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Unformatted text preview: Contents 1 Nonstochastic regressors 1 1.1 Types of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Model A assumptions . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Properties of OLS estimators 5 2.1 Unbiasedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Hypothesis testing 11 3.1 Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Nulls and alternatives . . . . . . . . . . . . . . . . . . . . . . . . 14 4 More 19 4.1 Types of error, power of a test . . . . . . . . . . . . . . . . . . . 19 4.2 t and F tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1 Nonstochastic regressors Contents 1.1 Types of data Contents Basically three types of data that we might run regressions on: 1. Crosssectional data observations at a single moment in time of many similar entities (countries, people, firms ...) e.g. wages across individuals 2. Time series data repeated observations of the same single entity (country, person, firm...) over time e.g. wages of a single person over time 3. Panel data repeated observations of the same multiple entities over time mix of crosssectional and time series e.g. wages of a sample of people over time The book covers all three types of regression on Xsectional, time series & panel data We will probably only cover Xsectional regressions in the course basic insights/procedures carry over to other types of data We will follow the book and distinguish between two types of Xsectional regression according to the properties of the regressors (explanatory variables) so far only one regressor (simple regression) Two types of crosssectional regression Model A  with nonstochastic regressors This means that the explanatory variables are not random variables they are completely deterministic, with no random component This is an unusual property, and really only applies to variables that we (the econometricians) construct e.g. say I want to run a regression of 281 assignment performance on students overall GPA, using a sample of students from this course but, I want my sample to be representative of the GPA distribution at Northwestern generally, and so pick the students accordingly then the GPAs (the regressors) would not be random variables Two types of crosssectional regression Model B  with stochastic regressors This means that the explanatory variables are random variables we do not choose our data directly, but instead treat the regressors as draws from some underlying probability distribution This describes most variables/models that econometricians investigate wages, height, gender, eye colour e.g. say I ran that regression of 281 performance on GPA, but using everyone in this class I didnt choose your GPA, and so for my purposes it is a random variable 2...
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This note was uploaded on 01/14/2012 for the course ECON 201 taught by Professor Witte during the Spring '08 term at Northwestern.
 Spring '08
 Witte
 Macroeconomics

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