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Lecture Applied econometrics course - Chapter 3: Statistic inference and hypothesis testing

Lecture "Applied econometrics course - Chapter 3: Statistic inference and hypothesis testing" has content: The distribution of the parameters, hypotheses testing, testing multiple linear restrictions,. and other contents. | Chapter III Statistic Inference and Hypothesis Testing APPLIED ECONOMETRICS COURSE NGUYEN BA TRUNG - 2016 I. THE DISTRIBUTION OF THE PARAMETERS Assumpt 6. Ui ~ N(0, 2) Theorem 4.1: Normal Distribution of the parametors I. THE DISTRIBUTION OF THE PARAMETERS Under the assumptions from 1-6, we have the following theorem: Theorem 4.2: Student Distribution II. HYPOTHESES TESTING (1). Manifest the hypothesis: (2). Compute t-statistics: (3). Search to find t (n-k-1), for example, α=5%, n-k-1=28, t0.05 (28)=1.701 ( excel: TINV(0.1,28)) (4). Decision Rule: Nếu t > t (n-k-1) thì có thể bác bỏ giả thiết H0 Nếu t t0.05 (8)=1.86, we therefore can reject the null hypothesis H0. In other word, we can accept the alternative hypothesis H1: 1 > 0 II. HYPOTHESES TESTING 2.2. Testing against One-Sided Alternatives: Left Hand Side (1). Suppose the hypothesis: (2).Compute t-statistics: (3).Search to find t (n-k-1) (4). Decision Rule : Nếu t t /2(n-k-1), we can reject the null hypothesis H0 if t t /2(n-k-1), we can accept the null hypothesis H0 II. HYPOTHESES TESTING Example: Whether income affects to expenditure? Manifest the hypothesis: Compute s-statistics: With = 5%, we have: t0.025(n-k-1) = t0.025(8) = 2.306 Because t =14.243 > t0.025(8) = 2.36, we can reject the null hypothesis H0: β1= 0. This means that income significantly impacts to expenditure. Solution: Example: | Chapter III Statistic Inference and Hypothesis Testing APPLIED ECONOMETRICS COURSE NGUYEN BA TRUNG - 2016 I. THE DISTRIBUTION OF THE PARAMETERS Assumpt 6. Ui ~ N(0, 2) Theorem 4.1: Normal Distribution of the parametors I. THE DISTRIBUTION OF THE PARAMETERS Under the assumptions from 1-6, we have the following theorem: Theorem 4.2: Student Distribution II. HYPOTHESES TESTING (1). Manifest the hypothesis: (2). Compute t-statistics: (3). Search to find t (n-k-1), for example, α=5%, n-k-1=28, t0.05 (28)=1.701 ( excel: TINV(0.1,28)) (4). Decision Rule: Nếu t > t (n-k-1) thì có thể bác bỏ giả thiết H0 Nếu t t0.05 (8)=1.86, we therefore can reject the null hypothesis .