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Policy Evaluation Antoine Bozio Institute for Fiscal Studies University of Oxford - January 2008

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Outline I.Why is policy evaluation important? 1.Policy view 2.Academic view II.What are the evaluation problems? 1.The Quest for the Holy Grail: causality 2.The generic problem: the counterfactual 3.Specific problems: selection, endogeneity III.The evaluation methods 1.Randomised social experiments 2.Controlling for observables: regression, matching 3.Natural experiments: diff-in-diff, regression discontinuity 4.Instrument variable strategy

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I. Why is policy evaluation important? (policy view) 1.Policy interventions are very expensive: UK government spends 41.5 % of GDP Need to know whether money is well spent There are many alternative policies possible 2.Evaluation is key to modern democracies –Citizens can differ in their preferences, in the goals they want policy to achieve => politics –Policies are means to achieve these goals –Citizens need to be informed on the efficiency of these means => policy evaluation

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I. Why is policy evaluation important? (policy view) 3.Its rarely obvious to know what are a policys effects –Unless you have strong beliefs (ideology), policies can have wide-ranging effects (economy is very complex and hard to predict) –Economic theory is very useful but leaves many of the policy conclusions indeterminate => it depends on parameters (individuals behaviour, markets…) –Correlation is not causation…

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I. Why is policy evaluation important? (academic view) Evaluation is now a crucial part of applied economics: -To estimate parameters -To test models and theories Evaluations techniques have become a field in themselves -Many advances in the last ten years -Turning away from descriptive correlations, and aiming at causal relationship

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I. Why is policy evaluation important? (academic view) Many fields of economics now rely heavily on evaluations work Labour market policies Impact of taxes Impact of savings incentives Education policies Aid to developing countries use of micro data different from macro analysis (cross-country…)

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II. What are the evaluation problems? 1.The Quest for the Holy Grail: causal relationships 2.The generic problem: the counterfactuals are missing 3.Specific obstacles: selection, endogeneity

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II -1. The Quest for Causality Correlation is not causality! Post hoc, ergo propter hoc : looking at what happens after the introduction of a policy is not proper evaluation. –Long term trends –Macroeconomics changes –Selection effects Rubins model for causal inference: the experience setting and language - See Holland (1986)

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II- 1. The Quest for Causality We want to establish causal inference of a policy T on a population U composed agents u To measure how treatment or the cause (T) affects the outcome of interest (Y) Define Y(u) as the outcome of interest defined over U (It can measure income, employment status, health, …)

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II – 2. Looking for counterfactuals Looking for counterfactual: What would have happened to this persons behaviour under an alternative policy ? E.G.: -Do people work more when marginal taxes are lower ? -Do people earn more when they have more education ? -Do unemployed find more easily a job when unemployment benefit duration is reduced ?

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II – 2. Looking for counterfactuals Treated: agent that has been exposed to treatment (T) Control: agent that has not been exposed to treatment (C, non T) The role of Y is to measure the effect of treatment (causes have effects) Y T (u) and Y C (u) outcome that would be observed had unit u been exposed to treatment outcome that would be observed had unit u not been exposed to treatment

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II – 2. Looking for counterfactuals The causal effect of treatment T on unit u as measured by outcome Y is α(u) = Y T (u) - Y C (u) Its a missing data problem Fundamental problem of causal inference It is impossible to observe Y T (u) and Y C (u) simultaneously on the same unit Therefore, it is impossible to observe α(u) for any unit u

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II – 2. Looking for counterfactuals time Y(u ) k T C α(u) = Y T (u)- Y C (u)

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The statistical solution Use population to compute the average causal effect of T over U Need data on many individuals (micro data) Average outcome of the treated: E[Y T (u) | T] Average outcome of the control : E[Y C (u) | C] Compute the difference between averages: D = E[Y T (u) | T] - E[ Y C (u)| C]

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II – 2. Selection bias Compute the difference between averages: D = E[Y T (u) | T] - E[ Y C (u)| C] D= E[Y T (u) - Y C (u)| T ] + E[Y C (u) | T] - E[ Y C (u)| C] D = α + E[Y C (u) | T] - E[ Y C (u)| C] D = average causal effect + selection bias

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Illustration: impact of advanced course in maths Treatment: advanced course in maths (against standard course in maths) Treated: students scoring above x in maths test at beginning of year Outcome of interest: score in maths test at end of year Measure impact of treatment by comparing average score of treated and controls by the end of year Problem? On average, treated students are better at maths than control students Best students would always perform better on average!! Selection bias : E[Y C (u) | T] - E[ Y C (u)| C] > 0 Overestimation of the true effect of the course

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Illustration: impact of advanced course in maths (cont) Compare before (t-1) and after treatment (t+1): before the advanced class and after. D = E[Y T (u) | T, t+1] - E[ Y T (u)| T, t-1] Problems? -Many other things might change : student grow older, smarter (trend issue) -Hard to disentangle the impact of the advanced class from the regular class -Grading before and after might not be equivalent… => Estimates likely to be biased

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III. Evaluation methods: how to construct the counterfactual 1.Randomised social experiments 2.Controlling for observables: OLS, matching 3.Natural experiment: Difference in difference, regression discontinuity design 4.Instrument variable methodology 5.Other methods : Selection model and structural estimation

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III- 1. Randomized social experiments Experiments solve the selection problem by randomly assigning units to treatment Because assignment to treatment is not based on any criterion related with the characteristics of the units, it will be independent of possible outcomes E[Y C (u) | C] = E[Y C (u) | T] now holds D = E[Y T (u) | T] - E[Y C (u) | C] D = α = E[Y T (u) - Y C (u)] = causal effect Convincing results More and more randomized policies

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Reform to incapacity benefits Source: House of Commons Work and Pensions Select Committee Report (2006). October 2003 April 2004 Six-month off-flow rate from incapacity benefits

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Is the policy working? Source: House of Commons Work and Pensions Select Committee Report (2006). October 2003 April 2004 Six-month off-flow rate from incapacity benefits

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Is the policy working? Source: House of Commons Work and Pensions Select Committee Report (2006). October 2003 April 2004 Six-month off-flow rate from incapacity benefits

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Is the policy working? Source: House of Commons Work and Pensions Select Committee Report (2006). October 2003 April 2004 Six-month off-flow rate from incapacity benefits

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Drawbacks to social experiments Experiments are costly and therefore rare (less rare now) –Cost and ethical reasons, feasibility Threats to internal validity –Non response bias. Non-random dropouts –Substitution between treated and control Threats to external validity –Limited duration –Experiment specificity (region, timing…) –Agents know they are observed –General equilibrium effects Threats to power –Small sample

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Non-experimental approaches Aim at recovering randomisation, thus recovering the missing counterfactual E(Y C |T) This is done in different ways by different methods Which one is more appropriate depends on the treatment being studied, question of interest and available data

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III 2. Controlling on observables 1/ Regression analysis (OLS) Y = a + b X1 + c X2 + d X3 Problems : a/ Omitted variables lead to bias and some variables may be unobservable Example: Effect of education on earnings Ability or preference to work is hardly observable b/ Explanatory variables might be endogenous Example: Effect of unemployment benefit duration When unemployment increases, policies tend to increase unemployment benefit duration => Correlation is NOT causality !!

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III 2. Controlling on observables 2/ Matching on observables: It is possible to compare groups that are similar relative to the variables we observe (same education, income…) Explores all observable information Take X to represent the observed characteristics of the units other than Y and D It assumes that units with the same X are identical with respect to Y except possibly for the treatment status Formally, what is being assumed is E[Y C |D=T,X] = E[Y C |D=C,X]

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Matching (cont) time Y kk+1 α M (X) = Y D=T (k+1,X) – Y D=C (k+1,X) α T|D=C,X T|D=T,X C|D=C Use X characteristics to ensure comparable units are being compared C|D=C,X

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III - 3. Natural experiments Explore sudden changes or spatial variation in the rules governing behaviour Typically involve one group that is affected by the phenomena (the treated) and one other group that is not affected (the control) Observe how behaviour (outcome of interest) changes as compared to change in unaffected group Difference in difference Regression discontinuity estimation

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Difference in differences (DD) Suppose a change in policy occurs at time k We observe agents affected by policy change before and after the policy change, say at times k-1 and k+1 : A= E[Y T |t=k+1] – E[Y T |t=k-1] We also observe agents not affected by the policy change at the same time periods: B=E[Y D |t=k+1] – E[Y D |t=k-1] DD =A- B = true effect of the policy

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Difference in differences time Y kk+1k-1 α T|D=C T|D=T C|D=C Use fact that difference between T and C remains fixed over time in C regime

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Under certain conditions 1.No composition changes within groups 2.Common time effects across groups Checking the strategy -Checks the DD strategy before the reform -Use different control groups -Use an outcome variable not affected by the reform Has to be a careful study ! Can take into account unobservable variables !

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Difference in differences: differential trends time Y kk+1k-1 E[Y C (k+1) - Y C (k-1)|D=C] E[Y C (k+1) - Y C (k-1)|D=T] α T|D=C T|D=T C|D=C Time trend in T and C groups are different

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Difference in differences: Ashenfelters dip time Y kk+1k-1 DD assumption holds only in certain periods α T|D=C T|D=T C|D=C T often experience particularly bad shocks before deciding to enrol into treatment k-2

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Diff-in-Diff : Esther Duflo (AER 2001) Policy: school construction in Indonesia Regional difference: low and high Children young enough to be affected = treated Children too old = control Estimate the impact of building school on education Estimate the impact of education on earnings

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Diff-in-Diff : Esther Duflo (AER 2001)

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Common problems with DD Long-term versus reliability trade-off: -Impact most reliable in the short term -True impact might take time Heterogeneous behavioural response –Average effect might hide high/low effect for certain groups Local estimation –Truly DD estimates are hard to generalize Need many estimations to establish general causal effect

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Regression discontinuity design (RD) Use the discontinuity in the treatment Example: New deal for young people in the UK Program targeted to young unemployed aged 18 to 24 Unemployed just older than 25 are in the control group Unemployed just younger than 25 are in the treated group

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De Giorgi (2006) : New deal for young people

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III - 4. Instrumental variable Use the fact that a variable Z (the instrument) might be correlated with the endogenous variable X BUT not with the outcome Y Except through the variable X E.G.: number of student per class is endogenous to outcomes test scores => How to find a good instrument ?

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Angrist and Lavy (QJE 1999)

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III - 5. Other methods Matching mixed with diff-in-diff Selection estimator Structural estimation There is a trade-off between reliability of the causal inference (identification) and the generalization of the results

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Conclusion Policy evaluation is crucial –For conducting efficient policies –For improving scientific knowledge Correlation is not causality Beware of the selection effect or of endogenous variable ! Methods to draw causal inference are available => Need careful analysis !

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