Deck 16: Simultaneous Equations Models

Question 1

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.

Answer 1

A
Explanation: Exclusion restrictions are said to be imposed in a two-equation simultaneous equations model if it is assumed that certain exogenous variables do not appear in the first equation and others are absent from the second equation.

Question 2

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.

Answer 2

D
Explanation: 2SLS should be applied to simultaneous equation models with panel data only after removing the unobserved effects from the equations of interest.

Question 3

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.

Answer 3

A
Explanation: Most time series have variables with a unit root and 2SLS is complicated when applied to equations with such variables.

Question 4

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.

Question 5

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

Question 6

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.

Question 7

The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q_i = ₁P_i + ₁z_i1 + u_i1
Q_i = ₂P_i + ₂z_i2 + u_i2
Which of the following are the endogenous variables in this model?

A)Pi_, zi_1, and z_i2
B)P_i and Q_i
C) zi_1, and z_i2
D) u_i1 and u_i2

Question 8

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.

Question 9

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.

Question 10

The following equations represent a simultaneous equations model: K₁ = ₁K₂ + ₁z₁ + u₁
K₂ = ₂K₁+ 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.

Question 11

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.

Question 12

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.

Question 13

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

Question 14

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.

Question 15

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

Question 16

A predetermined variable in a simultaneous equations model is:

A)a constant.
B)the error term.
C) a lagged variable.
D) an omitted variable.

Question 17

The following equations represent a two-equation model:​ y₁ = β_{10 +} α₁y₂ + z₁β₁ + u₁
Y₂ = β_{20 +} α₂y₁ + z₂β₂ + u₂
Where, y₁ and y₂ are the:

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

Question 18

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.

Question 19

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

Question 20

The following equations represent a simultaneous equations model: K₁ = ₁K₂ + ₁z₁ + u₁
K₂ = ₂K₁+ 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.

Question 21

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.

Question 22

​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.

Question 23

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

Question 24

​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.

Question 25

The instrumental variables in the two stage least squares estimation method consists of endogenous variables appearing in either equation.