Instrumental variables (IV) estimation can provide consistent estimates of alinear equation’s parameters when ordinary least squares (OLS) is biasedbecause an explanatory variable in the equation is correlated with theequation’s disturbance. The necessary ingredient for consistent IV estimation isa “valid” instrument, which is a variable correlated with the offendingexplanatory variable but uncorrelated with the equation’s disturbance term. IVestimation was first used to overcome biases in OLS by Phillip Wright (Wright 1928).
If the attractive large sample properties of the instrumental variable estimator are to be well approximated in finite samples, the correlation between the instrument and the troublesome explanatory variable must be sufficiently high (Nelson and Startz 1990). Instruments lacking such correlation are called “weak.” IV can consistently estimate an equation’s parameters if there is for each troublesome explanatory variable at least one valid instrument that is not...
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References and Further Reading
Andrews DWK, Stock JH (eds) (2005) Identification and inference for econometric models – essays in honor of Thomas Rothenberg. Cambridge University Press, Cambridge
Andrews DWK, Moreira M, Stock JH (2006) Optimal two-sided invariant similar tests for instrumental variables regression. Econometrica 74(3):715–752
Cragg JG, Donald SG (1993) Testing identifiability and specification in instrumental variable models. Economet theor 9:222–240
Davidson R, MacKinnon JG (1993) Estimation and inference in econometrics. Oxford University Press, New York
Fuller WA (1977) Some properties of a modification of the limited information maximum likelihood estimator, Econometrica 45(4):939–954
Hahn J, Hausman J, Kuersteiner G (2004) Estimation with weak instruments: accuracy of higher order bias and MSE approximations. Economet J 7:272–306
Heckman JJ, Vytlacil E (2005) Structural equations, treatment effects and econometric policy evaluation. Econometrica 73(3):669–738
Imbens G, Angrist JD (1994) Identification and estimation of local average treatment effects. Econometrica 62:467–476
Moreira M (2003) A conditional likelihood ratio test for structural models. Econometrica 71(4):1027–1048
Nelson C, Startz R (1990) The distribution of the instrumental variables estimator and its F-ratio when the instrument is a poor one. J Bus 63(1):125–140
Stock JH, Yogo M (2005) Testing for weak instruments in IV regression. In: Donald WK, Andrews, James H, Stock (eds) Identification and inference for econometric models: A Festschrift in honor of Thomas Rothenberg, Cambridge University Press, pp 80–108
Wright PG (1928) The tariff on animal and vegetable oils. Macmillan, New York
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Murray, M.P. (2011). Instrumental Variables. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_304
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