prefecture. Most of them are operated with the cooperation of social welfare organizations, and are not considered to be proprietary. This survey was performed through city/town/villages in Tokyo Prefecture. They collected detailed information on all child care workers in each facility, from 40 percent of licensed private facilities within the area of individual local governments, which were randomly selected $ ^{6} $ . As in the non-licensed data set, we are able to match employer and employees in each child care center, which enables us to study nonprofit wage premiums while controlling for various facility-related factors.

Focusing on the wage differentials between for-profit and nonprofit child care centers, we choose six municipal areas within Tokyo Prefecture, where the data on care workers in both non-licensed for-profit and private licensed not-for-profit facilities are available. For eliminating any factors affected by regional differences between urban and rural areas, therefore, we included only the municipal areas where both non-licensed and licensed facilities data are accessible. Moreover, we eliminated the samples of which the data necessary for our estimation are missing. We ended up with 911 (84 percent) and 173 (16 percent) workers in nonprofit and for-profit centers, both subsidized by the local government, respectively.

Before explaining the basic statistics, we have two reminders. In this study, we focus on the wage differences between private nonprofit and private for-profit centers; we exclude public facilities. Noguchi, Shimizutani, and Suzuki (2003) observe substantial differences in age of workers between publicly owned and private centers, and the wage age profiles are much steeper in public facilities, which are not related with worker productivity. Their findings suggest that the labor market for child care workers is segregated between the public and private sectors.
Table 1 describes some basic statistics of major characteristics of both employees and facilities that could affect wages in nonprofit and for-profit child care centers. Mean hourly wages are, remarkably, 52.7 percent higher in nonprofit facilities (1,604 yen in not-for-profit centers; the mean wage is 1,051 yen in for-profit centers) $ ^{7} $ . We are able to observe the nonprofit wage premiums very clearly.

The summary statistics demonstrate that individual employee characteristics between both sectors are not heterogeneous in our samples. The differences in mean years of age and market experience between both sectors are subtle. Workers in the nonprofit sector tend to be slightly younger, but have about 1.1 years more market experience compared to employees in the proprietary sector. Regarding educational backgrounds, two-year community college graduates seem to occupy around 50 percent of all employees in both sectors. The share of university graduates is slightly higher in for-profit centers than not-for-profit facilities, by 4.4 percentage points. More than two-thirds of employees in the child care centers are qualified and the share of qualified workers are 5.2 percentage points higher in the not-for-profit sector than in the for-profit sector. As for worker status, the shares of regular workers in nonprofit and for-profit centers are 67.8 percent and 72.8 percent, respectively. Unfortunately, we do not have information on marital and family status, which is controlled for in previous works as proxy indicators for employee stability $ ^{8} $ . Further, the data do not contain information on non-wage benefits such as insurance or professional training.

Contrary to the homogeneity among employees, we observe the difference in facility-related characteristics between nonprofit and for-profit sectors. The number of employees indicating firm size is apparently larger in nonprofit centers than for-profit organizations. This distinct difference in firm size might be accounted for by the positive relation between the number of employees and wage rates that a large number of studies
have shown $ ^{9} $ . Interestingly, not-for-profit centers are more likely to provide care for extra hours; total hours of care are 1.4 hours longer than for-profit centers, which is thoroughly contradictory to the general belief that non-licensed centers are inclined to operate for much longer hours than licensed facilities $ ^{10} $ .

In sum, the basic statistics reveal that workers in nonprofit centers enjoy higher hourly wages by approximately 34 percentage points than for-profit facilities. However, worker characteristics are not seen to be various among our samples in both sectors. Not-for-profit facilities are somewhat advantageous in employees' years of market experience, two-year community college education, and qualifications as child caregivers, while proprietary centers are slightly advantageous in worker age, four-year university education, and full-time status. Regarding facility characteristics, nonprofit facilities tend to operate for longer hours and to employ more workers, while for-profit centers provide supplemental types of care such as temporary and post acute care.

To examine the effects of these factors on wage determination, we first run a simple semi-logarithmic human capital wage function for a pooled full sample, using a dummy variable that indicates whether or not the ownership is proprietary. The results demonstrate that the dummy variable is large and statistically significant; they indicate that daily wages are higher in nonprofits by 32.9 percent (37.5 percent and 25.7 percent for monthly and hourly wages, respectively), after controlling for various worker and facility characteristics. However, simple least square regressions are not appropriate, since the allocation of workers with various characteristics in our data to the for-profit and nonprofit sectors is nonrandom. Therefore, applying Heckman’s two-stage approach (Lee (1978), we decided that Heckman (1979)) is an appropriate procedure to obtain reliable estimates on the effects of a variety of individual and firm factors on the sectoral allocation and wage
rates. There are only a few studies that address self-selection of workers into different sectors, in particular, with control for firm effects.

### 5. Results

Tables 2-1, 2-2, and 2-3 show the estimated coefficients of the for-profit selection equation and monthly, daily, and hourly wage equations. Since regular and non-regular workers are paid by these different types of wages, we need these to standardize the results. The results of the sector allocation probit regression in the first column basically replicate unadjusted comparisons between the two sectors in Table 1. At the 5-percent-level significance, workers who are relatively young and who have fairly long labor market experience and a two-year community college degree remain less likely to self-select into proprietary homes. Also, we observe that both regular and nonregular employees with long hours of work, at firms with larger numbers of employees, and longer hours of care are significantly preferable for nonprofit organizations.

The rest of the columns in these tables show the estimated coefficients of wage equations for proprietary and not-for-profit centers, corrected for self-selection bias. Focusing on hourly wages (Table 2-1), male, older, and more experienced employees with higher degree of education and qualifications seem to be more appreciated in the not-for-profit sector than the proprietary sector, where none of these factors are statistically significant. Coefficients of squared years of age and experience in Table 2-2 designate a familiar pattern of wage profile that does not linearly increase along with age and market experience in the not-for-profit sector. On the other hand, the profit-seeking sector rewards regular and non-regular workers with long hours, more than the not-for-profit sector, which is consistent with the propensity of these workers to self-allocate into for-profit centers.

Moving down to the effects of facility characteristics, larger proprietary firms offer lower wage rates, which is inconsistent with previous studies. In the not-for-profit sector, at the 5-percent-level significance, the effects of the firm size on wage rates are positive, yet
they remain almost the same magnitude along with the size of firm. Workers in for-profit facilities providing extra hours of care are valued more than those in the not-for-profit sector, although employees in facilities that actually operate for longer hours are less appreciated in both sectors.

Finally, it is important to point out the coefficients of truncated mean adjustment factors for selection bias, $ \theta^{1} $ and $ \theta^{2} $ in the wage equations. The estimates in this study show that both $ \theta^{1} $ and $ \theta^{2} $ are significantly positive, which implies that unobserved factors extensively affect employee allocation and wage rates. Although observed variables show that workers are not heterogeneous as discussed above, $ \theta^{1} > \theta^{2} $ shows that the relations between unobserved factors and both sectoral allocation and wage rates are larger in the proprietary than nonprofit sectors. Our estimates show that a worker who has tendency to choose for-profit earns 21.8 percent higher wages than a worker who is inclined to choose nonprofit facilities if he is employed in for-profit center. He also earned more than his counterpart if he works for a nonprofit center, but the difference is smaller. Therefore, our estimates demonstrate that there is a self-selection pattern between two sectors along with comparative advantage among workers who tend to choose the sector offering the highest wages. This implicitly means that the mean wages of employees who are actually self-allocated into profit facilities are greater than wages that would have been observed if they chose to work in not-for-profit facilities. On the contrary, the mean wages of employees who in fact chose to work in the nonprofit sector are greater than wages that would have been observed if employees with observed similar characteristics self-allocated into the profit sector.

### 6. Factor Decomposition Analysis of Wage Differentials Between Two Sectors

Based on the estimates from the wage equations corrected for self-selection bias in Tables 2-1, 2-2, and 2-3, we apply a simple decomposition analysis to the wage differential to distinguish the contributions of attributes from differential contributions in valuation of
key explanatory factors between for-profit and not-for-profit centers to the nonprofit wage premium. The total effects are broken down in the following way:

$$ \begin{aligned}&\sum\mathrm{W}_{\mathrm{i}}^{2}-\sum\mathrm{W}_{\mathrm{i}}^{1}=\sum\left(\mathrm{X}_{\mathrm{i}}^{2}\delta^{2}+\lambda_{\mathrm{i}}^{2}\theta^{2}\right)-\sum\left(\mathrm{X}_{\mathrm{i}}^{1}\delta^{1}+\lambda_{\mathrm{i}}^{1}\theta^{1}\right)\\&=\left\{\sum\delta^{2}\left(\mathrm{X}_{\mathrm{i}}^{2}-\mathrm{X}_{\mathrm{i}}^{1}\right)+\sum\theta^{2}\left(\lambda_{\mathrm{i}}^{2}-\lambda_{\mathrm{i}}^{1}\right)\right\}+\left\{\sum\left(\delta^{2}-\delta^{1}\right)\mathrm{X}_{\mathrm{i}}^{1}+\sum\left(\theta^{2}-\theta^{1}\right)\lambda_{\mathrm{i}}^{1}\right\}\\ \end{aligned} $$

where $ \left\{\sum\delta^{2}\left(\mathrm{X}_{\mathrm{i}}^{2}-\mathrm{X}_{\mathrm{i}}^{1}\right)+\sum\theta^{2}\left(\lambda_{\mathrm{i}}^{2}-\lambda_{\mathrm{i}}^{1}\right)\right\} $ is the summation of each factor's qualitative differential contributions and $ \left\{\sum\left(\delta^{2}-\delta^{1}\right)\mathrm{X}_{\mathrm{i}}^{1}+\sum\left(\theta^{2}-\theta^{1}\right)\lambda_{\mathrm{i}}^{1}\right\} $ is the sum of differential contributions in valuation of each explanatory variable. The results are shown in Tables 3 and 4. Looking at the daily wage differences in the first panel of Table 3, the summation of hourly wage differentials between the nonprofit and for-profit sectors over all explanatory variables is 28.3 percentage points (398 yen in real value) after controlling for unobserved self-selection bias. The characteristics of employees and facilities (attributes) and sector valuation account for 44.8 percentage points (761 yen) and minus 16.5 percentage points (-362 yen) of the total, respectively. Table 4 shows the breakdown of sectoral wage differentials in real value by factor, where positive (or negative) values enlarge (or reduce) the total nonprofit wage differential. The last column reports that employee demographic characteristics, market experience, education, qualifications, and the size of firms contribute to the higher observed wage in not-for-profit facilities. For all these factors other than gender, market experience, and education, the magnitude of effect is largely due to the higher value on characteristics in the not-for-profit sector than the for-profit sector. In other words, not-for-profit facilities value these attributes much more than they do in the proprietary centers. Therefore, as previous studies found (Idson and Feaster (1990) and Holtmann and Idson (1993)), nonprofit managers are less likely to be cost-sensitive in total under the non-distributional constraint. They are, therefore, more likely to value worker productivity associated with the quality of services related to age, market experience, education, qualifications, and the size of firms. This result is seen to be completely consistent with the property-rights hypothesis.
Focusing on the selectivity, we found that the total effect of selectivity is negative (-42 yen) and the net of selectivity (reducing the effect of selectivity from the total effect) is 440 yen. Also, since the truncated mean is positive in the for-profit sector, the positive coefficient on $ \lambda_{i}^{1} $ entails that wages for the average observed self-selected for-profit employees are higher than would be observed if employees are randomly allocated across two sectors. This implies that a random allocation of employees would lead to even lower wages in the for-profit sector relative to wages in the nonprofit sector, and would enlarge the wage differential between two sectors. In contrast to the results of Holtmann and Idson (1993), our result shows that a large number of workers who actually chose to work in nonprofit centers according to their comparative advantage are redistributed to for-profit centers by a random reallocation procedure, decreasing for-profit relative to nonprofit wages. As shown in Table 4, this negative selectivity effect is mostly attributed to differential characteristics rather than to sector valuation of the selectivity. However, the magnitude of the selectivity is not large enough to conclude that the presence of a larger number of workers who have unmeasurable comparative advantage in the not-for-profit relative to for-profit sectors is a serious cause of nonprofit wage premium. Rather, to improve efficiency in child care management and to break through the bottleneck of child care supply, the policy should shed light on the lavish and inefficient rate of return to workers in the not-for-profit sector.

### 7. Conclusion

The activities and enhanced presence of the nonprofit sector are still remarkable in various Japanese industries. Those employed in the nonprofit sector account for up to 3.8 percent $ ^{11} $ of total employment in 2000. An increase in the demand for child care due to the rapid growth of female labor participation rates would lead to a strong political incentive.
for the Japanese government to achieve market efficiency in the child care industry. This in turn will lead to accelerating the entry of for-profit firms into the conventional nonprofit sector and to stimulating competition between different types of firms in the market. Under such a drastic change in socio-economic circumstance, the empirical assessment of the child care industry, where both for-profit and nonprofit sectors coexist, will give us significant clues regarding policy implications from various aspects.

In this paper, we focus on the differences in economic behavior on wage setting between for-profit and nonprofit facilities. We hypothesize that the nonprofit wage premium in the child care market may be accounted for by the segregated labor market between two sectors, providing observed and unobserved different quality of services owing to “non-distributional constraints.” Under “non-distributional constraints,” nonprofit centers are prohibited from distributing net earnings, which makes nonprofit providers raise the quality of services to avoid the opportunistic behavior often observed in for-profit facilities. Since child care is a labor-intensive product, the difference in quality of workers between for-profit and nonprofit facilities will most likely clarify the quality of the service provided.

We have an empirical challenge in this context: sample selection bias caused by the endogeneity problem such that both sector affiliation of workers and wage rates are correlated with various unobserved individual and facility characteristics. We present three major empirical findings. First, our empirical results confirm that there is a significant magnitude of nonprofit wage premiums in the child care labor market in Japan before and after controlling for nonrandom unobserved self-selection bias, even after controlling for differences in subsidies for each area and facility. Second, nonprofit firms are more likely to value workers with respect to age, market experience, education, qualifications, and the size of firms than are for-profit firms. Third, the child care market is segregated between for-profit and not-for-profit facilities in Japan as a consequence of the presence of comparative advantage on worker self-allocation procedures. More experienced workers with higher levels of education and qualifications, who therefore may provide a higher quality of care, tend to choose working in nonprofit centers because they are more likely to
be valued in the not-for-profit sector compared to the proprietary sector. Fourth, the significant amounts of nonprofit wage premiums in the child care market are most likely to be caused by the high value on not-for-profit workers rather than on the presence of a larger number of workers who have unmeasurable comparative advantage in the nonprofit sector.
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