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1、Introduction to Econometrics, 3e (Stock)Chapter 13 Experiments and Quasi-Experiments13.1 Multiple Choice1) The following are reasons for studying randomized controlled experiment in an econometrics course, with the exception ofA) at a conceptual level, the notion of an ideal randomized controlled ex
2、periment provides a benchmark against which to judge estimates of causal effects in practice.B) when experiments are actually conducted, their results can be very influential, so it is important to understand the limitations and threats to validity of actual experiments as well as their strength.C)
3、randomized controlled experiments in economics are common.D) external circumstances sometimes produce what appears to be randomization.Answer: C2) Program evaluationA) is conducted for most departments in your university/college about every seven years.B) is the field of study that concerns estimati
4、ng the effect of a program, policy, or some other intervention or ntreatment.*C) tries to establish whether EViews, SAS or Stata work best for your econometrics course.D) establishes rating systems for television programs in a controlled experiment framework.Answer: B3) In the context of a controlle
5、d experiment, consider the simple linear regression formulation Yj = 00 + uj. Let the Yf be the outcome, X/ the treatment level, and uj contain all the additional determinantsof the outcome. ThenA) the OLS estimator of the slope will be inconsistent in the case of a randomly assigned X/ since there
6、are omitted variables present.B) Xj and uj will be independently distributed if the Xj be are randomly assigned.C) po represents the causal effect of X on Y when X is zero.D) E(Y | X = 0) is the expected value for the treatment group.Answer: B4) In the context of a controlled experiment, consider th
7、e simple linear regression formulation Yf = 00 +plXj + uj. Let the Yj be the outcome, Xf the treatment level when the treatment is binary, and uj containAall the additional determinants of the outcome. Then calling 01a differences estimatorA) makes sense since it is the difference between the sample
8、 average outcome of the treatment group and the sample average outcome of the control group.AB) and the level estimator is standard terminology in randomized controlled experiments.C) does not make sense, since neither Y nor X are in differences.D) is not quite accurate since it is actually the deri
9、vative of Y on X.Answer: A3) Earnings functions provide a measure, among other things, of the returns to education. It has been argued these regressions contain a serious omitted variable bias due to differences in abilities. Furthermore, ability is hard to measure and bound to be highly correlated
10、with years of schooling. Hence the standard estimate of about a 10 percent return to every year of schooling is upward biased. Suggest some ways to address this problem. One famous study looked at earnings of identical twins. Explain how this can be viewed as a quasi-experiment, and mention some of
11、the threats to internal and external validity that such a study might encounter.Answer: Answers will vary by student. The omitted variable bias should play a central part in the discussion.| X工 Wi/,., Wr() = 0 will not hold if one of the Ws is years of education and u containsunobserved ability. If
12、ability causes individuals to have higher earnings and longer years of education, perhaps through obtaining university scholarships easier, then the returns to education are biased upward. One way to circumvent this problem is, as some studies have done in the past, to approximate ability by IQ scor
13、es. If IQ scores measure ability with error, then instrumental variable techniques can be employed. These were discussed in Chapter 10 of the textbook. Another possibility is to model ability as an omitted variable that remains constant over time. In that case, panel estimation methods with fixed ef
14、fects, presented in Chapter 8 of the textbook, can be used. Data can be differenced to eliminate the entity fixed effects or binary variables can be added to capture them. At any rate, this approach requires data being available for more than a single point in time. The use of data from identical tw
15、ins is fascinating since these have identical genes and, typically, identical family backgrounds. The suggestion is therefore to assume that they have identical ability as well. If some twins have different years of schooling while others do not, then this can be treated as a quasi-experiment since
16、the researcher can view this choice as if it had been randomly assigned. Obviously it cannot count as a randomized controlled experiment, since the difference in schooling was not determined by the flip of a coin, say. But it may also run into problems in providing an as if randomization. The text f
17、lagged some of the potential problems in section 11.1: Initially, one might think that an ideal experiment would take two otherwise identical individuals, treat one of them, and compare the difference in their outcomes while holding constant all other influences. This is not, however, a practical ex
18、perimental design, for it is impossible to find two identical individuals: even identical twins have different life experiences, so they are not identical in every way.1 Finally, if identical twins are different, from the general population, then there is also a threat to external validity by genera
19、lizing the results for the population of all individuals.4) Describe the major differences between a randomized controlled experiment and a quasi-experiment. Answer: Answers will vary by student. Some of the following points should appear.A randomized controlled experiment relies on the random selec
20、tion of entities from a population of interest, and the random assignment of these individuals into either a treatment or control group. To study the causal effects, a simple regression model with a single regressor can be specified. This regressor can either be a binary variable or a variable indic
21、ating treatment levels. Since | Xf) = 0 is guaranteed if the assignment and selection was random, then the causal or treatment effect can be measured through E(Yf | X = %) - E(Y； | X = 0). The random selection and assignment assures that there is no omitted variable bias, and therefore the OLS estim
22、ator is unbiased. Adding additional regressors can result in increased efficiency. Alternatively a di仔erences-in-di仔erences estimator with or without additional regressors is also available if the entities have been observed for two periods, one before and one after the treatment. In the case of mor
23、e than two observations per entity, panel methods can be employed. There are various threats to internal and external validity. These include failure to randomize, failure to follow treatment protocol, attrition, experiment effects, and small samples (threats to internal validity), and nonrepresenta
24、tive sample, nonrepresentative program or policy, general equilibrium effects, and treatment vs. eligibility effects (threats to external validity).A quasi-experiment is also called a natural experiment1 since the treatment of some entities resulted from an external event. The treatment is administe
25、red as if it was random. The reason for observing quasi-experiments more often in economics is that they are less expensive and raise less of an ethical concern. The as if randomly assigned treatment is the result of, as the textbook puts it, vagaries in legal institutions, location, timing of polic
26、y or program implementation, natural randomness such as birth dates, rainfall, or other factors that are unrelated to the causal effect under study. There are two types of quasi-experiments, one whereby treatment is viewed as if randomly determined, the other whereby the as if randomization provides
27、 an instrumental variable. Threats to internal and external validity are the same as for randomized controlled experiments once they are modified. For example, experimental effects are typically absent since individuals are not aware that they are part of an experiment. Small samples are replaced by
28、 instrument validity in quasi-experiments.5) Roughly ten percent of elementary schools in California have a system whereby 4th to 6th graders share a common classroom and a single teacher (multi-age, multi-grade classroom). Suggest an experimental design that would allow you to assess the effect of
29、learning in this environment. Mention some of the threats to internal and external validity and how you would attempt to circumvent these. Answer: Students should be selected randomly within a school and should be randomly assigned to a treatment group (multi-age, multi-grade classroom) and a contro
30、l group (traditional grade assignment; 4th, 5由,and 6th grade only per room). Alternatively, and depending on the size of the experiment, a subset of schools could be chosen and some pupils would randomly be assigned to traditional grade assignments while others would be moved into multi-age, multi-g
31、rade classrooms. Another alternative would be to simply choose some schools randomly which would have multi-age, multi-grade classrooms only. The causal effect could then be estimated in a simple regression model with a binary regressor. Random selection and random assignment would assure Eg | X。= 0
32、 and thereby eliminate one threat to internal validity through omitted variable bias.Another threat to internal validity would be if the worst or best performing schools were chosen instead of using a random selection, or if parents in the district were allowed to vote whether or not to have the sch
33、ool selected for the experiment. This would imply a failure to randomize. If students were allowed to refuse to participate by transferring to a neighboring school, then this would represent failure to follow treatment protocol. Double blind experiments are obviously not feasible since both instruct
34、ors and students know into which setting they are being placed (experimental effects). There are few threats to external validity except for the situation whereby students would be allowed to opt in or out of the experimental group (treatment vs. eligibility effect).6) Assume for the moment that the
35、 student-teacher ratio effect on test scores was large enough that you would advocate reducing class sizes in elementary schools. In 1996, the State of California reduced class sizes from K-3 to no more than 20 students across all public elementary schools (Class Size Reduction Act) at a cost of app
36、roximately $2 billion. In a short essay, discuss why the general equilibrium effects might differ from the results obtained using experiments.Answer: The General Equilibrium effects are the result of the additional demand for teachers. Each elementary school needed additional teachers in order to re
37、duce the class size to 20 or less think of a school that had perhaps 3 Kindergarten classes of 25 students each. In that case, one additional classroom had to be created typically some temporary structure. The question arises where the additional teacher came from. If your school district was a desi
38、rable district to teach in, perhaps because of having a reputation of well behaved children or classrooms that were well equipped, then teachers from other districts, perhaps less desirable ones, would apply to the better school district. Presumably the desirable school district would pick the best
39、teacher(s) available, leaving the less desirable school district with a lower level of teacher quality. The same phenomenon would repeat itself at the lower level school district, and so forth, until you would get to the least desirable school district, which would have to hire new teachers from a c
40、ohort that could not find a job elsewhere. Given the size of the State of California, the General Equilibrium effect could be substantial, perhaps even drawing quality teachers from other states.13.3 Mathematical and Graphical Problems1) Your textbook mentions use of a quasi-experiment to study the
41、effects of minimum wages on employment using data from fast food restaurants. In 1992, there was an increase in the (state) minimum wage in one U.S. state (New Jersey) but not in neighboring location (Eastern Pennsylvania). To calculatethe/ diffs-in-diffsyou need the change in the treatment group an
42、d the change in the control group. Todo this, the study provides you with the following informationPANJFTE Employment before23.3320.44FTE Employment after21.1721.03Where FTE is full time equivalent1 and the numbers are average employment per restaurant.(a) Calculate the change in the treatment group
43、, the change in the control group, and finally0 山diffs since minimum wages represent a price floor, did you expect p ;小in-d,卜 topositive or negative?(b) If you look at 0出话 number primarily due to a change in the treatment group or the control group? Is this what you expected?(c) The standard error f
44、or 0，於一山一，小 !s i 36. Test whether or not the coefficient is statistically significant, given that there are 410 observations. If you believed that the benefit from small minimum wage increases outweighed the cost in terms of employment loss, would finding that this coefficient was not statistically
45、significant discourage you?Answer:(a) change in treatment group: + 0.59, change in control group:-2.16, 2 %ffs-2d加=2.75.Standard economic theory suggests a negative, not positive, change.(b) The overall change of 2.76 is primarily due to the change in Eastern Pennsylvania (2.16), i.e.z the control g
46、roup. Following standard economic theory, if employment fell in Eastern Pennsylvania, then you would expect employment in New Jersey to fall by even more than in Eastern Pennsylvania. Not only did employment in New Jersey not fall by less, it actually increased.(c) The f-statistic is 2.03, thereby m
47、aking the coefficient statistically significant at the 5% level (two-sided test). Even if the coefficient was not statistically significant, it is not negative. Hence finding an insignificant coefficient should be discouraging since it suggests that there is no negative employment effect of a small
48、increase in minimum wages.2) Define the：diffs-in-diffsP 1in terms of observable deferences in the treatment and control group, beforeand after the treatment. Explain why this presentation is the equivalent of calculating the coefficient in a regression framework.Answer: p in-diffs _treatment, after
49、_ y treatment before)_ control .after y contwl,before=Ay treatment - controlt Consider the following regression二的 + 肉 Xi + uiwhere Y is the value for the，出 individual after the experiment is completed, minus the value of Y before it starts, and X is a randomly assigned binary treatment variable, which takes on the value of one if treatment was received and is zero otherwise. Then for an individual