# Econometrics

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• Created by: Caroline
• Created on: 19-05-16 08:41
Consequences of serial correlation?
OLS is not BLUE, standard errors are no longer valid, estimates are still unbiased
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Consequence of using Koyck?
There is now serial correlation and MA(1) error. Lagged dependant variable, combination of LDV and serial correlation make OLS biased and inconsistent, OLS is not attractive to estimate Koyck, use IV method.
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Sources of lagged variables?
Perception, decisions, inertia, expectations
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Maximum lag may not be known, need big sample for consistency and multicollinearity
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Definition of serial correlation?
Correlation between error terms in different time periods
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Consequences of trends of time series data?
Spurious correlation, seasonality, univariate modelling, structural break
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What is the ad hoc method?
Keep adding lagged variables until the coefficient on the last variable included is insignficant
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Problems with the White test method?
Many regressors mean many degrees of freedom with just moderate number of independent variables. White test can be influenced by unusual observations.
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Limitations of residual plots?
For multiple regression need multiple plots, cannot use for dummy variables and only visual not very sophiticated
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Consequences of using instrumental variables?
Estimates are consistent, preferable to OLS, however in geometric lag does not solve serial correlation problem, issues with small samples and estimates are still biased
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Definition of endogenous?
Explanatory variable is correlated with error term
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How to correct heteroscedasticity when the form is known?
Estimation by weighted least squares - e.g. var(u|x)=sigma^2h(x) - divide equation through by square root of h
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What is heteroscedasticity robust standard errors?
Adjusts errors so they are valid in the presence of heteroscedasticity, makes them consistnat
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What is the Koyck approach?
Suggests the further back in time we go the less important the factor. Follows a geometric progression still depends on infinite lags
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Concept of weighted least squares?
Gives greater weights to observations with the smaller error variance
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What is feasible GLS?
Used when the form of heteroscedasticity is unknown. For large samples FGLS is more attractive than OLS but is still biased as is based on same data so cannot be BLUE. However, FGLS is asymptotically more efficient than OLS but is still biased so cannot b
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Causes of serial correlation?
Cross sectional (each piece of data relates to geographic area), Spillover effects (inertia - events can spill over to multiple years), differencing correct relationship and misspecification (wrong functional form and omitted variables.
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Consequence of violation of MLR5 (heteroscedascity)?
OLS will be unbiased and consistent. Is not efficient however OLS will not be BLUE. Will affect standard errors and therefore t/F tests. Does not affect R-squared.
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Limitations of the Breusch-Pagan-Godfrey Test?
Cannot observe the error term or expected value of error term. Only looking for linear relationship between errors and explanatory variables.
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Causes of violation of MLR4?
Misspecification, omitted regressors, measurement error, proxy variables, simultaneous equations and lagged dependant variables.
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Consequences of violation of MLR4?
OLS will be biased, inconsistent and not BLUE
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How does the RESET test work?
If an equation satisfies MLR4 then nonlinear functions of the independent variable should insignificant when added to the regression (F test for subset of regressors)
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Consequence of MLR6?
MLR1-MRL6 says that under large samples OLS estimates will be approximately BLUE.
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Tests for heteroscedascitiy?
Residual plots, Breush-Pagan-Godfrey, White Test and Goldfeld Quant test
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Tests for heteroscedascitiy?
When the dependant variable is a binary variable
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Consequences of binary dependant variable?
Heteroscedasticity and non normality
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What is spurious correlation?
Finding a relationship between two or more trending variables because they are both growing time. Adding a time trend eliminates this problem
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Other problems of linear probability model?
R squared can never be high, some probabilities fall outside range of 1-0 and a probability cannot be linearly related to the independent variables for all their possible values.
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Size effects - e.g. error term increases as I increases. Dummy depen variable - two values for error. Group means - errors become averaged (not constant - divided by n) unless n is same. Misspecification - missing explan variable. Functional form.
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If an equation satisfies MLR4, then no non linear function of independent variable should be significant when added to the equation.
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How do you use GLS in LPM?
Use OLS to find estimate of coefficients and errors/variances, then use feasible GLS.
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Problems of Durbin-Watson Test?
Only tests for AR(1), depends on assumptions MLR1-MLR6, there is an inconclusive region and is biased with LDV
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Problems of Durbin-Watson Test?
Skewness is a measure of symmetry and kurtosis is a measure of the thickness of tails and height of peaks
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What approximation does the Jarque bera test use?
Chi squared (needs large samples)
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What is inconsistency?
When the error term is correlated with any of the explanatory variables?
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What is the autoregressive process?
Error term depends on own previous value.
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What is the method for Breush-Godfrey test?
Residuals are regressed on original regressors and lagged residuals.
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What is the logit model?
Solves problems of the linear probability model - produces non-linear functions for probabilities (e^x/1+e^e) probability when y=1
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What causes OLS is be biased and inconsistent?
Violation of MLR4
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What is asymptotic efficiency?
unbiased estimate with the smallest error variance
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What does the central limit theorem say about MLR6?
If the sample size is large enough than OLS estimate will be approximately asymptotically normally distributed.
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What does the central limit theorem say about MLR6?
Mean the variance can only take two values.
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What is the method for the Brusch-Pagan-Godfrey test?
Regress squared residuals from original OLS against independent variables.
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What is the method for the White Test?
Regress squared residuals from original OLS against independent variables and their cross products.
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What is the method for the Goldfeld Quant test?
Sample is divided into ranges and groups and fit regression line to each group. Compare the RSS for each group. If the error term is homoscedastic there should be no systematic difference between the RSS in each group.
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What is the moving average process?
Error term will depend on past random shocks.
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What is the method for FGLS?
Run regression of y on independent variables. Take the log of the squared residuals and regress against independent variables and obtain fit values g^. Exponate g^=h^. Divide equation by h^.
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For y=Bo+B1x1 what is the ex-ante and ex-post probability?
Ex-ante is Bo, this is before the experiment takes place (x1=0) and B1 is the ex-post probability.
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What is seasonality?
When data contains seasonal patterns. There is the possibility for it to be seasonally adjusted or including seasonal dummy variable.
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Rejections regions for Durbin Watson test Ho:p=0 H1:p>0?
DW
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Rejection regions for Durbin Watson test Ho:p=0 H1:p
4-DW
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When will measurement error not cause OLS estimates to be biased and inconsistent?
When x* (the variable where data is missing) is uncorrelated with other variables (unlikely)
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Problems of proxy variables?
If proxy variable is not perfectly correlated with missing variable, estimate will contain measurement error, OLS are unlikely to be unbiased/consistent. If the unobserved variable x* is correlated with other variables there will be +/- bias.
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How do simultaneous equation cause bias?
If the dependant variable in one equation is correlated with the error in the second equation there will be simultaneity bias.
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What is the cause of including irrelevant variable?
No effect on bias but may increase error variance.
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What is omitted variable bias?
When a variable is omitted from a regression, but due to its correlation with other variables, MLR4 is now violated.
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When is an instrumental variable used?
When an explanatory variable is correlated with error term (MLRS)
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Requirements for an instrumental variable?
Must be correlated with endogenous variable but not error term.
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## Other cards in this set

### Card 2

#### Front

Consequence of using Koyck?

#### Back

There is now serial correlation and MA(1) error. Lagged dependant variable, combination of LDV and serial correlation make OLS biased and inconsistent, OLS is not attractive to estimate Koyck, use IV method.

### Card 3

#### Front

Sources of lagged variables?

### Card 5

#### Front

Definition of serial correlation?