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RANKTEST: Stata module to test the rank of a matrix using the Kleibergen-Paap rk statistic

Author

Listed:
  • Frank Kleibergen

    () (Brown University)

  • Mark E Schaffer

    () (Heriot-Watt University)

Abstract

ranktest implements the Kleibergen-Paap (2006) rk test 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. Both the Anderson and Cragg-Donald 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form; when this is not so, e.g., when disturbances are heteroskedastic or autocorrelated, the test statistics are no longer valid. The Kleibergen-Paap (2006) rk statistic is a generalization of the Anderson canonical correlation rank test to the case of a non-Kronecker covariance matrix. The implementation in ranktest will calculate rk statistics that are robust to various forms of heteroskedasticity, autocorrelation, and clustering.

Suggested Citation

  • Frank Kleibergen & Mark E Schaffer, 2007. "RANKTEST: Stata module to test the rank of a matrix using the Kleibergen-Paap rk statistic," Statistical Software Components S456865, Boston College Department of Economics, revised 24 Jan 2015.
  • Handle: RePEc:boc:bocode:s456865
    Note: This module should be installed from within Stata by typing "ssc install ranktest". Windows users should not attempt to download these files with a web browser.
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    Keywords

    matrix; rank; collinearity; cointegration;

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