Silviase/jgov_v1.4_full_ann huggingface dataset:
settings.

Moving down to the effects of facility characteristics, consistent with previous studies, wage rates become greater along with the firm size, and the statistical significance is slightly higher in for-profit than nonprofit homes. As regards non-wage benefits, for either full-time or part-time workers, proprietary facilities offering public pensions would lower wage rates. The provision of employment insurance and wages are appeared to be trade-offs in nonprofit homes. In general, non-wage compensations other than insurance such as professional trainings and various supports to employees seem to have negative influences on wage rates in both sectors. However, the results are slightly more significant in for-profit than in nonprofit homes. Consequently, it seems that nonprofit facilities would recompense workers' identifiable experience, some human capital with advanced skills, and their stability more than for-profit homes, while some non-wage compensation benefits appear to lower wage rates in both sectors.

Finally, it would be important to discuss that the coefficients of truncated mean adjustment factors for selection bias, $ \theta^{1} $ and $ \theta^{2} $ in the wage equations, to test the hypothesis that the labor market in the nursing home industry is segregated between the for-profit and not-for-profit sectors providing different quality of services. The estimates in this study show that both $ \theta^{1} $ and $ \theta^{2} $ are significantly positive, which implies that unobserved factors extensively affect employees' allocation and wage rates. Further, the necessary condition ( $ \theta^{1} > \theta^{2} $ ) for the comparative advantage theory suggested by Trost (1981) is met. $ \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. Therefore, our estimates on the coefficients of truncated mean adjustment factors for selection bias are seen to demonstrate that there is a self-selection pattern between two sectors along with comparative advantage among workers who tend to be choosing 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 were self-allocated into the profit sector. The result is entirely inconsistent with the strict hierarchical sorting assumption such that employees who do better performance than average in the proprietary sector would always do better than average in the nonprofit sector. In other words, they are valuating seemingly similar workers with various unobserved characteristics somehow differently in a way that nonprofit homes value workers with longer market experience and higher level of skills or education who suppose to provide better quality of care than for-profit homes. Therefore, we can conclude that the market is segregated between for-profit and not-for-profit facilities that are assume to be providing different quality of services. Since proprietary firms just started entering in the long-term care market, we suspect that the quality of service in the for-profit sector has not caught up yet with the one in the nonprofit 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 Table 3, we will apply a simple decomposition analysis to the wage differential, in order for distinguishing the contributions of attributes from differential contributions in valuation of key explanatory factors between for-profit and not-for-profit homes to the nonprofit wage premium. The total effects are decomposed 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 4 and 5. Looking at Table 4, the summation of wage differentials between nonprofit and
for-profit sectors over all explanatory variables is 17.8 percentage points (433 yen in real value) after controlling for unobserved self-selection bias, which is different from a simple linear estimate without controlling for self-allocation that might be biased in Table 2. The characteristics of employees and facilities (attributes) and the sector valuation account for 3.2 percentage points (-437 yen) and 14.5 percentage points (870 yen) of total, respectively. Table 5 shows the decomposition of sectoral wage differentials in real value by factor, where positive (or negative) values enlarge (or reduce) total nonprofit wage differential. In other words, without the positive (or negative) contribution of a factor, the total nonprofit wage premium will be reduced (or enlarged). Both qualifications and various non-wage supports to employees other than insurance are seen to contribute to the higher observed wage in not-for-profit facilities. For qualifications, the magnitude of effect is largely due to the attributes, whereas, for non-wage supports, it is mainly due to higher value on the characteristics. Age as a proxy of experience does also increase wages in nonprofits above proprietary homes, which depends on higher valuation on the attributes in the not-for-profit sector. On the other hand, the rest of the factors are affected in the opposite way: the pattern of male, full-time status, and most notably facility characteristics such as size of facility, insurance, hiring status, and professional training. For these factors, for-profit facilities value these attributes much higher than in the nonprofit sector. Therefore, wages in the proprietary sector are seen to grow at a faster rate with size, the presence of insurance, current hiring status, and the provision of professional training, than in the nonprofit sector. These are consistent with the previous empirical results shown by Idson and Feaster (1990) and Holtmann and Idson (1993) $ ^{11} $ .

Focusing on the selectivity, we found that the total effect of selectivity is negative (-592 yen) and the net of selectivity (reducing the effect of selectivity from the total effect) is 1025 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 that 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 to 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 homes according to their comparative advantage are redistributed to for-profit institutions by random reallocation procedure, decreasing for-profit relative to nonprofit wages. As shown in Table 5, this negative selectivity effect is mostly contributed by differential characteristics rather than sector valuation of the selectivity that performs in the positive direction, which are canceled with each other, eventually helping to expand the wage differential between two sectors as total. We would like 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 would be a more serious cause of nonprofit premium rather than the not-for-profit sector's lavish and inefficient rate of return to workers in the long-term care market in Japan.

### 7. Conclusion

Unlike the long-term care market in the United States, the Japanese nursing care market had been legally restricted to be run by the nonprofit sector. The recent introduction of the long-term care insurance lastly allows for -profit facilities to enter only the home-help market and for-profit and not-for-profit firms have just started to compete in the long-term care market in Japan. The current strong political incentive for the Japanese government to restructure administrative and industrial organizations 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 same market. Under such a drastic change in socio-economic circumstance, employment in the labor market where both for-profit and nonprofit sectors coexist will also expand. Therefore, the empirical
assessment of the introduction of for-profit into the nursing industry as a social experiment gives 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 long-term 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 constraint.” Under “non-distributional constraint,” nonprofit homes 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 long-term care is a labor-intensive product, the difference in quality of workers between for-profit and nonprofit facilities is the most likely to clarify the quality of product provided.

We have a couple of empirical and theoretical challenges in this context. An empirical challenge is 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 support to confirm that there is nonprofit wage premium in the long-term care labor market in Japan before and after controlling for nonrandom unobserved self-selection bias. Second, nonprofit firms are more likely to value workers with respect to age as a proxy of market experience and the qualifications as proxies of education than for-profit firms. Third, the long-term care market is segregated between for-profit and not-for-profit facilities in Japan as a consequence of the presence of comparative advantage on workers' self-allocation procedure. More experienced workers with higher level of education, therefore who may provide the higher quality of care, tend to choose working in nonprofit homes because they are more likely to be valued in the not-for-profit sector compared to the proprietary sector.

Our theoretical challenge is related to how to measure and interpret the quality of services provided by both sectors. Most previous studies positing that higher quality of products in the not-for-profit sector produced by high-quality workers might account for
nonprofit wage premium control for various individual and facility characteristics like education, market experience, marital and family status, full-time or part-time status, facility affiliation, non-wage compensations, and professional supports, and so forth, as observed quality measures (Preston (1988), Preston (1989), Holtmann and Idson (1993), Mocan and Viola (1997), Mocan and Tekin (2000), Leete (2001)). Although proprietary firms have just started entering into the long-term care market, we observe that several verifications that nonprofit facilities might be producing better quality of care than proprietary institutions. For example, those who are supposed to have relatively long market experience (measured by age as a proxy indicator) and advanced level of skills and education (assessed by qualification as a proxy factor) are more likely to be self-allocated into the nonprofit sector and they are unsurprisingly given a greater rate of return for their high-quality work in not-for-profit firms.

We also suspect that for -profit and nonprofit institutions would be producing completely different contents of products, rather than high and low quality of services, in the sense that for-profit nursing homes are more likely to supply daily needs to the elderly, as opposed to intensive long-term care such as rehabilitation, nursing care, and medical treatments often performed at special nursing homes operated merely by nonprofit organizations due to legal restrictions. To avoid multicollinearity, dummy variables for contents of services are not included into our previous estimation procedure. As regards home helpers, care managers, staff nurses, and service managers that appear to have nonprofit wage premiums based on simple semi-logarithmic wage functions, we applied the same empirical procedure separately, controlling for service dummies. Tables 6 and 7 show the results.

These separated regression analyses clarify a significant aspect more clearly than our previous over-all regression; that is, for-profit firms might unfairly value both observed and unobserved productivity-related workers' attributes, leading to a much larger number of workers with comparative advantage in the not-for-profit sector. After correcting for selection bias, the summations of wage differentials between nonprofit and profit sectors over all explanatory variables are 1.8 percent (1,006 yen) for home helpers; -1.7 percent
(-226 yen) for care managers whose nonprofit wage differential turns negative; 3.9 percent (884 yen) for staff nurses; and 18.3 percent (2,161 yen) for service managers. In particular for home helpers and staff nurses, the sector valuation on their attributes related to productivity such as age, full-time status, and professional training, which are supposed to guarantee the quality of service provided, appears to contribute to the majority of the nonprofit wage premium. In contrast, the sectoral valuation on service contents is slightly higher for home helpers or even largely lower for staff nurses in nonprofit homes, relative to for-profit facilities, implying that the nonprofit sector is not necessarily behaving inefficiently. Nevertheless, focusing on the selectivity, again we found that the total effect of selectivity is slightly negative, lending to expand the wage differential between two sectors. Examining our suspicion that the presence of unmeasured comparative advantage in the nonprofit to for-profit sector remains a crucial challenge for further theoretical and empirical investigations. Further, we should continue to investigate empirically how the difference in wage setting probably associated with the quality of care in the for-profit sector and the nonprofit sector will be changing after proprietary firms settle down in the long-term care industry in Japan.
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Note:

Table 2: For-profit logarithmic wage differential by occupation

Full sample(n=24,967)	Helper(n=6,075)	Care Manager(n=2,218)	Staff nurse(n=3,686)	Service manager(n=814)
Unadjusted	-0.047(0.007)	a	-0.011(0.008)	0.031(0.018)	b	-0.009(0.017)	-0.179(0.025)	a
Adjusted for all characteristics	-0.016(0.007)	a	-0.053(0.011)	a	-0.037(0.024)	c	-0.029(0.018)	c
by semi-logarithmic wage function	0.505	0.332	0.268	0.453	0.455

(1) As regards physicians, social workers, social care workers, and physical/occupational therapists,

the regressions adjusted for all characteristics are statistically insignificant.

level of 5%, 10%, and 15%, respectively.

(3) Values in parenthesis are standard errors.
Table 4: Decomposition analysis of nonprofit sectoral wage differentials

logarithmic value	real value
(1) The predicted wage of not-for-profit facility	9.164	10302.264
(2) The predicted wage of for-profit facility	8.986	9869.107
(3) The predicted wage differential due to attributes	0.032	-436.775
(4) The predicted wage differential due to valuation	0.145	869.933
(5) Total predicted wage differential	0.178	433.158
between for-profit and nonprofit facilities

Note:

(1) $ \sum\left(\mathbf{X}_{\mathrm{i}}^{2}\boldsymbol{\delta}^{2}+\lambda_{\mathrm{i}}^{2}\boldsymbol{\theta}^{2}\right) $

(2) $ \sum\left(\mathbf{X}_{\mathrm{i}}^{1}\boldsymbol{\delta}^{1}+\lambda_{\mathrm{i}}^{1}\boldsymbol{\theta}^{1}\right) $

(3) $ \left\{\sum\delta^{2}\left(\mathbf{X}_{\mathrm{i}}^{2}-\mathbf{X}_{\mathrm{i}}^{1}\right)+\sum\theta^{2}\left(\lambda_{\mathrm{i}}^{2}-\lambda_{\mathrm{i}}^{1}\right)\right\} $

(4) $ \left\{\sum\left(\delta^{2}-\delta^{1}\right)\mathbf{X}_{\mathrm{i}}^{1}+\sum\left(\theta^{2}-\theta^{1}\right)\lambda_{\mathrm{i}}^{1}\right\} $

(5) (1)-(2)=(3)+(4)
Table 5: Decomposition analysis of nonprofit sectotal wage differentials by factors

Due to differentials of attributes a/	Due to differentials of valuations b/	Total wage differentials c/
Male	19.999	-162.974	-142.975
Age	-153.333	402.479	249.146
Full-time	283.496	-394.343	-110.847
Part-time, but regular	-26.469	-166.157	-192.626
Qualifications	709.533	37.695	747.228
Size	8.981	-186.649	-177.668
Insurance	76.317	-445.139	-368.822
Hiring status, stability	4.037	-322.542	-318.505
Professional training	73.097	-501.870	-428.773
Various supports	70.422	167.198	237.620
Other	115.302	-920.112	-804.810
Prefecture	-523.450	-1443.770	-1967.220
Selectivity	-1094.709	502.788	-591.921
Intercept	-	4303.329	4303.329
Total	-436.775	869.933	433.158
-3433.3964	d/	1025.0785 e/

Note:

$$ \begin{array}{r l}{\mathrm{a/}}&{{}\left\{\sum\delta^{2}\left(\mathrm{X}_{\mathrm{i}}^{2}-\mathrm{X}_{\mathrm{i}}^{1}\right)+\sum\theta^{2}\left(\lambda_{\mathrm{i}}^{2}-\lambda_{\mathrm{i}}^{1}\right)\right\}}\end{array} $$

$$ \begin{aligned}\mathbf{b}/\quad\left\{\sum\left(\delta^{2}-\delta^{1}\right)\mathbf{X}_{i}^{1}+\sum\left(\boldsymbol{\theta}^{2}-\boldsymbol{\theta}^{1}\right)\boldsymbol{\lambda}_{i}^{1}\right\}\end{aligned} $$

$$ \mathrm{c}/\quad\sum\left(X_{i}^{2}\delta^{2}+\lambda_{i}^{2}\theta^{2}\right)-\sum\left(X_{i}^{1}\delta^{1}+\lambda_{i}^{1}\theta^{1}\right) $$

d/ Net of the intercept

e/ Net of selectivity