The Classical Model Flashcards
Classical Model
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…
1) The regression model is linear, correctly specified and has an additive error term.
2) The error term has zero population mean.
3) All explanatory variables are uncorrelated with the error term.
4) Observations of the error term are uncorrelated with each other (no serial correlation)
5) The error term has a constant variance (no heteroskedasticity)
6) No explanatory variable is a perfect linear function of any other explanatory variables (no perfect multicollinearity)
7) The error term is normally distributed (this assumption is optional but usually is invoked)
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:
1) We assume that the equation is correctly specified. If an equation has an omitted variable or an incorrect functional form, the odds are against that equation working well.
2) 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 if the unexplained value of Y
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 form 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 3 is violated most frequently when..
a researcher omits an important independent variable from an equation
The violation of assumption 5 is referred to as…
heteroskedasticity
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
The major application of normal distribution of the error term is…
in hypothesis test, which uses the estimated regression coefficient to investigate hypotheses about economic behavior
Even though Assumption 7 is optional, its usually advisable to add the assumption of normality to the other six assumption, for two reasons…
1) 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
2) The t-statistic and the F-statistic are not truly applicable unless the error term is normally distributed
The probability 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 referred to as a biased estimator
A estimator beta is an unbiased estimator if its 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 model
The Gauss-Markov Theorem states that…
Given Classical assumptions 1-6 (assumption 7 (normality) is not needed for this theorem), the OLS estimator of beta parameter is the minimum variance estimator from among the set of all linear unbiased estimates of beta, 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” (Best (meaning minimum variance) Linear Unbiased Estimator)
