# Shared Flashcard Set

## Details

Econometrics Midterm Definitions
Beginning Econometrics Definitions
60
Economics
10/15/2011

Term
 5 Properties of OLS estimators
Definition
 1) β's are unbiased 2) β's are consistent 3) β's are minimum variance of any unbiased estimator 4) MLE=OLS 5) β's are normally distributed
Term
 OLS normal equations
Definition
 ∑et=0 (sum of errors=0) ∑etxt=0 (sum of (errors*x's)=0 In matrix form, X'e=0 or X'Xβ^=X'Y. This means the predicted Y's and the errors are orthogonal.
Term
 Properties of OLS estimators if A1 fails
Definition
 1) β's are unbiased 2) β's are consistent 3) β's are NOT minimum variance of any unbiased estimator, but ARE minimum variance of linear unbiased estimators (BLUE) 4) OLS≠MLE 5) NOT normally distributed, but approximately are
Term
 When does OLS=MLE?
Definition
 When A1-A5 hold.
Term
 When does OLS=BLUE?
Definition
 If A2-A5 hold.
Term
 Properties of BLUE
Definition
 Best linear unbiased estimator. If A5 it is consistent
Term
 Biased
Definition
 When E(β^)=E(β)
Term
 Consistent
Definition
 limitn→∞Bias(β^)=0 limitn→∞Var(β^)=0
Term
Definition
 1-(SSE/(n-k)/(SST/(n-1)) This is a measure of the overall goodness of fit that has the property that adding an additional variable will only increase the adjusted R2  if the absolute value  of the t-statistic is greater than 1
Term
 Asymptotic Distribution (asymptotic chi square)
Definition
 f(θ^) is the asymptotic distribution of θ^ if  the exact distribution of θ^ approaches f(θ^) as n increases. The actual distribution can equal the asymptotic distribution. For example, if the errors aren't distributed normally, the t-statistic (θ^-θ)/(sθ^) is not an exact t-statistic, but it may have an asymptotic normal distribution.
Term
 Autocorrelation
Definition
 In time-series data, if the error terms between different times are correlated, this violates A4 and the OLS estimator would not be BLUE.
Term
 ANOV table
Definition
 Source Sum of squared errors Degrees of freedom Mean squared error Model SSR k-1 SSR/(k-1) Error SSE n-k SSE/(n-k) =s2 Total SST n-1 SST/(n-1)
Term
 Binary/Dummy Variable
Definition
 Variables that take the values of 0 or 1.
Term
 Chow Test
Definition
 To test joint hypothesis. [(SSE*-SSE)/r]/[SSE/(n-k)]~F(r, n-k) where r=(n-k)*-(n-k) or the number of equal signs in constraint * meaning the restrained model Can also look like [(R2*-R2)/r]/[(1-R2)/(n-k)]~F(r, n-k)
Term
 Confidence Interval
Definition
 a rule used to construct a random interval so that a certain percentage of all data sets, determined by the confidence level, yields an interval that contains the population value. CI for θ=(θ^-t(sθ^), θ^+t(sθ^). Where sθ^ is the standard error.
Term
 Cross Sectional Data
Definition
 a data set corresponding to sampling a population at a given point in time
Term
 Dummy Variable Trap
Definition
 With binary variables, you can only include an intercept if you don't include one of the binary options. (If variable can be 0, 1, or 2 you can eithe include two of those choices with an intercept or all three with no intercept)
Term
 Efficiency
Definition
 Minimum variance estimator.
Term
 endogenous regressor
Definition
 when a explanatory variable is correlated with the error term. Causes OLS to be biased and inconsistent.
Term
 Most common F-test
Definition
 Can test multiple hypothesis. Most common is to test that all variables have no explanatory power. The test is [SSR/(k-1)/[SSE/(n-k)] or [R2/(k-1)]/[(1-R2)/(n-k)]~F(k-1, n-k)
Term
 Hedonic pricing model
Definition
 Expresses the price or ln(price) of something in terms of its attributes. i.e. pricehome=f(squarefootage, bedrooms, bathrooms, age, size,...)
Term
 heteroskedasticity
Definition
 Violation of A3 meaning that Var(εt)=σt2≠σ2. OLS is not BLUE.
Term
 3 Characteristics of Instrumental Variables
Definition
 1) variable does not appear in equation 2) uncorrelated with error 3) correlated with endogenous regressor
Term
 Instrumental Variables Explanation
Definition
 To solve endogenous regressor problem. Use instrumental variable Z which satisfies 3 characteristics and then it will be consistent again.  IV=OLS if Z=X
Term
 interaction terms
Definition
 A regressor where two explanatory variables are multiplied together. The marginal impact of one independent variable depends on another explanatory variable.
Term
 kurtosis
Definition
 E(Y-μ)4/σ4 This is a measure of peakedness and tail thickness. Kurtosis value for normal is 3.
Term
 Likelihood Ratio Test
Definition
 Test validity of joint hypothesis. LR=2(l-l*)~χ2(r) where r is the number of equal signs in hypothesis.
Term
 Linear Probability Model
Definition
 When Y is a binary dependent variable and is estimated with OLS. There are 3 problems with this. 1) violates A1, 2) violates A3, 3) it is possible for predictions to be outside of (0, 1)
Term
 Logit model
Definition
 Model for binary dependent variables. Pr(Y=1|X)=the integral from -∞ to Xβ of f(s)ds =F(Xβ). f(s) is the log-logistic pdf (es/(1+es)2). Marginal effect is βiF(Xiβ).
Term
 Mean
Definition
 E(Y)=μ meaning the measure of central tendency.
Term
 multicollinearity
Definition
 non-zero correlations between explanatory variables in model. Increased collinearity makes the estimators less precise with significant F-test, and insignificant t-tests.
Term
 Panel Data
Definition
 Time-series data. Repeated cross-sectional data over time. Balanced if the same number of data appears each time.
Term
 PDF
Definition
 Probability Density Function. Satisfies the conditions that f(s)≥0 and that the integral of f(s) from -∞ to ∞ is 1. Also the Pr(a
Term
 Probit Model
Definition
 Binary dependent variable model. Pr(Y=1|X)=integral from -∞ to Xβ of f(s) ds=F(Xβ) where f(s)=(e-s^2/2/√2π). The marginal effect is βF(Xβ).
Term
 P-value
Definition
 Probability of a higher value of the test statistic under the null hypothesis. Smaller p-values mean you can reject the hypothesis.
Term
 Qualitative Response Model
Definition
 Probit or Logit models.
Term
 R2
Definition
 SSR/SST or 1-SSE/SST. It is the fraction of the model that is explained by the independent variables.
Term
 Reduced Form
Definition
 representation of model where each dependent variable is expressed in terms of explanatory variables
Term
 Skewness
Definition
 E(Y-μ)3/σ3 Measures symmetry or asymetry. Positive skewness means long thick tail to right.
Term
 Stepwise Regression
Definition
 data mining. No theory behind it so it is a bad word in economics.
Term
 Structural Representation of a Model
Definition
 This is a mathematical representation of the relationship between economic variables implied by economic theory and may include endogenous regressors (endogenous variables) along with exogenous variables on the right hand side of the equations.
Term
 T-statistic
Definition
 tests hypothesis that coefficient is equal to a number. Test is (θ^-θ)/sθ~t(n-k). Also used to test that a linear combination of coefficients is equal to a number.
Term
 "Useful" Theorem
Definition
 If Y~N[μy, ∑y] then Z=AY~N[Aμy, A∑yA'] We use this to determine the OLS distribution, predictions, and linear combinations of estimators.
Term
 Variance Inflation Factor
Definition
 1/(1-ρi.) Measures collinearity. ρi. is defined as the R2 obtained from regression the ith X on the other X's.
Term
 estimator and distribution of β1
Definition
 Ybar-β2^Xbar ~N[β1, σ2/n +Xbar2σ2/∑(Xt-Xbar)2
Term
 Estimator and Distribution of β2^
Definition
 Cov(X, Y)/Var(X) ~N[β2, σ2/∑(Xt-Xbar)2]
Term
 Estimator and Distribution of β (Matrix Form)
Definition
 (X'X)-1X'Y ~N[β, σ2(X'X)-1]
Term
 σ2yhat
Definition
 σ2/n +(Xt-Xbar)2σ2/∑(Xt-Xbar)2  σ2X0(X'X)-1X'0
Term
 σ2FE
Definition
 σ2-σ2yhat
Term
 Testing for σ2
Definition
 (n-k)s2β/σ2β~χ2(n-k) where s2=SSE/(n-2)
Term
 Autoregressive Model
Definition
 Includes lagged dependent variables. Can use the Koyck method for estimating.
Term
 Granger Causality Test
Definition
 Regress Y on lagged Y's and lagged X's. If the coefficients of the X's are nonzero then, X granger-causes Y. The test can be done using an F or Chow test.
Term
 Correlogram
Definition
 A plot of the correlation between a variable at different lag lengths.
Term
 Dickey-Fuller Test
Definition
 Tests if the ΔY=μ+ut is homoskedastic and uncorrelated. Null hypothesis is that you should use differences.
Term
 Difference in Differences Model
Definition
 Use when examining policies with two different time periods (before and after). The interaction term between the two tells you the D in D.
Term
 Distributed Lag Models
Definition
 Time series model that includes lagged explanatory variables. Can use Koyck and PDL to get rid of multicollinearity issues.
Term
 Koyck Distributive Lag Model
Definition
 Time series regression with lagged explanatory variables. Additional restriction that βi=λiβ0.
Term
 Polynomial Distributed Lag Model
Definition
 Time series regression model that includes lagged explanatory variables. Additional restriction that βi=a0+a1i+a2i2+...
Term
 Poisson Regression
Definition
 A regression model with an integer valued dependent variable which is distributed as a poisson variable with a mean value that is a linear function of the explanatory variables.
Term
 Spurious Regression
Definition
 When the independent variables show correlation but there is zero explanatory power. The regression is just showing that there is a trend. This can be fixed by adding a time variable.
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