1、APPLIED ECONOMETRICSLecture 1 - Identification,Defining Identification,Experiments,Natural Experiments,Instrumental variables,Econometric Identification,WHAT IS IDENTIFICATION?,Graduate and professional economics mainly concerned with identification in empirical workConcept of understanding what is
2、the causal relationship behind empirical results:This is essential for learning from empirical researchTime-series example: Interest rates and GDPCross-section example: Management & Productivity,WHAT IS DRIVING THIS RELATIONSHIP?,Correlation = 0.233,REASONS FOR CORRELATION,Imagine variables Yt and X
3、t are correlated:There can be three reasons for this, which are not mutually exclusive:Cause: Changes in Xt drive changes in YtReverse Cause: Changes in Yt drive changes in XtCorrelated variable: Changes in Zt drives Xt and Yt,WHAT IS DRIVING THIS RELATIONSHIP?,SO HOW DO WE GET IDENTIFICATION,Four b
4、road approaches for identificationExperiments you generate the variationNatural Experiments you know what generated the variationInstrumental variables you have a variable that can provide you variationEconometric Identification you rely on (testable) econometric assumptions for identification,Defin
5、ing Identification,Experiments,Natural Experiments,Instrumental variables,Econometric Identification,EXPERIMENTS (1),Experiments are totally standard in Science & MedicineFor example:Set up a treatment and control group for a new drug, making sure these are comparable (or randomly selected)Ensure th
6、e sample sizes are large enough to obtain statistical significanceEnsure the experiment is unbiased i.e. the drug and the placebo are as similar as possibleRun the experiment,EXPERIMENTS (2),Economists like to use the language of ScienceFor example the UK considered introducing an Education Maintena
7、nce Allowance, to pay kids to stay on at school. But want to test first to see if this would this work.Set up a treatment and control regions to match these in characteristicsSelect enough regions to get large sample sizesObserve agents actions to evaluate impact (rather than self reported outcomes)
8、Run the experiment,EXPERIMENTS (3),Experiments are rare in economics because they are expensive, although they becoming more popular:Typical areas for running experiments include:Development economics cheaper to run experiments in the third World (water supply or management practices)Consumer econom
9、ics small stakes experiments that are easy to administer (credit cards)Individual business applications firms can finance these (retail store layout)But some fields will never have experiment for example macroeconomics,Defining Identification,Experiments,Natural Experiments,Instrumental variables,Ec
10、onometric Identification,NATURAL EXPERIMENTS (1),Natural experiments are where fortunate situations create good underlying identification:Typically several approaches:Tax e.g. Response of R&D to the cost of capital (Bloom, Griffith & Van Reenen, 2002), (Chetty and Saez, 2003)Discontinuity (see over)
11、Shock - financial crisis and Kibutzim (Abramitzky, 2007)Disasters - Ethiopian Jews airlift (Gould, Levy & Passerman, 2004),NATURAL EXPERIMENTS (2),Natural experiments are almost the holly grail of modern applied economicsIn the absence of true experiments they provide the best way to provide simple
12、identificationCouple of standard way to use natural experiments in practiceDiscountinunity analysis and/orDifference in differences,DISCONTINUITY ANALYSIS example 1,Region A(no tax),Region B(50% tax),Imagine a 50% tax is levied on investment in the rich coastal region A but not in the poor inland re
13、gion B. If you saw the graph below could you say what the impact of the tax is on investment?,Investment,Estimated impact of the tax,DISCONTINUITY ANALYSIS example 2,Impact of telephones on price of fish in Kerala (India),DIFFERNCES IN DIFFERENCES,Identification comes from the differential change be
14、tween the two groups pre and post-treatmentdifference out unobserved fixed effectsdifference out common time effectsKey assumption of common time effects for the two groups,POLICY EXAMPLE OF “DIFF-IN-DIFF”,Small firms R&D tax credit introduced in 2000 for firms with 250 or less employeesSo could loo
15、k at firms before and after creditBut other things also changing (2000 peak of dotcom boom etc)So need to set up a control group of companies look similar to firms getting the credit except dont get the creditCompare firms with 240 employees to those with 260This is double-diff (or diff in diffs) to
16、 compare differences:Between pre and post the credit (1999 versus 2001)Between the treated (240 employees) and untreated firms (260 employees),Defining Identification,Experiments,Natural Experiments,Instrumental variables,Econometric Identification,INSTRUMENTAL VARIABLES (1),Want to look at effect o
17、f schooling (Si) on earnings (Yi)Assume the true model is : Yi = + 1 Si + 2 Ai + viwhere Ai is (unobserved) ability which is positively correlated with Si, and vi is random independent noiseWhat would happen if we estimated the following instead? Yi = a + b1 Si + eiwhere ei = 2 Ai + vi,INSTRUMENTAL
18、VARIABLES (2),-BackgroundAssume estimating equation below in Ordinary Least SquaresY = + X + eThe estimate of = E(YX)/E(XX)= E(X + e )X)/E(XX)= + E(eX)/E(XX)= only if e and X are independentBut if e and X are correlated then the estimated is biased, and X is called “endogenous” (correlated with the
19、error)-,INSTRUMENTAL VARIABLES (3),Thus, estimation of the following would be biased:Yi = a + b1 Si + eibecause Si and ei are correlated as ei is a function of ability Eb1=EYS/ESS=E(1Si+2Ai+vi)S / ESS= 1 + E(2Ai+vi)S / ESS= 1 + 2EAiS / ESS 1So because ignore ability, which is correlated with schooli
20、ng, we overestimate the impact of schooling on earnings,INSTRUMENTAL VARIABLES (4),Imagine we had a variable called an instrument Z that was correlated with schooling but not ability. We could then use this to explain variation in schooling as it is not correlated with abilityOne example of this wou
21、ld be if the Government paid everyone born on even days to stay in schoolThen “born on an even day” would be an instrument for schooling correlated with schooling but not abilityIn practice instruments are often hard to find,INSTRUMENTAL VARIABLES (5),Assume that Z is correlated with S but not A. Th
22、en the following instrumental variable estimator is consistent Eb1IV=EYZ/ESZ=E(1Si+2Ai+vi)Z / ESZ=E1SiZ + 2AiZ +viZ / ESZ= 1 + (2EAiS + EviZ) / ESZ= 1Stata will calculate this for you. All you need to find is a variable that only affects your dependent variable via the variable you are interested in
23、,INSTRUMENTAL VARIABLES,Any questions on this?Imagine you wanted to evaluate the impact of crop yields on farmers behavior can anyone suggest a good instrument,Defining Identification,Experiments,Natural Experiments,Instrumental variables,Econometric Identification,ECONOMETRIC IDENTIFICATION,Another
24、 way to obtain identification is try to model everythingFor example, we claim we know how ability is correlated with schooling and so model the whole systemThe problem with this is:It is a lot more complicatedIt requires strong assumptionsThus, this is usually only undertaken when there is no obvious instrument or natural experiment,SUMMARY,Identification understanding the causality in a regression is essential for generating meaningful resultsThere are a range of approaches but they all need some prior economic thought (i.e. is their a natural experiment?),
