LN+7+OLS+SE+and+F-test

# LN+7+OLS+SE+and+F-test - Empirical Methods II(API-202A...

This preview shows pages 1–4. Sign up to view the full content.

Empirical Methods II (API-202A) Kennedy School of Government Harvard University 1 Lecture Notes 7 OLS Standard Errors and F-test I – OLS Standard Errors SE ( 1 ˆ ) Refresher: The need for hypothesis testing Regressions: estimate partial association in the population using a sample Any sample is subject to sampling variation Need hypothesis testing to test hypotheses about population coefficients – Is 1 ˆ statistically significant? Refresher: we need the standard deviation of our estimator 1 ˆ , also called the standard error of 1 ˆ , SE ( 1 ˆ ) , to test for the statistical significance of 1 ˆ . Hypothesis Test : 1) 0 : 1 0 H , 0 : 1 A H 2) ) ˆ ( 0 ˆ 1 1 SE t 3) Reject the null if |t|>1.96 (N>120) Refresher: the (robust) SE ( 1 ˆ ) is computed as (K=1):  2 2 2 2 1 ) ( ˆ ) ( ) ˆ ( X X X X SE i i i TODAY: Where does the formula for the SE ( 1 ˆ ) come from and what is its key determinant? -Key determinant: What makes our SE ( 1 ˆ ) smaller, and thus, our t-test bigger? -In other words, what makes our estimation more or less accurate (ie, with higher or lower variance).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Empirical Methods II (API-202A) Kennedy School of Government Harvard University 2 Where does the formula for the SE ( 1 ˆ ) comes from? A Big Picture View (the math involved is beyond the scope of this course) i) Recall from LN4 that we can write the formula that computes 1 ˆ in demeaned terms (K=1). 2 2 1 ) ( ) )( ( ) ( ) )( ( ˆ d i d i d i i i i X Y X X X Y Y X X ii) And that we can replace d i Y with the SEQ written also in demeaned terms, yielding: 2 1 1 ) ( ˆ d i i d i X X iii) With this formulation, we can start thinking about how to compute the SE ( 1 ˆ ): 2 2 1 1 1 ) ( ) ( ) ˆ ( ) ˆ ( d i i d i d i i d i X X Var X X Var Var SE iv) One can show that for large N (>120) the formula above can be estimated with our formula for SE ( 1 ˆ ) pasted below - the math involved is beyond the scope of this course. 1  2 2 2 2 1 ) ( ˆ ) ( ) ˆ ( X X X X SE i i i 1 See Stock and Watson page 180 or Wooldridge page 264 for more details.
Empirical Methods II (API-202A) Kennedy School of Government Harvard University 3 Which is the key determinant of SE ( 1 ˆ )? The key determinant of SE ( 1 ˆ ) is the variance of the error term: 2 ) ( i i Var The larger the error terms i are, the bigger 2 i is, the bigger SE( 1 ˆ ) is and the more imprecise our estimation is . PRACTICAL IMPLICATION : Adding relevant control variables not only allow us to reduce the risk of OVB, but also to reduce the size and variance of the errors, and as a result, obtain more accurate estimates of 1 ˆ . “…we are taking something out of the error term. ..” For example . Adding control variables to a randomized experiment (eg Tennessee STAR) o Define TREAT = 1 if person is in treatment group (smaller classes) 0 if person is in control group (regular classes) o Two alternative estimates: test scores = 0 ˆ + 1 ˆ TREAT + ˆ test scores = 0 ˆ + 1 ˆ TREAT + 2 ˆ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 15

LN+7+OLS+SE+and+F-test - Empirical Methods II(API-202A...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online