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前言

理論與假設檢驗

Economists develop and evaluate theories about economic behavior. Hypothesis testing procedures are used to test these theories. In Chapter 5, we developed t-tests for null hypotheses consisting of a single restriction on one parameter βk from the multiple regression model, and null hypotheses consisting of a single restriction that involves more than one parameter. In this chapter we extend our earlier analysis to testing a null hypothesis with two or more restrictions on two or more parameters. An important new development for such tests is the F-test. A large sample alternative that can be used under weaker assumptions is the χ2-test.

• 經濟學家發展並評估有關經濟行為的理論，並使用假設檢驗程序來測試這些理論。
  
• 第五章介紹了針對單一參數的t檢驗和涉及多個參數的假設檢驗。
  
• 本章擴展了分析，介紹了對兩個或多個參數的零假設進行檢驗的新方法，包括F檢驗和在較弱假設下使用的χ²檢驗。

限制最小二乘法

The theories that economists develop sometimes provide nonsample information that can be used along with the information in a sample of data to estimate the parameters of a regression model. A procedure that combines these two types of information is called restricted least squares. It can be a useful technique when the data are not information-rich—a condition called collinearity—and the theoretical information is good. The restricted least squares procedure also plays a useful practical role when testing hypotheses. In addition to these topics, we discuss model specification for the multiple regression model, prediction, and the construction of prediction intervals. Model specification involves choosing a functional form and choosing a set of explanatory variables.
- 經濟學理論有時提供非樣本信息，這些信息可以與樣本數據結合來估計回歸模型的參數。
- 限制最小二乘法是一種將這兩種信息結合的程序，特別在數據不夠豐富（如共線性情況下）且理論信息良好時非常有用。

模型規範與預測

• 討論了多重回歸模型的規範，包括選擇函數形式和解釋變數集。
  
• 根據模型用途（預測或因果分析），選擇解釋變數的方法不同：因果分析中需考慮遺漏變數偏誤，而預測則需選擇與因變數高度相關的變數。

數據問題與非線性最小二乘法

Critical to the choice of a set of explanatory variables is whether a model is to be used for prediction or causal analysis. For causal analysis, omitted variable bias and selection of control variables is important. For prediction, selection of variables that are highly correlated with the dependent variable is more relevant. We also discuss the problems that arise if our data are not sufficiently rich because the variables are collinear or lack adequate variation, and summarize concepts for detecting influential observations. The use of nonlinear least squares is introduced for models that are nonlinear in the parameters.
- 提到如果數據不夠豐富（如變數共線性或缺乏足夠變異）可能出現的問題，以及如何檢測影響觀察值。 - 引入非線性最小二乘法，用於參數非線性的模型。

以上這段文字強調了經濟學研究中假設檢驗、模型規範及其在預測和因果分析中的應用。

章節

p.261 6.1 Testing Joint Hypotheses: The F-test
p.271 6.2 The Use of Nonsample Information
p.273 6.3 Model Specification
p.282 6.4 Prediction
p.288 6.5 Poor Data, Collinearity, and Insignificance
p.294 6.6 Nonlinear Least Squares
p.297 6.7 Exercises
p.311 Appendix 6A The Statistical Power of F-Tests
p.315 Appendix 6B Further Results from the FWL Theorem