BUSN5000 - Part 2

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 The test statistic for the null hypothesis that β2=1 is ________..

(βhat2−1)/se(β2)

If treatment assignment is randomized, then TERM 2 equals ______ and TERM 1 equals the ______.

0, ATE

yi = β0 + β1xi1 + ui, i = 1, ..., N. If E(ui|xi1)=0 in (1), the sampling error of β̂ 1 converges to _____ and β̂ 1 is ______.

0, consistent

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 If you omit xi2 , β̂ 1 will be unbiased only if β2= ______ or xi1 and xi2 are ______.

0, uncorrelated

The parameter δ represents the _____ (refer to hw 9).

ATT

The ______ captures how the population average of one random variable varies with the values of another random variable.

CEF

In a sharp RD design, the _____ holds automatically because treatment assignment is determined solely by the _____ value of the _____ variable.

CIA, cutoff, running

Suppose yi=β0+β1xi1+β2xi2+β3xi3+β4xi4+ui. To test the null that β3=β4=0, you use an ______ test, which compares the fit of a short regression that ______ x3 and x4 with the fit of a long regression that ______ them.

F, omits, includes

yi = β0 + β1xi1 + ui, i = 1, ..., N. The ______ theorem says you can control for other explanatory variables in estimating the effect of an x on y by either including the other variables directly or regressing y on the ______ from a regression of x on the other variables.

FWL, residual

Under the assumptions of a sharp RD design, you identify an average treatment effect on the untreated. average treatment effect measured at the cutoff. intent to treat effect. average treatment effect on the treated.

average treatment effect measured at the cutoff.

The parameter η reflects the average difference in outcomes _____ and _____ treatment for the _____ group (refer to hw 9).

before, after, untreated

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 Let's say you don't omit xi2, but it is measured with error. Then β̂ 2 will be ______ . (unbiased/ biased down/ biased up)

biased down

The basis for an RD analysis should be apparent in a _____ scatter plot of the outcome and _____ variable.

binned, running

Basic OLS inference is grounded in the application of the _____, which says that the ______ of the OLS estimator can be regarded as approximately _____ for large samples.

central limit theorem, sampling distribution, normal

yi = β0 + β1xi1 + ui, i = 1, ..., N. The coefficient β1 measures the _____ in y _____ with a _____ in x1, holding all of the unobservables constant.

change, associated, unit change

Computing the correct standard errors for TWFE estimates usually requires _____ at the group level to account for _____ and _____ correlation.

clustering, heteroscedasticity, serial

In the DAG, Z is a _____.

confounder

You can't observe the effect of a treatment on an individual because you can't observe the ______ outcome. In this sense, causal inference is a ______ data problem.

counterfactual, missing

The parameter η also reflects the _____ average difference in outcomes between periods 0 and 1 for the _____ (refer to hw 9).

counterfactual, treated

An RD analysis of baseline _____ should show no evidence of _____ among them.

covariates, discontinuities

Including the baseline _____ in the regression model (should/should not) _____ affect the estimated treatment effect.

covariates, should not

In a fuzzy RD design, the _____ value of the _____ variable determines the _____ of treatment.

cutoff, running, probability

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 R^2 measures how much of the variance of the ______ variable is accounted for by the ______ variables.

dependent, explanatory

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 If xi1 is education and xi2 is labor market experience, and you omit xi2from (2), then β̂ 1 will be biased ______ because β2 is _____ and cov(xi1,xi2) are _____ correlated.

downward, positive, negatively

The test statistic for whether a explanatory variable has a statistically significant association with the dependent variable is the ratio of explanatory variable's ______ to its _____.

estimator, standard error

A regression formulation of a DD design is appealing because it

facilitates standard error estimation, generalizes for multiple time periods and treatment groups, accommodates covariates

True or false. If corr(x,y)=0, y does not depend on x.

false

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 True or false: R^2 is centrally important for doing causal inference.

false

If we say E(y|x)=β1+β1x, where β0and β1solve the population least-squares problem, then the CEF is the population regression _____ and β0 and β1 are population regression _____.

function, coefficients

The standard 2×2 DD analysis can be carried out by regressing the outcome on a _____ dummy, a period _____, and their _____.

group, dummy, interaction

We described a TWFE model as a regression model for data with both a _____ and _____ dimension.

group, time

The R function lm gives the wrong standard errors, test statistics and confidence intervals because it ignores ______.

heteroscedasticity

The modern approach to regression inference is to allow for the variance of the regression errors to allow for _____, which implies the variance of the errors depends on the ______.

heteroscedasticity, explanatory variables

Estimating a TWFE model with data on multiple groups and variation in treatment timing can identify the ATT if the treatment effect is _____ .

homogenous

The conditional independence assumption (CIA) is a claim that there is a set of covariates that once you control for them, you can consider the potential outcomes to be ______ of treatment assignment. The CIA is a claim of un______ and is un______.

independent, confoundedness, testable

However, if the potential outcomes are ______ of treatment assignment, the assignment mechanism is ______ and the difference in sample average outcomes for treated and untreated individuals will identify the ATE.

independent, ignorable

Potential outcomes will be ______ of treatment assignment if individuals are ______ assigned to treated and untreated groups.

independent, randomly

Using the difference in sample average outcomes for treated and untreated individuals generally won't work for estimating the ATE because potential outcomes are not ______ of treatment assignment, which results in ______ bias.

independent, selection

The population regression function provides the best ______ to the CEF.

linear approximation

The population regression function provides the best _____ of the dependent variable, given the explanatory variables

linear predictor

yi = β0 + β1xi1 + ui, i = 1, ..., N. If E(ui|xi1)=0 in (1), xi1 is _____ of ui and the sampling error of β̂ 1 equals ______ on average, which implies that β̂ 1 is ______.

mean independent, zero, unbiased

yi = β0 + β1xi1 + ui, i = 1, ..., N. If β0 and β1 solve the population least-squares problem their values ______ the expected value of the _____ difference between the dependent variable and the CEF.

minimize, squared

The distribution of the running variable should show

no evidence of manipulation because it is smooth through the cutoff.

Unlike in standard regression analysis, however, there is no _____ in a sharp RD design, because individuals with different values of D have different values of the covariate by construction.

overlap

If η varied by group, the _____ assumption would not hold (refer to hw 9).

parallel trends

The key identifying assumption in a DD analysis is that the treated and untreated outcomes would follow _____ trends in the _____ of the treatment.

parallel, abscence

yi = β0 + β1xi1 + ui, i = 1, ..., N. When the PRF includes more than one x, we say that β1 measures the _____ effect of x1 (without necessary giving a causal interpretation).

partial

In general, the RD specification should include a low-order _____ in the running variable and _____ of the running variable with the treatment indicator.

polynomial, interactions

While individual treatment effects are not observable, you may be able to identify the average treatment effect (ATE), which is the difference in average ______ outcomes.

potential

The key identifying assumption of an RD design is that the average _____ outcomes are _____ through the cutoff.

potential, continuous

If you have a set of control variables for which a CIA holds, you can identify the average effect of the treatment on the outcome using a ______ of the outcome on a ______ dummy and ______ .

regression, treatment, control variables

As an alternative to the procedure sketched out in the previous question, by the Frisch-Waugh-Lovell theorem, you could simply run a regression of the outcome on the ______ from a regression of the treatment indicator on the controls.

residuals

The modern approach means we should always report _____ standard errors and test statistics.

robust

yi = β0 + β1xi1 + ui, i = 1, ..., N. If there were more than one x in (1), then the formula for β1 would be the _____, except xi1 would be replaced with the _____ from a regression of xi1 on the other xs.

same, residuals

yi = β0 + β1xi1 + ui, i = 1, ..., N. The OLS estimator for β1 can be obtained by plugging in the _____ of xi and yi for their ______ and plugging in another _____ for each outer expectation.

sample averages, population averages, sample average

A simple comparison of treated vs control observations after treatment misses factors that cause non-random _____ into treatment.

selection

TERM 2 in (1) is selection bias the average treatment effect on the treated the average treatment effect on the untreated the average treatment effect

selection bias

Larger ______ statistics and smaller ______ values indicate ______ evidence against the null hypothesis.

t, p, greater

refer to hw 7: TERM 1 in (1) is the average treatment effect the average treatment effect on the untreated selection bias the average treatment effect on the treated

the average treatment effect on the treated

A DD analysis targets the average treatment effect on the _____ or E(y1i−y0i|Di=_____).

treated, 1

The standard 2×2 DD analysis compares the difference in average outcomes for the _____ observations _____ and _____ treatment with the difference in mean outcomes for the controls _____ and _____ treatment.

treated, before, after, before, after

The parameter γ reflects the average difference between _____ and _____ outcomes (refer to hw 9)

treated, untreated

To estimate the ATE under a CIA, you also need overlap, which is the ability to observe ______ and ______ units for any set of covariate values.

treated, untreated

A simple before vs after comparison of treated observations misses _____ that are shared by the control group.

trends

True or false. If x causes y, the conditional distribution of y given x must depend on x.

true

The target estimand cannot be estimated directly because E(y0i|Di=1) is _____.

unobserved

yi = β0 + β1xi1 + β2xi2 + ui, i = 1, ..., N where E(ui | xi1, xi2) = 0 If you omit xi2 , β̂ 1 will be biased ______ if β2 and cov(xi1,xi2) have the same ______.

upward, sign

A formal expression of the DD regression consistent with Table 2 is:

y=μ+γtreat+ηafter+δtreat⋅after+u

yi = β0 + β1xi1 + ui, i = 1, ..., N. The value of β1 that solves the population least-squares problem is:

β1=cov(xi1yi)/E(xi1^2)