TAILIEUCHUNG - Lecture Undergraduate econometrics, 2nd edition - Chapter 4: Properties of the least squares estimators

In this chapter, students will be able to understand: The least squares estimators as random variables, the sampling properties of the least squares estimators, the Gauss-Markov theorem, the probability distribution of the least squares estimators, estimating the variance of the error term. | Chapter 4 Properties of the Least Squares Estimators Assumptions of the Simple Linear Regression Model SR1. yt 01 02Xt et SR2 . E et 0 E yt 01 02Xt SR3. var et Ơ2 var yt SR4. cov ei ej cov yi yj 0 SR5. xt is not random and takes at least two values SR6 . et N 0 ơ2 yt N 01 02xt Ơ2 optional 1 Slide 4. Undergraduate Econometrics 2nd Edition -Chapter 4 The Least Squares Estimators as Random Variables To repeat an important passage from Chapter 3 when the formulas for b1 and b2 given in Equation are taken to be rules that are used whatever the sample data turn out to be then bl and b2 are random variables since their values depend on the random variable y whose values are not known until the sample is collected. In this context we call b1 and b2 the least squares estimators. When actual sample values numbers are substituted into the formulas we obtain numbers that are values of random variables. In this context we call bl and b2 the least squares estimates. 2 Slide 4. Undergraduate Econometrics 2nd Edition -Chapter 4 The Sampling Properties of the Least Squares Estimators The means expected values and variances of random variables provide information about the location and spread of their probability distributions see Chapter . As such the means and variances of b1 and b2 provide information about the range of values that b1 and b2 are likely to take. Knowing this range is important because our objective is to obtain estimates that are close to the true parameter values. Since bl and b2 are random variables they may have covariance and this we will determine as well. These predata characteristics of bl and b2 are called sampling properties because the randomness of the estimators is brought on by sampling from a population. 3 Slide 4. Undergraduate Econometrics 2nd Edition -Chapter

• Quản trị kinh doanh
• Undergraduate econometrics
• Lecture Undergraduate econometrics
• Kinh tế lượng
• The least squares estimators
• Least squares estimators
• Random variables
• Econometric model
• Experimental data
• Statistical inference
• Probability concepts
• Probability density
• Linear regression model
• Economic model
• Simple regression model
• Interval estimation
• Hypothesis testing
• Simple linear regression model
• Coefficient of determination
• Regression analysis
• Multiple regression model
• Model specification
• The least squares estimator
• Hypothesis tests
• Collinear economic variables
• Intercept dummy variables
• Slope dummy variables
• Dummy variables
• Nonlinear models
• Interaction variables
• Logistic growth curve
• Nature of heteroskedasticity
• Proportional heteroskedasticity
• Distributed lag models
• Finite distributed lag models
• Geometric lag
• Time series data
• Stationary time series
• Spurious regressions