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The main advantage of using panel data over cross sectional data is that it

allows you to control for some types of omitted variables without actually observing them.

The difference between an unbalanced and balanced panel is that

an unbalanced panel contains missing observations for at least one time period or one entity.

the "before and after" specification, binary variable specification, and "entity-demeaned" specification produce identical OLS estimate

as long as T=2 and the intercept is excluded from the "Before and after" specification.

In the panel regression anlysis of beer taxes on traffic deaths, the estimation period is 1982088 for the 48 contiguous US states. You are using a binary variable specification and you want to test the significance of entity fixed effects. Then, you should calculuate the F statistic and compare it to the critical value from your F1, infinity distriubtion, where q equals

47.

Time fixed effects regression are useful in dealing with omitted variables

if these omitted variables are constant across entities but not over time.

Failure to follow the treatment protocol means that

instrumental variables estimation of the treatment effect should be used where the initial random is the instrument for the treatment actually received.

Conditional randomization

is a randomization in which the probability of assignment to the treatment group depends on one or more observable variables W.

having more relevant instruments

is like having a larger sample size in that the more information is availalbe for use in the IV regressions

The distinction between endogenous and exogenous variables

is whether or not the variables are correlated with the error term.

The following estimation methods should not be used to test for randomization and when Xi, is binary:

linear probability model (OLS) with homoskedasticity-only standard errors.

In the context of a controlled experiment, consider the simple linear regression formulation Yi=Bo+BiXi+Ui. let the Yi be the outcome, Xi the treatment level when the treatment is binary, and ui contain all the addtional determinants of the outcome. Then calling B1 a difference estimator

makes sense since it is the difference between the sample average outcome of the treat group and the sample average outcome of the control group.

Consider the special panel data case where T=2. If some of the omitted variables, which you hope to capture in the changes analysis, in fact change over time, then the estimator on the included change regressor

may still be unbiased

The following are reasons for studying randomized controlled experiments in an econometrics course, with the exception of

randomized controlled experiments in economics are common.

In a quasi-experiment

randomness is introduced by variations in individual circumstances that make it appear as if the treatment is randomly assigned.

Weak instruments are a problem because

the TSLS estimator may not be normally distributed, even in large samples.

The interpretation of the coefficients in a distributed lag regression as causal dynamic effects hinges on

the assumption that X is exogenous.

The Hawthorne effect refers to

the phenomenon that subjects in an experiment can change their behavior merely by being experiment.

The major flaw of the linear probability model is that

the predicted values can lie above 1 and below 0.

When estimating probit and logit models,

the t-statistic should still be used for testing a single restriction.

If the fifth assumption in the Fixed Effects regression (cov(uit,uis| Xit,Xis)=0 for t =/= s) is violated, then

you can use the simple homoskedasticity-only standard errors calculated in your regression package.

If you included binary variables to represent both time and entity fixed effects in the regression model which includes a constant, then

you must exclude one of the entity binary variables and one of the time binary variables to be ables to estimate the regression.

To test for randomization when Xi is binary

you regress Xi, on all W's and compute the F-statistic for testing that all the coefficients on the W's are zero. (The W's measure characteristics of individuals, and these are not affected by the treatment.)

consider the regression exaple from your textbook, which estimates the effect of beer taxes on fatality rates across 48 contiguous US states. If beer taxes were set nationally by the federal government rather than by the states, then

you should not use time fixed effects since beer taxes are the same at a point in time across states.

In the context of a controlled experiment, consider the simple linear regression formulation Y

Xi and ui will be independently distributed if the Xi are randomly assigned.

The following does not represent a threat to internal validity of randomized controlled experiments

a large sample size.

Assume that for the T=2 time periods case, you have estimated a simple regression in changes and found a statistically significant positive intercept. This implies

a positive mean change over time in the LHS variable in the absence of a change in the RHS variable.


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