The Eﬀect of Transportation Beneﬁts on Health and Consumption Among the Elderly: Quasi-Experimental Evidence from Urban China


 This study estimates the causal eﬀect of transportation subsidies or similar beneﬁts on the health of the elderly. We exploit a discontinuity in the probability of receiving transportation beneﬁts induced by an age-based policy to take account of the endogeneity of treatment status. Our baseline IV results indicate that receiving public transportation beneﬁts signiﬁcantly improves elderly people’s health condition by approximately 10 percentage points. The results are robust under diﬀerent speciﬁcations and placebo tests. Further tests on possible channels show that the health eﬀect is driven by increasing food consumption and health care utilization, but not by the amount of exercise done.


Introduction
Public transportation is a key component of our lives that offers a safer, more economical, and more environmentally friendly transit choice. The demands on public transit have increased rapidly over the last decade in the context of an aging population.
More than one-fifth of Americans over age 65 do not drive due to poor health, limited physical or mental abilities, concerns over safety, or lack of access to a car (Bell and Cohen, 2009). Would public transit be a better alternative for them than personal vehicles? On the one hand, public transit is supposed to reduce air pollution and traffic congestion (Anderson, 2014), increase mobility (Green et al., 2014), and thus improve public health. On the other hand, promoting public transit requires a huge amount of subsidies to pay for operating costs above passenger fare revenues received. According to Parry and Small (2009), average passenger fare subsidies account for 65% of operating costs across the twenty largest transit systems in the U.S. Despite the huge cost of granting them, reduced fare and free ride permits for senior citizens and individuals with disabilities are offered in many cities. But do these public transit programs really benefit citizens' health?
The transportation literature has mainly focused on the impact of transit benefits on people's travel behavior, while its causal impact on people's health remains unknown. Coronini-Cronberg et al. (2012) studied the impact of a free elderly bus pass on active travel and regular walking in England, and found that having a free pass is positively associated with incidental physical activity. Webb et al. (2011) also reports similar results for other parts of England. Edwards et al. (2013) studied the impact of free bus travel for young people in London. However, he found little impact on active travel overall. Bueno et al. (2017) studied employees' travel behavior using data from New York and New Jersey, where employer-funded benefits for transit passes and bike reimbursements could be substituted for personal vehicle use.
However, it is difficult to evaluate the causal impact of transportation benefits on public health. Potential endogeneity issues are as follows: (1) Omitted variable bias: If unobserved factors are common between subsidy participation and health, then the effect of transportation benefits on health is biased. Supposing that unobserved health awareness is both positively correlated to subsidy participation and health, then the estimates would be upwardly biased; (2) Self-selection: Generally, transportation benefits are not mandatory. Even when a person is eligible for a subsidy, he has to apply to participate. If an elderly person with a low budget self-selects himself into treatment, then the marginal health impact will likely be exaggerated. Craig et al. (2012) points out that natural experiments are necessary for policy evaluation in the field of public health.
Furthermore, multicollinearity among eligible ages for transit, retirement, and health care benefits makes the impact of transportation subsidies ambiguous or unidentifiable.
For instance, in the U.S., elderly people who are eligible for reduced fare permits (age 65 or older) have higher chance of being retired, as the full retirement age ranges from 65 to 66 for this cohort 1 . At the same time, senior citizens become eligible for the Medicare program, which basically covers hospital and medical insurance for all people who are 65 or older. Any estimates solely relying on variation in age would capture a mixture of these policies in U.S. Isolating the impact of transit benefits from other aging policies is a near-impossible task, as multiple aging benefits are given at a certain age simultaneously.

As of 2015
This paper contributes to the literature in the following three ways. First, this paper includes a credible identification strategy to evaluate the health benefits arising from transportation subsidies. Using data from Shanghai, which is comparable to larger cities in Western countries, we take account of the endogeneity of transit subsidy participation and overcome the multicollinearity issue by the unique policy design in China.
In Shanghai, elderly persons who are age 70 or older are eligible for free transportation, while those who are under age 70 are not. Using the sudden change in the probability of receiving transportation benefits around age 70, we clearly identify the causal effect of transportation on health status among the elderly by a fuzzy regression discontinuity design (FRD), which is equivalent to the instrumental variable (IV) approach. Moreover, one must take note of the fact that the mandatory retirement age in China is 60 for men and 50 for women 2 , providing a sufficient window of time between retirement age and becoming eligible for transit benefits to ensure that our estimates do not suffer from multicollinearity problems.
Second, our estimates are probably very close to the average treatment effects (ATE) that capture the health impacts of free public transit on the overall aging population.
Under the IV framework, different instruments measure different local average treatment effects (LATE) among different subpopulations (Imbens and Angrist, 1994). If treatment effects are heterogeneous across subpopulations, then estimated LATE would not be informative in terms of how the average health status of elderly has been improved by transit subsidies. Economists have started to search for robust instruments that influence larger and more representative subpopulations, which should not be systematically different from their untreated peers (Oreopoulos, 2006;Ebenstein, 2009). In the 2 55 for female cadres transit subsidy case, self-selected treatments or any application requirements other than age would prevent us from understanding the ATE. Mah and Mitra (2017) shows that lower-income elderly have a higher likelihood of using their free passes in Canada, by which one would be able to capture the LATE among the lower-income group instead of just using the average population. This paper relies on a remarkable natural experiment in Shanghai, where 82.5% eligible elderly people receive free transit benefits, to estimate the average impacts of transit subsidies on senior citizens' health statuses.
Third, we clearly identify the mechanisms by which public transportation benefits affect the elderly's health status. We examine three possible channels: amount of exercise, food consumption, and health care utilization. According to conventional wisdom, free transit programs may encourage people to use public transit instead of personal vehicles, thus increasing incidental physical activity and even that amount of exercise could potentially improve public health. We argue that the health impact of free transit programs through added exercise will be limited, or at least statistically insignificant.
On the contrary, we show that the greater health impacts will be driven by increased food consumption and expanded health care utilization. Free transit programs improve the elderly's access to markets and hospitals. Specifically, households with low food budgets may substitute transportation consumption with more food; and people living close to the hospital (no more than two kilometers) will visit their doctors more frequently and thus spend more on health care.
Our baseline IV results show that free public transportation significantly improves the elderly's health by approximately 10.1 percentage points, while the corresponding OLS indicates 10.8 percentage points. We show that the treatment group of elderly free transit recipients are no different from the control group in terms of gender, schooling, number of children, marital status, exercise levels, and pensions around the eligibility cutoff. We have also conducted a battery of robustness checks and placebo tests to determine whether our results are sensitive to functional forms of the forcing variable in FRD, and whether our results are driven by cohort-specific unobserved factors other than transit benefits.
The remainder of this paper organized as follows. Section 2 briefly introduces the institutional background. Section 3 provides the identification strategy. Section 4 describes the dataset and lists the descriptive statistics. The following section presents our baseline results. Section 6 discusses the mechanisms. Section 7 checks the robustness of our results. Section 8 concludes.

Institutional Background
Shanghai has always been one of the most populous cities in the world, with a permanent population estimated to have been approximately 24.15 million in 2015 3 . Senior citizens aged 65 or over account for 19.6% among the registered population, which is comparable to global cities such as London (21% 4 ), New York City (13.2% 5 ), and Tokyo (23.3% 6 ). In the context of the rapid aging process, Shanghai has enhanced its healthcare insurance system and old-age pension to improve the quality of life of the elderly.
Beginning in 2009, Shanghai has carried out a free ride permits for senior citizens who are at least 70 years old. After applying to the free transit program, eligible citizens obtain a public transit pass that entitles them to unlimited travel by metro and bus It is worthwhile to emphasize some unique features of the free transit program in Shanghai. First, age is the only requirement for applying the senior pass, and free public transit is for all senior citizens aged 70 or above. In other global cities, the application requirements sometimes include age and income. For example, in Chicago, although all older adults aged 65 years or older are eligible for a reduced fare permit, the ride free permits are only for those who are enrolled in the Illinois Benefit Access Program (IBAP). The income levels for IBAP eligibility range from $27,610 or less for an individual, $36,635 for a two-person household, and $45,657 for a household of three or more people. In Tokyo, the annual cost of a senior pass is only 1,000 Japanese yen for both non-taxpayers and the low-income population, while it costs 20,510 yen for taxpayers whose annual incomes are over 1.25 million yen.
Second, community committees (Juweihui ) help to promote the use of free transit pass in Shanghai. In almost all global cities such as Chicago, London, New York City and Tokyo, the senior pass is based on older people's voluntary application. The elderly may enjoy reduced fare or ride-free permits if and only if they had applied. In such cases, more price-sensitive elderly would positively select themselves into subsidy participation. However, the implementation of a free transit pass is semi-mandatory in Shanghai. The community committees are in charge of promoting laws and policies, family planning, population administration, social welfare, etc. under the guidance of local government. Especially in the case of free transit passes, the committees remind el-igible elderly persons to apply for and receive the free transit pass through door-to-door visitation.
Third, the mandatory retirement age is 60 for men and 50 for women 8 in Shanghai, which assures the free transit program is not tainted by other aging policies. The multicollinearity among eligible ages for transit, retirement, and health care benefits makes the impact of transit benefits hard to clearly identify. For instance, in major cities in the United States, people aged 65 years or older are eligible for both transit subsidies and Medicare. It is an almost impossible task to isolate the impact of transit subsidies from others when multiple events happen at the same time. However, the clear policy design in Shanghai offers a good opportunity to estimate the impact of transit subsidies on senior citizens.

Identification Strategy
We begin with a simple model of the relationship between health status and receiving free transportation subsidies: where Healthy i indicates health status, Subsidy i indicates receiving transportation subsidy or not, X i is a vector of individual characteristics.
To account for the potential endogeneity of OLS, we estimate the effect of trans-8 55 for female cadres portation subsidy on health status using a fuzzy regression discontinuity design.
where the binary instrument 1[Age i ≥ 70] indicates whether one's age is greater than or equal to age 70, f (Age i ) is an unknown function of age. As Gelman and Imbens (2017) shows that using high-degree polynomials of the running variable in regression discontinuity design could lead to noisy estimates, sensitivity to the degree of the polynomial, and poor coverage confidence intervals, we assume a quadratic form of age to approximate f (Age i ) as our baseline model. Local linear estimates would be shown in the section of robustness checks.

Data
Our data source is the 2015 Chinese Living Conditions Survey for Rural and Urban Aged Population 9 (hereinafter abbreviated as CLCS), which is designed to collect information on demographics, economic and health status, living conditions, social inclusion, routine activities, and social welfare among the elderly who are at least 60 years old.
It is the largest and most representative survey for the elderly population in the history of China, covering approximately 224 thousand individuals from 466 counties in 31 provinces. In this study, we use the Shanghai sub-sample 10 that consists of 4,301 senior citizens in the most modern city in China, which is comparable to other global cities with respect to social security and welfare.
The CLCS data has three unique features. First, this survey includes information on both self-reported health status and transit subsidy participation, which are the dependent and the key independent variables in estimating the health impact of free transportation. The respondents were directly asked whether or not they are receiving reduced fare or free ride permits benefits. Previous studies have either indirectly measured health by physical activities (Coronini-Cronberg et al., 2012) and obesity (Webb et al., 2011), or treatment status by policy eligibility (Edwards et al., 2013

Results
In this section, we discuss the estimates of FRD design, which were designed to analyze the policy impact of transportation subsidies on health status among the elderly. We first discuss the first-stage estimates of subsidy eligibility upon receiving those benefits, and then we show the results of baseline FRD estimation. In our baseline estimation, models are fitted by the global polynomial method in a quadratic form.
In all regressions, we use standard errors clustered at the district level for inference.
Among four specifications, the estimates with full controls are our preferred results, and these estimates are the focus of the discussion in the following subsections. In the final subsection, we discuss the validity of our FRD estimates. Figure 1 graphs the probability of receiving transportation subsidy against age in decimal years. The hollow circles indicate means of observed probability of receiving subsidy within each age cell, which are weighted by the number of observations in each corresponding cell. The red curve shows a quadratic fit for who are younger than 70, while the blue curve is fitted for those who are greater than or equal to 70. Figure 1 also shows clear discontinuous changes in the probability of receiving subsidy around age 70. Visually, the probability of receiving subsidy is approximately 80 percentage points higher among the elderly who had just turned 70, compared to their younger peers who were still 69 years old. Table 2 reports the first stage of IV estimates corresponding to Figure 1. Columns 1 to 4 use four specifications of covariates. We control for covariates of basic demographic information, marital status, amount of exercise, and pension. Column 4 sets full controls for our preferred results. According to Column 4, the elderly who were just on the right tail of eligibility cutoff are more likely to receive transportation subsidies by 76.3 percentage points, which is highly robust across specifications. The age-based transportation subsidy is probably executed strictly within a few self-selection issues.

First Stage
The F-statistics of excluded instruments are consistently over 400, indicating that weak instruments might not be a concern in this paper. Smoothness tests on covariates will be discussed later.

Baseline Results
Figure 2 graphically shows the health status around the eligibility cutoff at age 70. Like in Figure 1, each hollow circle indicates a weighted mean of observed health status within each age cell. Red and blue curves fit the data in a quadratic form, while corresponding dashed lines use a local linear form. Figure 2 shows consistently positive health effects regardless of the fitting methods used. Health status is not monotonically decreasing in age. Surprisingly, the elderly over age 70 are in better health than their younger peers. The particularly strong instrument, as shown in Table 2, indicates that age is the dominant factor for subsidy participation rather than any other observed factors. In this paper, the treatment group is probably homogenous with the control group in covariates.

Smoothness Tests
According to Column 4 in Table 1, those who are at least age 70 are not different from their younger peers in covariates of gender, schooling, amount of exercise, and pension. However, slight differences were noted in numbers of children and marital status. If these differences occurred around the eligibility cutoff point, then our FRD estimates would be invalid and misleading. To directly test this possibility, we test whether these covariates were correlated to some discontinuity in the probability of receiving transportation benefits. Figure 3 shows that no clear jumps are observed in each covariate, which is robust to both quadratic and linear fits. In Figure 3, we graph each covariate against age in six panels. As marital status and exercising are category variables, we use the probability of being widowed and exercising instead for consciousness sake. In China, variations in marital status among the elderly basically come from widowhood, only 1% and 2% persons are never married and divorced in our final sample (see Table 1). Using a binary variable to measure marital status might not be problematic. Table 4 reports the estimated coefficients corresponding to Figure 3, indicating no statistical correlation between the cutoff and each covariate. In each column, the covariate itself is the dependent variable and excluded from the vector of covariates. Figure 3, the eligibility cutoff is not correlated to gender, schooling, number of children, widowhood, undertaking exercise, and pension, indicating these covariates are smooth at age 70.

Mechanisms
Our baseline results in Table 3 suggest that those elderly who receive free transit benefits are substantially healthier than those who do not. In this section, we propose three possible channels through which transportation may consequently affect senior citizens' health status, which are (1) exercise and routine activities, (2) health care utilization, and (3) improved food consumption. We use the same FRD estimation strategy as shown in Equation 2 and include a full set of covariates for causal inference.
Different dependent variables and subsamples are used to investigate how the elderly respond to the free-transit benefit.
First, we argue that the health impact of free transit through exercise and routine activities should be very limited, at least statistically insignificant. In Column 5 of Table 4, as well as in Panel E of Figure 3, we have already shown that free public transportation does not have any effect on the elderly's exercise preferences. To test whether receiving transit benefits may affect older people's health through incidental activities, we regressed 12 kinds of routine activities against subsidy-receiving status. In Table 5, we show that free transit is not related to either indoor or outdoor activities.
We then test whether the elderly's consumption of food and medical care are impacted by the free transportation program. Table 6 shows the impact of free transit pass on food and medical care expenditures, in Panel B and Panel C, respectively. Panel A shows the estimates on transit expenditures by way of comparison. We construct subsamples according to food budget and distance from the hospital to investigate the heterogeneous effects. Panel B and Panel C of Table 6 offer some evidence that the health impact resulting from the free transportation program could be through attaining a better diet via increased food intake among households with smaller food budgets, and increased in medical care expenditures among those who lived close to the hospital or physicians' offices.

Selection on Bandwidth
So far, we presented our results based on the global polynomial method. Our baseline model assumes a quadratic form of running variable. To test whether our baseline results are sensitive to different methods, we also present a nonparametric means-a local linear regression-to estimate the fuzzy regression discontinuity equation.
where Age i = Age i − Age 0 , and Age 0 is 70. In these local linear regressions, we use 1-year, 2-year, 3-year, and 4-year banding.
Results of local linear regressions with different bandwidths are shown in Table 7.
Regardless of where bands fall relative to the cutoff, consistent positive health effects are observed (columns 2, 3, 4, and 5), which are similar to our baseline model assuming a quadratic form of age.

Placebo Tests
In this subsection, we use four placebo treatments to test the robustness of the fuzzy RD estimates. These placebo treatments are two-years prior, one-year prior, one- year posterior, two-years posterior to the actual treatment received. These placebo treatments should not have any effect on health. If we find an impact from a placebo treatment, the real treatment-based results might be driven by other unobserved factors rather than the transportation benefit. Congruently, the following reduced-form equation is estimated, where p denotes the placebo treatment relative to the real treatment of age 70. The reduced form estimates of placebo treatments are displayed in Table 8, and the estimate of real treatment is also listed by way of comparison. Again, none of these placebo treatments had any significant effect on health.

Concluding Remarks
This paper estimates the causal effect of transportation benefits on health status among the elderly. Using a unique survey with detailed information on month of birth, we exploit a fuzzy regression discontinuity design to investigate the difference in health status between who are below or above age 65. We offer clear evidence that transporta-        Notes: Standard errors are clustered at the district level. All specifications include basic controls, marital status, amount of exercise, and pension. *** p<0.01, ** p<0.05, * p<0.1 Notes: Standard errors are clustered at the district level. All specifications include basic controls, marital status, amount of exercise, and pension. *** p<0.01, ** p<0.05, * p<0.1