Your textbook mentions use of a quasi-experiment to study the 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 calculate the $\widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ you need the change in the treatment group and the change in the control group. To do this, the study provides you with the following information $\begin{array}{|l|c|c|} \hline& \text { PA } & \text { NJ } \\ \hline \begin{array}{l} \text { FTE Employment } \\ \text { before } \end{array} & 23.33 & 20.44 \\ \hline \begin{array}{l} \text { FTE Employment } \\ \text { after } \end{array} & 21.17 & 21.03 \\ \hline \end{array}$ Where $F T E$ is "full time equivalent" and the numbers are average employment per restaurant. W (a) Calculate the change in the treatment group, the change in the control group, and finally $\widehat { \beta } _ { 1 } ^ { d i f f - i n - d i f f s }$. Since minimum wages represent a price floor, did you expect $\widehat { \beta } _ { 1 } ^ { d i f f s - i n - d i f f s }$ to be positive or negative?

The t-statistic is 2.03, thereby making

A) provide a bridge between the econometric analysis of observational data sets and the statistical ideal of a true randomized controlled experiment. B) are not the same as experiments, and lessons learned from the use of the latter can therefore not be applied to them. C) most often use difference-in-difference estimators, which are quite different from OLS and instrumental variables methods studied in earlier chapters of the book. D) use the same methods as studied in earlier chapters of the book, and hence the interpretation of these methods is the same. A) provide a bridge between the econometric analysis of observational data sets and the statistical ideal of a true randomized controlled experiment. B) are not the same as experiments, and lessons learned from the use of the latter can therefore not be applied to them. C) most often use difference-in-difference estimators, which are quite different from OLS and instrumental variables methods studied in earlier chapters of the book. D) use the same methods as studied in earlier chapters of the book, and hence the interpretation of these methods is the same.

Exam 13: Experiments and Quasi-Experiments

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 learning in this environment. Mention some of the threats to internal and external validity and how you would attempt to circumvent these.

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Students should be selected randomly within a school and should be randomly assigned to a treatment group (multi-age, multi-grade classroom) and a control group (traditional grade assignment; 4th, 5th, 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-grade 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 $E \left( u _ { i } \mid X _ { i } \right) = 0$ 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 school 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 instructors 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").

Assume that data are available on other characteristics of the subjects that are relevant to determining the experimental outcome.Then including these determinants explicitly Results in

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C

With panel data, the causal effect

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Question 3

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C

To analyze the effect of a minimum wage increase, a famous study used a quasiexperiment for two adjacent states: New Jersey and (Eastern) Pennsylvania. A $\widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ was calculated by comparing average employment changes per restaurant between to treatment group (New Jersey) and the control group (Pennsylvania). In addition, the authors provide data on the employment changes between "low wage" restaurants and "high wage" restaurants in New Jersey only. A restaurant was classified as "low wage," if the starting wage in the first wave of surveys was at the then prevailing minimum wage of \$4.25. A "high wage" restaurant was a place with a starting wage close to or above the $\$ 5.25$ minimum wage after the increase. (a)Explain why employment changes of the "high wage" and "low wage" restaurants might constitute a quasi-experiment.Which is the treatment group and which the control group?

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Question 4

Your textbook gives a graphical example of $\widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ , where outcome is plotted on the vertical axis, and time period appears on the horizontal axis. There are two time periods entered: " $\mathrm { t } = 1$ " and " $\mathrm { t } = 2$ ." The former corresponds to the "before" time period, while the latter represents the "after" period. The assumption is that the policy occurred sometime between the time periods (call this " $\mathrm { t } = \mathrm { p }$ "). Keeping in mind the graphical example of $\widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ , carefully read what a reviewer of the Card and Krueger (CK) study of the minimum wage effect on employment in the New Jersey-Pennsylvania study had to say: "Two assumptions are implicit throughout the evaluation of the 'natural experiment:' (1) $\left[ \widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } } \right]$ would be zero if the treatment had not occurred, so a nonzero $\left[ \widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } } \right]$ indicates the effect of the treatment (that is, nothing else could have caused the difference in the outcomes to change), and (2) ... the intervention occurs after we measure the initial outcomes in the two groups. ... Three conditions are particularly relevant in interpreting CK's work: (1) $[ \mathrm { t } = 1 ]$ must be sufficiently before $[ \mathrm { t } = \mathrm { p } ]$ that [the treatment group] did not adjust to the treatment before $[ \mathrm { t } = 1 ] -$ otherwise $\left[ \bar { Y } ^ { \text {treatment,before } } - \bar { Y } ^ { \text {conrol,hefofor } } \right]$ will reflect the effect of the treatment; (2) $[ \mathrm { t } = 2 ]$ must be sufficiently after $[ \mathrm { t } = \mathrm { p } ]$ to allow the treatment's effect to be fully felt; and (3) we must be sure that the same difference $\left[ \bar { Y } ^ { \text {treatment } , b \text { before } } - \bar { Y } ^ { \text {control, byfore } } \right]$ would have been observed at $[ \mathrm { t } = 2 ]$ if the treatment had not been imposed, that is, [the control group must be good enough] that there is no need to adjust the differences for factors other than the treatment that might have caused them to change." Use a figure similar to the textbook to explain what this reviewer meant.

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Question 5

Experimental data are often

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Question 6

Your textbook mentions use of a quasi-experiment to study the 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 calculate the $\widehat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ you need the change in the treatment group and the change in the control group. To do this, the study provides you with the following information PA NJ FTE Employment before 23.33 20.44 FTE Employment after 21.17 21.03 Where $F T E$ is "full time equivalent" and the numbers are average employment per restaurant. W (a) Calculate the change in the treatment group, the change in the control group, and finally $\widehat { \beta } _ { 1 } ^ { d i f f - i n - d i f f s }$ . Since minimum wages represent a price floor, did you expect $\widehat { \beta } _ { 1 } ^ { d i f f s - i n - d i f f s }$ to be positive or negative?

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Question 7

Quasi-experiments

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Question 8

The New Jersey-Pennsylvania study on the effect of minimum wages on employment mentioned in your textbook used a comparison in means "before" and "after" analysis. The difference-in-difference estimate turned out to be 2.76 with a standard error of 1.36. The authors also used a difference-in-differences estimator with additional regressors of the type $\Delta Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } W _ { 1 , i } + \ldots + \beta _ { 1 + r } W _ { r , i } + u _ { i }$ where $i = 1 , \ldots , 410 . X$ is a binary variable taking on the value one for the 331 observations in New Jersey. Since the authors looked at Burger King, KFC, Wendy's, and Roy Rogers fast food restaurants and the restaurant could be company owned, four $W$ -variables were added. (a)Given that there are four chains and the possibility of a company ownership, why did the authors not include five W-variables?

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Question 9

Causal effects that depend on the value of an observable variable, say $W _ { \mathrm { i } }$

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Question 10

Heterogeneous population

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Question 11

Let the vertical axis of a figure indicate the average employment fast food restaurants. There are two time periods, t=1 and t=2 , where time period is measured on the horizontal axis. The following table presents average employment levels per restaurant for New Jersey (the treatment group) and Eastern Pennsylvania (the control group). PA NJ FTE Employment before 23.33 20.44 FTE Employment after 21.17 21.03 Enter the four points in the figure and label them $\bar { Y } ^ { \text {treatment,before } } , \bar { Y } ^ { \text {treatment,after } } , \bar { Y } ^ { \text {cantrol,before } }$ and $\bar { Y } ^ { \text {control, after } }$ . Connect the points. Finally calculate and indicate the value for $\widehat { \beta } _ { 1 } ^ { \text {ditss-in-diffs } } .$

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Question 12

The following estimation methods should not be used to test for randomization when $X _ { \mathrm { i } }$ is binary:

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Question 13

In the context of a controlled experiment, consider the simple linear regression formulation $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \text {. Let the } Y _ {i}$ be the outcome, $X _ { \mathrm { i } }$ the treatment level, and $u _ { i }$ contain all the additional determinants of the outcome. Then

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Question 14

Experimental effects, such as the Hawthorne effect,

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Question 15

A repeated cross-sectional data set a. is also referred to as panel data. b. is a collection of cross-sectional data sets, where each cross-sectional data set corresponds to a different time period. c. samples identical entities at least twice. d. is typically used for estimating the following regression model $Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \beta _ { 2 } W _ { 1 , i t } + \ldots + \beta _ { 1 + r } W _ { r , i t } + u _ { i t }$

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Question 16

(Requires Appendix material)Discuss how the differences-in-differences estimator can be extended to multiple time periods.In particular, assume that there are n individuals and T time periods.What do the individual and time effects control for?

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Question 17

All of the following are reasons for using the differences estimator with additional regressors, with the exception of

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Question 18

In a quasi-experiment a. quasi differences are used, i.e., instead of $\Delta Y$ you need to use $\left( \bar { Y } ^ { \text {after } } - \lambda \times \bar { Y } ^ { \text {before } } \right)$ , where $0 < \lambda < 1$ . b. randomness is introduced by variations in individual circumstances that make it appear as if the treatment is randomly assigned. c. the causal effect has to be estimated through quasi maximum likelihood estimation. d. the $t$ -statistic is no longer normally distributed in large samples.

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Question 19

Describe the major differences between a randomized controlled experiment and a quasi- experiment.

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Question 20

Assume that data are available on other characteristics of the subjects that are relevant to determining the experimental outcome.Then including these determinants explicitly Results in

With panel data, the causal effect

Experimental data are often

Quasi-experiments

Causal effects that depend on the value of an observable variable, say $W _ { \mathrm { i } }$

Heterogeneous population

The following estimation methods should not be used to test for randomization when $X _ { \mathrm { i } }$ is binary:

Experimental effects, such as the Hawthorne effect,

(Requires Appendix material)Discuss how the differences-in-differences estimator can be extended to multiple time periods.In particular, assume that there are n individuals and T time periods.What do the individual and time effects control for?

All of the following are reasons for using the differences estimator with additional regressors, with the exception of

Describe the major differences between a randomized controlled experiment and a quasi- experiment.

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Exam 13: Experiments and Quasi-Experiments

Assume that data are available on other characteristics of the subjects that are relevant to determining the experimental outcome.Then including these determinants explicitly Results in

With panel data, the causal effect

Experimental data are often

Quasi-experiments

Causal effects that depend on the value of an observable variable, say WiW _ { \mathrm { i } }Wi​

Heterogeneous population

The following estimation methods should not be used to test for randomization when XiX _ { \mathrm { i } }Xi​ is binary:

Experimental effects, such as the Hawthorne effect,

(Requires Appendix material)Discuss how the differences-in-differences estimator can be extended to multiple time periods.In particular, assume that there are n individuals and T time periods.What do the individual and time effects control for?

All of the following are reasons for using the differences estimator with additional regressors, with the exception of

Describe the major differences between a randomized controlled experiment and a quasi- experiment.

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Causal effects that depend on the value of an observable variable, say $W _ { \mathrm { i } }$

The following estimation methods should not be used to test for randomization when $X _ { \mathrm { i } }$ is binary: