Midterm II

Question 1

Can we run a simple regression to obtain model parameters?

Answer 1

No, the variables being studied are not constant.

Question 2

What is the implicit claim underlying a regression of two variables?

Answer 2

That the results are not going to be affected by anything else in the model.

Question 3

What does the Lucas Critique specify about policy?

Answer 3

That policy changes will alter variables beyond the immediate analysis, making it problematic.

Question 4

How can economists bypass the Lucas critique in analyzing policy?

Answer 4

By utilizing the deep parameters of the model that are unlikely to be affected by changes.

E. g. Patience, Subsistence Consumption, Risk Aversion, etc.

Question 5

What is the basic autoregressive model?

Answer 5

y(t) = B(0) + B(1)y(t-1) + u(t)

Question 6

What sets the AR process apart from a normal regression?

Answer 6

Its propensity to explode

Question 7

When is an autoregression stable?

Answer 7

When |B(1)| < 1

Question 8

How many eigenvectors are in a matrix?

Answer 8

K

Question 9

What is an eigenvector?

Answer 9

The dimension along which things do not get disorted by the matrix transformation.

Question 10

What is the stability condition for VAR(1)?

Answer 10

When all eigenvalues of A(1) are less than one in absolute value.

Question 11

What does the Wold Decomposition Theorem say?

Answer 11

Any stationary process can be decomposed into a deterministic and stochastic process.

Question 12

What is a deterministic process?

Answer 12

One where the system always produces the same result from teh given iniatials.

Question 13

What is a stochastic process?

Answer 13

A collection of random variables indexed by time.

Question 14

What is a stationary process?

Answer 14

A stochastic process with correlations that do not change over time.

Question 15

Using the WDT, which process is represented with a moving average?

Answer 15

The Stochastic one

Question 16

Why is recursive subsitution preformed in the VAR(1)?

Answer 16

To obtain the moving average form.

Question 17

What does the moving average of VAR(1) show?

Answer 17

That it is fully characterised by the infinite past realizations of the process.

Question 18

What does the moving average of VAR(1) imply about shocks?

Answer 18

That: (I) the process is nothing more than the joint effect of shocks to it; & (II) that recent shocks matter more.

Question 19

What is the unconditional expectation of x(t) [in VAR(1) MA form]?

Answer 19

E[x(t)] = pi = (I-A)^(-1) c

The stochastic term is cancelled as all the u’s have means of 0.

Question 20

What is Matrix sum(u)?

Answer 20

It tells us by how much the shocks co-move.

Question 21

What is true if the time subscripts of two U(t) terms don’t match?

Answer 21

The expectations are zero.

They must be uncorrelated over time.

Question 22

What is are expectations of two u(t) terms?

Answer 22

The corresponding value in Matrix sum(u).

Question 23

How do you obtain the MA form of VAR(p)?

Answer 23

By forcing it into a VAR(1) form and using an extractor matrix.

Question 24

Which variable tranforms the VAR(1)?

Answer 24

A(1)

Question 25

When do we consider a modelled IRF function to be true?

Answer 25

When the predicted IRF is equal to the IRF from actual data.

Question 26

Can you use coefficients to estimate the impact of one variable on another in a VAR?

Answer 26

No, as the variables indirectly affect one another. | E. g. a shock might affect x(t) and not y(t), but x(t) affects y(t+1).

Question 27

How do you estimate the impact of a shock in one period on a variable of interest?

Answer 27

By looking at the variable's moving average coefficients at the relevant time period. | The impulse response function is contained in MA coefficent matrices.

Question 28

Can you use OLS to estimate a systems of equations?

Answer 28

Yes, but only when all the regressors are the same. Otherwise you must use GLS.

Question 29

What is the IS curve?

Answer 29

The combination of interest rates and GDP that is consistent with the goods market equilibrium.

Question 30

After a positive demand shock, how is the steady state achieved again?

Answer 30

Households take notice of higer prices and revise their expectations, shifting SRAS left.

Question 31

Under neoclasiccal theory, what drives economic growth?

Answer 31

Technology

Question 32

What do square matrices do to a vector space?

Answer 32

They deform it.

Question 33

What is the scaling factor of a matrix?

Answer 33

It's eigenvalues

Question 34

**Why** do VARs explode?

Answer 34

The more you apply matrix A, the more deformation will occur. Applying it T times will cause it to grow to infinity. | Unless |eigenvalues(A)| < 1, so repeated multiplication =/= deformations

Question 35

How do you force a VAR(p) into a VAR(1)?

Answer 35

By forcing the all the lagged matrices into new container matrices and then writing them in VAR(1) form. | Subsequant equations should simply be algebraic identities.

Question 36

What does stationarity refer to?

Answer 36

The rules of a particular stochastic process' evolution and there resistence to change.

Question 37

Under the Wold Decomposition Theorem, what represents the trend compenent?

Answer 37

The deterministic process y(t)

Question 38

Under the Wold Decomposition Theorem, what is true about the relationship between y(t) and x(t)?

Answer 38

They are uncorrelated.

Question 39

Mathematically, how does the moving average of VAR(1) show that recent shocks matter more?

Answer 39

The increasingly higher powers of A(1) make the coefficent smaller, as it is less than one.

Question 40

Why does the MA's second term cancelled upon deriving the unconditional expectation?

Answer 40

The u terms have means of zero.

Question 41

What is the main assumption underlying the shock process?

Answer 41

That it is IID with variance-covaraince matrix sum(u).

Question 42

What is always true about shocks under our assumptions?

Answer 42

They are uncorrelated over time.

Question 43

What period do we start at when applying OLS to a VAR?

Answer 43

(- p) + 1