Ch11 Model selection

1. Ch11 Model selection 估計 母體的實際值 在其他條件不變之下，但實際上呢？ ☆ omitted variable bias => biased estimation ＊may even change sign(正號變負號或負號變正) Ex: • Law of demand : ex:龍蝦不符合Law of demand, 因為還有其他變數會影 響龍蝦的需求量，如:所得、替代品的價格等。

2. Ch11 Model selection • Fallacy of causation (因果的繆誤):當兩個變數同時發生或出現，並不代表有因果關係。 • Two variables appear together not means causal relation between X and Y. • 康老師出生後，台灣的國民所得都呈上升狀，是否表示康老師的出生和國民所得成長有關？ Ans:跑出來的 >0 且R²>60%，但實際上 GDP與康老師的年紀無關。 ＊因為影響一件事的因素非常多，omitted variable bias => 爭功委過

3. Ch11 Model selection • 11.4 inclusion of irrelevant variables(納入不相關變數) True Model: Estimated Model: *產生的後果: (p.342) • OLS estimators still unbiased • 還是correct estimate=> • Standard C.I. 和假設檢定 or F and t test remains valid. • OLS 估計的estimators are LUE, not BLUE =>省略了重要變數的後果比較嚴重。

4. Ch11 Model selection • 11.5 incorrect functional form True Model: Estimated Model: => If we choose the wrong functional form, the estimated coeff. May be biased of the true coeff. (i.e. may be biased)

5. Ch11 Model selection • 11.6 Errors of Measurement (p.345) 到目前為止，我們假設X、Y在衡量上是沒有誤差的，如果有衡量誤差的話: • If dependent variable 衡量錯誤: 1. OLS的估計值unbiased 2. OLS 估的variance unbiased 3. 的估計值會比較大 • If independent variable 衡量錯誤=> 嚴重性較高 ＊在統計的世界: • Uncertainty • 誤差到處存在(在不完美下過日子)

6. Ch11 Model selection • 11.7 Detecting specification errors: • (p.347) Detecting the presence of unnecessary variables • => => use t test, if reject H0 => x4 belongs to the model (x4 is a superfluous variables) 2. Suppose we are not sure x3 and x4 are relevant variables => => use F test, if reject H0, then x3 and x4 should be included in the model.