Hypothesis testing and OLS Regression

[Pages:28]Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Hypothesis testing and OLS Regression

NIPFP 14 and 15 October 2008

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Overview

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A Monte-Carlo simulation Model Specification

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

The OLS estimator continued

As we discussed yesterday, the OLS estimator is a means of obtaining good estimates of 1 and 2, for the relationship Y = 1 + 2X1 +

Let us now move towards drawing inferences about the true 1 and 2, given our estimates ^1 and ^2. This requires making some valid assumptions about Xi and . These assumptions also evoke certain useful statistical properties of OLS, as constrasted with the purely numerical properties which we saw yesterday.

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumptions of OLS regression

Assumption 1: The regression model is linear in the parameters. Y = 1 + 2Xi + ui . This does not mean that Y and X are linear, but rather that 1 and 2 are linear.

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumptions of OLS regression

Assumption 1: The regression model is linear in the parameters. Y = 1 + 2Xi + ui . This does not mean that Y and X are linear, but rather that 1 and 2 are linear.

Assumption 2: X values are fixed in repeated sampling.

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumptions of OLS regression

Assumption 1: The regression model is linear in the parameters. Y = 1 + 2Xi + ui . This does not mean that Y and X are linear, but rather that 1 and 2 are linear.

Assumption 2: X values are fixed in repeated sampling. Assumption 3: The expectation of the disturbance ui is zero.

Thus, the distribution of ui given a value of Xi (in the population) is symmetric around its mean. (Show figure).

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumption 4: The variance of ui is the same for all observations, i.e. in the above distribution, the distribution of ui given each value of Xi has the same variance. This is an important property called homoskedasticity.

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumption 4: The variance of ui is the same for all observations, i.e. in the above distribution, the distribution of ui given each value of Xi has the same variance. This is an important property called homoskedasticity.

Assumption 5: There is no correlation between the ui (disturbances) of different observations. This is called auto-correlation or serial-correlation. It is seen more in time series analysis than cross-sectional analysis.

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