Introduction to econometrics II eco 356 faculty of social sciences course guide course Developers: Dr. Adesina-Uthman
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- 2.2.1.0 INTRODUCTION INTRODUCTION TO ECONOMETRICS II ECO 306
| INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 53 UNIT 2: PROPERTIES OF THE REGRESSION COEFFICIENTS AND HYPOTHESIS TESTING CONTENTS 2.2.1.0 Introduction 2.2.2.0 Objectives 2.2.3.0 Main Content 2.2.3.1 The Random Components of the Regression Coefficients 2.2.3.2 Assumptions Concerning the Disturbance Term 2.2.3.2.1 Gauss–Markov Condition 1: E(μ i ) = 0 for All Observations 2.2.3.2.2 Gauss–Markov Condition 2: Population Variance of μ i Constant for All Observations 2.2.3.2.3 Gauss–Markov Condition 3: μ i Distributed Independently of μ j ( ) 2.2.3.2.4 Gauss–Markov Condition 4: u Distributed Independently of the Explanatory Variables 2.2.3.3 The Normality Assumption 2.2.3.4 Unbiasedness of the Regression Coefficients 2.2.3.5 Precision of the Regression Coefficients 2.2.3.6 Testing Hypotheses Relating to the Regression Coefficients 2.2.3.6.1 Formulation of a Null Hypothesis 2.2.3.6.2 Developing the Implications of a Hypothesis 2.2.3.7 Compatibility, Freakiness, and the Significance Level 2.2.3.8 What Happens if the Standard Deviation of is Not Known 2.2.4.0 Conclusion 2.2.5.0 Summary 2.2.6.0 Tutor-Marked Assignment 2.2.7.0 References/Further Reading 2.2.1.0 INTRODUCTION INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 54 This unit firstly attempts giving an appropriate explanation to the concept of GAUSS- MARKOV THEOREM before proceeding into the discussion of the properties of regression coefficients and hypothesis testing. However, to properly understand this unit, a brief discussion would be made of some knowledge areas like i. Estimators ii. Assumptions underlying the Classical Linear Regression Model (CLRM) iii. Properties of Ordinary Least Square (OLS) estimator iv. Statistical inference (hypothesis testing) like null and alternative hypotheses. The basic knowledge of the aforementioned areas are what the students must be equipped with before proceeding in this unit. - Estimators A rule for calculating an estimate of a given quantity based on observed data is referred to as an estimator. Hence in the calculation three quantities are distinguished the quantity of interest, referred to as an estimand, the result (estimate) and the rule (estimator. The properties of estimators are the concerns of Estimation theory. The theory defines and determines properties that can be used under given circumstances to relate different estimators or different rules for creating estimates for the same quantity which are built on the same data. A simple example of an estimator is given by a sample mean equation of a population mean shown below. 1 1 N i i k k N where, k is an estimator for the population mean - Assumptions underlying Classical Linear Regression Model (CLRM) This model is the basis of most econometric theory and provides a description of the method of ordinary least squares (OLS). It also explains |