First, we will load data from Graddy (1995) who observes daily fish prices and quantities from the Fulton Fish Market in NYC.

The goal of this paper is to estimate the demand elasticity of fish prices $$ Q = \alpha + \delta P + \gamma X + \varepsilon $$ Since price and quantity are simultaneous equations, we need an instrument that shocks $P$. Graddy (1995) uses the two-day lagged weather which determines that day's market price for fish.

Load the Fulton Fish Market data from https://github.com/Mixtape-Sessions/Causal-Inference-1/raw/main/Lab/IV/Fulton.dta

1. Run OLS of q on p controlling for indicators for day of the week (Mon, Tue, Wed, Thu). Interpret the elasticity.

2. Estimate the Wald estimator using reduced form and first stage regressions with day of week fixed effects using Stormy as the instrument. Interpret the elasticity.

3. Instrument for p using the variable Stormy which is an indicator for it being stormy in the past two days. Interpret the elasticity. Compare your answer to the Wald estimator.

4. Calculate the Olea and Pfleuger effective F-statistic and interpret the strength of the instrument.

5. Calculate the Anderson-Rubin confidence intervals.

6. What might be a great figure of the reduced form and the first stage separately?

Next, we will turn to the classical IV example of Card (1995). Card aims to estimate the returns to college education, but is worried about omitted variable bias when regressing wages on years of education. In this case, the coefficient on education is likely biased upwards by unobserved ability since it is plausibly positively correlated with education and with wages.

Load the Card data from https://raw.github.com/scunning1975/mixtape/master/card.dta

1. Regress the log wage lwage on years of education educ controlling for experience (exper), an indicator for being Black (black), an indicator for being in the South (south), an indicator for being married (married), and an indicator for living in an urban area (smsa). Interpret the coefficient on schooling.

2. Using the same set of controls, run an instrumental variables regression instrumenting educ by nearc4 which is an indicator for being near a 4-year college/university. Interpret the coefficient on schooling

3. Calculate the strength of the first stage using the Olea and Pfleuger effective F statistic. Interpret the result.

4. Calculate the Anderson-Rubin confidence intervals and interpret your result.

5. Compare the two results, does the IV estimate move in the direction we predicted above? Use the concept of LATE to describe why the coefficient moved in the direction it did.

6. If your schooling result is a LATE, then what do the five assumptions mean in the context of this study?

7. What might be a great figure of the reduced form and the first stage separately?

Note: for Stata, you can use -weakivtest- for the Olea and Pfleuger effective F and -twostepweakiv- for the Anderson-Rubin confidence intervals. For R, you can use the {} and {} packages