Question 1

What does it mean for a structural equation to be unidentified?&#10;A)too many endogenous variables are included in the equation to estimate a unique parameter value&#10;B)the sample size is not large enough to rely on asymptotic estimator properties&#10;C)the simultaneous nature of the equations makes random samples impossible to obtain&#10;D)the sample size is not large enough to allow M*(M-1)degrees of freedom

Accepted Answer

An unidentified structural equation means that too many endogenous variables are included in the equation to estimate a unique parameter value. This can lead to estimation difficulties and biased results.

Question 2

What estimation technique should be used to estimated parameters in an unidentified structural equation?&#10;A)none-no techniques exist&#10;B)OLS&#10;C)2SLS&#10;D)GLS

Accepted Answer

If a structural equation is unidentified, it means that there is not enough information available to uniquely estimate the parameters of the model. Therefore, no estimation technique can be used to estimate parameters in an unidentified structural equation.

Question 3

What does 2SLS abbreviate?&#10;A)twice squared linear series&#10;B)second summed linear sample&#10;C)second order stationary logical sequence&#10;D)two stage least squares

Accepted Answer

2SLS abbreviates two stage least squares, a statistical technique used to address endogeneity or simultaneity in regression models.

Question 4

Why is it best to use specialized software to estimate 2SLS?&#10;A)specialized t-values are needed for inference and hypothesis testing&#10;B)the  $ \tau $distribution is not widely available otherwise&#10;C)it is algebraically difficult to find structural parameter estimates from reduced form estimates,so the software needs to use specialized algorithms when algebra does not work&#10;D)it is too easy to make a data handling mistake when capturing predicted values to use as regressors in the second stage

Accepted Answer

The answer of Why is it best to use specialized...

Question 5

What is the 2^nd stage of 2SLS? A)estimate parameters of reduced form equations and find predicted values B)find a random sample large enough to divide into 2 separate samples for the two stages C)estimate parameters of the structural equations using predicted values from reduced form equations D)use reduced form parameter estimates as explanatory variables

Accepted Answer

The 2^nd stage of 2SLS refers to the second stage of two-stage least squares, where the parameters of the structural equations are estimated using predicted values from the reduced form equations. Therefore, option C is the correct choice. Option A refers to the first stage, where the parameters of the reduced form equations are estimated and predicted values are calculated. Option B is not relevant to this particular stage of 2SLS, as it pertains to sample size determination. Option D is incorrect, as the reduced form parameter estimates are used as instruments and not explanatory variables in the second stage of 2SLS.

Question 6

How does the least squares estimator perform on a simultaneous equation model with an endogenous regressor?&#10;A)unbiased and consistent in large samples&#10;B)unbiased but inconsistent in all sample sizes&#10;C)biased but consistent in large samples&#10;D)biased and inconsistent for structural equations,but unbiased and consistent for reduced form equations

Accepted Answer

The least squares estimator is biased and inconsistent for structural equations due to the endogeneity of the regressor, but it can be unbiased and consistent for reduced form equations where the endogenous variables are expressed as functions of the exogenous variables only.

Question 7

What are the implications for 2SLS estimators if reduced form parameter estimates are statistically insignificant?&#10;A)still consistent in large samples,but no longer BLUE&#10;B)there will be correlation in the structural equations,causing estimators to be inconsistent&#10;C)there are no consequences,only structural parameters matter&#10;D)small sample properties no longer hold,but asymptotic properties still apply

Accepted Answer

If the reduced form parameter estimates are statistically insignificant, it means that the instruments are weak and not strongly related to the endogenous variable. As a result, there will be correlation in the structural equations, which will cause the 2SLS estimators to be inconsistent. Therefore, option B is the correct answer. Option A is not entirely correct because 2SLS estimators will no longer be consistent in small samples if reduced form parameter estimates are not statistically significant. Option C is incorrect because the structural parameters are estimated using the 2SLS estimators, which are affected by the weakness of the instruments. Finally, option D is incorrect because small sample properties are not the only issue, as even asymptotic properties will not hold if the instruments are weak.

Question 8

In a system of M simultaneous equations,at least M-1 variables must be excluded from each equation for the equation to be identified.What does it mean if the equation is not identified?&#10;A)unique coefficient estimates for each variable cannot be identified using least squares&#10;B)the economic value of the predicted value cannot be identified&#10;C)the economic relationships are unclear and the equation should be dropped form the system&#10;D)the exogenous variables have been incorrectly identified

Accepted Answer

If an equation is not identified, it means that unique coefficient estimates for each variable cannot be identified using least squares. This makes it impossible to obtain meaningful estimates of the parameters and to make reliable predictions based on the equation. Therefore, the equation cannot be used in the system and should be dropped or modified until it becomes identified.

Question 9

In a system of 4 simultaneous equations,how many endogenous variables must be excluded from an equation in the system for the parameters to be identified?&#10;A)1&#10;B)2&#10;C)3&#10;D)4

Accepted Answer

In a system of 4 simultaneous equations, 3 endogenous variables must be excluded from an equation in the system for the parameters to be identified, according to the order condition for identification. This ensures that there is enough variation in the data to estimate the parameters of the equation of interest.

Question 10

What are reduced form equations in a system of equations?&#10;A)the structural equations rewritten with endogenous variables as a function of exogenous variables&#10;B)the structural equations without the endogenous regressors&#10;C)the exogenous variables reworked as a function of the other exogenous variables&#10;D)the equations remaining when the parameters of structural equations are reduced to generate additional degrees of freedom

Accepted Answer

Reduced form equations are derived from structural equations by expressing the endogenous variables solely as functions of the exogenous variables, thereby isolating the direct effect of changes in exogenous variables on the endogenous variables.

Question 11

When estimating the structural parameters of simultaneous equation models,how do least squares estimates,compare to the true value of $\beta$?&#10;A) &#10;B) &#10;C) &#10;D)The direction of the bias depends on the sample correlation.

Accepted Answer

The answer of When estimating the structural parameters of simultaneous...

Question 12

What is the first stage of 2SLS?&#10;A)estimate parameters of reduced form equations and find predicted values&#10;B)find a random sample large enough to divide into 2 separate samples for the two stages&#10;C)estimate parameters of the structural equations using OLS&#10;D)use reduced form parameter estimates as explanatory variables

Accepted Answer

The answer of What is the first stage of 2SLS?&#10;A)estimate...

Question 13

In a multi-equation model the jointly determined variables are referred to as____________.&#10;A)exogenous&#10;B)explanatory&#10;C)regressors&#10;D)endogenous

Accepted Answer

The answer of In a multi-equation model the jointly determined...

Question 14

If a structural model has M simultaneous equations,what is the necessary condition for a unique parameter value to be consistently estimated for each variable in the equation?&#10;A)The number of endogenous variables excluded from the equation must be at least as large as M-1&#10;B)the number of endogenous variables excluded must be at least M/2&#10;C)the number of exogenous variables in the equation must be greater than the number of endogenous variables in the equation&#10;D)the sample size must be large enough to allow M * (M-1)degrees of freedom

Accepted Answer

The answer of If a structural model has M simultaneous...

Question 15

How does the least squares estimator perform on a simultaneous equation model with an endogenous regressor?&#10;A)unbiased and consistent in large samples&#10;B)biased and inconsistent in all sample sizes&#10;C)biased but consistent in large samples&#10;D)unbiased but inconsistent unless collected through random sampling

Accepted Answer

The answer of How does the least squares estimator perform...

Deck 12: Simultaneous Equations Models