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Part IIA Economics > Cross-section Metrics > Flashcards

Cross-section Metrics Flashcards

1
Q

Sources of endogeneity

A

OVB, measurement error, reverse causality

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2
Q

Derive OVB

A

Derive on paper

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3
Q

Why adjust R^2?
And what is adjusted R^2?

A

Guaranteed to rise as we add variables: = 1-((n-1)/(n-k-1))(SSR/SST)

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4
Q

Unbiased estimate of S^2?
When uihat=Yi-b0hat-b1hatx1 etc

A

((1)/(n-betas))*sum of ui squared

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5
Q

GM Assumptions

A

Linearity / fixed or stochastic non identical regressors / exog / homeskedastic / no serial correlation / no perfect multicolinearity

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6
Q

If GM and e is normal dist?

A

(bhat - b)/(se(bhat)) ~t n-betas

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7
Q

Partialling out

A

OV to purify effect.
Reg ind on OV then reg Y on residual to get true effect!

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8
Q

Var of b1hat OLS one regressor

A

Var of error / Var(X)

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9
Q

Var of b1hat OLS with many regressors?

A

Var of error / (1-R^2 of X on other regressors)*SSTx

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10
Q

If large sample test b1=x

A

b1hat -b1 / (se b1hat) ~N(0,1) by CLT

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11
Q

F stat

A

F=((SSRr-SSRur)/(#restrictions))/(SSRur)/n-betas ~F#,n-betas

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12
Q

Linear combination test

A

t test

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13
Q

Non linear regressors / interactions

A

Test jointly (F).
Interactions: consider if compliments / substitutes!

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14
Q

Assumption of F test

A

All GM plus normal errors!

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15
Q

Law of Iterated Expectations

A

E(X)=E(E(X given Y))

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16
Q

Ramsey Reset what tests

A

Model specification. Should be add higher powers / cross terms

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17
Q

How to set up ramsey reset?

A

Reg yihat on xis and higher powers of yihat. Test (jointly coefficients on higher power yihats) F

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18
Q

Predict w if lnw=b0+b1x+b2y

A

Must remember Jensen’s inequality: Time e^(var of error/2)

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19
Q

Dummies thing to remember

A

Be precise and careful on comparison groups!

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20
Q

Chow test

A

Is model same for A and B groups? Just F test between the 2!

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21
Q

Asymptotics crucial when?

A

Not ~ N

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22
Q

Chebyshev’s inequality

A

As n to infinity, we can say confidence interval of xbar to correct value becomes very small!

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23
Q

Preservation of unbiasedness/ consistency by continuous transform?

A

Unbiasedness: no (see Jensen).
Consistency: Yes by continuous mapping theorem!

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24
Q

Slutsky’s theorem

A

If Xn converges to dist X and Yn converges in prob to C, then Xn/Yn converges in dist to X/C!

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25
Q

Use Slutsky’s on beta1hat - beta1

A

CLT on numerator and LLN on denom

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26
Q

Lagrange Multiplier test

A

nR^2 ~a~ Chi squared dof betas

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27
Q

Effect of hetero

A

inefficiency, increasing Var(b1hat ols)

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28
Q

Causes of hetero

A

Model misspecification (eg OVB/subpopulation differences/wrong functional forms)
IVs
Measurement error
Also genuine hetero!

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29
Q

Tests for Hetero

A

Goldfield Quandt (archaic)/Breusch Pagan/ White

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30
Q

GQ hetero test

A

Split sample in 2. Thus must be monotonic hetero

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31
Q

BP assumption

A

Assumes normality of errors.

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32
Q

Logit distribution?

A

e^x/(1+e^x) = 1/(e^-x+1)

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33
Q

BP type 1:

A

1: Test if variance of errors linear in one regressor (regress uihat squared on that regressor and test if coefficient =0)

34
Q

BP type 2:

A

2: test if variance of errors linear in all regressors

35
Q

BP type 3:

A

Reg uihat squared on predicted Y and test if significant

36
Q

White’s test

A

Include square and cross terms: reg uihat squared on higher powers of predicted y (F test)

37
Q

BP vs W

A

W+: Relaxes U~N. Flexible functional form so can find any form of hetero
W-: Doesn’t determine form of hetero. Loses power fast as increases #regressors.

38
Q

GLS

A

If we know form of hetero, adjust each value by sqrt of scaling to variance!

39
Q

Feasible GLS

A

GLS but when we must estimate form of hetero

40
Q

Outliers

A

Anomalous (eg not from same population).

41
Q

Random error in outcome

A

Derive on paper. No effect on estimate, but larger se

42
Q

Random error in regressor

A

Derive on paper.
Attenuation bias!

43
Q

Proxy variables difficulty

A

Eg if we use IQ as a proxy for innate ability, we must have IQ uncorrelated with all other parts of abil!

44
Q

Cov(X,Y)

A

E(XY)-E(X)E(Y)

45
Q

How to derive beta IV

A

Take Cov wrt IV on both sides and becomes very simple. By LLN, beta1hat IV converges in prob to beta1

46
Q

Wald Estimator

A

Binary IV:
Reg Y on Z and Y on X to get:
beta1hatIV=(Ybar1-Ybar0)/(Xbar1-Xbar0)

47
Q

betaIV aymptotics

A

Normal by Slutsky’s and CLT

48
Q

Weak instruments issue

A

Relevance is barely met and so se is very large

49
Q

Exog fails IV

A

Inconsistent

50
Q

2sls stages

A

1- Reg X1 on Z and other controls. (can test relevance)
2- Use X1hat as regressor for Y

51
Q

Over-ID for IV?

A

More z vs endog regressors.
Hausmann test

52
Q

Hausmann test for IV over-ID

A

Assume one IV valid. H0: beta1 same for both Zs. H1: different.
Test stat: Chi-squared with one restriction.

53
Q

What to do if weak instruments

A

Regress endog on IVs and compare to restriction of all = 0. Weak if F<10. Find better ones or drop weaker ones

54
Q

Anderson Rubin Test

A

Weak zs and want to test H0: beta1=beta1 nought.
Suppose we have lwage=beta0 + beta1educ…
Then lwage=lwage-beta1educ
Reg lwage on all else.
AR test stat is F stat for IVs and so reject if AR > Chi squared(#)/#

55
Q

Test for endog
Why
How

A

If exog, 2sls is unnecessary and inefficient vs OLS
Assume: valid instruments.
ei is residual from regressing X1 on Z
Endog: ui=gamma*ei +epsiloni. Exog:Cov(ui,ei)=0
Thus, reg y on all plus ei and t test if significant on ei!

56
Q

Reduced form simultaneous

A

Rearrange for outcome variables.
Simply regressing gives us a weighted average of the two elasticities (each curve)

57
Q

Treatment effects what do we observe

A

Assignment prob and avg outcomes, but not counterfactuals!

58
Q

Observed diff=

A

Add and subtract (E(Y(1)givenD=1)).
This gives us ‘Average effect of Treatment on Treated’ plus selection effect

59
Q

selection effect on obs diff

A

Often, whether or not treated is endogenous and so biases obs away from ATT (down if being treated is desirable)!

60
Q

Problems affecting validity

A

Contamination, non compliance, hawthorn, john henry, placebo
Internal- contamination (treated even though not in group) and non compliance (other way)
Hawthorne effect - Participants change behaviour due to being in trial
John Henry - Control group changes behaviour
Placebo- Perceived changes (not actual) change outcomes

61
Q

Conditional independence assumption

A

Assignment to treatment ind. of outcome given covariates.
If true, leads to OBS dif given Xi=x) = ATT = ATE (Avg treatment effect)

62
Q

CIA vs IV

A

CIA: Fix selection bias by zooming in on closely defined subgroups
CIA may not be practical: may need to specify v specific group!

63
Q

FD Goal

A

Goal: Destroy time invariant effects (may be correlated with obs regressors)

64
Q

FD assumptions

A

strict exog (tough often) and other GM! For blue
If also, normal errors then valid for small samples

65
Q

Arellano-Bond

A

IV for panel data when feedback from the past leads to violation of strict exogeneity! Z is xi1
Relevance: Cov(xi1,deltaxi3)=/=0
Exclusion: cov(xi1,delta epsiloni3)=0

66
Q

AB method

A

Reg delta yi3 on delta xi3 using 2sls (instrument is xi1) to estimate beta1

67
Q

Fixed effects

A

Subtract time mean from each observation.

68
Q

FE vs FD

A

T=2: identical
T>=3: Close but non identical.
FE is more efficient if no serial correlation in epsilonit.
Must be careful with FE if n is small relative to t!
FD can eliminate serial correlation if error follows a random walk

69
Q

MLE

A

Choose theta hat s.t. we max out (ln)likelhood function. Clearly, MLE depends on sample we observe!

70
Q

MLE properties

A

MLE effectively exploits all info in data for parametric estimation.
Consistent, asymptotically normal, asymptotically efficient (although generally biased)

71
Q

Asymptotic MLE to ~

A

Converges ~ to N(parameter,Inverse of Fisher information/n)
Think of I^-1(parameter) as asymptotic variance of parameter MLE

72
Q

Likelihood ratio test

A

2(logLikelihood ur − logLr) ~ Chisquared1

73
Q

Probit assumes

A

Homoskedastic required for consistency. Assumes normality of errors in latent!
P(Y=1givenX)=P(Y*>0givenX)=
1-P(ui<=-Xibeta given X)
Use Normal CDF

74
Q

Marginal effects of probit

A

Average marginal partial effect or partial effect at average
Dummy- Evaluate using CDF
Continuous- Evaluate using normal PDF = beta1*normalPDF at that point!

75
Q

To choose betas in MLE

A

Set del l / del beta = 0 for all betas! This maximizes likelihood by choosing betas

76
Q

Logit easier to work with?

A

Residuals always sum to zero (unlike probit) implying all have same weights in the FOC

77
Q

Logit marginals

A

Dummy: Just compute at =0,1
Continuous: Differentiate leads to marginal = β1Λ (Xβ) (1 − Λ(Xβ)).

78
Q

Pseudo R^2 MLE

A

1-(lur/lr)
Restricted to only one intercept!

79
Q

Goodness of Fit

A

Percentage of time that Yi is correctly predicted

80
Q

Probit/logit endogeneity

A

Use 2SLS control function method

81
Q

Control function method

A

Include both residual (exogenous variation in endog variable) and the variable to separate the endogenous and exogenous effects!

Part IIA Economics (10 decks)

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