Wooldridge PPT ch9

Fall 2008 under econometrics prof keunkwan ryu 7

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Fall 2008 under Econometrics Prof. Keunkwan Ryu 7 Nonnested Alternatives (cont) More difficult if one model uses y and the other uses ln( y ) Can follow same basic logic and transform predicted ln( y ) to get ŷ for the second step In any case, Davidson-MacKinnon test may reject neither or both models rather than clearly preferring one specification

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Fall 2008 under Econometrics Prof. Keunkwan Ryu 8 Proxy Variables What if model is misspecified because no data is available on an important x variable? It may be possible to avoid omitted variable bias by using a proxy variable A proxy variable must be related to the unobservable variable – for example: x 3 * = δ 0 + δ 3 x 3 + v 3 , where * implies unobserved Now suppose we just substitute x 3 for x 3 *
Fall 2008 under Econometrics Prof. Keunkwan Ryu 9 Proxy Variables (continued) What do we need for for this solution to give us consistent estimates of β 1 and β 2 ? E( x 3 * | x 1 , x 2 , x 3 ) = E( x 3 * | x 3 ) = δ 0 + δ 3 x 3 That is, u is uncorrelated with x 1 , x 2 and x 3 * and v 3 is uncorrelated with x 1 , x 2 and x 3 So really running y = ( β 0 + β 3 δ 0 ) + β 1 x 1 + β 2 x 2 + β 3 δ 3 x 3 + ( u + β 3 v 3 ) and have just redefined intercept, error term x 3 coefficient

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Fall 2008 under Econometrics Prof. Keunkwan Ryu 10 Proxy Variables (continued) Without out assumptions, can end up with biased estimates Say x 3 * = δ 0 + δ 1 x 1 + δ 2 x 2 + δ 3 x 3 + v 3 Then really running y = ( β 0 + β 3 δ 0 ) + ( β 1 + β 3 δ 1 ) x 1 + ( β 2 + β 3 δ 2 ) x 2 + β 3 δ 3 x 3 + ( u + β 3 v 3 ) Bias will depend on signs of β 3 and δ j This bias may still be smaller than omitted variable bias, though
Fall 2008 under Econometrics Prof. Keunkwan Ryu 11 Lagged Dependent Variables What if there are unobserved variables, and you can’t find reasonable proxy variables? May be possible to include a lagged dependent variable to account for omitted variables that contribute to both past and current levels of y Obviously, you must think past and current y are related for this to make sense

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Fall 2008 under Econometrics Prof. Keunkwan Ryu
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