Nonlabor Income and Age at Marriage: Evidence From China’s Heating Policy

We exploit China’s heating policy to investigate how nonlabor income affects marriage. From the mid-1950s, the policy gave substantial subsidies to urban residents north of the Huai River. Applying geographic regression discontinuity, we find that with the policy, urban men in the north married 15 months earlier than men in the south. The difference is substantial given that the average age at first marriage is 24.9 years for urban men in the south. The effect is larger for later birth cohorts, which is consistent with the progressive implementation of the policy. The effect is smaller among women, consistent with women having less power in the household than men. There is no effect among rural residents, who did not benefit from the heating policy. Electronic supplementary material The online version of this article (10.1007/s13524-018-0732-1) contains supplementary material, which is available to authorized users.


Appendix B. Data and Supplementary Estimates
To further check whether our estimated north/south difference in age of first marriage is driven by factors than are not related to heating policy, we run another 20 counterfactual analyses by setting hypothetical policy boundaries at 50 km intervals from 500 kms south to 500 kms north of the Huai River. Figure A2 plots these hypothetical boundaries. The figure shows that while the Huai River is in the middle of a flat region (the Huang-huai and Jiang-huai plains), most of the hypothetical policy boundaries cross mountains as well as plains. Obviously, mountainous areas are thinly populated, and so, the bulk of the people on the two sides of a hypothetical boundary crossing mountains could live hundreds of kms apart. Hence, people living on different sides of the boundary could behave quite differently, which a smooth function of distance would not properly control for. This violates a fundamental assumption of GRD, and the GRD estimate is likely to be sensitive to the choice of the boundary.
The estimates using hypothetical boundaries are reported in Table A4 and plotted in Figure A3. Most of the coefficients are not significantly different from zero. The coefficients that are statistically significant are unstable. For instance, among the three clusters of coefficients that are significant ˗ between 450 and 250 kms south, between 150 and 200 kms north, and between 350 and 450 kms north, the estimates oscillate between positive and negative. The instability of these estimates could be due to the hypothetical boundaries crossing mountains. The only robust estimate is that for the actual Huai River boundary. These estimates provide further support to our conclusion that the heating policy indeed affected the age of first marriage of the affected cohorts. B-2 Figure A1. Possible confounds (urban men born in 1956-65) Notes: Sample comprises male residents with urban hukou born in 1956-65. Graphs depict fitted values from local polynomial estimate of the possible confounds (as labeled in each graph and explained in Table 2, Panel B) on distance from the Huai River, and corresponding 95 percent confidence intervals. Dots represent average of possible confounds within 50 km bins. All estimates are at individual level, except for rice culture, gender ratio, and GDP per capita by county, and Confucianism and SOE employment by prefecture. B-3 Figure A2. Hypothetical policy boundaries Notes: The solid line on the map is the Huai River and the black dotted lines are the hypothetical policy boundaries at 100-km intervals from 500 kms south to 500 kms north of the Huai River. B-4 Figure A3. Regression discontinuity estimates with hypothetical policy boundaries Notes: Coefficients of north and corresponding confidence intervals from GRD estimates with hypothetical policy boundaries at 50-km intervals from 500 kms south to 500 km north of the Huai River (Table A4).  Vol. 18 No. 25,Labor,Chapter 7.5,    Notes: Estimated by OLS (except columns (6)-(7) by Stata routine, rdrobust), with quadratic distance polynomials and MSE-optimal bandwidth; Sample comprises married male residents in the 2000 census with urban hukou within MSE-optimal bandwidth, born in 1956-65, who did not move from neighborhood of birth; Dependent variable is age at first marriage; Standard errors clustered by county in parentheses (***p < 0.01, **p < 0.05, *p < 0.1). Column (1): Preferred estimate from Table 5, column (6); Column (2) repeats column (1) but replaces the urban sample by its rural counterpart; Column (3) specifies boundary as 32.5 o N and assigns distance by latitude, with optimal bandwidth of 0.93 o ; Columns (4)-(5) specify boundary as 50 kms north or south of the Huai River; Column (6) repeats column (1) with linear distance polynomials; Columns (7)-(8) repeat column (1) with alternative density functions; Column (9) repeats column (1) using a multi-level model that includes county fixed effects, county-specific random coefficients for age, Han Chinese, education, occupation, living with parents, and province-specific coefficients for Confucianism, rice culture, gender ratio and GDP per capita; Column (10) excludes men whose wife holds rural hukou; Column (11) includes urban men in adjacent provinces (Shandong, Hebei, Shanxi, Hubei, Jiangxi, Zhejiang, and Shanghai); Column (l) repeats column (12) with parametric RD method.
B-8  Notes: Panels A and B estimated by OLS, using parametric GRD with quadratic distance functions; Panels C and D estimated by Stata routine, rdrobust, using non-parametric GRD with quadratic distance functions and asymmetric MSE-optimal bandwidths (reported as "south/north"). Sample: men and women with urban hukou in all cohorts; Standard errors clustered by county in parentheses (***p < 0.01, **p < 0.05, *p < 0.1).  (3): Estimates on individuals with below and above median years of education; Columns (4)-(6): Estimates on individuals in government or professional occupation or otherwise.

Appendix C: Differences in Differences
The GRD analyses estimate the local average treatment effect (LATE) of the heating policy in the neighborhood of the Huai River. Besides, it is also useful to understand the average treatment effect (ATE) of the heating policy, which is the effect on the broader population.
To investigate, we apply an empirical strategy of Differences in Differences (DID) and estimate a regression of the age at first marriage among all people with urban hukou: where C jt = 1 if individual j was born in cohort t, λ 0 is a constant, λ 1 represents the northsouth difference in age at first marriage across all urban birth cohorts, λ 2t represents the common time trend for birth cohort t, and λ 3t represents the north-south difference in the time trend for cohort t, which is due to the heating policy, and ε ji represents a random error term. The other variables and coefficients are as defined in (8) and (11).
Besides identifying the ATE rather than the LATE, the DID analysis is also helpful as it relies on different identification assumptions from the GRD analyses. DID analyses assume that the outcome of interest follows the same trend in both the control and treatment groups subject to a possible time invariant difference. Typically, this would be validated by showing a common pre-treatment trend. Unfortunately, our sample contains only one cohort  which married before the heating policy, and so, we cannot test the existence of a common pre-treatment trend. Nevertheless, since counties in the north and south of the Huai River belong to the same provinces, and so, are subject to similar regulations, the common trend hypothesis is justifiable. By comparison, the GRD analyses rely on the assumption that the heating policy is the only factor that affects marriage which is discontinuous at the Huai River. Although we have checked the robustness of the GRD finding in various ways, it is useful to apply tests that rely on different assumptions.
As a preliminary, Table A7 reports the age at first marriage among men and women in the various birth cohorts with urban hukou resident in areas north and south of the Huai River.

C-1
Among all cohorts of men and all cohorts of women except those born between 1946-55, the age at first marriage is significantly lower in the north than south. Table A8 reports estimates for men and women with urban hukou, and including controls, X ji , comprising prefecture fixed effects and demographic, social, cultural, and other factors that affect marriage. The coefficient of north represents the north-south difference in the age at first marriage in the oldest cohort . The coefficient of north for the later cohorts represents the difference in the north-south difference in the age at first marriage between the respective cohort and the oldest cohort.
Referring to The estimate of the ATE is smaller than the corresponding GRD estimate of the LATE in Table 5, column (5). Apparently, the heating policy had a smaller effect on the age at first marriage in the north vis-à-vis south as a whole as compared with the immediate north vis-à-vis south of the Huai River. Referring to Figure 3(d), the age at first marriage increased with distance from the Huai River towards the south and north. The DID estimate suggests that, controlling for province and other controls, the north-south difference becomes smaller with distance from the Huai River.
1 For women, the coefficient of north for the 1956-65 cohort is negative but imprecise. Combined with the coefficient of north for the 1926-35 cohort, the estimated north-south difference in the 1956-65 cohort is 0.43 years and significant. A puzzle is that the coefficient of north for the 1946-55 cohort is positive.
C-2 C-3 Notes: Sample comprises residents in the 2000 census in Henan, Anhui, and Jiangsu born in 1926-65, with urban hukou, who did not move from neighborhood of birth. Upper rows report mean values, standard deviations in parentheses and frequencies in brackets; Lower rows report difference in means between north and south with tstatistics (***p < 0.01, **p < 0.05, *p < 0.1). Notes: Sample comprises residents in 2000 census with urban hukou born in 1926-65 who did not move from neighborhood of birth; Estimated by OLS with prefecture fixed effects and covariates (as listed in Table 5); Dependent variable: age at first marriage; Column (1): Men; Column (2): Women. Standard error clustered by county in parentheses (***p < 0.01, **p < 0.05, *p < 0.1). North-south difference is the sum of the coefficient of North and the coefficient of the interaction of North with the respective birth cohort.