Problem 1

Describe the major differences between a randomized controlled experiment and a quasi-experiment. Consider yourself a Chief Experiment Visionary (CEV) of a small fastfood restaurant chain. Rumor has it that some shifts are more productive because of advertisement videos with funny frogs which occasionally appear on your restaurants digital menu boards on Wednesdays. To test this hypothesis you decide to design a randomized controlled experiment. Given that it is in your power to control the digital menu boards, for your experimental protocol you have to define

Unit of observation i

Outcome variable Yi

Treatment T

Describe both treatment and control groups

Mechanism of assignment to treatment

Under what condition can you carry out the test for the hypothesis using just one statistical test?

Which test would that be? State the null hypothesis.

Problem 2

After conducting a few statistical tests you remember how good econometrician you are and decide to estimate the impact on productivity numerically with regression model. Consider the simple population regression model, where the treatment is the same for the members of the treatment group, and hence X is a binary variable. Explain why the coefficient on X represents the difference between two means. How is the test for the statistical significance of the coefficient on X related to the test you employed earlier? Write down the null and alternative hypothesis in each case (Hint: See Section 4.7 from Stock- Watson), formulate the regression model, indicate the coefficient of interest and interpret it. Under which conditions this estimate of the effect is unbiased and consistent?

Problem 3 Now, thinking that maybe you are just too focused on funny frogs videos, you decide to hypothesize that maybe the installation of the digital menu boards in 2015 somehow affected the performance of said restaurants. You remember your good friend Viktor who manages the restaurant chains regional branch in the neighboring country of Krakozhia a country somewhat like yours. The only exception is that in Krakozhia people do not tolerate digital displays in any form, so the restaurants in the regional branch have never received the upgrade! Victor does not want to share his data unless you present him the properly planned quasi-experimental protocol with the following:

Unit of observation i

Outcome variable Yi

Treatment T

Describe both treatment and control groups

After some consideration he sends you what seems to be two repeated cross-sections with n observa tions from period prior to 2015, and another n observations from after 2015. Write down the formula for the DD estimator and provide graphical interpretation of the approach, explain the idea of Diff-in-Diff. Under what conditions (assumptions) should you be estimating the effec of such upgrade on performance with differences-in-differences estimator? List two potential threats to internal and external validity when comparing performances of the restaurants in Krakozhia to your country.