Quantitative Economics for the Evaluation of the European Policy
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1 Quantitative Economics for the Evaluation of the European Policy Dipartimento di Economia e Management Irene Brunetti Davide Fiaschi Angela Parenti 1 25th of September, ireneb@ec.unipi.it, davide.fiaschi@unipi.it, and aparenti@ec.unipi.it. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
2 Plan of the Course Plan of the Course Module 1: Quantitative methods to evaluate economic policy Statistical, non-experimental methods for policy evaluation: the problem of causality, the counterfactual approach (Dr. Irene Brunetti) The estimate of the counterfactual (Dr. Irene Brunetti) The impact of estimating counterfactual (Dr. Irene Brunetti) Module 2: Quantitative methods for economics Introduction to non-parametric techniques (Prof. Davide Fiaschi) Introduction to bootstrap (Prof. Davide Fiaschi) Introduction to panel (Dr. Angela Parenti) Introduction to spatial econometrics (Dr. Angela Parenti) Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
3 Plan of the Course Plan of the Course Module 3: European Regional policy and economic convergence Causes and effects of regional imbalance: economic theory and empirical evidence (Prof. Davide Fiaschi) Regional policies: theoretical models (Prof. Davide Fiaschi and Dr. Angela Parenti) Historical development of European Regional Policy (Dr. Angela Parenti) Econometric models for convergence (Prof. Davide Fiaschi and Dr. Angela Parenti) Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
4 Plan of the Course Resources and Materials for the Course Some books chapters and papers Some handouts on R ( Website of the course: Web resources for the EU Regional Policy: Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
5 Plan of the Course Methods of evaluation Two homeworks for each couple of students (randomly formed) First homework: at the end of the course (Module 1) Second homework: at the end of the course (Modules 2 and 3) Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
6 Main Questions of the Course Main Questions of the Course How is the inequality across European regions and how is evolving? Which type of inequality we are interested in? (income, health, happiness, unemployment, productivity, concentration of economic activities, etc.) Is there a theoretical model able to explain such types of inequality? Which are the main goals of European Regional Policy? How can we verify if European Regional Policy achieves its goals?. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
7 Introduction Module 1 Example 1 Suppose we have a group of unemployed individuals who are in training and who are looking for a job. Six months after the end of the training program we check their employment situation and find that 40% of the group is working. Can we conclude that 40% of those that were unemployed before the training, found work because of the training program? In order to make a comprehensive evaluation one needs to take into account many things how can we isolate the effect so it can be attributed solely on the treatment (the training)? Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
8 Introduction Why evaluate? Programs and policies are usually designed to change outcomes, for example, to increase incomes, to reduce unemployment, or to raise human capital. Understand if these changes are achieved is a crucial question. Learn to evaluate the impact of programs/policies helps you to address interesting and policy-relevant questions from many different areas. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
9 Introduction What is causality? A causal question is a simple question involving the relationship between two theoretical concepts: a cause and an effect. Cause = Effect? Does X cause Y? Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
10 Introduction Why is causality so important? The primary aim of all sciences. Understanding of causal relationships leads to accurate predictions of the future. It provides the scientific basis for policy intervention. It advances our theoretical knowledge of the world. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
11 Introduction Program evaluation Program evaluation is the systematic process of studying a program, or a policy, to discover how well it is working to achieve intended goals. The goal in program evaluation is to assess the causal effect of public policy interventions. Examples include effects of: Job training programs on earnings and employment. Class size on test scores. Minimum wage on employment. Military service on earnings and employment. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
12 Introduction Preliminary questions To measure the effect of a program/policy is essentially to understand: Effect about what?: identify the outcome-variable. Effect of what?: specify the treatment-variable. Effect for whom?: identify the target population. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
13 Causality Rubin Causal Model, (Rubin and Imbens, 2010) The Rubin Causal Model (RCM) is a formal mathematical framework for causal inference. Two essential parts to the RCM: the use of potential outcomes to define causal effects in all situations. An explicit probabilistic model for the assignment of treatments to units the assignment mechanism. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
14 Causality Causality with potential outcome Treatment: D i : Indicator of treatment for unit i { 1, if unit i received the treatment D i = 0, otherwise Outcome: Y i : Observed outcome variable of interest for unit i. Potential Outcomes: Y 1i : Potential outcome for unit i with treatment; Y 0i : Potential outcome for unit i without treatment (the counterfactual). Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
15 Causality Causality with potential outcome Treatment Effect The treatment effect (or causal effect) on the outcome for unit i is the difference between his/her two potential outcomes: Observed Outcomes Observed outcomes are realized as: i = Y 1i Y 0i Y i = Y 1i D i + Y 0i (1 D i ) (1) { Y 1i, if D i = 1 or Y i = Y 0i, if D i = 0 Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
16 Causality An example Imagine a population with 4 units Tabella: A numerical example i D i Y i Y 1i Y 0i i Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
17 Causality Connection to linear model How to estimate the effect of treatment? Suppose we wish to measure the impact of treatment on an outcome, Y. For the moment, we abstract from other covariates that may impact on Y. D is the treatment indicator: a dummy variable assuming the value 1 if the individual has been treated and 0 otherwise. The potential outcomes for individual i at any time t are denoted by Y 1it and Y 0it. These outcomes are specified as: Y 1it = β + ρ i + ɛ it if D it = 1 Y 0it = β + ɛ it if D it = 0 (2) where β is the intercept parameter, ρ i is the effect of treatment on individual i and ɛ is the unobservable component of Y. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
18 Causality Connection to linear model The observable outcome is then: so that Y i = Y 1i D i + Y 0i (1 D i ) Y it = β + ρ i D it + ɛ it (3) where E(ɛ) = 0 and cov(ɛ, D) = 0. Estimating Eq.(3) by OLS we obtain the estimate of the causal effect of D. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
19 Causality Identification problem for causal inference Fundamental Problem of Causal Inference Cannot observe both potential outcomes (Y 1i,Y 0i ) = How can we find Y 1i Y 0i? A large amount of homogeneity would solve this problem: (Y 1i, Y 0i ) constant across individuals; (Y 1i, Y 0i ) constant across time. Unfortunately, often there is a large degree of heterogeneity in the individual responses to participation in public programs/policy. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
20 Causality Quantities of interest Instead of the individual treatment effect, we might be interested in the average treatment effect (ATE): α ATE = E[Y 1i Y 0i ] = E[Y 1i ] E[Y 0i ] (4) If ATE > 0 = E[Y 1i ] > E[Y 0i ] = The policy is good; if ATE < 0 = E[Y 1i ] < E[Y 0i ] = The policy is bad; if ATE = 0 = E[Y 1i ] = E[Y 0i ] = The policy has no impact BUT we can not find the ATE because of the unobserved potential outcomes. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
21 Causality Average Treatment Effect (ATE) Imagine a population with 4 units: Tabella: A numerical example i D i Y i Y 1i Y 0i i E[Y 1 ] 1.5 E[Y 0 ] 0.5 E[ ] 1 α ATE = E[ ] = 3 (1/4) + 0 (1/4) + 1 (1/4) + 0 (1/4) = 1 Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
22 Causality Quantities of interest We might also be interested in the average treatment effect on the treated (ATET): α ATET = E[Y 1 Y 0 D = 1] = E[Y 1i D = 1] E[Y 0i D = 1] (5) BUT we can not find the ATET because of unobserved potential outcomes. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
23 Causality Average Treatment Effect on the Treated (ATET) Imagine a population with 4 units: Tabella: A numerical example i D i Y i Y 1i Y 0i i E[Y 1 D = 1] 2 E[Y 0 D = 1] 0.5 E[ 1] 1.5 α ATET = E[ D = 1] = 3 (1/2) + 0 (1/2) = 1.5 Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
24 Causality ATE vs ATET ATE is relevant when the treatment has universal applicability. ATET is relevant when we want to consider the average gain treatment for the treated. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
25 Causality Estimating ATE Both Y 0i and (Y 0i D = 1) are unobserved = we can estimate the ATE as: ˆ ATE = E[Y 1t Y 0c ] = E[Y 1t ] E[Y 0c ] (6) where Y 1t is the outcome of treated and Y 0c is the outcome of untreated (the control group). Both quantities are observed. We basically find the average Y for observations that received treatment and average Y for observations that received control. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
26 Causality Selection bias What are we measuring if we compare the outcomes for the treated to the untreated? Is this the causal effect we want (i.e., the effect of treatment on the outcome)? NO E[Y D = 1] E[Y D = 0] = E[Y 1 D = 1] E[Y 0 D = 0] = E[Y 1 D = 1] E[Y 0 D = 1] + E[Y 0 D = 1] E[Y 0 D = 0] (7) = E[Y 1 Y 0 D = 1] + E[Y 0 D = 1] E[Y 0 D = 0] }{{}}{{} ATET BIAS where the bias term is the difference between no-treatment outcomes of individuals that are treated and those that are not treated. If no selection bias, then we get the ATET. The ATET is of interest but note that it is not the same as the ATE (except in special cases). If there is selection bias, estimate of the ATE based on comparing the average outcomes of the treated to the untreated will be misleading (biased). Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
27 Causality Selection Bias The bias term is not likely to be zero for most public policy. The goal is to minimize/eliminate it. Sources of bias Self-selection positive bias causal effect will be overstated; Targeting negative bias causal effect will be understated; Observables vs. Unobservables. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
28 Assumptions for unbiased estimate Assumptions for unbiased estimate What assumptions do we need for the estimate to be unbiased? Stable Unit Treatment Value Assumption (SUTVA); Unconfoundedness/ignorability.; Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
29 Assumptions for unbiased estimate Stable Unit Treatment Value Assumption (SUTVA) The stable unit treatment value assumption (SUTVA) assumes that: the treatment status of any unit does not affect the potential outcomes of the other units (non-interference); the treatments for all units are comparable (no variation in treatment). Violations: Vaccination (interference); Fertilizer A and B on crop yield, but each fertilizer has a lot of versions (variation in treatment). This assumption may be problematic, so we should choose the units of analysis to minimize interference across units. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
30 Assumptions for unbiased estimate Unconfoundedness/Ignorability Conditional independence assumption: Given a vector of observable variables x (vector of covariates), the assumption states that, conditional on x, the outcomes are independent of treatment: (Y 1, Y 0 ) D x (8) Unconfoundedness (strong ignorability): (Y 1, Y 0 ) D (9) Treatment assignment is independent of the outcomes (Y ). Technically, unconfoundedness is a stronger assumption. Most people just say ignorability. Violations: Omitted Variable Bias Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
31 Assumptions for unbiased estimate Assignment mechanism Assignment Mechanism Assignment mechanism is the procedure that determines which units are selected for treatment intake. Examples include: random assignment; selection on observables: matching, regression discontinuity; selection on unobservables: Diff-in-Diff, control function approach, instrumental variable estimation. Most models of causal inference attain identification of treatment effects by restricting the assignment mechanism in some way. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
32 Assumptions for unbiased estimate Key ideas Causality is defined by potential outcomes, not by realized (observed) outcomes; Estimation of causal effects of a treatment (usually) starts with studying the assignment mechanism. Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
33 Assumptions for unbiased estimate Readings Textbook: J.D. Angrist and J.S. Pischke (2015), Mastering Metrics: The Path from Cause to Effect; Princeton University Press. Imbens, G.W. and J.M. Wooldridge (2009) Recent Developments in the Econometrics of Program Evaluation, Journal of Economic Literature, Vol. 47(1), Holland P.W. (1986) Statistic and Causal Inference, Journal of the American Statistical Association, Vol.81(396). Lectures slides and reading lists are available from the website: Brunetti-Fiaschi-Parenti Quantitative Economics 25th of September, / 33
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