Term

Definition
The model is Linear in the Coefficients and the Error Term
Means:
 You must always write your model so it is Linear in the coefficients
 You Assume an error term is added on the end
Problem:
 Ols will give you no solution
Problem Found in:
 Equations which in theory cannot be written linearly
Solution:
 "Iterative" Computer techniques called NonParametric Methods



Term

Definition
The Error Term has a Zero Population Mean
Means: The distribution of the error term must have an expected value of zero.
Problem: An error term which has a mean other than zero will influence the estimated coefficients. The error term is zero tso that we can assume all the changes in the dependent variable have to do with independent variable.
Problem Found in: All Linear Regressions
Solution: Use a constant term 


Term
Classical Assumption #3 (Last of Theory) 

Definition
No independent variable is correlated with the error term
Means:
 There is no relationship between the error term and the independent variables
 All independent variables have to be determined outside of the model and not with each other or the independent variable.
Problem: Simultaneous equation bias. Coefficients are biased. (example supply and demand together determine effect of price on quantity)
Problem found in: The dependent variable could be in a second regression model that explains an independent variable.
Solution: Create instrumental variables by "TwoStage" least squares instead of OLS



Term

Definition
Error term observations are not correlated with each other
Means: The error for one observation should in no way influence the error for the next observations.
Problem: Serial Correlation
 Pure Serial Correlation: Comes from theory, not biased, increased variance
 Impure Serial Correlation: When you leave out an important variable. Biased. Increased Variance.
Problem Found In: Time Series Models
Solutions: First, test for serial correlation, then:
 Pure: Use Generalized Least Squares, not OLS
 Impure: Find the missing variable



Term

Definition
The error term has a constant variance.
Means: The variance of the error term will stay the same, regardless of independent variables used.
Problems: Two Types
 Pure Heteroskedasticity: Comes from theory. Not biased. Increases Variance.
 Impure Heteroskedasticity: When you leave out an important variable. Biased. Increase Variance.
Problem Found in: CrossSectional Data
Solutions: First, test for heteroskedasticity, then:
 Pure: Redefine variables or use Weighted Least Squares
 Impure: Find the Missing Variable



Term

Definition
Independent Variables are not perfect linear functions of each other
 Means: There is no relationship between any two or more independent variables
Problem: Multicollinearity
 Perfect Multicollinearity: Exact mathematical relationship, cannot solve for coefficients
 Imperfect Multicollinearity: Strong fuctional relationship, unbiased. Increase variance for affected variables.
Problem Found In: Both timer series and cross sectional models.
 Perfect: Comes from specification
 Imperfect: May come from chance of samples or two independent variables are really related
Solutions: First, test for multicollinearity, then:
 Perfect: Drop one of the perfect multicollinearity variables.
 Imperfect: DO NOTHING (avoid specification bias)



Term
Classical Assumption #7
(Not necessary, but used in Hypothesis testing) 

Definition
The error term is normally distributed
Means: The error term will only have a bellshaped distribution (this allows for t and F tests)
Problems: When this doesn't hold, we cant use the simple t and F tests for significance.
Problem Found In: Models where theory tells you assuming normal is inappropriate.
Solutions: Assume normal or assume some other more theoretically appropriate distributions 


Term

Definition
 Pure: Comes from theory. Not Biased. Increased Variance
 Use generalized least squares, not OLS
2. Impure: When you leave out an important variable. Biased. Increased Variance
 Find the missing variables



Term

Definition
 Pure: Comes from Theory. Not Biased. Increased Variance.
 Redefine the variables or use weighted least squares
2. Impure: When you leave out an important variable. Biased. Increased variance
 Find the Missing Variable



Term

Definition
Perfect: Exact mathematical relationship. Cannot solve for coefficients
 Drop one of the variables
Imperfect: Strong functional relationship. Unbiased. Increased variance for affected variables
 Do nothing to avoid specification bias



Term

Definition
An unbiased estimator with the smallest variance 


Term

Definition
Tells us that if classical assumptions 1 through 6 are met, OLS is the minimum variance estimator from among the set of all lineal unbiased estimators 


Term

Definition
Standard error of the equation 


Term

Definition
Standard Error of the estimated Coefficients 


Term

Definition
= √ ε^{e}²/n3
ε(_{X1i}x̄_{1})2(1r^{2} _{12})



Term

Definition
The Standard error gets smaller the bigger your sample 


Term

Definition


Term

Definition
Original Theoretical Justification 


Term

Definition
Substitute for theoretically desired variables when data on variables are incomplete or missing. Must move proportional to variable being measured.
(Ex: Zip code as a prozy quite successfully for income) 


Term

Definition
When using timer series data, a certain variable in one period may be affected by something that happened in a previous period.
β_{t1} 


Term

Definition
Taking qualitative measurements and converting them into quantitative variables for use in OLS
Two Methods:
From a baseline  always pick a base and drop it
Incremental Change 


Term

Definition
Sometimes you are not interested in the total value of a variable, but how it changes from one period to the next.
Δβ 

