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Econometrics > Estimation > Flashcards

Estimation Flashcards

1
Q

What is y?

A

Dependent variable

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2
Q

What is Bo?

A

Intercept/constant coefficient

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3
Q

What are B1-Bk?

A

Slope coefficients

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4
Q

What are X1-Xk?

A

Explanatory/independent variables

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5
Q

What is u?

A

Error term

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6
Q

What is the definition of the causal effect of x on y (under notion of ceteris paribus)?

A

How y changes if variable x changes, when all other relevant factors are held constant

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7
Q

What does linearity imply about effect of x on y?

A

Implies a one unit change in x always the same effect on y
- y increases by same value with each 1 unit change in x

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8
Q

What assumptions must hold to ensure the estimators are unbiased in the simple regression model?

A
  • model is linear in parameters
  • data is from a random sample
  • there must be some variation in our explanatory variable
  • no perfect Collinearity between explanatory variables
  • there should be no statistical relationship between the error term and regressor (Zero conditional mean assumption)
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9
Q

What is E(U)?

A

Zero

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10
Q

What is the zero conditional mean assumption?

A

E(U/X1,X2,……,Xk = 0
- explanatory variables must not contain info about the mean of the unobserved factors

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11
Q

What is the aim of the line/plane of best fit?

A

We want the residuals to be as small as possible

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12
Q

What does the estimated error term equal?

A

Estimated u = true value of y - estimated y

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13
Q

What are the algebraic properties of OLS?

A
  • Sum of residuals = 0
  • sample covariance between regressors and OLS residuals is zero
  • sample averages of y and regressors lie on regression line
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14
Q

What is SST?

A

Total sum of squares
- represents total variation in dependent variable

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15
Q

What is SSE?

A

Explained sum of squares
- represents variation explained by regression

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16
Q

What is SSR?

A

Residual sum of squares
- represents variation not explained by regression

17
Q

What is SST equal to?

A

SST = SSE + SSR

18
Q

What is R-squared?

A
  • measures the proportion of the sample variation in y that is explained by the regression model/explanatory variables
19
Q

What does R-squared equal?

A

R-squared = SSE/SST = 1 - SSR/SST

20
Q

What is the definition of an unbiased estimator?

A

The expected value of the estimated coefficient = true population value

21
Q

What assumptions must hold on MLR model so that OLS estimators are unbiased?

A

MLR.1- Linear in parameters
MLR.2- Random Sampling
MLR.3- No Perfect Collinearity
MLR.4-Zero conditional mean

22
Q

Describe MLR.1?

A
  • Linear in parameters
  • model must be correctly specified
  • error term is additive
23
Q

Describe MLR.2

A
  • Random Sampling
  • observations in the sample are randomly selected from the population
24
Q

Describe MLR.3

A
  • No Perfect Collinearity
  • must be variation on all of the independent variables
  • there are no exact relationships among the independent variables
25
Q

Describe MLR.4

A

-Zero conditional mean
- value of the explanatory variables must contain no info about the mean of the unobserved factors

26
Q

What is meant by an endogenous explanatory variable?

A
  • an explanatory variable that is correlated with the error term
  • endogeneity is a violation of MLR.4
27
Q

What is meant by an exogenous explanatory variable?

A
  • explanatory variable is uncorrelated with error term
  • if all explanatory variables are exogenous MLR.4 holds
28
Q

What is simultaneity?

A

When causality doesn’t just run from the regressors to the regressand but also in the other direction

29
Q

Interpret unbiasedness

A

It is an average property in repeated samples.
- on average the estimated coefficient will equal the true value

30
Q

What is omitted variable bias?(OVB)

A
  • occurs when one or more explanatory variables are correlated with a relevant omitted variable subsumed in the error term)
  • results in biased estimated coefficients
  • more generally, in MLR if omitted variable is correlated with only one explanatory variable all estimates coefficients are likely to be biased
31
Q

What is MLR.5?

A

Homescedasticity
- the value of the explanatory variables must contain no info about the variance of the unobserved factors

32
Q

What is the effect of a high error variance on the sampling variance?

A
  • High error variance leads to an increase in sampling variance.
  • As a result a large error variance makes estimates more imprecise.
  • error variance does not decrease with sample size
33
Q

What is the effect of a higher sample variation in the explanatory variable on the OLS estimates?

A
  • More sample variation leads to more precise estimates
  • total sample variation increases with sample size
34
Q

Effect of a high Rj-Squared.

A

High Rj-Squared means there is a strong correlation between explanatory variable Xj and the other explanatory variables
- higher Rj-Squared increases variance of estimate Bj
- problem of almost linearly dependent explanatory variables is called multi Collinearity
- Occurs as Rj approaches 1

35
Q

Is multi Collinearity a violation of our assumptions?

A
  • does not violate any of our assumptions
  • but troublesome
36
Q

How can we lessen effect of multi Collinearity?

A

Increase sample size

37
Q

What is Gauss-Markov theorem?

A

Under assumptions MLR.1-MLR.5 Bo, B1……. Are the Best Linear Unbiased Estimators (BLUE) of the true population values

38
Q

How to tell if a regression suffers from multi Collinearity.

A
  • VIF > 10 indicates m/c in regression
  • t-tests reject the individual significance of several coefficients but overall R-Squared of regression is still high
  • Estimates are imprecise
  • Estimates will be sensitive to changes in specification of the model

Econometrics (7 decks)

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