Shared Flashcard Set

Details

Econometrics
Advanced Stats
36
Economics
Graduate
04/28/2013

Additional Economics Flashcards

 


 

Cards

Term
Causes of Autocorrelation
Definition

1. Incorrect specification of form of a relationship (eg – non-linear)

2. Omission of variable (misspecification)

3. Measurement error in the dependent variable

4. Variables move smoothly over time (sluggishness – lag e.g. GDP)

 

In 1 & 2 included IVs the error term is picking up the missing variables

 

3&4 are true autocorrelation

Term
Durbin Watson range
Definition
  • 0-4,
  • 0=positive autocorrelation,
  • 4=perfect negative autocorrelation.
  • 2=no autocorrelation
Term
Whites test procedure (preferred with small # IVs and sufficient sample size)
Definition
  • Carry out auxiliary regression in which the squared residuals (ui) from the main regression are regressed on all of the IVs
  • υ_i^2=α_1+α_2 X_2i+α_3 X_3i+α_4 X_2i^2+〖α_5 X_3i^2+α〗_6 X_2i X_3i+ν_i
  • Obtain raw R2
  • Df = number of regressors (not u) so 5 in above
  • N* R2~χ2df
  • If calculated chi-squared > critical chi-squared reject the null hypothesis of homoscedasticity
Term

Durbin Watson hypothesis test for 1st order autocorrelation

Definition

• If d=2 – no autocorrelation

• If 0≤d≤2 – positive correlation

• If 2≤d≤4 then negative autocorrelation

 

d<dl - reject H0

d>du - do not reject

dl<d<du - indeterminate range

Term
Cochrane-Orcutt estimation of rho
Definition

1. Run OLS on original equation

2. Regress residuals on lagged residuals to estimate rho. 3. Transform variables using this estimate of rho.

4. Run OLS on the transformed variables.

 

Cochrane-Orcutt Iterative Process - uses GLS approximations in an iterative process to converge on a reliable estimate of ρ for first-order serially correlated disturbances; based on minimizing the sum of squared residuals (RSS) for different values of ρ until a stable value for the RSS is obtained (i.e., one that does not change between iterations)

Term

Origins of simultaneous equation bias

Definition

 

When the dependent variable from one equation becomes the independent variable in another there is a violation of the assumption that the IV has no relation to the error term. This results in inconsistent estimates and bias.

 

 

 

Term
Purpose of Concordance/discordance
Definition

To measure goodness of fit of a logit model. 60 - fair, 70 - good, 80 - vg, 90-excellent

Term
Concept and use of instrumental variable
Definition
An instrumental variable is used to correct for endogeneity. The instrumental variable needs to be (hopefully strongly) correlated for another IV but NOT the error term.
Term

Interpretation of the parameter estimate from a Logit regression.

Definition

Beta is the change in the log of the odds of y occurring given a one unit change in x holding the effects of other variables constant

Term
Interpretation of the Odds Ratio from a Logit regression
Definition
  •  The odds of y occurring is the odds ratio multiplied by (parameter estimate) given a one unit increase in the independent variable holding the effects of the other variables contstant.
  • Or the multiplicative increase in the odds of the dependent event occurring if the event represented by the independent variable occurs, holding the effects of the other variables contstant.
Term
Characteristics of the Logit model.
Definition

1. The probability of the event (Pi) is between 0 and 1 ( or 0% to 100%)

2. S shaped curve – so as the value of the IV approaches zero, Pi decreases at a decreasing rate and is asymptotic to 0.

3. Conversely, as the IV get large,Piincreases at a decreasing rate and is asymptotic to 1.

 

Term
Theory of Two-stage least Squares
Definition
Theory - Replaces each endogenous with a proxy variable which is obtained by replacing each endogenous variable that is on the right with its predicted value from the regression
The predicted value for the endogenous variable, (which is unrelated to the error term) is then substituted for Y on the right side of each equation in which it appears. The result will still be biased, and the proxy has specification error – but the estimates are now consistent – best that can be hoped for
Term
Durbin Watson Decision Rule
Definition

 

Decision rule – range because d depends not only on p but also values of the x variables.

 

·       H0: p=0

 

·       If d<dL – reject

 

·       If d > du  - do not reject

 

·       If dL < d < du   - cannot confirm or deny

 

Term
Interpretation of the parameter estimate from a Logit regression.

 

Definition

Beta is the change in the log of the odds of y occurring given a one unit change in x holding the effects of other variables constant

Term
Interpretation of the Odds Ratio from a Logit regression.
Definition

The odds of y occurring is the odds ratio multiplied by (parameter estimate) given a one unit increase in the independent variable holding the effects of the other variables contstant. Or the multiplicative increase in the odds of the dependent event occurring if the event represented by the independent variable occurs, holding the effects….

 

Term
Characteristics of the Logit model.
Definition

1. The probability of the event (Pi) is between 0 and 1 ( or 0% to 100%) and 2. S shaped curve – so as the value of the IV approaches zero, Pi decreases at a decreasing rate and is asymptotic to 0. Conversely, as the IV get large,Pi increases at a decreasing rate and is asymptotic to 1.

 

Term
Use Two-Stage Least Squares (TSLS). – used for simultaneous equations
Definition

 

Process:

 

1.      Regress the endogenous variables (right side) on all the predetermined variables of the model

 

2.      Replace them with their predicted values

 

3.      Perform OLS to the transformed version of the equation

 

Term
What are the effects of omitting a relevant variable that is uncorrelated with the included variables in an OLS regression?
Definition

1.Beta-hat is biased if there is any correlation with any other included IV.

 

2.If at all correlated, its effects are picked up by its friends.

 

3.If at all correlated the variances for the other betas will be smaller than that of the true model

 

4.The stronger the relationship btw the omitted variable and another IV, the larger the bias.

 

5.The estimate of the variance of beta-hat is always biased upwards. –what does this mean?

 

6.Still best

 

7.F and t-stats are no longer accurate

 

Term
What are the effects of inclusion of an irrelevant variable in an OLS regression?
Definition

 

1.Does not cause bias.

2.Also inflates the standard error of the estimates.

3.OLS is still BLUE.

4.We get an unbiased estimate of a generally inflated variance.

5.F and t-stats are accurate

Term
Contextual problem involving estimation of an OLS regression where the researcher discovers that he/she has left out two critical variables.
Definition

 

1.Beta-hat is biased if there is any correlation with any other included IV.

2.If at all correlated, its effects are picked up by its friends.

3.If at all correlated the variances for the other betas will be smaller than that of the true model

4.The stronger the relationship btw the omitted variable and another IV, the larger the bias.

5.The estimate of the variance of beta-hat is always biased upwards. – what does this mean?

6.Still best

7.F and t-stats are no longer accurate

 

Term
Contextual problem involving estimation of an OLS regression where the researcher discovers that he/she has left out two critical variables. Explain why a variable from the first regression becomes insignificant in the revised regression.
Definition
/Because they were on the friends and family plan and then they got divorced.  - Do more work
Term
Contextual problem involving estimation of an OLS regression where the researcher discovers thathe/she has left out two critical variables. What can you conclude about the relationship between this variable and the two critical variables that were left out of the original model.
Definition

They are correlated. Look at STB, R-sq, and p. It could be that it is not as critical in the model. I would want to do a third regression and drop the now insignificant variable and watch what happens to the R-sq and parameter estimates.

Term
For the SAS output of a Logit regression, carry out all appropriate hypothesis tests and interpret the results.
Definition

 

·  Likelihood ratio – overall significance ~F. rejection shows a sig. relation

 

·  Pseudo R-squared – interpreted the same. Cannot be used between models

 

·  Parameter estimates – change in the log of the odds of y occurring given a one unit chand in x holding the effects of all other IVs constant

 

·  Chi-square/ chi-square p-values – just like t-stat and p. report standard error

 

·  Interpretation of odds ratios – the odds that Y is occurring is multiplied by (odds ratio) given a one unit change in X holding the effect….

 

·  Concordant – 60% fair, 70% good, 80% very good, 90% exc

 

o   Pair 1s and 0s

 

·  AIC and SC – across models – lower is better

 

o   Predicted probability. Multiply parameter estimate by given values. Complete the model calculation. The result becomes the power to which e is raised. Ex/(1+ Ex)

 

Term
Logit Likelihood ratio
Definition

– overall significance ~F. rejection shows a sig. relation

 

 

Term
Logit Pseudo R-squared
Definition

 interpreted the same as OLS R-squared. Cannot be used between Logit models

 

 

Term
Logit Parameter estimates
Definition

– change in the log of the odds of y occurring given a one unit chand in x holding the effects of all other IVs constant

 

 

Term
Logit Chi-square/ chi-square p-values
Definition

Just like t-stat and p in an OLS regression. Report standard error

 

 

Term
Logit Interpretation of odds ratios
Definition

– the odds that Y is occurring is multiplied by (odds ratio) given a one unit change in X holding the effect….

 

 

Term
Concordant / discordant interpretation
Definition

– 60% fair, 70% good, 80% very good, 90% exc

 

oPair 1s and 0s

 

Term
Shortcomings of Logit
Definition

 

·Shortcomings – dependent variable is bivariate. Not used for forecasting, need more data to achieve meaningful stable results – at least greater than 100. Needs to use WLS.Interpretation is not as intuitive

 

Term
Logit AIC and SC
Definition

Compares significance of the logit regression across models – lower is better

 

Term
Logit Predicted probability process.
Definition

Multiply parameter estimate by given values. Complete the model calculation. The result becomes the power to which e is raised.

 

ex/(1+ ex)

Term
Goldfeld Quandt procedure
Definition
  1. sort data by IV in which HTS is suspected
  2. Divide data into two datasets (high and low)
  3. Remove center observations    (n/5 < c < n/4)
  4. RSS-high/RSS-low
  5. Calculate df (n-c-2k)/2
  6. Compare to critical F
  7. null hypothesis is homoscedasticity
  8. Transform variables - run again and check for HTS again
Term
After WLS write out model
Definition

Take SAS output and use the parameter estimate of the transformed variable as the intercept and the entercept as the Beta for the transformed variable

Term
Causes of HTS
Definition

 

1.     Error learning

 

2.     Increased choice

 

3.     Data measurement error

 

4.     Outliers

 

5.     Correct specification

 

6.     Skewness

 

7.     Incorrect form

 

Term
Effects of HTS on OLS
Definition

 

1.     Still unbiased

 

2.     Not best – no longer minimum variance

 

3.     Not efficient

 

4.     Affects t and F

 

5.     Affects parameter estimates

 

Supporting users have an ad free experience!