Meeting Dates

Wednesday, November 16, 2022

Upcoming Assignment

Problem Set 5 is due on Monday November 28.

## Overview

Today, we begin our brief look at panel data, where we track multiple individuals over time. Panel data contains its own unique challenges, because it contains a time series component for every individual, giving potential sources of bias.

We now need to understand the third assumption about $$u_i$$: no autocorrelation. The errors of our observations are likely going to be correlated within each individual and within each time period.

We can correct for these with a fixed effects model that isolates and absorbs some of that bias. In general, for a two-way fixed effects model:

$\widehat{\text{Y}}_{it} = \beta_0+\beta_1 \text{X}_{1it} + \beta_2 \text{X}_{2it}+\alpha_{i} + \theta_{t} + \nu_{it}$

Each observation is an individual $$i$$ at time $$t$$ (pay attention to the subscripts).

• Let $$Y_{it}$$ be our dependent variable, and $$X_{1it}$$ be the independent variable of interest. We would like to estimate the causal effect of $$X_{1it} \rightarrow Y_{it}$$.
• $$\alpha_i$$ is the group fixed-effect. It absorbs all unobservable factors that vary by group but don’t change over time.
• $$\tau_t$$ is the time fixed-effect. It absorbs all unobservable factors that do not vary by group but change over time.
• Since the fixed effects do not pick up factors that both vary by group and change over time, we need to include other variables that might cause $$X_{1it}$$ to be endogenous: hence, $$X_{2it}$$
• $$\nu_{it}$$ is the remaining (random) error term (after we have pulled $$\alpha_i$$ and $$\tau_t$$ out of $$u_{it}$$.

• Ch. 8.1—8.4 in Bailey, Real Econometrics

## Assignments

### Problem Set 5 Due Mon Nov 28

Problem Set 5 is due by the end of the day on Wednesday, November 28.

## Slides

Below, you can find the slides in two formats. Clicking the image will bring you to the html version of the slides in a new tab. The lower button will allow you to download a PDF version of the slides.

I suggest printing the slides beforehand and using them to take additional notes in class (not everything is in the slides)!