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.

Accepted Answer

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.

Accepted Answer

2SLS should be applied after removing the unobserved effects from the equations of interest in order to avoid bias in the estimation. Choice A is incorrect as the White test is used to test for heteroscedasticity and not serial correlation in panel data. Choice B is incorrect as t statistic can be used to test for serial correlation in panel data, but it may not be the most efficient test. Choice C is incorrect as instrumental variables are only required for endogenous variables and not exogenous variables in panel data. 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.

Accepted Answer

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.

Accepted Answer

Simultaneity arises when one or more explanatory variables are jointly determined with the dependent variable. This means that the dependent variable and at least one of the explanatory variables are determined by the same underlying factors or that they affect each other in some way. As a result, the regression coefficients may be biased and inconsistent, making it difficult to identify the causal effect of each variable on the dependent variable. In econometrics, simultaneity arises when one or more of the explanatory variables is jointly determined with the dependent variable, typically through an equilibrium process.

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

Accepted Answer

y₁ = α₁₂y₂ + α₁₃y₃ + β₁₁z₁ + u₁is an overidentified equation because we need only two IVs (for y₂ and y₃) but we have three available (z₂, z₃, and z₄); there is one overidentifying restriction in this equation.

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.

Accepted Answer

Using fixed effects transformation helps to account for time-invariant variables and reduces potential endogeneity issues. Applying 2SLS can further address endogeneity concerns by instrumenting for the endogenous variables. This approach is often preferred to OLS after first differencing because differencing can result in loss of information and may not be appropriate for some variables. Converting the equations into reduced form and applying feasible generalized least squares can also be a valid approach, but it may be computationally more complex and may not always be necessary. Using OLS after converting to reduced form is not recommended because it can lead to biased estimates due to endogeneity and omitted variable bias. An alternative to using simultaneous equation models with panel data is to use fixed effects transformation on the equations and then apply 2SLS.

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

Accepted Answer

In this model, the endogenous variables are the variables that are determined within the model itself, and are not exogenously determined. In this case, the endogenous variables are the equilibrium price (P_i) and quantity (Q_i) of the good. The other variables (zi_1,, z_i₂, u_i₁ and u_i₂) are exogenous variables, which are determined outside of the model and affect the equilibrium price and quantity. Therefore, the best choice is B, as it includes only the endogenous variables. P_i and Q_i are the endogenous variables in the given simultaneous equation model.

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.

Accepted Answer

An exogenous variable is determined outside of the model and is not affected by the other variables in the model. Therefore, it is not determined endogenously within the model. In a simultaneous equations model, if any variable is determined outside of the model, then it is considered an exogenous 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.

Accepted Answer

A structural equation should have a behavioral, ceteris paribus interpretation on its own. This means that the equation should be able to give an idea about how the variables behave and change in relation to each other while holding other relevant variables constant. The other choices are not correct as structural equations can have unequal numbers of dependent and independent variables (A), endogenous and exogenous variables (B), and can contain structural errors (D). A structural equation should have a behavioral, ceteris paribus interpretation on its own.

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.

Accepted Answer

For the given simultaneous equations model, the reduced form equation for K₂ will express K₂ as a function of exogenous variables and the error terms.

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.

Accepted Answer

The reduced form error from the reduced form equation for K₂ will be a 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.

Accepted Answer

An equation in the simultaneous equations model satisfies the order condition for identification if 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

Accepted Answer

Two stage least squares estimation is a commonly used method for estimation in simultaneous equations models where endogeneity is a concern. It involves instrumenting for endogenous variables by identifying exogenous variables that are correlated with the endogenous variables and using them as instruments in a first-stage regression. The fitted values from this first-stage regression are then used in place of the endogenous variables in a second-stage regression to obtain consistent estimates of the parameters of interest. Options A, B, and C are methods for dealing with autocorrelation in time-series data and are not directly applicable to estimation in simultaneous equations models. The two stage least squares estimation can be used in simultaneous equations models.

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.

Accepted Answer

Identification of simultaneous equations with three or more equations is based on matrix algebra.

Question 15

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

Accepted Answer

This is true because OLS assumes that the endogenous variables are not correlated with the error term, which is not the case in a structural equation in a simultaneous equations system. This leads to biased and inconsistent parameter estimates. Special techniques, such as two-stage least squares, are required to obtain consistent estimates in this case. 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.

Accepted Answer

A predetermined variable in a simultaneous equations model is a lagged variable.

Question 17

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.

Accepted Answer

The endogenous variables are the variables that are determined by the model itself, and their values depend on the values of the other variables in the model. In this case, y₁ and y₂ are both determined by the equations in the model and therefore are endogenous variables. In the two-equation model, y₁ and y₂ are the endogenous variables.

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.

Accepted Answer

The rank condition for identification of a structural equation states that the first equation in a two-equations simultaneous equations model is identified if, and only if, the second equation contains at least one exogenous variable (with a nonzero coefficient) that is excluded from the first equation.

Question 19

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

Accepted Answer

Just because two variables are determined simultaneously, it does not imply that a simultaneous equations model is suitable. The criteria for using a simultaneous equations model is that each equation in the model should make sense in isolation from the other equation.

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.

Accepted Answer

In the given simultaneous equation model, OLS will suffer from simultaneity bias if K₂ is correlated with u₁.

Quiz 16: Simultaneous Equations Models

Exclusion restrictions are said to be imposed in a two-equation simultaneous equations model if it is assumed that:

Which of the following statements is true?

Which of the following correctly highlights a limitation of applying simultaneous equation models to time series data?

In econometrics, simultaneity arises when:

Which of the following equations is an overidentified equation?

An alternative to using simultaneous equation models with panel data is:

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?

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

Which of the following correctly identifies a characteristic of structural equations?

The following equations represent a simultaneous equations model: K₁ = ₁K₂+ ₁z₁ + u₁ K₂ = ₂K₁+ ₂z₂ + u₂ The reduced form equation for K₂ will express:

Refer to the simultaneous equations model above. The reduced form error from the reduced form equation for K₂ will be a:

An equation in the simultaneous equations model satisfies the order condition for identification if:

Which of the following is a method which can be used for estimation in simultaneous equations models?

Which of the following statements is true?

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

A predetermined variable in a simultaneous equations model is:

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

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

The following equations represent a simultaneous equations model: K₁ = ₁K₂ + ₁z₁ + u₁ K₂ = ₂K₁+ ₂z₂ + u₂ OLS will suffer from simultaneity bias if:

Quiz 16: Simultaneous Equations Models

Exclusion restrictions are said to be imposed in a two-equation simultaneous equations model if it is assumed that:

Which of the following statements is true?

Which of the following correctly highlights a limitation of applying simultaneous equation models to time series data?

In econometrics, simultaneity arises when:

Which of the following equations is an overidentified equation?​

An alternative to using simultaneous equation models with panel data is:

The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Qi = 1Pi + 1zi1 + ui1 Qi = 2Pi + 2zi2 + ui2 Which of the following are the endogenous variables in this model?

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

Which of the following correctly identifies a characteristic of structural equations?

The following equations represent a simultaneous equations model: K1 = 1K2 + 1z1 + u1 K2 = 2K1+ 2z2 + u2 The reduced form equation for K2 will express:

Refer to the simultaneous equations model above. The reduced form error from the reduced form equation for K2 will be a:

An equation in the simultaneous equations model satisfies the order condition for identification if:

Which of the following is a method which can be used for estimation in simultaneous equations models?

Which of the following statements is true?

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

A predetermined variable in a simultaneous equations model is:

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

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

The following equations represent a simultaneous equations model: K1 = 1K2 + 1z1 + u1 K2 = 2K1+ 2z2 + u2 OLS will suffer from simultaneity bias if:

Which of the following equations is an overidentified equation?

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?

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

The following equations represent a simultaneous equations model: K₁ = ₁K₂+ ₁z₁ + u₁ K₂ = ₂K₁+ ₂z₂ + u₂ The reduced form equation for K₂ will express:

Refer to the simultaneous equations model above. The reduced form error from the reduced form equation for K₂ will be a:

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

The following equations represent a simultaneous equations model: K₁ = ₁K₂ + ₁z₁ + u₁ K₂ = ₂K₁+ ₂z₂ + u₂ OLS will suffer from simultaneity bias if: