This paper develops a general framework for conducting inference on the rank of an unknown matrix Π0. A defining feature of our setup is the null hypothesis of the form . The problem is of first-order importance because the previous literature focuses on by implicitly assuming away , which...

This paper develops a general framework for conducting inference on the rank of an unknown matrixΠ0. A defining feature of our setup is the null hypothesis of the form<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>:</mo><mi mathvariant="normal">rank</mi><mo stretchy="false">(</mo><msub><mrow><mi>Π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo>≤</mo><mi>r</mi></math>. The problem is of first‐order importance because the previous literature focuses on<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>:</mo><mi mathvariant="normal">rank</mi><mo stretchy="false">(</mo><msub><mrow><mi>Π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mi>r</mi></math>by...