Kraay, Aart2012-05-302012-05-302008-05https://hdl.handle.net/10986/6693The validity of instrumental variables (IV) regression models depends crucially on fundamentally untestable exclusion restrictions. Typically exclusion restrictions are assumed to hold exactly in the relevant population, yet in many empirical applications there are reasonable prior grounds to doubt their literal truth. In this paper I show how to incorporate prior uncertainty about the validity of the exclusion restriction into linear IV models, and explore the consequences for inference. In particular I provide a mapping from prior uncertainty about the exclusion restriction into increased uncertainty about parameters of interest. Moderate prior uncertainty about exclusion restrictions can lead to a substantial loss of precision in estimates of structural parameters. This loss of precision is relatively more important in situations where IV estimates appear to be more precise, for example in larger samples or with stronger instruments. The author illustrates these points using several prominent recent empirical papers that use linear IV models.CC BY 3.0 IGOABSOLUTE VALUEBAYESIAN ANALYSISBENCHMARKBILATERAL TRADECAUSATIONCONFIDENCE INTERVALSCONSUMERSCONTROL VARIABLESCORRELATIONSCOUNTRY DUMMIESCOVARIANCEDEGREES OF FREEDOMDEPENDENT VARIABLEDISTRIBUTIONAL ASSUMPTIONSDUMMY VARIABLEECONOMETRIC THEORYECONOMIC ACTIVITYECONOMIC DEVELOPMENTECONOMIC GROWTHENDOGENOUS VARIABLEENDOGENOUS VARIABLESEQUATIONSERRORERROR TERMERROR TERMSEXCLUSIONEXPERIMENTAL DATAFINANCIAL DEVELOPMENTFINANCIAL SERVICESFITTED VALUESGAMMA DISTRIBUTIONGDPGDP PER CAPITAGROWTH RATEGROWTH RATESHUMAN CAPITALINFLATIONINSTRUMENTAL VARIABLEINSTRUMENTAL VARIABLESINSTRUMENTAL VARIABLES ESTIMATORINSTRUMENTAL VARIABLES REGRESSIONINTERNATIONAL BANKLIKELIHOOD FUNCTIONLINEAR FUNCTIONLINEAR REGRESSIONLINEAR REGRESSION MODELMACROECONOMICSMATRIXMORTALITYNORMAL DISTRIBUTION0 HYPOTHESISPER CAPITA INCOMESPRECISIONPROBABILITYPROBABILITY DISTRIBUTIONPROPERTY RIGHTSRANDOM VARIABLERANDOM VARIABLESREGRESSION MODELROBUSTNESS CHECKSSAMPLE MEANSAMPLE SIZESENSITIVITY ANALYSISSLOPE COEFFICIENTSLOPE COEFFICIENTSSTANDARD DEVIATIONSTANDARD ERRORSSTRUCTURAL PARAMETERSTEST STATISTICSTRADE EQUATIONTRADE OPENNESSTRADE POLICYTRADE SHAREUNCERTAINTYUNKNOWN PARAMETERVALIDITYVARIABLE ESTIMATIONVARIANCE-COVARIANCE MATRIXWorld Bank10.1596/1813-9450-4632