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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
Use Slutsky's on beta1hat - beta1
CLT on numerator and LLN on denom
26
Lagrange Multiplier test
nR^2 ~a~ Chi squared dof betas
27
Effect of hetero
inefficiency, increasing Var(b1hat ols)
28
Causes of hetero
Model misspecification (eg OVB/subpopulation differences/wrong functional forms) IVs Measurement error Also genuine hetero!
29
Tests for Hetero
Goldfield Quandt (archaic)/Breusch Pagan/ White
30
GQ hetero test
Split sample in 2. Thus must be monotonic hetero
31
BP assumption
Assumes normality of errors.
32
Logit distribution?
e^x/(1+e^x) = 1/(e^-x+1)
33
BP type 1:
1: Test if variance of errors linear in one regressor (regress uihat squared on that regressor and test if coefficient =0)
34
BP type 2:
2: test if variance of errors linear in all regressors
35
BP type 3:
Reg uihat squared on predicted Y and test if significant
36
White's test
Include square and cross terms: reg uihat squared on higher powers of predicted y (F test)
37
BP vs W
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
GLS
If we know form of hetero, adjust each value by sqrt of scaling to variance!
39
Feasible GLS
GLS but when we must estimate form of hetero
40
Outliers
Anomalous (eg not from same population).
41
Random error in outcome
Derive on paper. No effect on estimate, but larger se
42
Random error in regressor
Derive on paper. Attenuation bias!
43
Proxy variables difficulty
Eg if we use IQ as a proxy for innate ability, we must have IQ uncorrelated with all other parts of abil!
44
Cov(X,Y)
E(XY)-E(X)E(Y)
45
How to derive beta IV
Take Cov wrt IV on both sides and becomes very simple. By LLN, beta1hat IV converges in prob to beta1
46
Wald Estimator
Binary IV: Reg Y on Z and Y on X to get: beta1hatIV=(Ybar1-Ybar0)/(Xbar1-Xbar0)
47
betaIV aymptotics
Normal by Slutsky's and CLT
48
Weak instruments issue
Relevance is barely met and so se is very large
49
Exog fails IV
Inconsistent
50
2sls stages
1- Reg X1 on Z and other controls. (can test relevance) 2- Use X1hat as regressor for Y
51
Over-ID for IV?
More z vs endog regressors. Hausmann test
52
Hausmann test for IV over-ID
Assume one IV valid. H0: beta1 same for both Zs. H1: different. Test stat: Chi-squared with one restriction.
53
What to do if weak instruments
Regress endog on IVs and compare to restriction of all = 0. Weak if F<10. Find better ones or drop weaker ones
54
Anderson Rubin Test
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
Test for endog Why How
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
Reduced form simultaneous
Rearrange for outcome variables. Simply regressing gives us a weighted average of the two elasticities (each curve)
57
Treatment effects what do we observe
Assignment prob and avg outcomes, but not counterfactuals!
58
Observed diff=
Add and subtract (E(Y(1)givenD=1)). This gives us 'Average effect of Treatment on Treated' plus selection effect
59
selection effect on obs diff
Often, whether or not treated is endogenous and so biases obs away from ATT (down if being treated is desirable)!
60
Problems affecting validity
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
Conditional independence assumption
Assignment to treatment ind. of outcome given covariates. If true, leads to OBS dif given Xi=x) = ATT = ATE (Avg treatment effect)
62
CIA vs IV
CIA: Fix selection bias by zooming in on closely defined subgroups CIA may not be practical: may need to specify v specific group!
63
FD Goal
Goal: Destroy time invariant effects (may be correlated with obs regressors)
64
FD assumptions
strict exog (tough often) and other GM! For blue If also, normal errors then valid for small samples
65
Arellano-Bond
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
AB method
Reg delta yi3 on delta xi3 using 2sls (instrument is xi1) to estimate beta1
67
Fixed effects
Subtract time mean from each observation.
68
FE vs FD
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
MLE
Choose theta hat s.t. we max out (ln)likelhood function. Clearly, MLE depends on sample we observe!
70
MLE properties
MLE effectively exploits all info in data for parametric estimation. Consistent, asymptotically normal, asymptotically efficient (although generally biased)
71
Asymptotic MLE to ~
Converges ~ to N(parameter,Inverse of Fisher information/n) Think of I^-1(parameter) as asymptotic variance of parameter MLE
72
Likelihood ratio test
2(logLikelihood ur − logLr) ~ Chisquared1
73
Probit assumes
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
Marginal effects of probit
Average marginal partial effect or partial effect at average Dummy- Evaluate using CDF Continuous- Evaluate using normal PDF = beta1*normalPDF at that point!
75
To choose betas in MLE
Set del l / del beta = 0 for all betas! This maximizes likelihood by choosing betas
76
Logit easier to work with?
Residuals always sum to zero (unlike probit) implying all have same weights in the FOC
77
Logit marginals
Dummy: Just compute at =0,1 Continuous: Differentiate leads to marginal = β1Λ (Xβ) (1 − Λ(Xβ)).
78
Pseudo R^2 MLE
1-(lur/lr) Restricted to only one intercept!
79
Goodness of Fit
Percentage of time that Yi is correctly predicted
80
Probit/logit endogeneity
Use 2SLS control function method
81
Control function method
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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