A weak instrument F-test in linear IV models with multiple endogenous variables

Journal of Econometrics, 2013

480 citations recorded by the source corpus.

We consider testing for weak instruments in a model with multiple endogenous variables. Unlike Stock and Yogo (2005), who considered a weak instruments problem where the rank of the matrix of reduced form parameters is near zero, here we consider a weak instruments problem of a near rank reduction of one in the matrix of reduced form parameters. For example, in a two-variable model, we consider weak instrument asymptotics of the form π1=δπ2+c/n where π1 and π2 are the parameters in the two reduced-form equations, c is a vector of constants and n is the sample size. We investigate the use of a conditional first-stage F-statistic along the lines of the proposal by Angrist and Pischke (2009) and show that, unless δ=0, the variance in the denominator of their F-statistic needs to be adjusted in order to get a correct asymptotic distribution when testing the hypothesis H0:π1=δπ2. We show that a corrected conditional F-statistic is equivalent to the Cragg and Donald (1993) minimum eigenvalue rank test statistic, and is informative about the maximum total relative bias of the 2SLS estimator and the Wald tests size distortions. When δ=0 in the two-variable model, or when there are more than two endogenous variables, further information over and above the Cragg–Donald statistic can be obtained about the nature of the weak instrument problem by computing the conditional first-stage F-statistics.

Subfields: Aerospace Engineering, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93f6b553e2f5f143cbab43ed98b357000acfbdfe

Citations in the corpus

• Firm Life Cycle, Corporate Risk Taking, and Investor Sentiment (2017, unknown): “To address this problem, we follow the approach proposed by Angrist and Pischke (2008) and recently modified by Sanderson and Windmeijer (2013) and estimate a corrected version of the first stage F statistic that is suitable for our setting of more than three endogenous variables.”
• Does Institutional Quality Foster Economic Complexity? (2019, unknown): “Second, the value of the Sanderson and Windmeijer (2016) F-test for the excluded instrument is bigger than the rule-of-thumb value of 10 in all cases, which implies that UV-R is not a weak instrument.”
• Unity in Diversity? How Intergroup Contact Can Foster Nation Building (2019, unknown): “At the bottom of the table, Sanderson and Windmeijer (2016) Wald statistics reject the null of weak instruments on the two endogenous variables.”
• Services trade policy and manufacturing productivity: The role of institutions (2017, unknown): “31 The test statistics are derived in Sanderson and Windmeijer (2016) and are consistent with the diagnostic approach presented in Angrist and Pischke (2008).”
• Endogeneity and marketing strategy research: an overview (2019, unknown): “Additionally, the researcher can bolster their theoretical reasoning for an IV by considering the Sanderson-Wodmeijer multivariate F-test to inform the strength of their chosen instrument(s), and report it along with results (Sanderson and Windmeijer 2016).”
• Corporate Life Cycle and Cost of Equity Capital (2015, unknown): “To address this problem, we follow the approach proposed by Angrist and Pischke (2008) and recently modified by Sanderson and Windmeijer (2013) and estimate a corrected version of the first stage F statistic that is suitable for our setting of more than three endogenous variables.”
• Multivariable Mendelian Randomization and Mediation. (2020, unknown): “If this assumption is not satisfied then there will be multicollinearity between the predicted exposures and the MVMR estimates obtained will suffer from weak-instrument bias (Cragg and Donald 1993; Sanderson and Windmeijer 2016).”