RANKTEST: Stata module to test the rank of a matrix

ranktest implements various tests for the rank of a matrix. Tests of the rank of a matrix have many practical applications. For example, in econometrics the requirement for identification is the rank condition, which states that a particular matrix must be of full column rank. Another example from econometrics concerns cointegration in vector autoregressive (VAR) models; the Johansen trace test is a test of a rank of a particular matrix. The traditional test of the rank of a matrix for the standard (stationary) case is the Anderson (1951) canonical correlations test. If we denote one list of variables as Y and a second as Z, and we calculate the squared canonical correlations between Y and Z, the LM form of the Anderson test, where the null hypothesis is that the matrix of correlations or regression parameters B between Y and Z has rank(B)=r, is N times the sum of the r+1 largest squared canonical correlations. A large test statistic and rejection of the null indicates that the matrix has rank at least r+1. The Cragg-Donald (1993) statistic is a closely related Wald test for the rank of a matrix. The standard versions of these tests require the assumption that the covariance matrix has a Kronecker form; when this is not so, e.g., when disturbances are heteroskedastic or autocorrelated, the test statistics are no longer valid. ranktest implements various generalizations of these tests - Kleibergen-Paap, Cragg-Donald, and J-type 2-step GMM and CUE GMM tests - to the case of a non-Kronecker covariance matrix. The implementation in ranktest will calculate test statistics that are robust to various forms of heteroskedasticity, autocorrelation, and clustering.