1. Empirical methods take real-world data estimate size of relationship between variables two types  regression analysis  natural experiments take real-world data estimate size of relationship between variables two types  regression analysis  natural experiments

2. Regression analysis two variables: X and Y fit a linear relationship  Y = a + bX + u X is independent variable Y is the dependent variable how does a change in X cause Y to change? two variables: X and Y fit a linear relationship  Y = a + bX + u X is independent variable Y is the dependent variable how does a change in X cause Y to change?

3. Y = a + bX + u get data on Y, X  multiple observations use regression analysis to estimate a and b Y = a + bX + u get data on Y, X  multiple observations use regression analysis to estimate a and b

4. multiple regression  many independent variables  X1, X2, X3, X4, … how many indep. variables to include?  tough question  if wrong, estimates may be biased multiple regression  many independent variables  X1, X2, X3, X4, … how many indep. variables to include?  tough question  if wrong, estimates may be biased

5. Natural experiment In medical research: random assignment experiment  one group gets treatment  one group gets nothing  people randomly assigned to group  then different outcomes due to treatment In medical research: random assignment experiment  one group gets treatment  one group gets nothing  people randomly assigned to group  then different outcomes due to treatment

6. in economics: natural experiment  like random assignment  researcher did not plan experiment  the experiment results from an event or policy natural experiment  like random assignment  researcher did not plan experiment  the experiment results from an event or policy

7. example: EITC income subsidy to low income families expanded 1986  women w/ children get EITC  women w/ out children do not EITC increases labor force participation income subsidy to low income families expanded 1986  women w/ children get EITC  women w/ out children do not EITC increases labor force participation