ENDOGENEITY - SIMULTANEITY Development Workshop

What is endogeneity and why we do not like it? [REPETITION] Three causes: – X influences Y, but Y reinforces X too – Z causes both X and Y fairly contemporaneusly – X causes Y, but we cannot observe X and Z (which we observe) is influenced by X but also by Y Consequences: – No matter how many observations – estimators biased (this is called: inconsistent) – Ergo: whatever point estimates we find, we can’t even tell if they are positive/negative/significant, because we do not know the size of bias + no way to estimate the size of bias

The magic of „ceteris paribus” Each regression is actually ceteris paribus Problem: data may be at odds with ceteris paribus Examples?

Problems with Inferring Causal Effects from Regressions Regressions tell us about correlations but ‘correlation is not causation’ Example: Regression of whether currently have health problem on whether have been in hospital in past year: HEALTHPROB | Coef. Std. Err. t PATIENT | _cons | Do hospitals make you sick? – a causal effect

The problem in causal inference in case of simultaneity Confounding Influence Treatment Outcome Observed Factor Unobserved Factor

Any solutions? Confounding Influence Treatment Outcome Observed Factor Unobserved Factor

Instrumental Variables solution… Confounding Influence Treatment Outcome Instrumental Variable(s) Observed Factor Unobserved Factor

Fixed Effects Solution… (DiD does pretty much the same) Confounding Influence Treatment Outcome Fixed Influences Observed Factor Unobserved Factor

Short motivating story – ALMPs in Poland Basic statement: 50% of unemployed have found employment because of ALMPs Facts: – 50% of whom? – only those, who were treated (only those were monitored) – only 90% of treated completed the programmes – of those, who completed, indeed 50% work, but only 60% of these who work say it was because of the programme So how many actually employed because of the programme?

Short motivating story – ALMPs in Poland ??? 90 % Product Gross effectiveness Net effectiveness Net efficiency? Completed training …... found employment thanks to programme…

Basic problems in causal inference Compare somebody „before” and „after” – If they were different already before, the differential will be wrongly attributed to „treatment”  can we measure/capture this inherent difference?  does it stay unchanged „before” and „after”?  what if we only know „after”? If the difference stays the same => DiD estimator => assumption that cannot be tested for If the difference cannot be believed to stay the same?

Faked counterfactual or generating a paralel world o MEDICINE: takes control groups – people as sick, who get a different treatment or a placebo => experimenting o What if experiment impossible? Seminarium magisterskie - zajęcia 4 12

What if experiment impossble? Only cross-sectional data Panel data „Regression Discontinuity Design“ „Propensity Score Matching“ Instrumental variables Before After Estimators Difference in Difference Estimators (DiD) „Propensity Score Matching“ + DiD

Propensity Score Matching Confounding Influence Treatment Outcome Treatment Observed Factor Unobserved Factor

Propensity score matching GroupY1Y0 Treated (D=1) Observedcounterfactual – (does not exist) Nontreated (D=0) counterfactual – (does not exist)observed Average treatment effect E(Y)=E(Y1-Y0)=E(Y1)-Y0 Average treatment effect for the untreated E(Y1-Y0|D=0)=E(Y1|D=0)-E(Y0|D=0) Average treatment effect for the treated (ATT) E(Y1-Y0|D=1)=E(Y1|D=1)-E(Y0|D=1)

Propensity Score Matching Idea – Compares outcomes of similar units where the only difference is treatment; discards the rest Example – Low ability students will have lower future achievement, and are also likely to be retained in class – Naïve comparison of untreated/treated students creates bias, where the untreated do better in the post period – Matching methods make the proper comparison Problems – If similar units do not exist, cannot use this estimator

How to get PSM estimator? – First stage: run „treatment” on observable characteristics – Second stage: estimate the probability of „treatment” – Third stage: compare results of those „treated” and similar non-treated („statistical twinns”) – The less similar they are, the less likely they should be compared one with another

The obtained propensity score is irrelevant (as long as consistent) NEAREST NEIGHBOR (NN) Pros => tzw. 1:1 Cons => if 1:1 does not exist, completely senseless

The obtained propensity score is irrelevant (as long as consistent) CALIPER/RADIUS MATCHING(NN) Pros => more elastic than NN Cons => who specifies the radius/caliper?

The obtained propensity score is irrelevant (as long as consistent) Stratification and Interval Pros => eliminates discretion in radius/caliper choice Cons => within strata/interval, units don’t have to be „similar” (some people say 10 strata is ql)

The obtained propensity score is irrelevant (as long as consistent) KERNEL MATCHING (KM) Pros => uses always all observations Cons => need to remember about common support TreatmentControl * ** * * *

What is „common support”? Distributions of pscore may differ substantially across units Only sensible solutions!

Real world examples

Next week – practical excercise Read the papers posted on the web I will post one that we will replicate soon…