2. Highlights of Chapter 12

3. 2 Scientific truth always goes through three stages. First, people say it conflicts with the Bible; next they say it has been discovered before; and lastly they say that they always believed it Louis Agassiz, Swiss naturalist We do not now a truth without knowing its cause Aristotle, Nicomachean Ethics Development of Western science is based on two great achievements: the invention of the formal logical system (Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance) Albert Einstein

4. 3 Preliminary causal glossary Independent (exogenous, cause) variables – are the direct policy/program interventions and socio-economic control Dependent (endogenous, effect) variables – represent the outcomes Intervention variables are a special class of independent variables that represent policy/programming, often as a discrete (dummy) variable marking the boundary between the program and counterfactual Counterfactual – the state of affairs that would have occurred without the program Gross impact - observed change in the outcome (s) Net impact - portion of gross impact attributable to the program intervention Experiment – the purposeful manipulation of independent and intervention variables to observe the change in outcomes. Quasi-experiment – the replication of manipulation within the context of a statistical model.

5. 4 Cause and effect Necessary causes: For X to be a necessary cause of Y, then if Y occurs, X must also occur. The fact that X occurs does not imply that Y will occur. Sufficient causes: For X to be a sufficient cause of Y, then the presence of X always implies that y will occur. The fact that Y occurs does not imply that X has occurred since another variable Z, could be the cause. Contributory causes: A cause X may contribute to the occurrence of Y, if X occurs before Y and varying X varies Y.

6. 5 Causal logic models Verbal models National Child Benefit (NCB) The NCB Initiative is a joint initiative of federal and provincial/territorial governments intended to help prevent and reduce the depth of child poverty, as well as promote attachment to the workforce by ensuring that families will always be better off as a result of working. It does this through a cash benefit paid to low income families with children, a social assistance offset and various supplementary programs provided by provinces and territories.

7. 6 NCB Verbal models have limits in presenting the causal logic

8. 7 Causal Analysis I X 1, X 2 are independent (causal) variables also known as exogenous variables. Y 1 is a dependent (effect) or endogenous variables. e 1 is an error term, reflecting measurement imprecision, poor model design, failure to include all the relevant variables, external factors… Y 1 = a 0 + a 1 X 1 + a 2 X 2 + e 1

9. 8 Graphical logic for the National Child Benefit

10. 9 Causal Analysis II X 1, X 2 are independent (causal) variables also known as exogenous variables. Y 1, Y 2 are dependent (effect) or endogenous variables. e 1 and e 2 as above Y 1 = a 0 + a 1 X 1 +a 2 X 2 + e 1 Y 2 = b 0 + b 1 X 1 +b 2 X 2 + b 3 Y 1 +e 2 X 1 = c 1 X 2

11. Root cause analysis Root cause analysis is a structured process for reviewing an event, with the goals of determining what happened, why it happened and what can be done to reduce the likelihood of recurrence. “On August 22nd, 2006, a 43 year old woman died after a medication incident that occurred while she was receiving outpatient care at the Cross Cancer Institute in Edmonton, Alberta. The cause of death as determined by the coroner was “sequelae of fluorouracil toxicity”. On July 31, the woman had inadvertently received an infusion of fluorouracil over 4 hours that was intended to be administered over 4 days. She was being treated for advanced nasopharyngeal carcinoma, according to a standard protocol that included high-dose fluorouracil and cisplatin in the ambulatory setting. The medication incident was recognized within 1 hour after the infusion was completed. The patient was admitted to hospital 4 days after the incident occurred. Profound mucositis and pancytopenia developed, and the patient experienced hemodynamic collapse and multi-organ failure before her death.” Source: http://www.cancerboard.ab.ca/NR/rdonlyres/4107CCF0-2608-4E4D-AC75- E4E812F94FD6/0/Incident_Report_UE.pdf

12. 11 Herald of Free Enterprise sinking – causal analysis ROOT CAUSE ANALYSIS of a ferry sinking

13. 12 The mother of all causal diagrams A PowerPoint diagram that portrays the complexity of American strategy in Afghanistan as having succeeded. http://www.nytimes.com/2010/04/27/world/27powerpoint.html?src=me&ref=general

14. Concept of causality Causality often implies inevitability, but the reality is that causal statements usually reflect degrees of uncertainty. Causality and probability are fundamentally connected because we want to : –Know the causes of an event –Measure the relative strength of these causes

16. Randomized experiments Classic experiment is the random, double- blind experiment (RDE): –subjects are selected randomly into a treatment and control group –each subject received a code –an independent third party assigns codes randomly to treatment and control group members. –the treatment is not identifiable (i.e., the real and fake pill are identical. –those administering the treatments and placebo have no knowledge of what subject receives.

17. Key benefits of the RDE randomization creates statistically equivalent groups in the absence of any interventions (the drug under tests), the incidence of disease is the same for both groups the groups are the “same” (statistically, except that one gets the drug and the other a placebo analysis can be done by difference of means tests or other basic techniques.

19. Limits of RDE In social science, randomized double blind experiments are often not feasible: –human subjects are unreliable (they move, die or otherwise fail to participate in the full experiment). –many see the administration of a placebo as withholding a treatment. –social policy cannot be masked (creating a placebo is difficult).

20. Quasi-experimental designs Most policy testing in social sciences uses a quasi-experimental design. Two approaches exist –Multivariate (regression) models specify dependent variable outcome, and include dummy variables to identify those in the program. Other covariates are included to control for the interventions. –Matching: Program participants and non-participants serve as the basis for the treatment and control groups.

21. Four potential models for evaluating policy 1.Randomized control (RC) 2.Natural experiments (difference-in- difference, discontinuity) 3.Quasi-experimental methods –Heckman two step –Statistical Matching 4.Instrumental variables (treated separately)

22. Randomized control Attempts to create a situation where Cov (X’,  ) = 0, or E(T’,  ) = E(T”, W), where W are the omitted variables that determine selection into treatment.

23. Natural experiments Create a “split” in the sample, where treated and untreated are classified by a variable that is not related to the the treatment. This split occur “naturally” where the program change occurs in one area/jurisdiction, not in others that are “closely similar.” Difference-in-differences (DID) methods are a common evaluation framework.

24. Difference in Differences The DID estimator uses the average before and after values for an outcome variable for the program and comparison group. DID = [Y p (t=a) – Y p (t=b) ] – [Y c (t=a) - Y c (t=b) ] Example: –Avg. earned income before - program group = $4500 –Avg. earned income after - program group = $6500 –Avg. earned income before - comparison group = $10,500 –Avg. earned income after - comparison group = $11,000 DID = [6500 - 4500] – [11,000 – 10,500] = $1,500 = net impact attributable to the program (treatment)

25. Net impact using DID

26. Causal Inference – comparison in regression Problem: Estimate effect of treatment (T) on observed outcome (Y), or estimate B in Y i = B 0 + B 1 T i +  i = X i B +  I (where X = [1, T] Assume –dichotomous treatment variable: T=1 if treated, 0 otherwise –homogeneous treatment effect (B) (every i experiences same effect) “average treatment effect” –Linear (no dose) –no covariates mediate the outcome

27. B hat = Y bar(T=1) – Y Bar (T=0) The simple comparison group model

29. OLS assumption E (X’,  ) = 0, or E (X’,  ) = X’ (Y- B OLS X) which then creates the OLS estimator B OLS = (X’X) –1 X’y But, with omitted variables, the validity of OLS requires the omitted variables to be uncorrelated with T (the treatment). This is the essence of the self-selection problem. No covariates is the key assumption

30. Selection and attrition Random samples may be upset by self-selection and attrition (or both)

31. The original motivation for this procedure was to correct evaluation studies for sample distortion caused by self-selection. Two steps: 1.Estimate the probability of participation for each participant and non-participant. Y i = B 0 + B 1 X i1 + B 2 X i2 + … B k X ik + e i (Y=1 for a participant, for a non-participant). 2.For each participant/non-participant a unique probability of participation will be estimated. Call this λ i Now, this is inserted into the outcome regression W i = B 0 + B 1 X i1 + B 2 X i2 + … B k X ik + B l λ i + e i, where Wi is the outcome for person i (wages, hours worked, etc.) Heckman two step procedure (basic)

32. Matching In social experiments, participants differ from non- participants because: –failure to hear of program –constraints on participation or completion –selection by staff Matching participants and non-participants can be accomplished via –pair-wise –statistical

33. Matching Process

34. Pair wise matching The theory will indicate those attributes that are likely to make a difference in the quasi- experiment. –For labour markets, gender, education and rural- urban location are important –For health policy, age, rural-urban, and family history might be important. The analyst starts with the first variable, and divides the participants and non-participants into two sets. Within the sets the samples are classified with respect to the second, variable and so on.

35. Pair wise Matching

36. Statistical Matching Matching is needed because we cannot randomly allocate clients to the program and comparison groups. Program benefits cannot be withheld. Logit model provides the estimate of the propensity to participate for participants and non-participants. The key idea is that we estimate that propensity to participate is based on observed attributes of the participants and non-participants. Participants are assigned a “Y”value of 1 and non-participants are assigned a “Y” value of 0. A logistic regression then estimates the propensity to participate. Note that even though a non-participant actually did not participate the model will assign a score between 0 and 1. Typically non-participants will have lower scores than participants, but there will be an overlap. The overlap is termed the region of common support.

37. Rationale for statistical matching Matching is needed because we cannot randomly allocate EI clients to the program and comparison groups. Part II benefits cannot be withheld. Logit model provides the estimate of the propensity to participate for participants and non-participants. The key idea is that we estimate that propensity to participate is based on observed attributes of the participants and non-participants. Participants are assigned a “Y”value of 1 and non-participants are assigned a “Y” value of 0. A logistic regression then estimates the propensity to participate. Note that even though a non-participant actually did not participate the model will assign a score between 0 and 1. Typically non-participants will have lower scores than participants, but there will be an overlap. The overlap is termed the region of common support.

38. Statistical matching simplified

39. The logit model LPM Model P i = E(Y = 1| X i ) = B 1 + B 2 X 2 + B 3 X 3 +..+B k X k Logit Model P i = E(Y = 1| X i ) = 1/[1+ e – (  BiXi) ] In Log Odds format L i = ln(P i /1-P i ) = Z i =  B i X i

40. Region of Common Support Each participant has the value of 1 for P and each non-participant has the value 0. However, once the model is estimated, each participant and non-participant has a score between 0 and 1. Participants tend to have scores closer to 1 and non-participants are closer to 0. The distribution of scores can be graphed.

41. Statistical Matching

42. Statistical Matching: The region of common support

43. Issues in Matching The matching is limited to the variables available in the administrative files. The balancing test compares the program and participant groups for each covariate using a t test for differences in means. Two key weaknesses are: –matching on the observed variables may not align the program and comparison groups on the non-observed variables. –The statistical quality of the match is very important Every additional variable that is introduced to the matching equation process, potentially improves the closeness of the match.

44. Application of the DID estimator in a matching context When combined with control, it measures the impact of the observed differences between the two groups, which is participation in treatment (program) Cannot measure the net impact of different interventions unless these are added as covariates. This requires a 1 – 1 match between a program participant and a non-participant (i.e.., matched program and comparison groups) DID i-j = B 1 T 1,i-j + B 2 T 2,i-j +..B k T k,i-j + u i-j

46. Effect of training programs – wages and hours increase Measures of outcome Increase in earnings (I) Increase in hours (I) Reduction in social assistance payments (G) W 0 = market wage at h o and W 1 = market wage at h 1 Increase in surplus arises from increase in market wages and increase in hours) A is the net increase due to wage increase at old hours B = C is the increase in hours times the new wage C = loss of leisure If individuals were under-employed or find virtue in work, then C is part of the social surplus. If individuals value leisure but cannot regulate the time they work (a fixed work day/week). Labour supply

47. Effect of training programs – hours increase When only hours increase, the social surplus lies above the supply survey (and below the wage rate). Market wages remain stable. Note the similarity with the concept of producer surplus.

48. Workfare This policy requires a minimum number of hours (h*, where h* = grant/min wage) W m is the min wage which is assumed to be equal to the market wages associated with S 0 and S 1. The reservation wage is the payment needed to bring forth one hour of work … W 0 r and W 1 r If the policy reduces/eliminates social assistance payments, then labour supply shifts right (S 0 – S 1 ). W 1 r falls below the min wage. The recipient if offered h* hours at W m