2.1. The Theoretical Model
Previous theoretical research presents a model of monocentric cities with decentralized employment [
8]. This model proposes if the work location is assumed to be fixed, longer commuting will be compensated by lower house prices, or by higher wages when residential location is assumed to be fixed. Although the effect of commuting on labor supply can be analyzed based on White’s model, a large amount of the literature casts doubt on the ability of the monocentric model to explain actual commuting behavior in the US [
9,
10,
11,
12].
The model we set up in this paper does not assume that the city is monocentric and that work places are located in the center of city. On the contrary, work locations can be altered if workers change their jobs. Since the data we use is longitudinal, in which people surveyed stay in the same residential location, we assume that people do not change their residential locations. Hourly wage is a function of distance from residential location to work location, that is, , in which is the hourly wage and is the round-trip commute distance.
Assume that the individual utility function is given by
, and that a worker wants to maximize utility subjected to their budget constraint:
in which
is consumption;
is leisure,
is non-labor income;
is the commute time for each unit of commute distance;
is the round trip commute time; and
the is the monetary cost of each unit of commute distance. The budget constraint can be rewritten as:
Putting the above specification into the utility function and maximizing the utility function:
The optimal values of
and
are then as follows:
We assume that all workers have the same utility level; differentiate with respect to distance (
) and apply the envelope theorem:
in which
is the labor supply.
implies that higher wage compensates longer commute distance or commute time.
First, the marginal effect of commute distance on labor supply is:
in which:
Note that the superscript “h” denotes Hicksian. Combining the two equations above, the marginal effect of commute distance on labor supply will be:
According to economic theory, given the individual’s utility is unchanged, the increase of hourly wage will substitute leisure time, that is, . Considering also , if the absolute value of or is large enough, the commute distance will have a positive effect on labor supply, that is, . Furthermore, given constant commute time per unit of commute distance, commute time increases labor supply. However, if the absolute value of the product is not large enough, the commute distance will decrease labor supply, that is, .
In addition, the change of commute time per unit of commute distance
can be understood as the variation of transport condition in an urban area. Then, the marginal effect of transportation condition on labor supply is given by:
in which
is used to denote the total income of a worker, that is,
. Due to the positive income effect, the increase of total income will increase the leisure time, that is,
. Under this specification, when
or
is large enough, the commute time per unit of commute distance or the deterioration of transportation condition will have a positive effect on labor supply, that is,
. Therefore, commute time will have a positive effect on working hours given that commute distance is held constant. Nevertheless, when the product of
and
is small, the deterioration of transportation condition will then decrease labor supply.
To summarize, the derivation of theoretical model leads to the following propositions.
Proposition 1. The change of commute distance, such as induced by job change, has a positive effect on the wage, but its effect on labor supply is uncertain.
Proposition 2. Better transportation conditions do not affect the wage, and its effect on labor supply is uncertain.
2.2. Data and Descriptive Statistics
The dataset adopted in this study was drawn from the China Health and Nutrition Survey (CHNS) provided by the Chinese Center for Disease Control and Prevention and the Population Research Center of the University of North Carolina in the USA. The first round was in 1989. The next eight waves followed in 1991, 1993, 1997, 2000, 2004, 2006, 2009, and 2011. The study population is composed of respondents from the provinces of Guangxi, Guizhou, Heilongjiang, Henan, Hubei, Hunan, Jiangsu, Liaoning, and Shandong in China. This sample is diverse, with variation found in a wide-ranging set of socioeconomic factors, which include income, employment, education, and modernization and other related health, nutritional and demographic measures. The detailed information on commute time and other data at both individual and household levels make it ideal for examining the effect of commute time on labor supply.
To take advantage of controlling individual-specific, time-invariant effects, attention was restricted to a longitudinal subsample in the dataset. We further limited the sample to workers aged between 16 and 60 years who were surveyed in the urban areas. Note that urban areas in this paper include all urban, suburban, and town communities in the CHNS. For the purpose of this study, we also limited the sample to surveys after 2004 since CHNS only included questions on commute time for workers from 2004. We defined three variables relating to labor supply in this study, that is, workhours per day, workdays per week, and weekly workhours.
In line with the previous studies on labor supply, some variables reflecting socioeconomic and demographic characteristics of the respondents were specified. As illustrated in numerous economics studies, an individual’s status relating to smoking and chronic conditions is a signal of health and affects that individual’s labor supply decision, and was thus included in the labor supply function. In addition to health status, other demographic characteristics involved in the empirical analysis included age, the number of children less than or equal to 6 years old, and the number of family members in the household. In order to capture the wealth effect on labor supply, we also controlled for family wealth in the regression. Family wealth included house value and values of appliances, vehicles, machines, and equipment owned. Family income affects individual labor supply and thus was also controlled in our analysis. Family income, in this study, was defined as household non-labor income, other family members’ labor income, and housing subsidy, in which housing subsidy was calculated by subtracting the annual rent the family pays from the annual fair market rent.
To correct the endogenous problem of individual commute time, we used the average commute time in the city, which was constructed as the average of individual workers’ commute times in the city, as the instrumental variable for individual commute time. To avoid the problem that city characteristics may be potentially correlated with city average commute time and individual labor supply, we controlled for city-level human capital, measured by city average education level, and the ratio of employment from the non-public sector, as a variable from the labor demand side. We further controlled the fraction of workers changing job in the city to reflect the city labor market condition.
Finally, after excluding those observations with relevant missing information, a total sample of 1077 individuals and 2727 observations was retained. The descriptive statistics of commute time, labor supply variables, and other important variables in 2004, 2006, 2009 and 2011 are presented in
Table 1.
On average, round trip commute time increased from 29.17 min in 2004 to 36.09 min in 2009 and then decreased to 34.68 min in 2011. All three labor supply variables decreased in 2006 first and then increased. For example, typical workers worked 8.05 h per day, 5.51 days per week, and 44.56 h per week in 2004. In 2006, daily working hours decreased to 7.93, working days decreased to 5.43, and weekly working hours also decreased. However, from 2009 to 2011, people worked longer per day, more days per week, and also had higher weekly working hours.
Family wealth and family income had a similar increasing trend. The proportion of smoking people was consistently around 33% across different years. The number of children aged less than 6 years in the household was around 0.14–0.17 and the number of family members in the household was around 3.2. The percentage of job changing workers ranged from 11% to 16%. Average years of education in the city was around 11 years. The ratio of non-public employment increased from 29% in 2004 to 44% in 2011.
2.3. Empirical Methodology
In this paper, we aim to investigate the causal effect of commute time on labor supply, measured by working hours per day, number of workdays per week, and weekly workhours. However, following the standard labor supply literature, controlling commute time, hourly wage, and other variables in regressions cannot provide a consistent estimator for such a causal effect, due to the following two reasons.
First, commute time is endogenous, especially when residential location and work location can be chosen by individual workers and such a decision is made based on the working hours. For example, long workhours may cause workers to move to places closer to the work places. In this research, worker’s residential location is assumed to be fixed in the longitudinal data. However, there are still two factors accounting for the change of commute time, that is, the changes of work location and transportation conditions in the city. As a result, the reverse causal effect of labor supply on work location decision cannot be ruled out, resulting in the endogeneity problem. Nevertheless, since city transportation conditions provide a good instrumental variable for commute time, we adopted the average commute time in the city to measure the city transportation conditions. Note that as the city average commute time is an aggregate variable, it can at least partially correct the endogeneity of individual commute time. From this perspective, although the city average commute time is not flawless, it might work as a valid instrumental variable to some extent.
Second, wages may also be endogenous. Given the residence location, workers can find jobs based on job characteristics, such as daily workhours, number of workdays per week, total weekly workhours, hourly wage, and commute time. Labor supply, wage, and commute time are simultaneously chosen. In this research, as hourly wage was not the variable of interest, in order to avoid the endogeneity problems, a totally reduced form was adopted first, and hourly wage was not included in the regression. Hourly wage was included in a subsequent regression to perform a robustness check.
The basic regression form is:
in which
measures labor supply variables, that is, daily workhours, working days per week, and weekly workhours;
is the round trip commute time;
are other time-varying independent variables, controlling for individual, household, demographic, and city characteristics;
is the individual time-invariant unobserved heterogeneity;
captures the year fixed effect; and
is the error term.
is the elasticity of labor supply with respect to commute time. The fixed effect is the model that fit using the above equation.
The first-stage regression for commute time is:
in which
is the average commute time in city
j where individual
i lives, and
is the error term. We also applied a fixed effect model to the above equation.
Note that by using the modified Wald test and the Cumby–Huizinga test, we found that the problems of heteroscedasticity and autocorrelation in the error terms exist. Therefore, in all regressions, we adjusted standard errors by clustering around individuals.