計量經(jīng)濟學導論ch15課件

1、計量經(jīng)濟學導論ch15課件計量經(jīng)濟學導論ch15課件Example: Education in a wage equationDefinition of a instrumental variable:1) It does not appear in the regression2) It is highly correlated with the endogenous variable3) It is uncorrelated with the error termReconsideration of OLS in a simple regression modelError terms c

2、ontains factors such as innate ability which are correlated with educationand assumeInstrumental Variables and Two Stage Least SquaresExample: Education in a wage eAn simple consistency proof for OLS under exogeneity:(Exogeneity)This holds as long as the data are such that sample variances and cova-

3、riances converge to their theoretical counterparts as n 1, i.e. if a LLN holds. OLS will basically be consistent if, and only if, exogeneity holds.Instrumental Variables and Two Stage Least SquaresAn simple consistency proof foAssume existence of an instrumental variable :(but )IV-estimator:The inst

4、rumental variable is un-correlated with the error termThe instrumental variable is correlated with the explanatory variableInstrumental Variables and Two Stage Least SquaresAssume existence of an instrumExample: Fathers education as an IV for educationOLS:IV:Is the education of the father a good IV?

5、It doesnt appear as regressorIt is significantly correlated with educIt is uncorrelated with the error (?)The estimated return to education decreases (which is to be expected)It is also much less precisely estimatedReturn to education probably overestimatedInstrumental Variables and Two Stage Least

6、SquaresExample: Fathers education asOther IVs for education that have been used in the literature:The number of siblings1) No wage determinant, 2) Correlated with education because of resource constraints in hh, 3) Uncorrelated with innate abilityCollege proximity when 18 years old1) No wage determi

7、nant, 2) Correlated with education because more education if lived near college, 3) Uncorrelated with error (?)Month of birth1) No wage determinant, 2) Correlated with education because of compulsory school attendance laws, 3) Uncorrelated with errorInstrumental Variables and Two Stage Least Squares

8、Other IVs for education that hProperties of IV with a poor instrumental variableIV may be much more inconsistent than OLS if the instrumental variable is not completely exogenous and only weakly related to IV worse than OLS if:e.g.There is no problem if the instrumental variable is really exogenous.

9、 If not, the asymp-totic bias will be the larger the weaker the correlation with x.Instrumental Variables and Two Stage Least SquaresProperties of IV with a poor iIV estimation in the multiple regression modelConditions for instrumental variable1) Does not appear in regression equation2) Is uncorrel

10、ated with error term3) Is partially correlated with endogenous explanatory variableendogenousexogenous variables This is the so called reduced form regression“In a regression of the endogenous explanatory variable on all exogenous variables, the instrumental variable must have a non-zero coefficient

11、.Instrumental Variables and Two Stage Least SquaresIV estimation in the multiple Computing IV estimates in the multiple regression case:as well asExogeneity conditions:Use sample analogs of the exogeneity conditions:This yields k+1 equations from which the k+1 estimates can be can be obtained.Instru

12、mental Variables and Two Stage Least SquaresComputing IV estimates in the Two Stage Least Squares (2SLS) estimationIt turns out that the IV estimator is equivalent to the following procedure, which has a much more intuitive interpretation:First stage (= reduced form regression):Second stage (= OLS w

13、ith y2 replaced by its prediction from the first stage):The endogenous explanatory variable y2 is predicted using only exogenous informationAdditional exogenous variable (= instrument)Instrumental Variables and Two Stage Least SquaresTwo Stage Least Squares (2SLS)Why does Two Stage Least Squares wor

14、k?All variables in the second stage regression are exogenous because y2 was replaced by a prediction based on only exogenous informationBy using the prediction based on exogenous information, y2 is purged of its endogenous part (the part that is related to the error term)Properties of Two Stage Leas

15、t SquaresThe standard errors from the OLS second stage regression are wrong. However, it is not difficult to compute correct standard errors.If there is one endogenous variable and one instrument then 2SLS = IVThe 2SLS estimation can also be used if there is more than one endo-genous variable and at

16、 least as many instrumentsInstrumental Variables and Two Stage Least SquaresWhy does Two Stage Least SquarExample: 2SLS in a wage equation using two instrumentsTwo Stage Least Squares estimation results:First stage regression (regress educ on all exogenous variables):Education is significantly parti

17、ally correlated with the education of the parentsThe return to education is much lower but also much more imprecise than with OLSInstrumental Variables and Two Stage Least SquaresExample: 2SLS in a wage equatiUsing 2SLS/IV as a solution to errors-in-variables problemsIf a second measurement of the m

18、ismeasured variable is available, this can be used as an instrumental variable for the mismeasured variableStatistical properties of 2SLS/IV-estimationUnder assumptions completely analogous to OLS, but conditioning on . rather than on , 2SLS/IV is consistent and asymptotically normal2SLS/IV is typically much less precise because there is more multicolli-nearity and less explanatory variation in the second stage regressionCorrections for heteroscedasticity/serial correlatio