Deck 8: Modelling Long-Run Relationships in Finance

Question 1

A variable x is defined as ??________ if its value is determined outside of the equation or system of equations. What is the blank?

A) Endogenous
B) Exogenous
C) Homogeneous
D) Heterogeneous

Answer 1

Exogenous

Question 2

Which of these is an approach used to determine the appropriate lag lengths of VAR models?

A) Graphically plotting the time series of the data
B) Selecting the number of lags that maximises the information criteria
C) Selecting the number of lags that minimises the information criteria
D) None of the above

Answer 2

Selecting the number of lags that minimises the information criteria

Question 3

Which of the following statements is true concerning VAR impulse response functions?
(I) Impulse responses help the researcher to investigate the interactions between the variables in the VAR.
(ii) An impulse response analysis is where we examine the effects of applying unit shocks to all of the variables at the same time.
(iii) Impulse responses involve calculating the proportion of the total forecast error variance of a given variable is explained by innovations to each variable.
(iv) If the $\pm$ 2 standard error bars around the impulse responses for a given lag span (i.e. include) the x-axis, it would be said that the response is statistically significant.

A) (i), (ii), (iii), and (iv)
B) (i), (ii) and (iii) only
C) (i) only
D) (i) and (ii) only

Answer 3

(i) and (ii) only

Question 4

Which of these statements is true about vector autoregressive models?
(I) They allow the value of a variable to depend on more than just its own lags
(II) All variables are endogenous
(III) The researcher does not need to specify which variables are endogenous or exogenous
(IV) All variables are exogenous

A) I only
B) I and II only
C) I, II and III only
D) I, II, III and IV

Question 5

Which of these assumptions is violated when an equation is estimated using OLS where is in fact part of a simultaneous structural system?

A)
B)
C)
D) None of the above

Question 6

Which of these is not an appropriate method of estimating equations that are from a simultaneous system?

A) Indirect least squares
B) Two-stage least squares
C) Aggregate least squares
D) Instrumental variables

Question 7

Comparing the information criteria approach with the likelihood ratio test approach to determining the optimal VAR lag length, which one of the following statements is true?

A) The choice of stiffness of penalty term will not affect the model choice
B) The validity of information criteria relies upon normal residuals
C) Conducting a likelihood ratio test could lead to a sub-optimal model selection
D) An application of the univariate information criteria to each equation will give identical results to the application of a multivariate version of the criteria to all of the equations jointly

Question 8

Estimation of equation (2) on its own using OLS would result in

A) Consistent and unbiased coefficient estimates
B) Consistent coefficient estimates which might be biased in small samples
C) Inconsistent but unbiased coefficient estimates
D) Coefficient estimates that are neither unbiased nor consistent.

Question 9

Consider the following bivariate VAR(2): Which of the following coefficient significances are required to be able to say that y₁ Granger-causes y₂ but not the other way around?

A) $\alpha$ ₁₃ and $\alpha$ ₁₄ significant; $\alpha$ ₂₁ and $\alpha$ ₂₂ not significant
B) $\alpha$ ₂₁ and $\alpha$ ₂₂ significant; $\alpha$ ₁₃ and $\alpha$ ₁₄ not significant
C) $\alpha$ ₂₁ and $\alpha$ ₂₃ significant; $\alpha$ ₁₁ and $\alpha$ ₁₃ not significant
D) $\alpha$ ₁₁ and $\alpha$ ₁₃ significant; $\alpha$ ₂₁ and $\alpha$ ₂₃ not significant

Question 10

Which of the following are characteristics of vector autoregressive (VAR) models?
(I) They are typically a-theoretical and data driven
(ii) they can easily lead to overfitting
(iii) all variables on the right hand side of the equation are pre-determined
(iv) their interpretation is often difficult from a theoretical perspective

A) (i), (ii), (iii) and (iv)
B) (i), (ii), and (iv) only
C) (i) and (ii) only
D) (i) and (iv) only
For questions 2 and 3, consider the following set of simultaneous equations:

Assume that the Y's are endogenous and the X's exogenous variables, and that the error terms are uncorrelated.

Question 11

Assuming that you have a VAR model with 2 variables (A and B) including many lags, how can you test whether A cause Granger-causes changes in B?

A) By observing if the differences in correlation between A and B are statistically significant
B) Impose restrictions that all the coefficients of the lags of A are equal to 0 in the equation for B of the VAR model and test the joint hypothesis within the F-test framework
C) Impose restrictions that all the coefficients of the lags of B are equal to 0 in the equation for A of the VAR model and test the joint hypothesis within the F-test framework
D) None of the above

Question 12

Impulse responses:

A) Trace out the responsiveness of the dependent variables in the VAR to shocks to each of the variables
B) Are a different term for variance decompositions
C) Trace out the responsiveness of the residuals in the VAR to shocks to each of the variables
D) Give the proportion of the movements in the dependent variables that are due to their own shocks versus shocks to other variables

Question 13

Which of the following statements is incorrect?

A) Equations that are part of a recursive system can be validly estimated using OLS
B) Unnecessary use of two-stage least squares (2SLS) - i.e. on a set of right hand side variables that are in fact exogenous - will result in consistent but inefficient coefficient estimates.
C) 2SLS is just a special case of instrumental variables (IV) estimation.
D) 2SLS and indirect least squares (ILS) are equivalent for over-identified systems.

Question 14

In the context of simultaneous equations modelling, which of the following statements is true concerning an exogenous variable?

A) The values of exogenous variables are determined within the system
B) The exogenous variables are assumed to be fixed in repeated samples
C) Reduced form equations will not contain any exogenous variables on the RHS
D) Reduced form equations will contain only exogenous variables on the LHS

Question 15

Which of the following could be viewed as a disadvantage of the vector autoregressive (VAR) approach to modelling?

A) We do not need to specify which variables are endogenous and which are exogenous
B) Standard form VARs can be estimated equation-by-equation using OLS
C) VARs often contain a large number of terms
D) VARs can be expressed using a very compact notation.

Question 16

Variance decompositions

A) Trace out the responsiveness of the dependent variables in the VAR to shocks to each of the variables
B) Will always give the same conclusions as impulse responses
C) Trace out the responsiveness of the residuals in the VAR to shocks to each of the variables
D) Give the proportion of the movements in the dependent variables that are due to their own shocks versus shocks to other variables

Question 17

The second stage in two-sage least squares estimation of a simultaneous system would be to

A) Estimate the reduced form equations
B) Replace the endogenous variables that are on the RHS of the structural equations with their reduced form fitted values
C) Replace all endogenous variables in the structural equations with their reduced form fitted values
D) Use the fitted values of the endogenous variables from the reduced forms as additional variables in the structural equations.

Question 18

Which of the following statement is true of equation (3)?

A) According to the order condition, it is not identified
B) According to the order condition, it is just identified
C) According to the order condition, it is over-identified
D) There is insufficient information given in the question to determine whether the equation is identified or not.