Testing Instrument Strength and Overidentifying Restrictions
The strength of the instruments can be directly assessed because both the endogenous covariates and the instruments are observable (Stock, Wright, and Yogo 2002). A common rule of thumb for models with one endogenous regressor is: the F-statistic against the null that the excluded instruments are irrelevant in the first-stage regression should be larger than 10.
The assumption that the instruments are not correlated with the error term in the equation of interest is not testable in exactly identified models. If the model is overidentified, there is information available which may be used to test this assumption. The most common test of these overidentifying restrictions, called the Sargan test, is based on the observation that the residuals should be uncorrelated with the set of exogenous variables if the instruments are truly exogenous. The Sargan test statistic can be calculated as (the number of observations multiplied by the coefficient of determination) from the OLS regression of the residuals onto the set of exogenous variables. This statistic will be asymptotically chi-squared with m − k degrees of freedom under the null that the error term is uncorrelated with the instruments.
Read more about this topic: Instrumental Variable
Famous quotes containing the words testing, instrument and/or strength:
“No testing has overtaken you that is not common to everyone. God is faithful, and he will not let you be tested beyond your strength, but with the testing he will also provide the way out so that you may be able to endure it.”
—Bible: New Testament, 1 Corinthians 10:13.
“We ought, says Kant, to become acquainted with the instrument, before we undertake the work for which it is to be employed; for if the instrument be insufficient, all our trouble will be spent in vain. The plausibility of this suggestion has won for it general assent and admiration.... But the examination can be only carried out by an act of knowledge. To examine this so-called instrument is the same as to know it.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“I believe that Harmon would be the easiest to defeat, though he might gain much strength from the Republicans. Clark would surely lose New York. I am beginning to feel that by some stroke of genius they may name Woodrow Wilson, and that seems a pretty hard tussle.”
—William Howard Taft (1857–1930)