Econometrica: Jul, 1984, Volume 52, Issue 4

Tests for the Bivariate Normal Distribution in Econometric Models with Selectivity

https://doi.org/0012-9682(198407)52:4<843:TFTBND>2.0.CO;2-M
p. 843-863

Lung-Fei Lee

The model considered is a two-equations model consisting of a binary choice equation and a regression equation. Tests for the bivariate normal distribution are derived for the truncated samples case and the censored samples case. The tests are Lagrangean multiplier tests for testing the bivariate normal distribution within the bivariate Edgeworth series of distributions. Simple intuitive interpretations for the statistics are provided.For the truncated case, the test compares with the estimated differences between some sample moments of order (r,s) for which r + s > 2 and the corresponding hypothesized moments of the disturbances. For the censored case, the test is equivalent to the testing of some sample semi-invariants for which r + s > 2 are zeros.