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.

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.

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.

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.

Causal inference in paired two-arm experimental studies under non-compliance with application to prognosis of myocardial infarction

Motivated by a study about prompt coronary angiography in myocardial infarction, we propose a method to estimate the causal effect of a treatment in two-arm experimental studies with possible non-compliance in both treatment and control arms. The method is based on a causal model for repeated binary outcomes (before and after the treatment), which includes individual covariates and latent variables for the unobserved heterogeneity between subjects. Moreover, given the type of non-compliance, the model assumes the existence of three subpopulations of subjects: compliers, never-takers, and always-takers. The model is estimated by a two-step estimator: at the first step the probability that a subject belongs to one of the three subpopulations is estimated on the basis of the available covariates; at the second step the causal effects are estimated through a conditional logistic method, the implementation of which depends on the results from the first step. Standard errors for this estimator are computed on the basis of a sandwich formula. The application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next two years, with a log-odds of about -2. Given that non-compliance is significant for patients being given the treatment because of high risk conditions, classical estimators fail to detect, or at least underestimate, this effect

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.

Fruit and vegetable intake: change with age across childhood and adolescence

Abstract Eating fruit and vegetables (FV) offers important health benefits for children and adolescents, but their average intake is low. To explore if negative trends with age exist as children grow, this study modelled differences in fruit and vegetable consumption from childhood to young adulthood. A pseudo-panel was constructed using Years 1-4 (combined) of the Rolling Programme of the UK National Diet and Nutrition Survey (2008/09 – 2011/12). Intake of fruits and vegetables in the NDNS was recorded using 4- day unweighted food diaries. Data consisted of 2131 observations of individuals aged 2 to 23 years. Age-year-cohort decomposition regression analyses were used to separate age effects from year and cohort effects in the data. Total energy intake was included to account for age differences in overall energy consumption. Fruit intake started to decrease from the age of 7 for boys and girls and reached its lowest level during adolescence. By 17 years boys were consuming 0.93 (p = 0.037) less fruit portions compared to the age of two. By 15 years, girls were consuming 0.8 fruit portions less (p = 0.053). Vegetable intake changed little during childhood and adolescence (p = 0.0834 and p = 0.843 for change between 7 and 12 years, boys and girls respectively). There was unclear evidence of recovery of FV intakes in early adulthood. Efforts to improve FV intake should consider these trends, and focus attention on the factors influencing intake across childhood and adolescence in order to improve the nutritional quality of diets during these periods

Are there asymmetries in the effects of training on the conditional male wage distribution?

Recent studies have used quantile regression (QR) techniques to estimate the impact of education on the location, scale and shape of the conditional wage distribution. In our paper we investigate the degree to which work-related training – another important form of human capital – affects the location, scale and shape of the conditional wage distribution. Using the first six waves of the European Community Household Panel, we utilise both ordinary least squares and QR techniques to estimate associations between work-related training and wages for private sector men in ten European Union countries. Our results show that, for the majority of countries, there is a fairly uniform association between training and hourly wages across the conditional wage distribution. However, there are considerable differences across countries in mean associations between training and wages

Treatment compliance and effectiveness of a cognitive behavioural intervention for low back pain : a complier average causal effect approach to the BeST data set

Background: Group cognitive behavioural intervention (CBI) is effective in reducing low-back pain and disability in comparison to advice in primary care. The aim of this analysis was to investigate the impact of compliance on estimates of treatment effect and to identify factors associated with compliance. Methods: In this multicentre trial, 701 adults with troublesome sub-acute or chronic low-back pain were recruited from 56 general practices. Participants were randomised to advice (control n = 233) or advice plus CBI (n = 468). Compliance was specified a priori as attending a minimum of three group sessions and the individual assessment. We estimated the complier average causal effect (CACE) of treatment. Results: Comparison of the CACE estimate of the mean treatment difference to the intention-to-treat (ITT) estimate at 12 months showed a greater benefit of CBI amongst participants compliant with treatment on the Roland Morris Questionnaire (CACE: 1.6 points, 95% CI 0.51 to 2.74; ITT: 1.3 points, 95% CI 0.55 to 2.07), the Modified Von Korff disability score (CACE: 12.1 points, 95% CI 6.07 to 18.17; ITT: 8.6 points, 95% CI 4.58 to 12.64) and the Modified von Korff pain score (CACE: 10.4 points, 95% CI 4.64 to 16.10; ITT: 7.0 points, 95% CI 3.26 to 10.74). People who were non-compliant were younger and had higher pain scores at randomisation. Conclusions: Treatment compliance is important in the effectiveness of group CBI. Younger people and those with more pain are at greater risk of non-compliance