4.) The Classical Model Flashcards
The term classical refers to a set of fairly basic assumptions required to hold in order for…
OLS to be considered the “best” estimator for regression models
The CLASSICAL ASSUMPTIONS must be…
met in order for OLS estimators to be the best available
The Classical Assumptions are…
- ) The regression model is linear, is correctly specified, and has an additive error term.
- ) The error term has zero population mean.
- ) All explanatory variables are uncorrelated with the error term.
- ) Observations of the error term are uncorrelated with each other (no serial correlation).
- ) The error term has a constant variance (no heteroskadasticity).
- ) No explanatory variable is a perfect linear function of any other explanatory variable(s) (no perfect multicollinearity)
- ) The error term is normally distributed (this assumption is optional but usually is invoked).
Assumption I
The regression model is linear, is correctly specified, and has an additive error term
Assumption II
the error term has a zero population mean
Econometricians add a stochastic (random) error term…
to regression equations to account variation in the dependent variable that is not explained by the model
The properties of the OLS estimator of the betas still hold because the equation is linear. Two additional properties also must hold.
- ) We assume that the equation is correctly specified. If an equation has omitted variable or an incorrect functional form, the odds are against that equation work ing well.
- ) We assume that a stochastic error term has been added to the equation. This error term must be an additive one and cannot be multiplied by or divided into any of the variables in the equation.
In essence, the constant term equals…
the fixed portion of Y that cannot be explained by independent variables whereas the error term equals the stochastic portion of the unexplained value of Y.
Assumption III
All explanatory variables are uncorrelated with the error term. It is assumed that the observed values of the explanatory variables are independent of the values of the error term.
Assumption IV
Observation of the error term are uncorrelated with each other. The observations of the error term are drawn independently from each other
If an explanatory variable and the error term were instead correlated with each other, the OLS estimates would be likely to attribute…
to the X some of the variation in Y that actually came from the error term
If the error term and X were positively correlated then…
the estimated coefficient would probably be higher than it would otherwise have been (biased upward). because the OLS program would mistakenly attribute the variation in Y caused by error term to X instead
Classical Assumption III is violated most frequently when…
a researcher omits an important independent variable from an equation.
Classical Assumption V
The error term has a constant variance
To meet classical assumption V, the variance of the distribution from which the observations of the error term are drawn is…
constant
The violation of assumption V is referred to as…
heteroskadasticity
Classical Assumption VI
No explanatory variable is a perfect linear function of any other explanatory variables(s).
Perfect collinearity between two independent variables implies…
that they are really the same variable, or that one is a multiple of the other, and/or that a constant has been added to one of the variables
Many instances of collinearity (or multicollinearity if more than two independent variables are involved)
are the result of the researcher not accounting for identities (definitional equaivalences) among the independent variables
Classical Assumption VII
The Error Term is normally distributed
Assumption VII states that …
the observations of the error term are drawn from a distribution that is normal
The major application of normal distribution of the error term is…
in hypothesis test, which uses the estimated regression coefficient to investigate hypotheses about econ behavior
Even though Assumption VII is optional, it’s usually advisable to add the assumption of normality fo the other six assumption for two reasons….
- ) The error term can be though of as the sum of a number of minor influences or errors. As the number of these minor influences gets larger, the distribution of the error term tends to approach the normal distribution
- ) The t-statistic and the F-statistic are not truly applicable unless the eror term is normally distributed
The probability distribution of betas values across different samples
is called the sampling distribution of Beta
An estimator is a…
formula, such as the OLS formula
An estimate is…
the value of beta computed by the formula for a given sample
A desirable property of a distribution of estimates is that its mean equals…
the true mean of the variable being estimated
If an estimator produces betas that are not centered around the true beta…
the estimator is refered to as a biased estimator
a estimator beta is an unbiased estimator if it sampling distribution has…
as its expected value the true value of beta
E(Beta Predicted) = Beta
The Mean Square Error is equal to..
the variance plus the square of the bias.
The lower the Mean Square Error (MSE) …
the better
The Gauss-Markov Theorem States that…
Given Classical assumptions I through VI (Assumption VII, normality, is not needed for this theorem), the Ordinary Least Squares estimator of beta parameter is the minimum variance estimator from among the set of all linear unbiased estimates of beta k, for k = 0,1,2,…,K.
Since the standard error of the estimated coefficient is the square root of the estimated variance of the betas…
it is similarly affected by the size of the sample and the other factors we’ve mentioned
An unbiased estimator with the smallest variance is called…
efficient, and that estimator is said to have the property of efficiency
If all seven assumptions are met, OLS is…
“BLUE”
OLS is BLUE (stands for…)
Best (meaning minimum variance) Linear Unbiased Estimor
