# Shared Flashcard Set

## Details

Econometrics
Classical Assumptions, Dummy Variables, Standard Error
22
Economics
03/11/2013

Term
 Classical Assumption #1
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 Non-Parametric Methods
Term
 Classical Assumption #2
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 "Two-Stage" least squares instead of OLS
Term
 Classical Assumption #4
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
 Classical Assumption #5
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: Cross-Sectional Data Solutions: First, test for heteroskedasticity, then: Pure: Redefine variables or use Weighted Least Squares Impure: Find the Missing Variable
Term
 Classical Assumption #6
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 bell-shaped 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
 Serial Correlation
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
 Heteroskedasticity
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
 Multicollinearity
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
 Efficient
Definition
 An unbiased estimator with the smallest variance
Term
 Gauss-Markov Theorm
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
 SEE
Definition
 Standard error of the equation
Term
 SE( βk)
Definition
 Standard Error of the estimated Coefficients
Term
 SE ( β1)
Definition
 = √ εe²/n-3 ε(X1i-x̄1)2(1-r2 12)
Term
 Consistency
Definition
 The Standard error gets smaller the bigger your sample
Term
 Functional Form
Definition
 Shape of the Graph
Term
 Priors
Definition
 Original Theoretical Justification
Term
 Proxy Variable
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
 Lag Variables
Definition
 When using timer series data, a certain variable in one period may be affected by something that happened in a previous period.   βt-1
Term
 Dummy Variable
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
 Difference Variables
Definition
 Sometimes you are not interested in the total value of a variable, but how it changes from one period to the next. Δβ
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