Least Squares Estimates
- yi = B0 + B1xi + ui
-ui is the error term for observation i because it contains all factors affecting yi other
-Assume u is uncorrelated with x.
-Then u has zero expected value and that the covariance between x and u is z
Units of Measurements
-Two important issues in applied economics are (1) understanding how changing the
units of measurement of the dependent and/or independent variables affects OLS
estimates and (2) knowing how to incorporate popular functional forms us
-Econometrics is based upon the development of statistical methods for estimating
economic relationships, testing economic theories, and evaluating and implementing
government and business policy.
-The most common application of
Expected Values and Variances
-now view B0 and B1 as estimators for the parameters B0 and B1 that appear in the
-In the population model, the dependent variable, y, is related to the independent
variable, x, and the error (or disturbance
Causality and Ceteris Ceribus
-the economists goal is to infer that one variable has a causal effect on another variable
-ceteris paribus means other (relevant) factors being equal
-For example, if we succeed in holding all other relevant factors fixed
-A cross-sectional data set consists of a sample of individuals, households, firms, cities,
states, countries, or a variety of other units, taken at a given point in time.
-An important feature of cross-sectional data is that we can often as
-Multiple regression analysis is more amenable to ceteris paribus analysis because
it allows us to explicitly control for many other factors that simultaneously affect the
-multiple regression analysis can be used t
Properties of OlS
-Given B0 and B1, we can obtain the fitted value yi for each observation
-The OLS residual associated with observation i, ui, is the difference between yi and its
-If ui is positive, the line under predicts yi
-if ui is nega
-y=B0 + B1x+u
-the simple linear regression model.
-also called the two-variable linear regression model or bivariate linear regression model
because it relates the two variables x and y.
-y is called the dependent variable, the explained
Variances of OLS Estimators
-it is important to know how far we can expect B1 to be away from B1 on average.
-this allows us to choose the best estimator among all, or at leasta broad class of,
-The measure of spread in the distributi