Estimating the Return to College in Britain Using Regression and Propensity Score Matching

College graduates tend to earn more than non-graduates but it is difficult to ascertain how much of this empirical association between wages and college degree is due to the causal effect of a college degree and how much is due to unobserved factors that influence both wages and education (e.g. ability). In this paper, I use the 1970 British Cohort Study to examine the college premium for people who have a similar ability level by using a restricted sample of people who are all college eligible but some never attend. Compared to using the full sample, restricting the sample to college-eligible reduces the return to college significantly using both regression and propensity score matching (PSM) estimates. The finding suggests the importance of comparing individuals of similar ability levels when estimating the return to college.return to college, regression, propensity score matching

Strongly Regular Graphs as Laplacian Extremal Graphs

The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. We find that the class of strongly regular graphs attains the maximum of largest eigenvalues, the minimum of second-smallest eigenvalues of Laplacian matrices and hence the maximum of Laplacian spreads among all simple connected graphs of fixed order, minimum degree, maximum degree, minimum size of common neighbors of two adjacent vertices and minimum size of common neighbors of two nonadjacent vertices. Some other extremal graphs are also provided.Comment: 11 pages, 4 figures, 1 tabl

Determining the nature of white dwarfs from low-frequency gravitational waves

An extreme-mass-ratio system composed of a white dwarf (WD) and a massive black hole can be observed by the low-frequency gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). When the mass of the black hole is around $10^4 \sim 10^5 M_\odot$, the WD will be disrupted by the tidal interaction at the final inspiraling stage. The event position and time of the tidal disruption of the WD can be accurately determined by the gravitational wave signals. Such position and time depend upon the mass of the black hole and especially on the density of the WD. We present the theory by using LISA-like gravitational wave detectors, the mass-radius relation and then the equations of state of WDs could be strictly constrained (accuracy up to $0.1\%$). We also point out that LISA can accurately predict the disruption time of a WD, and forecast the electromagnetic follow-up of this tidal disruption event.Comment: 7 pages, 2 figure

Earnings Returns to the British Education Expansion

We study the effects of the large expansion in British educational attainment that took place for cohorts born between 1970 and 1975. Using the Quarterly Labour Force Survey, we find that the expansion caused men to increase education by about a year on average and gain about 8% higher wages; women obtained a slightly greater increase in education and a similar increase in wages. Clearly, there was a sizeable gain from being born late enough to take advantage of the greater educational opportunities offered by the expansion. Treating the expansion as an exogenous increase in educational attainment, we obtain instrumental variables estimates of returns to schooling of about 6% for both men and women.return to education; higher education expansion

Are Discoveries Spurious? Distributions of Maximum Spurious Correlations and Their Applications

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries from these data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions about the exogeneity of the covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distributions of the maximum spurious correlations given a certain number of predictors, namely, the distribution of the correlation of a response variable $Y$ with the best $s$ linear combinations of $p$ covariates $\mathbf{X}$, even when $\mathbf{X}$ and $Y$ are independent. When the covariance matrix of $\mathbf{X}$ possesses the restricted eigenvalue property, we derive such distributions for both a finite $s$ and a diverging $s$, using Gaussian approximation and empirical process techniques. However, such a distribution depends on the unknown covariance matrix of $\mathbf{X}$. Hence, we use the multiplier bootstrap procedure to approximate the unknown distributions and establish the consistency of such a simple bootstrap approach. The results are further extended to the situation where the residuals are from regularized fits. Our approach is then used to construct the upper confidence limit for the maximum spurious correlation and to test the exogeneity of the covariates. The former provides a baseline for guarding against false discoveries and the latter tests whether our fundamental assumptions for high-dimensional model selection are statistically valid. Our techniques and results are illustrated with both numerical examples and real data analysis