Session 3: Dealing with Reverse Causality

1 IntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummarySession 3: Dealing with Reverse CausalityBen ShepherdPrincipal, Developing Trade Consultants Capacity Building Workshop for Trade Research:Gravity ModelingThursday, August 26, 2010 Ben ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOutline1 IntroductionOverviewEndogeneity and its Consequences2 Dealing with EndogeneityAd Hoc SolutionsIV Estimation3 Examples of IV Gravity Models Trading on Time (Djankov et al., 2008) Contract Enforcement (Ranjan & Lee, 2007)4 SummaryBen ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOverviewEndogeneity and its ConsequencesOutline1 IntroductionOverviewEndogeneity and its Consequences2 Dealing with EndogeneityAd Hoc SolutionsIV Estimation3 Examples of IV Gravity Models Trading on Time (Djankov et al.)

2 , 2008) Contract Enforcement (Ranjan & Lee, 2007)4 SummaryBen ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOverviewEndogeneity and its ConsequencesOverviewOne of the most important OLS assumptions is that theerrors are uncorrelated with the dependent number of possible reasons:Measurement errorOmitted variablesEndogeneity ( Reverse Causality )Endogeneity is particularly important in policy in trade facilitation ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOverviewEndogeneity and its ConsequencesOverviewTariffs are an obvious example of an endogeneity problemin many gravity suggests that tariffs should impact negatively onbilateral political economy suggests that greater importpenetration is likely to lead to increased demand forprotection by industry lobbies ( , Grossman andHelpman, protection for sale )What are the consequences for estimation and inference?

3 How can we deal with the problem?Ben ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOverviewEndogeneity and its ConsequencesOutline1 IntroductionOverviewEndogeneity and its Consequences2 Dealing with EndogeneityAd Hoc SolutionsIV Estimation3 Examples of IV Gravity Models Trading on Time (Djankov et al., 2008) Contract Enforcement (Ranjan & Lee, 2007)4 SummaryBen ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOverviewEndogeneity and its ConsequencesConceptualizing EndogeneityA simple example of endogeneity is the following:A=XB+EX=AC+WSince the current value of X depends on the current valueof A, X must be influenced by current shocks to A:X= (XB+E)C+WThus, X and E are correlated. This violates the ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryOverviewEndogeneity and its ConsequencesConsequences of EndogeneityEndogeneity bias is not a simple violation to deal is no equivalent to the robust estimators used toconduct inference in the presence of general patterns , it has serious consequences for our the presence of endogeneity, OLS can produce biasedand inconsistent parameter estimates.

4 Hypotheses testscan be seriously it takes is one endogenous variable to seriously distortALL OLS estimates of a ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationOutline1 IntroductionOverviewEndogeneity and its Consequences2 Dealing with EndogeneityAd Hoc SolutionsIV Estimation3 Examples of IV Gravity Models Trading on Time (Djankov et al., 2008) Contract Enforcement (Ranjan & Lee, 2007)4 SummaryBen ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationIntroductionWe need some way of separating out genuinely exogenousvariation in independent variables that might , we would also like some way of testing the extentto which endogeneity is a problem in our data, andensuring that the solution we have chosen is a good groups of solutions:Ad hoc approachesInstrumental variables estimationBen ShepherdSession 3.

5 Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationAd Hoc SolutionsIf a dependent variable is potentially endogenous, it isintuitively appealing to look for a proxy that does not sufferfrom the same most common approach is to lag the suspect variablesby one or more argument is that although current values of (eg) tariffsmight be endogenous to import penetration, it is unlikelythat past values of tariffs are subject to the same ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationAd Hoc SolutionsAdvantages of Lags/ProxiesVery simple to data requirements of Lags/ProxiesInterpretation becomes a little more difficult since thevariable in the regression is only a proxy for the variable weare interested of precision in some way of gauging empirically how serious theendogeneity problem is, and whether the solution isadequate to deal with ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationOutline1 IntroductionOverviewEndogeneity and its Consequences2 Dealing with EndogeneityAd Hoc SolutionsIV Estimation3 Examples of IV Gravity Models Trading on Time (Djankov et al.)

6 , 2008) Contract Enforcement (Ranjan & Lee, 2007)4 SummaryBen ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationIntroductionThe best way to deal with endogeneity concerns is throughinstrumental variables (IV) most common IV estimator is Two Stage LeastSquares (TSLS).Intuitively, IV estimation works as follows:Find a genuinely exogenous variable (instrument) that isstrongly correlated with the potentially that the instrument only influences the dependantvariable through the potentially endogenous ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationIntroductionIV estimation is intuitively appealing, and relatively simpleto implement on a technical most difficult part lies in the selection of main advantages of IV estimation are:Rigor and transparencyAmenability to empirical testing (appropriateness ofinstruments, extent of endogeneity, etc.

7 Ben ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTwo Stage Least SquaresAs the name suggests, this estimator proceeds in twosteps. Both of them involve the potentially endogenous variables in the gravitymodel on the exogenous variables from the model AND anumber of genuinely exogenous instruments equal to thenumber of potentially endogenous the gravity model using the predicted values from thefirst stage regressions in place of the potentiallyendogenous ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTwo Stage Least SquaresWhy does TSLS work? Intuitively:The first stage cleanses the endogeneity from thevariables we are worried about. By using predicted valuesbased on genuinely exogenous variables only, we obtainthe exogenous part of their second stage uses a variable that is now exogenousthanks to the first stage, and so the bias of parameters and hypothesis testing can alltake place as usual, following the same procedures ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTwo Stage Least SquaresThe hard part about TSLS is not the estimation, but one potentially endogenous variable, we need at leastone instrumental variable.

8 For two, we need at least two, is a valid instrument?It is strongly correlated with the potentially is exogenous to the gravity model, and does not influencebilateral trade EXCEPT through the potentially ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTwo Stage Least SquaresIn practice:1IV estimates are only as good as the instruments need to run some statistical tests and make sure themodel is working it s called two stage least squares, avoidrunning the two stages separately. You will get incorrectstandard errors (too small), and you might mistakenlyexclude exogenous variables from the main model acommon STATA s canned routes: ivreg, and ivreg2 (includesthe tests we are about to discuss). But make sure youknow what they re telling you!Ben ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationEstimation in StataTo make life easy, use the external ivreg2 and xtivreg2commands.

9 Use the first option to get the first stageregression a gravity model in which tariffs are potentiallyendogenous, we specify the following in Stata:ivreg2 ln_trade ln_dist (ln_tariff = instrument) [etc.]dummies, robust cluster(dist) firstxtivreg2 ln_trade ln_dist (ln_tariff = instrument) [etc.], robustfirstBen ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTesting TSLS ModelsOverviewTSLS provides a number of useful tests that can help indeciding whether IV estimation is necessary, and whether theinstruments chosen are test: Is there evidence that correlationbetween the potentially endogenous variables and theerror term is strong enough to result in substantivelybiased estimates?Instrument relevance test: Are the instruments sufficientlystrongly correlated with the potentially endogenousvariables?

10 Exogeneity/excludability of instruments: Are theinstruments genuinely uncorrelated with the main equationresiduals?Ben ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTesting TSLS ModelsTesting for Instrument RelevanceTSLS is only as good as the the presence of weak instruments, the TSLS estimatorcan actually produce worse results than simple the first step in testing must be to ensure that theinstruments are strongly enough correlated with thepotentially endogenous ShepherdSession 3: Dealing with Reverse CausalityIntroductionDealing with EndogeneityExamples of IV Gravity ModelsSummaryAd Hoc SolutionsIV EstimationTesting TSLS ModelsTesting for Instrument RelevanceTo test for instrument relevance, make sure to run the firststage regressions of the potentially endogenous variableson all of the exogenous the instruments individually statistically significant?