Equations and Key Interpretations Flashcards
Formula for the maximum or minimum point in a regression.
[beta 0 / (2*beta1]
What are the Gauss-Markov Assumptions?
- population model is linear, with additive error term.
- random sampling
- some sample variation
- the error term has a mean of 0 and shows no systematic pattern. ZCM
- Homoskadisiticy: same variance across all values of the IV.
Formula for SST
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Formula for SSE
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Formula for SSR
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What is Perfect Collinearity?
When there is a exact relationship between two linear variables.
What is the Normality Assumption?
The population error u is independent of the explanatory variables and is normally distributed with zero mean and variance.
Finding critical values in the t table what is the difference between for one tailed and two tailed tests.
One tailed use exact value.
Two tailed use half of the percentage you want to. Example 0.025 for 5% significance.
If the P value is very low this means there is…
Evidence against the null.
STATA generates p for a two sided test, for a one sided test divide the two sided p value by 2.
What is the df for an F test and what does each component mean?
(q, n-k-1)
q = number of exclusion restrictions. n = observations
Which equation is the restricted regression in an F test?
The smaller equation
Finding critical values in the F table what is the difference between for one tailed and two tailed tests.
Halved for a two tailed test.
The effect of multiplying y by a constant c on a regression.
y-hat = beta-hat(0) + beta-hat(1)x
cy-hat = cbeta-hat(0) + cbeta-hat(1)x
SE are also multiplied by c, test unchanged.
The effect of dividing / multiplying x1 by a constant c on a regression.
If you divide (multiply) the independent
variable x1 by a constant c and rerun the regression, the
estimated slope coefficient on x1 will be multiplied (divided) by c.
Log-Log elasticity equation
beta 1
Log-Level elasticity equation
beta-hat * x-bar
Level-Log elasticity equation
beta-hat * (1/y-bar)
Level-Level elasticity equation
beta 1 x (x-bar / y-bar)
Level-Level interpretation
A 1 unit change in x will result in a beta unit change in y.
Level-Log interpretation
A 1 percentage change in x will result in a (beta/100) unit change in y.
Log-Level interpretation
A 1 unit change in x will result in a (100 * beta) percentage change in y.
Log-Log interpretation
A 1 percentage change in x leads to a beta percentage change in y.
Interpretation of models with quadratics.
change in y-hat = (beta-hat 1 + 2beta-hatx) change in x
What is the dummy variable trap and what is the solution?
Perfect collinear relationship
One of the collinear dummies needs to be omitted.
Direction of omitted variable bias.
Relationship between omitted variable and other explanatory.
Relationship between omitted x and y
What are the consequences of omitted variable bias?
OLS estimator is bias and inconsistent.
The standard errors,
t-tests and F-test are also invalid
Draw the SSE, SST, SSR graph
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The effect of omitted variable bias on the R squared.
Does the omitted variable bias go in the opposite or same direction as the true effect of the included variable.
Bias in same direction as true effect: R2 biased upwards.
Bias in opposite direction to true effect: R2 biased downwards.
What are the effects of including irrelevant variables?
Unbiased but inefficient coefficients.
Valid standard errors.
Effects of including a proxy varible.
SE and t stat be the same.
R squared the same.
Not possible to obtain an estimate of beta 2.
Not be able to obtain beta 0.
What is homoskedasticty and write out mathematical condition?
The variance of the disturbance term (u) is constant.
What is heteroskadicity and write out mathematical condition?
The variance of the disturbance term (u) is not constant in every observation.
What are the causes of heteroskadicity?
Size issues, big x disturbance term is bigger.
When using aggregated data, industry or country data.
Incorrectly specifying the functional form.
What are the consequences of heteroskedasticity?
Does not bias estimators.
Estimates are inefficient.
Standard errors estimated wrongly.
Any t and f tests are invalid.
When do you reject the null hypothesis using the Goldfeld Quandt Test.
If the F value is larger than the critical.
Breusch Pagen test statistic equation and what is the df.
nR(squared)
df: number of explanatory variables.
What is auto correlation and write out the mathematical assumption?
Autocorrelation is when the disturbance term in each observation is correlated with the distrubance term in other observations.
cov(ui, uj) = 0 not auto correlation.
What is auto correlation AR(1)
First order auto correlation.
ut = pUt-1 + et
What causes auto correlation?
Omission of lagged variables that should be in the equation.
What are the consequences of auto correlation?
Does not bias estimated coefficients.
Estimates will be inefficient.
SE will be estimated wrongly, AR(1) underestimated.
T test and F test invalid.
If the d value is larger than 2 what do you do?
4 - dl
4 - du
What test do you use for auto correlation with lagged dependent variables?
Durbins h test
In Durbins h test what is p equal to?
p-hat = 1 - 0.5d
What is the degrees of freedom for the common factor test?
Number of explanatory variables in the original model
Interpretation of Common Factor Test of AR(1) restrictions.
If fail to reject null, restriction are valid.
If reject the null, restrictions not valid. Reject the AR(1) specification in favour of unrestricted version.
Caused by lagged variables.
What is another name for omitted variable bias?
Uncontrolled endogeneity or endogeneity
What is the Zero Conditional Mean assumption and lay it out mathematically?
E(U|X) = 0
U and X are independently distributed
X does not provide information on expected value of U.
When do you use proxy variables and when do you use instrumental variables?
Proxy: for missing variable(s).
Instrumental:
Have an endogenous explanatory variable whose value is determined by other variables.
