SarganTest

SarganTest, also known as the Sargan-Hansen test, is a statistical test used in econometrics to determine whether a model is over-identified. An over-identified model is one where there are more instruments than endogenous variables, which can lead to more precise estimates. The test was developed by James Sargan in 1958 and later refined by Hans Hansen in 1982.

The SarganTest is based on the principle that if a model is correctly specified, the instruments should be uncorrelated with the residuals of the model. If the model is over-identified, the instruments should be uncorrelated with the residuals even if the model is not correctly specified. The test statistic is calculated as the sum of the squared residuals of the instruments, weighted by the inverse of the variance-covariance matrix of the instruments.

The null hypothesis of the SarganTest is that the model is correctly specified and the instruments are uncorrelated with the residuals. If the test statistic is significantly large, the null hypothesis is rejected, indicating that the model is over-identified. The test is widely used in econometrics and finance to assess the validity of instrumental variables models.

The SarganTest has some limitations. It assumes that the instruments are valid and that the model is linear. It also assumes that the residuals are homoscedastic and normally distributed. If these assumptions are violated, the results of the test may be unreliable. Despite these limitations, the SarganTest remains an important tool for econometricians and researchers in related fields.