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Econometrics (382) > Final COPY > Flashcards

Final COPY Flashcards

1
Q

What is the stochastic error term?

A

A term added to the regression equation to account for any variation in Y that is not explained by X

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2
Q

What does TSS equal?

A

ESS+SSR

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3
Q

What is the SE?

A

Sq.Rt. of RSS/{(n-k-1) ∑(Xi-Xbar)2}

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4
Q

What are the four assumptions of the error term?

A
  1. The variation does not change as X changes 2. Its distribution is normal 3. Conditional mean=0 4. Independent for any two observations (i,j)
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5
Q

What can cause stochastic error?

A
  1. OVB 2. Measurement error 3. A misspecified function 4. Random occurrences
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6
Q

When are dummy variables useful?

A

When we want to quantify something that is inherently qualitative (race, gender, etc.)

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7
Q

What is Ŷ?

A

An estimated value of Y calculated from the regression at the i-th observation

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8
Q

What is a residual?

A

The difference between the estimated and actual values of the dependent variable

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9
Q

What changes between observations?

A

The values of Y, Xs, and error terms (but not the coefficients)

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10
Q

While adding a variable may not change TSS…

A

It will likely reduce SSR and, thus likely increase R-squared

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11
Q

OLS seeks to minimize….

A

The sum of squared residuals (or SSE)

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12
Q

K = ?

A

The # of independent variables

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13
Q

Why is a high degree of freedom desired?

A

It is likely that the errors will balance out

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14
Q

Yi - Ŷ is….

A

The residual (prediction mistake)

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15
Q

What are the three properties of estimators?

A
  1. Unbiasedness: The estimator is correct (on avg.) 2. Consistency: As observations increase, so does the probability that the estimator is close to the pop. parameter Efficiency: Estimator has smaller relative variance (converges to the pop. parameter more quickly)
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16
Q

How do we adjust for degrees of freedom?

A

Divide by (n-1)

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17
Q

What does ß0 equal? (Univariate)

A

Ybar - ß1(Xbar)

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18
Q

What does ß1 equal? (Univariate)

A

∑(Yi-Ybar)(Xi-Xbar)/∑(Xi-Xbar)2

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19
Q

What is the formula for sample variance?

A

1/(n-1) ∑(Xi-Xbar)2

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20
Q

What is the formula for sample covariance?

A

1/(n-1) ∑(Xi-Xbar)(Yi-Ybar)

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21
Q

What are the 7 OLS assumptions?

A
  1. The population regression function (DGP) is linear in parameters 2. Observations are randomly drawn from the population and i.i.d 3. X[vector] is fixed in repeated samples (no measurement error) 4. The error term has a conditional mean of 0 5. Homoskedasticity 6. Errors are independent (for every i, j) 7. Outliers are unlikely
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22
Q

If you specify a dummy variable for each possible outcome…..

A

You will induce perfect multicollinearity (nothing to compare dummy to)

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23
Q

If the omitted variable is correlated with a regressor and it has an effect on the dependent variable….

A

We have OVB

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24
Q

If the effect of the OV on Y and the correlation between OV and regressor are moving in the same direction…

A

Your estimator is too big

25
Q

How do you know if you have OVB?

A
  1. Use economic theory/knowledge of the subject 2. Run a robustness check
26
Q

What is ESS?

A

Sum of the squared differences between predicted values and the mean

27
Q

What is TSS?

A

Sum of the squared differences between actual values and the mean

28
Q

What is R2?

A

The % of variation in Y explained by the model

29
Q

What are the formulas for R2?

A
  1. ESS/TSS 2. 1 - SSR/TSS
30
Q

What is the formula for the adj. R2?

A
  1. 1 - [(n-1)/(n-k-1)] x SSR/TSS
31
Q

What is RMSE?

A
  1. Another goodness of fit measurement 2. Sqrt of SSR/(n-k-1)
32
Q

What happens if we have perfect multicollinearity?

A

OLS is impossible

33
Q

Why is perfect (or high) multicollinearity an issue?

A

A high degree of multicolinearity may be problematic because it inflates the variance of the estimator

34
Q

What can we use to quantify the severity of multicollinearity in our model?

A

We use the variance inflation factor (VIF)

35
Q

What is the VIF(ß1 hat?)

A

1/(1-R2)

36
Q

Formula for t-test?

A

(ß1 hat)-(H0: ß1) / SE(ß1 hat) p = 2(cdf)(-l t l)

37
Q

What is the extensive formula for R2?

A

(ß1) ∑(Xi-Xbar)(Yi-Ybar)/∑(Yi-Ybar)2

38
Q

What is the extensive formula for ESS?

A

(ß1)2 ∑(Xi-Xbar)2

39
Q

How do you standardize a normal distribution?

A

Subtract the mean and divide by sigma

40
Q

For a hypothesis test, what is the significance level and confidence level?

A

Significance = p Confidence = 1-p

41
Q

What must “t” be greater than equal to for: 1. 90% confidence 2. 95% confidence 3. 99% confidence

A

1) 1.645 2) 1.96 3) 2.58 ^^ For two-tailed tests

42
Q

If our causal effect depends on the level of another independent variable, what do we do?

A

Take the natural log of the variable

43
Q

If our causal effect depends on another variable (but not the level) what do we do?

A

Use an interaction terms

44
Q

What assumption do we make about the causal effect if we use a natural log?

A

That it is always positive or negative

45
Q

What are the advantages of using a non-linear specification other than a log?

A

No assumptions about direction, allows for inflection points, and increasing/decreasing rates

46
Q

What property about our OLS estimator is violated if we have homoskedasticity?

A

Efficiency

47
Q

What type of GLS do we use when the form of heteroskedasticity is unknown?

A

Feasible GLS

48
Q

How do we run feasible GLS?

A
  1. Estimate w/ OLS and calculate residuals 2. Run OLS w/ squared residuals on variance 3. Use predicted values from that to create weight (1/sq.rt(predicted values))
49
Q

What is iteratively re-weighted least squares?

A

Feasible GLS repeated until weights converge to a value

50
Q

Which hypothesis test do we use for the following situations?: 1. Single parameter (one restriction) 2. Multiple parameter (linear combination) 3. Multiple parameter (non-linear combination) 4. Multiple parameter (multiple restrictions)

A
  1. t-test (of one variable) 2. lincom (or t-test comparing two variables) 3. t-test/Taylor approximation (if one restriction) 4. F-test
51
Q

What is the formula for an F-test?

A

(SSRr - SSRu/r) ÷ (SSRu/n-k-1)

52
Q

What do you need to look at after running an F-test to determine if it is statistically significant?

A

The Chi-square critical values

53
Q

What is the advantage of BIC over AIC?

A

BIC gives you consistent estimates

54
Q

What should you do if you are asked about an effect? A change?

A

Effect = derivative Change = difference

55
Q

What do you do if asked which level of x has a max effect on y?

A

Take the derivative and solve for x

56
Q

What do you do if asked about the effect of x on y for a person w/ z years of x?

A

Plug z into x and solve **(Final answer * Ɛ)

57
Q

What do you do if asked about the difference in y due to a difference in x?

A

Plug in given values and take the difference

58
Q

What do you do if asked about the difference in the effect of x on y? (Someone w/ 10 years vs. someone w/ 20)

A

Take the derivative, plug in the numbers and take the difference

59
Q
A

Econometrics (382) (2 decks)

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