We study the rank of the instantaneous or spot covariance matrix Σ(t) of a multidimensional continuous semi-martingale X(t). Given highfrequency observations X(i=n), i = 0; : : : ;n, we test the null hypothesis rank (Σ(t)) ≤ r for all t against local alternatives where the average (r + 1)st...

This paper considers a fundamental question about the school environment - what are the long run effects of a student's ordinal rank in elementary school? Using administrative data from all public school students in Texas, we show that students with a higher third grade academic rank,...

This paper establishes a new fact about educational production: ordinal academic rank during primary school has lasting impacts on secondary school achievement that are independent of underlying ability. Using data on the universe of English school students, we exploit naturally occurring...