Chapter 16
1. In econometrics, simultaneity arises when:
a. strictly exogenous explanatory variables determine the dependent variable through a step-by-step
process.
b. the error term is correlated with both the dependent variable and explanatory variables.
c. one or more of the explanatory variables is jointly determined with the dependent variable.
d. both serial correlation and heteroskedasticity are present in an hypothesized model.
2. The following simultaneous equations describe the demand and supply for a particular good in a
competitive market.
Qi = α1Pi + β1zi1 + ui1
Qi = α2Pi + β2zi2 + ui2
Which of the following are the endogenous variables in this model?
a. Pi, zi1, and zi2
b. Pi and Qi
c. zi1, and zi2
d. ui1 and ui2
3. Which of the following correctly identifies a characteristic of structural equations?
a. A structural equation should contain equal number of dependent and independent variables.
b. A structural equation should contain equal number of endogenous and exogenous variables.
c. A structural equation should have a behavioral, ceteris paribus interpretation on its own.
d. A structural equation should not contain structural errors.
4. The following equations represent a simultaneous equations model:
K1 = α1K2 + β1z1 + u1
K2 = α2K1 + β2z2 + u2
The reduced form equation for K2 will express:
a. K1 as a function of K2 and the error terms.
b. K2 as a function of K1 and the error terms.
c. K2 as a function of exogenous variables and the error terms.
d. K1 as a function of exogenous variables, the error terms, and K2.
5. The following equations represent a simultaneous equations model:
K1 = α1K2 + β1z1 + u1
K2 = α2K1 + β2z2 + u2
OLS will suffer from simultaneity bias if:
a. u1 is correlated with z1.
b. z1 is correlated with z2.
c. K2 is correlated with u1.
d. K1 is correlated with u1.
6. Refer to the simultaneous equations model above. The reduced form error from the reduced form
equation for K2 will be a:
a. quadratic function of u1 and u2, and correlated with z1 and z2.
b. quadratic function of u1 and u2, and uncorrelated with z1 and z2.
c. linear function of u1 and u2, and correlated with z1 and z2.
d. linear function of u1 and u2, and uncorrelated with z1 and z2.
7. Exclusion restrictions are said to be imposed in a two-equation simultaneous equations model if it is
assumed that:
a. certain exogenous variables do not appear in the first equation and others are absent from the
second equation.
b. certain endogenous variables do not appear in the first equation and others are absent from the
second equation.
c. the error terms in each equation is uncorrelated with the exogenous variables.
b. the error terms in each equation is correlated with the exogenous variables.
8. Which of the following is a method which can be used for estimation in simultaneous equations
models?
a. Feasible generalized least squares estimation
b. Prais-Winsten transformation
c. Cochrane-Orcutt transformation
d. Two stage least squares estimation
9. The rank condition for identification of a structural equation states that the first equation in a two-
equation simultaneous equations model is identified if, and only if:
a. the first equation contains at least one exogenous variable (with a nonzero coefficient) that is
excluded from the second equation.
b. the first equation contains at least two exogenous variables (with a nonzero coefficient) that are
excluded from the second equation.
c. the second equation contains at least one exogenous variable (with a nonzero coefficient) that is
excluded from the first equation.
d. the second equation contains at least two exogenous variables (with a nonzero coefficient) that are
excluded from the first equation.
10. Which of the following statements is true?
a. The use of 2SLS is applicable to simultaneous equations model with at most two equations.
b. Identification of simultaneous equations with three or more equations is based on matrix algebra.
c. 2SLS method used in the estimation of simultaneous equations is an example of a system estimation
method.
d. The maximum number of equations permissible for a simultaneous equations model is four.
11. An equation in the simultaneous equations model satisfies the order condition for identification if:
a. the number of excluded endogenous variables from the equation is at most as large as the number of
right-hand side exogenous variables.
b. the number of excluded endogenous variables from the equation is at least as large as the number of
right-hand side exogenous variables.
c. the number of excluded exogenous variables from the equation is at most as large as the number of
right-hand side endogenous variables.
d. the number of excluded exogenous variables from the equation is at least as large as the number of
right-hand side endogenous variables.
12. A predetermined variable in a simultaneous equations model is:
a. a constant.
b. the error term.
c. a lagged variable.
d. an omitted variable.
13. Which of the following correctly highlights a limitation of applying simultaneous equation models to
time series data?
a. Most time series have variables with a unit root and 2SLS is complicated when applied to equations
with such variables.
b. 2SLS estimates are inefficient when applied to variables that are not in their levels but in first
differences.
c. It is difficult to form simultaneous equations which satisfy the rank and order conditions using time
series data.
d. The problem of serial correlation greatly limits the efficiency of simultaneous equation models and
leads to inefficient estimations.
14. An alternative to using simultaneous equation models with panel data is:
a. to use OLS estimates after first differencing the data.
b. to use fixed effects transformation on the equations and then apply 2SLS.
c. to convert the equations into reduced form and then apply feasible generalized least squares.
d. to convert the equations into reduced form and then apply OLS.
15. Which of the following statements is true?
a. White test can be used to efficiently determine the presence of serial correlation in panel data.
b. The t statistic is not an efficient test to determine serial correlation in panel data.
c. Instrumental variables for both endogenous and exogenous variables are required for estimating
simultaneous equation models concerned with panel data.
d. 2SLS should be applied to simultaneous equation models with panel data only after removing the
unobserved effects from the equations of interest.
16. A simultaneous equations model is suitable whenever two variables are determined simultaneously.
17. OLS is biased and inconsistent when applied to a structural equation in a simultaneous equations
system.
18. The instrumental variables in the two stage least squares estimation method consists of endogenous
variables appearing in either equation.
19. The order condition is a necessary and sufficient condition for identification of an equation in a
simultaneous equations model.
20. If a structured model contains a time trend—which may capture exogenous, trending factors that
are not directly modeled—then the trend acts as its own instrumental variable.