1. 政治大學中山所共同選修 課程名稱： 社會科學計量方法與統計－計量方法 Methodology of Social Sciences 授課內容： Nonlinear Models 日期： 2003 年 11 月 13 日

2. 政治大學 中山所共同選修 黃智聰 Ch10 Nonlinear Model First category: nonlinear in the variables, but still linear in terms of the unknown parameters y= α L β K γ lny= δ + β ln(L)+ γ ln(K)

3. 政治大學 中山所共同選修 黃智聰 10.1 Polynomial and Interaction Variables The slop of the regression model is continuously changing. TC= α 1 + α 2 Q+ α 3 Q 2 + α 4 Q 3 +e PIZZA= β 1 + β 2 AGE+ β 3 Y+e = β 2 :for any given level of income, the expected on pizza change by the amount β 2 with an additional year of age. α PIZZA α AGE

4. 政治大學 中山所共同選修 黃智聰 = β 3 :for individuals of any given age, an increase in income of $1 increases expected expenditures on pizza by β 3 How about: a person grows older, their marginal propensity to spend on pizza decline. the effect of income depends on the age of the individual. AGE×y PIZZA= β 1 + β 2 AGE+ β 3 Y+β 4 (AGE×y) +e α PIZZA αYαY

5. 政治大學 中山所共同選修 黃智聰 = β 2 + β 4 Y The effect of age now depends on income = β 3 + β 4 Age The effect of a change in income on expected pizza expenditure now depends on AGE. αE(PIZZA) αAGE αE(PIZZA) αY

6. 政治大學 中山所共同選修 黃智聰 What is the different b/w the follower two equations Pizza: 342.8848***-7.5756**AGE+0.0024***Y Pizza: 161.4654-2.9774AGE+0.0091**Y- 0.00016**(Y×AGE) AGE is no longer appears to be a significant explanatory factor. This suggests that AGE affects pizza expenditure through its interaction with income---that is, it affects the marginal propensity to spend on pizza. Estimate the marginal effect of AGE