The course Econometrics at Tilburg University is separated into two parts. This summary covers the first part, Lecture 1 - Lecture 7. The summary is based on the Lecture Notes, but is extended to clarify some derivations, which makes it easier to cope with some of the concepts. The summary is conc...
A common question in econometrics is to study the effect of one group of variables X, usually
called the regressors, on another Y, the dependent variable.
In cross-sections1 , the relationship between the regressors and the dependent variable is modelled
through the conditional expectation E[Yi | Xi ]. The deviation of Yi from its conditional expectation
is called the error or residual:
εi = Yi − E[Yi | Xi ]. (1.1)
In the parametric framework, it is assumed that the conditional expectation function depends on a
number of unknown constants or parameters, and that the functional form of E[Yi | Xi ] is known.
In the linear regression model, it is assumed that E[Yi | Xi ] is linear in the parameters:
Here, β is a vector of unknown constants. Thus, the error in (1.1) is not observable, as the
conditional expectation is unknown. With econometric theory we aim to estimate these unknowns.
1.1 Linear Regression Model Assumptions
Let us formally define the linear regression model. In the classical regression model, it is assumed
that the variance of the errors is independent of the regressors and the same for all observations.
Var(εi | Xi ) = σ 2
For some constant σ 2 > 0. This property is called homoscedasticity. The following are the four
classical regression assumptions.
(A1) y = Xβ + ε
(A2) E[ε | X] = 0
(A3) Var(ε | X) = σ 2 In
(A4) rank(X) = k
1 A cross-sectional data set consists of a sample of individuals, households, firms, cities, counties, or a variety
of other units, taken at a given point in time.
2
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