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Research Methods and Introductory Econometrics > Equations and Key Interpretations > Flashcards

Equations and Key Interpretations Flashcards

1
Q

Formula for the maximum or minimum point in a regression.

A

[beta 0 / (2*beta1]

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2
Q

What are the Gauss-Markov Assumptions?

A
  1. population model is linear, with additive error term.
  2. random sampling
  3. some sample variation
  4. the error term has a mean of 0 and shows no systematic pattern. ZCM
  5. Homoskadisiticy: same variance across all values of the IV.
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3
Q

Formula for SST

A

.

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4
Q

Formula for SSE

A

.

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5
Q

Formula for SSR

A

.

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6
Q

What is Perfect Collinearity?

A

When there is a exact relationship between two linear variables.

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7
Q

What is the Normality Assumption?

A

The population error u is independent of the explanatory variables and is normally distributed with zero mean and variance.

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8
Q

Finding critical values in the t table what is the difference between for one tailed and two tailed tests.

A

One tailed use exact value.

Two tailed use half of the percentage you want to. Example 0.025 for 5% significance.

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9
Q

If the P value is very low this means there is…

A

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.

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10
Q

What is the df for an F test and what does each component mean?

A

(q, n-k-1)

q = number of exclusion restrictions.
n = observations
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11
Q

Which equation is the restricted regression in an F test?

A

The smaller equation

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12
Q

Finding critical values in the F table what is the difference between for one tailed and two tailed tests.

A

Halved for a two tailed test.

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13
Q

The effect of multiplying y by a constant c on a regression.

A

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.

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14
Q

The effect of dividing / multiplying x1 by a constant c on a regression.

A

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.

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15
Q

Log-Log elasticity equation

A

beta 1

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16
Q

Log-Level elasticity equation

A

beta-hat * x-bar

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17
Q

Level-Log elasticity equation

A

beta-hat * (1/y-bar)

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18
Q

Level-Level elasticity equation

A

beta 1 x (x-bar / y-bar)

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19
Q

Level-Level interpretation

A

A 1 unit change in x will result in a beta unit change in y.

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20
Q

Level-Log interpretation

A

A 1 percentage change in x will result in a (beta/100) unit change in y.

21
Q

Log-Level interpretation

A

A 1 unit change in x will result in a (100 * beta) percentage change in y.

22
Q

Log-Log interpretation

A

A 1 percentage change in x leads to a beta percentage change in y.

23
Q

Interpretation of models with quadratics.

A

change in y-hat = (beta-hat 1 + 2beta-hatx) change in x

24
Q

What is the dummy variable trap and what is the solution?

A

Perfect collinear relationship

One of the collinear dummies needs to be omitted.

25
Q

Direction of omitted variable bias.

A

Relationship between omitted variable and other explanatory.

Relationship between omitted x and y

26
Q

What are the consequences of omitted variable bias?

A

OLS estimator is bias and inconsistent.
The standard errors,
t-tests and F-test are also invalid

27
Q

Draw the SSE, SST, SSR graph

A

.

28
Q

The effect of omitted variable bias on the R squared.

A

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.

29
Q

What are the effects of including irrelevant variables?

A

Unbiased but inefficient coefficients.

Valid standard errors.

30
Q

Effects of including a proxy varible.

A

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.

31
Q

What is homoskedasticty and write out mathematical condition?

A

The variance of the disturbance term (u) is constant.

32
Q

What is heteroskadicity and write out mathematical condition?

A

The variance of the disturbance term (u) is not constant in every observation.

33
Q

What are the causes of heteroskadicity?

A

Size issues, big x disturbance term is bigger.

When using aggregated data, industry or country data.

Incorrectly specifying the functional form.

34
Q

What are the consequences of heteroskedasticity?

A

Does not bias estimators.

Estimates are inefficient.

Standard errors estimated wrongly.

Any t and f tests are invalid.

35
Q

When do you reject the null hypothesis using the Goldfeld Quandt Test.

A

If the F value is larger than the critical.

36
Q

Breusch Pagen test statistic equation and what is the df.

A

nR(squared)

df: number of explanatory variables.

37
Q

What is auto correlation and write out the mathematical assumption?

A

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.

38
Q

What is auto correlation AR(1)

A

First order auto correlation.

ut = pUt-1 + et

39
Q

What causes auto correlation?

A

Omission of lagged variables that should be in the equation.

40
Q

What are the consequences of auto correlation?

A

Does not bias estimated coefficients.

Estimates will be inefficient.

SE will be estimated wrongly, AR(1) underestimated.

T test and F test invalid.

41
Q

If the d value is larger than 2 what do you do?

A

4 - dl

4 - du

42
Q

What test do you use for auto correlation with lagged dependent variables?

A

Durbins h test

43
Q

In Durbins h test what is p equal to?

A

p-hat = 1 - 0.5d

44
Q

What is the degrees of freedom for the common factor test?

A

Number of explanatory variables in the original model

45
Q

Interpretation of Common Factor Test of AR(1) restrictions.

A

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.

46
Q

What is another name for omitted variable bias?

A

Uncontrolled endogeneity or endogeneity

47
Q

What is the Zero Conditional Mean assumption and lay it out mathematically?

A

E(U|X) = 0

U and X are independently distributed

X does not provide information on expected value of U.

48
Q

When do you use proxy variables and when do you use instrumental variables?

A

Proxy: for missing variable(s).

Instrumental:
Have an endogenous explanatory variable whose value is determined by other variables.

Research Methods and Introductory Econometrics (1 decks)

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