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Econ 5420

HOMEWORK 2

You are encouraged to work together on assignments, but must turn in your own assign-ment, in your own words. All assignments are turned in through Carmen. (All home works will be checked for plagiarism through the turnitin app) There are no late assignments accepted. Assignments will be due at 11:59 pm on the due date. Each homework will have a bonus question worth up to 5 bonus points (total score capped at 100). Homeworks are to be submitted on Carmen and entirely typed in a single document. Tables must be written in estout or a similar format. STATA tables cut and pasted from the output window will not receive any credit. All tables and graphs should be labeled and numbered.

1. (10 points) Explain the difference between strict exogeneity and contemporaneous exogeneity.

2. (20 points) Suppose we have a scale of Covid-19 regulations Regt 6 [0,10] measuring regulations such as masks, vaccines, shutdowns, etc. The regulations are determined by public policy that can be approximated using the function:

(EQ 1) Regst = So + 5\Casest_i + ^2Political-Leant + u

We want to estimate the effect of regulations on cases with the following equation: (EQ 2) Casest = ao + a1Regst + a₂T emperaturet + et

Show that equation 2 violates the assumption of strict exogeneity, preventing us from unbiased results.

3. (40 points)In 1990, Whittington, et al published a study on the effect of tax ex

emptions on the general rate of fertility (births per 1000 women). The original article can be found on Carmen under the papers section. The general form of their estimating equation is: GFRt = So + SiPersonalExmption + income + ^^Unemployment + S^InfantMortality + ^^Immigration + S^FemaleWage + S₇BirthControl + SsWWII + S^t + + S^t³ + e. They try multiple estimation

techniques based on this equation, but vary the number of lags of each independent variable. For example, in their preferred estimation they include times t, t-1, t-2, t-3, and t-4 of each independent variable.

(a) Why would Female wage be included in the regression? (Think principles of microeconomics opportunity costs.)

(b) Why should availability of birth control, Infant Mortality, and WWII all be included?

(c) Why should lags be included?

(d) Why should a time trend be included and why include t²,t³?

(e) The authors state that coefficients on individual lags are not necessarily reliable, but the sum of those coefficients is reliable. Why would the individual lag coefficients be unreliable?

4. (30 Points) The data set FERTIL3_s22.dta is the same data set as used in the paper from number 3. (It is missing the first two time periods though.) Use the data set to complete the following tasks:

(a) Create a time series line of fertility rate and real value of personal exemption over time.

(b) Discuss any trends in the variables. Do they appear to move together? (There isn't necessarily a right or wrong answer, as long as your reply makes sense.)

(c) Regress fertility rate on personal exemption and 2 lags of personal exemption. Repeat the regression including the time trend t. Create a table with your regression results.

(d) What is the long-run propensity and short-run propensity of the personal exemption according to your results (with time trend included)? (Write out your answer in complete sentences in terms of dollars and births.)

5. (5 Bonus Points) Include other controls from the dataset in number 4 that make sense to include empirically. Run a regression with the appropriate lags included. Discuss the results.

Some helpful commands in STATA:

• You must first tell stata that the data is time ordered by some variable t ”tsset t”. In our case the time variable is year.

• To create a time series graph of y, type ”tsline y”