Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments

instrumental variables, natural experiment

Estimating the Payoff to Schooling Using the Vietnam-Era Draft Lottery

Between 1970 and 1973 priority for military service was randomly assigned to draft-age men in a series of lotteries. Many men who were at risk of being drafted managed to avoid military service by enrolling in school and obtaining an educational deferment This paper uses the draft lottery as a natural experiment to estimate the return to education and the veteran premium. Estimates are based on special extracts of the Current Population Survey for 1979and 1981-85. The results suggest that an extra year of schooling acquired in response to the lottery is associated with6.6 percent higher weekly earnings. This figure is about 10 percent higher than the OLS estimate of the return to education in this sample, which suggests there is omitted-variable bias in conventional estimates of the return to education. Our findings are robust to a variety of assumptions about the effect of veteran status on earnings.

Split Sample Instrumental Variables

Instrumental Variables (IV) estimates tend to be biased in the same direction as Ordinary Least Squares (OLS) in finite samples if the instruments are weak. To address this problem we propose a new IV estimator which we call Split Sample Instrumental Variables (SSIV). SSIV works as follows: we randomly split the sample in half, and use one half of the sample to estimate parameters of the first-stage equation. We then use these estimated first-stage parameters to construct fitted values and second-stage parameter estimates using data from the other half sample. SSIV is biased toward zero, rather than toward the plim of the OLS estimate. However, an unbiased estimate of the attenuation bias of SSIV can be calculated. We us this estimate of the attenutation bias to derive an estimator that is asymptotically unbiased as the number of instruments tends to infinity, holding the number of observations per instrument fixed. We label this new estimator Unbiased Split Sample Instrumental Variables (USSIV). We apply SSIV and USSIV to the data used by Angrist and Krueger (1991) to estimate the payoff to education.

The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples

This paper tests the hypothesis that compulsory school attendance laws, which typically require school attendance until a specified birthday, induce a relationship between the years of schooling and age at school entry. Variation in school start age created by children's date of birth provides a natural experiment for estimation of the effect of age at school entry. Because no large data set contains information on both age at school entry and educational attainment, we use an Instrumental Variables (IV) estimator with data derived from the 1960 and 1980 Censuses to test the age-at-entry/compulsory schooling model. In most IV applications, the two covariance matrices that form the estimator are constructed from the same sample. We use a method of moments framework to discuss IV estimators that combine moments from different data sets. In our application, quarter of birth dummies are the instrumental variables used to link the 1960 Census, from which age at school entry can be derived for one cohort of students, to the 1980 Census, which contains educational attainment for the same cohort of students. The results suggest that roughly 10 percent of students were constrained to stay in school by compulsory schooling laws.

Does Compulsory School Attendance Affect Schooling and Earnings?

This paper presents evidence showing that individuals' season of birth is related to their educational attainment because of the combined effects of school start age policy and compulsory school attendance laws. In most school districts, individuals born in the beginning of the year start school at a slightly older age, and therefore are eligible to drop out of school after completing fewer years of schooling than individuals born near the end of the year. Our estimates suggest that as many as 25 percent of potential dropouts remain in school because of compulsory schooling laws. We estimate the impact of compulsory schooling on earnings by using quarter of birth as an instrumental variable for education in an earnings equation. This provides a valid identification strategy because date of birth is unlikely to be correlated with omitted earnings determinants. The instrumental variables estimate of the rate of return to education is remarkably close to the ordinary least squares estimate, suggesting that there is little ability bias in conventional estimates of the return to education. The results also imply that individuals who are compelled to attend school longer than they desire by compulsory schooling laws reap a substantial return for their extra schooling.

Why do World War II Veterans Earn More Than Nonveterans?

Veterans of World War II are widely believed to earn more than nonveterans of the same age. Theoretical justifications for the World War II veteran premium include the subsidization of education and training, and preference for veterans in hiring. In this paper, we propose and test an alternative view: that the observed World War II veteran premium reflects the fact that men with higher earnings potential were more likely to have been selected into the Armed Forces. An empirical strategy is developed that allows estimation of the effects of veteran status while controlling for correlation with unobserved earnings potential. The estimation is based on the fact that from 1942 to 1947 priority for conscription was determined in chronological order of birth. Information on individuals' dates of birth may therefore be used to construct instruments for veteran status. Empirical results from the 1960, 1970, and 1980 Censuses, along with two other micro data sets, support a conclusion that World War II veterans earn no more than comparable nonveterans, and may well earn less. These results suggest that 015 estimates of the World War II veteran premium are severely biased by nonrandom selection into military service, and that the civilian labor market experiences of veterans of World War II were not very different from the experiences of Vietnam-era veterans.

Evaluating a bilingual education program in Spain: the impact beyond foreign language learning

Bilingual education programs, which consist of doing a substantial part of the instruction in a language different from the native language of the students, exist in several countries like the United States, India, and Spain. While the economic benefits of knowing a second language are well established, the potential effects over the learning of other subjects have received much less attention. We evaluate a program that introduced bilingual education (in English and Spanish) in primary education in a group of public schools of the Madrid region in 2004. Under this program, students not only study English as a foreign language but also some other subjects (at least Science, History, and Geography) are taught in English. In order to evaluate the program, a standardized test for all sixth grade students in Madrid on the skills considered indispensable at that age is our measure of the outcome of primary education. Our results indicate that there is a clearly negative effect on the exam results for the subject taught in English, for children whose parents have less than upper secondary education. This negative effect is a composite of two phenomena: the effect of the program on the student's knowledge of the subject and a reflection of the student ability to do the test in their native language when English is the medium of instruction. Although we are not able to separate quantitatively these two effects, the composite effect has a relevant interest, because the results for exams taken in Spanish are the measures that determine academic progression in the Spanish system. In contrast with the previous result, there is no significant effect for anyone on mathematical and reading skills, which were taught in Spanish. (JEL H40, I21, I28)We gratefully the support from the Spanish Ministry of Science and Technology from grants ECO2009-07530 and ECO2012- 31985 (B.A.), ECO2012-34581 (A.C.), ECO2009-11165 and ECO2012-31358 (J.M.C.), CONSOLIDER-INGENIO 2010—CSD2006-0016 (all), and Consejera de Educación de la Comunidad de Madrid under the Excelecon projec

Jackknife Instrumental Variables Estimation

Two-stage-least-squares (2SLS) estimates are biased towards OLS estimates. This bias grows with the degree of over-identification and can generate highly misleading results. In this paper we propose two simple alternatives to 2SLS and limited-information-maximum-likelihood (LIML) estimators for models with more instruments than endogenous regressors. These estimators can be interpreted as instrumental variables procedures using an instrument that is independent of disturbances even in finite samples. Independence is achieved by using a `leave-one-out' jackknife-type fitted value in place of the usual first-stage equation. The new estimators are first-order equivalent to 2SLS but with finite-sample properties superior to those of 2SLS and similar to LIML when there are many instruments. Moreover, the jackknife estimators appear to be less sensitive than LIML to deviations from the linear reduced form used in classical simultaneous equations models.

Blissful ignorance?: a natural experiment on the effect of feedback on students' performance

We provide evidence on whether providing university students with feedback on their past exam performance affects their future exam performance. Our identification strategy exploits a natural experiment in a leading UK university where different departments have historically different rules on the provision of feedback to their students. We find that the provision of feedback has a positive effect on students' subsequent test scores: the mean impact corresponds to 13% of a standard deviation in test scores. The impact of feedback is stronger for more able students and for students who have less information to start with about the academic environment, while no subset of individuals is found to be discouraged by feedback. Our findings suggest that students have imperfect information on how their effort translates into test scores and that the provision of feedback might be a cost-effective means to increase students' exam performance