Using unemployment rates as instruments to estimate returns to schooling.

• Author: Arkes, Jeremy

1. Introduction

   There have been significant societal efforts over time to keep children in school and to encourage people to pursue a college education. The basis of these efforts is the general consensus that schooling helps people develop the necessary skills that will help them compete in the labor market and reduce their chance of experiencing poverty. However, schooling involves an opportunity cost (from foregone earnings, in addition to any direct costs), so that understanding the true returns to schooling would be important for individuals making schooling decisions. Yet, estimating the returns to schooling has proved to be very difficult.

   The conventional thought in labor economics is that ability bias causes ordinary least squares (OLS) to overstate the monetary returns to schooling. That is, the higher earnings for more educated people would reflect, in addition to the causal effects of schooling, the effects of higher innate ability and motivation that cause some to obtain more schooling. Thus, a correction for ability bias should produce lower estimated returns to schooling. This result has been confirmed with studies on twins (Card 1999). However, as described in more detail below, a consistent result from two-stage least squares (2SLS) models that attempt to correct for ability and other biases is that the corrected estimates are higher. While each instrument can be questioned about its validity, together the estimates suggest that the ability-bias story is not the complete story.

   In this article, I introduce a new plausible instrumental variable: the state unemployment rate during a person's teenage years. The unemployment rate is indicative of the economic conditions in that state. A higher unemployment rate could affect one's educational attainment through an income effect and a substitution effect. The income effect would be that, with higher unemployment rates, family incomes would be lower. This would cause some families to have their teenage children quit school to work to help support the family. In addition, the lower income could make college unaffordable. The substitution effect would stem from the lower wages and fewer job opportunities for teenagers associated with higher unemployment rates. These factors would lower the opportunity costs of attending school, which should lead to an increase in educational attainment. It turns out that the substitution effect dominates. My findings support the contention that this is a valid instrument.

   Card (1999) reviews several recent analyses that use data on twins or a variety of other instruments in instrumental variables models to correct for these biases in estimating the returns to schooling. (1) The articles using twins almost all show that the cross-sectional OLS estimate is higher than the estimate based on differences across twins. Behrman and Rosenzweig (1999) confirm, based on a study of twins, that there is a positive ability bias on the estimated returns to schooling. In contrast, the articles that Card (1999) reviews based on instrumental variables models tend towards the opposite conclusion: The instrumental variables or 2SLS estimates in these articles exceed their OLS counterparts in almost every study and by up to 150%. For example, Card (1995) uses proximity to a four-year college as the instrumental variable and finds a coefficient estimate on years of schooling of 0.132, compared to the OLS estimate of 0.073. In about one-half of the studies Card (1999) reviews, the differences are statistically significant at least at the 10% level. (2)

   The analysis I consider the most persuasive is Angrist and Krueger (1991). They use quarter-of-birth dummy variables interacted with year-of-birth dummy variables as the instrumental variables, with the argument being that, given compulsory school attendance laws, individuals born earlier in the year turn 16 (the typical school-leaving age) earlier, and thus can quit school before their younger classmates. They report several sets of OLS and 2SLS estimates based on whether they include different sets of covariates. In four sets of OLS-2SLS estimates using the male 1930-1939 cohort from the 1980 Census, the 2SLS estimate is higher in all but one. (3)

   Despite the quarter of birth seeming to be a perfectly reasonable instrumental variable for years of schooling, its validity was called into question. Bound, Jaeger, and Baker (1995) cite evidence indicating that the quarter of birth may be associated with student performance, physical and mental health, and parental incomes. These factors may then have independent effects on a person's earnings. Although these independent effects may be small, Bound, Jaeger, and Baker (1995) argue that a weak correlation between the instrument and the endogenous variable would exacerbate any inconsistency. As an important side note, Bound, Jaeger, and Baker (1995) claim that Angrist and Krueger's estimates are marred by finite-sample bias due to overidentification, which occurs even if the instruments are exogenous in the population. The finite-sample bias always biases the estimates in the direction of OLS estimates.

   Using the same data set as Angrist and Krueger (1991), I estimate the returns to schooling with the unemployment rate during teenage years as the instrument and also with quarter-of-birth dummy variables as instruments. The 2SLS estimates from these two models are very close to each other, and they are higher than their OLS counterparts. Statistical tests support the contention that the instruments are valid. This lends more weight to the argument that the simple ability-bias story for the returns-to-schooling estimates is not complete. Furthermore, the results suggest that the returns to schooling are quite high for people whose schooling would be affected by the instrument.

2. The New Instrument

   The condition for a valid instrumental variable in the 2SLS models is that the variable affects the years of schooling, but has no impact on the earnings outcome other than through its effect on years of schooling. The estimated returns to schooling would then be based on variation in earnings due to variation in the instrumental variable.

   The new instrument I use is the average state unemployment rates over the three years in which the respondent turns 15, 16, and 17 years old. The unemployment rates (obtained from The Manpower Report of the President [various years]) are for workers who are covered by unemployment insurance (UI). This is the only state unemployment rate available from the late 1940s to the late 1950s, but it turns out to be an ideal instrumental variable, as will be described below. As described in the next section, I control for the state of birth and the year of birth so that the exogenous variation in educational attainment comes from the within-state changes over time in unemployment rates relative to other states. Over the 13 years that unemployment rates are used (1948 to 1959), the average standard deviation of the unemployment rate within states is 1.36 percentage points. With the three-year moving average unemployment rate (for ages 15 to 17), the average standard deviation is 0.75.

   State unemployment rates during one's teenage years can affect school enrollment and educational attainment through two forces. First, there is an income effect, or "additional worker" effect. With a higher unemployment rate, earnings will be lower so families may need their teenage children to quit school and work to help support them. Families experiencing spells of unemployment may also experience more difficulty in sending their children to college. As labor market conditions improve and unemployment rates come down, more families can afford to let their teenagers attend school; thus, the income effect results in higher unemployment rates being associated with lower enrollment rates and less educational attainment. Conversely, the substitution effect, or the "discouraged worker" effect, results in higher unemployment rates being associated with higher enrollment rates. In periods of high unemployment, wages are typically lower and jobs are scarcer. Thus, the opportunity cost of attending school is lower, which would, according to Barceinas-Paredes et al. (2001), increase the rate of return to schooling, and thus increase educational attainment. As shown in section 4, the substitution effect dominates the income effect.

   Previous research on the cyclical effects of school enrollment supports the result that the substitution effect dominates. Black et al. (2005) observe this with location-specific data, as they find that higher wages for low-skilled workers (related to coal booms) in Kentucky and Pennsylvania contributed to significantly lower high school enrollment rates. Using national-level data, Betts and McFarland (1995) find that enrollment of full-time students at community colleges increases by 0.5% and 4%, with a 1% increase in the unemployment rates, of recent high school...