Ch 9 Dummy Variables Multiple regression model y

Ch 9 Dummy Variables Multiple regression model y=β 0+β 1 X 1+β 2 X 2+…+βk. Xk+e All βk are the same for each and every observation βk the change in E(y) when is increased by one unit, and all other variables are held constant 政治大學 中山所共同選修 黃智聰

Dummy variable the regression parameters are different for some of the observations in a sample a very powerful total for capituring qualitative characteristic of individuals. Usage: gender, region, religion, event Interaction variables 政治大學 中山所共同選修 黃智聰

9. 2 Intercept Dummy Variables y=β 0+β 1 X 1+e 1 if characteristic is present D= 0 if characteristic is not present y=β 0+β 1 X 1+αD+e β 0+β 1 X 1+α when D=1 Y= β 0+β 1 X 1 when D=0 D is a intercept dummy variable: shift in the intercept 政治大學 中山所共同選修 黃智聰

Slop Dummy variables y=β 0+β 1 X 1+γ(DX 1) +e β 0+β 1 X 1+γX 1 when D=1 E(y) = β 0+β 1 X 1 when D=0 αE(y) αX 1 β 1+γ when D=1 = β 1 when D=0 政治大學 中山所共同選修 黃智聰

If D affects both intercept and the slope y=β 0+β 1 X 1+δD+γ(X 1 D)+e β 0+β 1 X 1+δD+γX 1 when D=1 E(y) = β 0+β 1 X 1 when D=0 αE(y) αX 1 β 1+γ when D=1 = β 1 when D=0 政治大學 中山所共同選修 黃智聰

9. 5 Common Applications of Dummy Variables Additive: the effect of each qualitative factor is added to the regression intercept, and the effect of any dummy variable is independent of any other qualitative factor. 政治大學 中山所共同選修 黃智聰

2. Several categories: educational level, region, religion, race, gender Include all the dummy variables for educational attainment exact collinearity exists. b/c E 0+ E 1+ E 2+ E 3=1 E 0=1 - E 1 -E 2 -E 3 violate The assumption (E) which is an explanatory variable is not exact linear of the other explanatory variables. Omit one dummy variable and define as a reference group 政治大學 中山所共同選修 黃智聰

3. Controlling for time Seasonal dummies: fertility Annual dummies Regime effect: political regime, unusual economic condition, change in the large environment Test: single qualitative effect: T test several qualitative effects: F test 政治大學 中山所共同選修 黃智聰

The Chow Test Are there different b/w the regressions for two categories or not? If no two categories can be pooled into one sample. y=β 0+β 1 X 1+δD+γ(X 1 D)+e =1 male D =0 female Test H 0: δ=0, γ=0 Or test the equivalence of the two regression y=α 0+α 1 X 1+e y=β 0+β 1 X 1+e 政治大學 中山所共同選修 黃智聰

If δ=0 then α 1= β 1 and if thenγ=0 then α 0=β 0 How we can simply estimate the pooled y=a 0+a 1 x 1+u If H 0 is not true, then pooling data together would be equivalent to imposing constraints which is not true cause the least squares estimator biased, no matter how large our sample 政治大學 中山所共同選修 黃智聰

Chow Test Estimate y=α 1+α 1 X 1+e y=β 1+β 1 X 1+ε y=a 1+a 1 X 1+u SSE 1 SSE 2 SSER (SSER-SSE 1 -SSE 2) /J (SSE 1+SSE 2) /(T-K) 政治大學 中山所共同選修 黃智聰 Sum=SSEu ~FJ , T 1 -T 2 -K 1 -K 2