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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.

E) A) and B)
F) C) and D)

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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.

E) A) and B)
F) A) and C)

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​The first step in estimating simultaneous equations models (SEMs) with panel data is to find instrumental variables for the endogenous variables in the transformed equation.

A) True
B) False

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False

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 correlated with the exogenous variables.
D) the error terms in each equation is uncorrelated with the exogenous variables.

E) B) and C)
F) A) and B)

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The order condition is a necessary and sufficient condition for identification of an equation in a simultaneous equations model.

A) True
B) False

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The following equations represent a simultaneous equations model: K1 = The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub> + <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: A) u<sub>1</sub> is correlated with z<sub>1</sub>. B) z<sub>1</sub> is correlated with z<sub>2</sub>. C) K<sub>2</sub> is correlated with u<sub>1</sub>. D) K<sub>1</sub> is correlated with u<sub>1</sub>. 1K2 + The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub> + <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: A) u<sub>1</sub> is correlated with z<sub>1</sub>. B) z<sub>1</sub> is correlated with z<sub>2</sub>. C) K<sub>2</sub> is correlated with u<sub>1</sub>. D) K<sub>1</sub> is correlated with u<sub>1</sub>. 1z1 + u1 K2 = The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub> + <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: A) u<sub>1</sub> is correlated with z<sub>1</sub>. B) z<sub>1</sub> is correlated with z<sub>2</sub>. C) K<sub>2</sub> is correlated with u<sub>1</sub>. D) K<sub>1</sub> is correlated with u<sub>1</sub>. 2K1+ The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub> + <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: A) u<sub>1</sub> is correlated with z<sub>1</sub>. B) z<sub>1</sub> is correlated with z<sub>2</sub>. C) K<sub>2</sub> is correlated with u<sub>1</sub>. D) K<sub>1</sub> is correlated with u<sub>1</sub>. 2z2 + 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.

E) None of the above
F) A) and D)

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​The number of overidentifying restrictions equals the total number of exogenous variables in the system plus the total number of explanatory variables in the equation.

A) True
B) False

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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.

E) A) and B)
F) None of the above

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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.

E) All of the above
F) A) and C)

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Which of the following equations is an overidentified equation?​


A) ​y1 = α12y2 + α13y3 + β11z1 + u1
B) ​y2 = α21y1 + β21z2 + β23z3 + u2
C) ​y3 = α32y1 + β31z1 + β32z2 + β33z3 + β34z4 + u3
D) ​y1 = β10 + α1y2+ z1β1 + u1

E) A) and B)
F) None of the above

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The following equations represent a two-equation model:​ y1 = β10 + α1y2 + z1β1 + u1 Y2 = β20 + α2y1 + z2β2 + u2 Where, y1 and y2 are the:


A) ​endogenous variables.
B) ​structural error terms.
C) ​exogenous variables.
D) ​intercepts.

E) None of the above
F) C) and D)

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A

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.

E) None of the above
F) C) and D)

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The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Qi = The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> = <sub>1</sub>P<sub>i</sub> + <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> = <sub>2</sub>P<sub>i</sub> + <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? A) Pi<sub>,</sub> zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> B) P<sub>i</sub> and Q<sub>i</sub> C) zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> D) u<sub>i</sub><sub>1</sub> and u<sub>i</sub><sub>2</sub> 1Pi + The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> = <sub>1</sub>P<sub>i</sub> + <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> = <sub>2</sub>P<sub>i</sub> + <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? A) Pi<sub>,</sub> zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> B) P<sub>i</sub> and Q<sub>i</sub> C) zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> D) u<sub>i</sub><sub>1</sub> and u<sub>i</sub><sub>2</sub> 1zi1 + ui1 Qi = The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> = <sub>1</sub>P<sub>i</sub> + <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> = <sub>2</sub>P<sub>i</sub> + <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? A) Pi<sub>,</sub> zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> B) P<sub>i</sub> and Q<sub>i</sub> C) zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> D) u<sub>i</sub><sub>1</sub> and u<sub>i</sub><sub>2</sub> 2Pi + The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> = <sub>1</sub>P<sub>i</sub> + <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> = <sub>2</sub>P<sub>i</sub> + <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? A) Pi<sub>,</sub> zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> B) P<sub>i</sub> and Q<sub>i</sub> C) zi<sub>1,</sub> and z<sub>i</sub><sub>2</sub> D) u<sub>i</sub><sub>1</sub> and u<sub>i</sub><sub>2</sub> 2zi2 + 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

E) None of the above
F) A) and B)

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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.

E) C) and D)
F) A) and C)

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In a simultaneous equations model, if any variable is determined outside of the model, then it is considered a(n) :​


A) ​endogenous variable.
B) ​random variable.
C) ​exogenous variable.
D) ​error variable.

E) B) and C)
F) A) and C)

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The following equations represent a simultaneous equations model: K1 = The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub><sup> </sup>+ <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: A) K<sub>1</sub> as a function of K<sub>2</sub> and the error terms. B) K<sub>2</sub> as a function of K<sub>1</sub>and the error terms. C) K<sub>2</sub> as a function of exogenous variables and the error terms. D) K<sub>1</sub> as a function of exogenous variables, the error terms, and K<sub>2</sub>. 1K2 + The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub><sup> </sup>+ <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: A) K<sub>1</sub> as a function of K<sub>2</sub> and the error terms. B) K<sub>2</sub> as a function of K<sub>1</sub>and the error terms. C) K<sub>2</sub> as a function of exogenous variables and the error terms. D) K<sub>1</sub> as a function of exogenous variables, the error terms, and K<sub>2</sub>. 1z1 + u1 K2 = The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub><sup> </sup>+ <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: A) K<sub>1</sub> as a function of K<sub>2</sub> and the error terms. B) K<sub>2</sub> as a function of K<sub>1</sub>and the error terms. C) K<sub>2</sub> as a function of exogenous variables and the error terms. D) K<sub>1</sub> as a function of exogenous variables, the error terms, and K<sub>2</sub>. 2K1+ The following equations represent a simultaneous equations model: K<sub>1</sub> = <sub>1</sub>K<sub>2</sub><sup> </sup>+ <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> = <sub>2</sub>K<sub>1</sub>+ <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: A) K<sub>1</sub> as a function of K<sub>2</sub> and the error terms. B) K<sub>2</sub> as a function of K<sub>1</sub>and the error terms. C) K<sub>2</sub> as a function of exogenous variables and the error terms. D) K<sub>1</sub> as a function of exogenous variables, the error terms, and K<sub>2</sub>. 2z2 + 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 K1and 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.

E) B) and C)
F) All of the above

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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.

A) True
B) False

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True

OLS is biased and inconsistent when applied to a structural equation in a simultaneous equations system.

A) True
B) False

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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.

E) None of the above
F) B) and C)

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A simultaneous equations model is suitable whenever two variables are determined simultaneously.

A) True
B) False

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