Weak Instruments and Identification Slides

# Weak Instruments - NBER Summer Institute Whats New in Econometrics Time Series Lecture 3 Weak Instruments Weak Identification and Many Instruments

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Revised July 22, 2008 3-1 NBER Summer Institute What’s New in Econometrics – Time Series Lecture 3 July 14, 2008 Weak Instruments, Weak Identification, and Many Instruments, Part I

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Revised July 22, 2008 3-2 Outline Lecture 3 1) What is weak identification, and why do we care? 2) Classical IV regression I: Setup and asymptotics 3) Classical IV regression II: Detection of weak instruments 4) Classical IV regression III: hypothesis tests and confidence intervals Lecture 4 5) Classical IV regression IV: Estimation 6) GMM I: Setup and asymptotics 7) GMM II: Detection of weak identification 8) GMM III: Hypothesis tests and confidence intervals 9) GMM IV: Estimation 10) Many instruments
1) W hat is weak identification, and why do we care? 1a) Four examples Example #1 (cross-section IV) : Angrist-Kreuger (1991), What are the returns to education? Y = log(earnings) X = years of education Z = quarter of birth; k = #IVs = 3 binary variables or up to 178 (interacted with YoB, state-of-birth) n = 329,509 ˆ A-K results: = .081 ( SE = .011) TSLS β Then came Bound, Jaeger, and Baker (1995)… The problem is that Z (once you include all the interactions) is weakly correlated with X Revised July 22, 2008 3-3

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Revised July 22, 2008 3-4 Example #2 (time-series IV): Estimating the elasticity of intertemporal substitution, linearized Euler equation e.g. Campbell (2003), Handbook of Economics of Finance Δ c t +1 = consumption growth, t to t +1 r i , t +1 = return on i th asset, t to t +1 linearized Euler equation moment condition: E t ( Δ c t +1 τ i ψ r i , t +1 ) = 0 Resulting IV estimating equation: E [( Δ c t +1 i r i , t +1 ) Z t ] = 0 (this ignores temporal aggregation concerns)
Revised July 22, 2008 3-5 EIS estimating equations: Δ c t +1 = τ i + ψ r i , t +1 + u i , t +1 ( a ) or r i , t +1 = μ i + (1/ ) Δ c t +1 + η i , t +1 ( b ) Under homoskedasticity, standard estimation is by the TSLS estimator in (a) or by the inverse of the TSLS estimator in (b). Findings in literature (e.g. Campbell (2003), US data): regression (a): 95% TSLS CI for is (-.14, .28) regression (b): 95% TSLS CI for 1/ is (-.73, 2.14) What is going on? Reverse regression: r i , t +1 = i + (1/ ) Δ c t +1 + Can you forecast Δ c t +1 using Z t ? Z t is weakly correlated with Δ c t +1

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Revised July 22, 2008 3-6 Example #3 (linear GMM): New Keynesian Phillips Curve e.g. Gali and Gertler (1999), where x t = labor share; see survey by Kleibergen and Mavroeidis (2008). Hybrid NKPC with shock η t : π t = λ x t + γ f E t t +1 + b t –1 + t Rational expectations: E t –1 ( t x t f t +1 b t –1 ) = 0 GMM moment condition: E [( t f t +1 b t –1 x t ) Z t ] = 0 Instruments: Z t = { t –1 , x t –1 , t –2 , x t –2 ,…} (GG: 23 total) Issues : Z t needs to predict t +1 – beyond t –1 (included regressor) But predicting inflation is really hard! Atkeson-Ohanian (2001) found that, over 1985-1999 quarterly sample, it is difficult to outperform a year-over-year random walk forecast at the 4-quarter horizon
Example #4 (nonlinear GMM): Estimating the elasticity of intertemporal substitution, nonlinear Euler equation With CRRA preferences, in standard GMM notation, h ( Y t , θ ) = 1 1 1 G t tG t C R C γ δ ι × + + ⎛⎞ ⎜⎟ ⎝⎠ where R t +1 is a G ×

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## This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Weak Instruments - NBER Summer Institute Whats New in Econometrics Time Series Lecture 3 Weak Instruments Weak Identification and Many Instruments

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