Midterm II Flashcards
Can we run a simple regression to obtain model parameters?
No, the variables being studied are not constant.
What is the implicit claim underlying a regression of two variables?
That the results are not going to be affected by anything else in the model.
What does the Lucas Critique specify about policy?
That policy changes will alter variables beyond the immediate analysis, making it problematic.
How can economists bypass the Lucas critique in analyzing policy?
By utilizing the deep parameters of the model that are unlikely to be affected by changes.
E. g. Patience, Subsistence Consumption, Risk Aversion, etc.
What is the basic autoregressive model?
y(t) = B(0) + B(1)y(t-1) + u(t)
What sets the AR process apart from a normal regression?
Its propensity to explode
When is an autoregression stable?
When |B(1)| < 1
How many eigenvectors are in a matrix?
K
What is an eigenvector?
The dimension along which things do not get disorted by the matrix transformation.
What is the stability condition for VAR(1)?
When all eigenvalues of A(1) are less than one in absolute value.
What does the Wold Decomposition Theorem say?
Any stationary process can be decomposed into a deterministic and stochastic process.
What is a deterministic process?
One where the system always produces the same result from teh given iniatials.
What is a stochastic process?
A collection of random variables indexed by time.
What is a stationary process?
A stochastic process with correlations that do not change over time.
Using the WDT, which process is represented with a moving average?
The Stochastic one
Why is recursive subsitution preformed in the VAR(1)?
To obtain the moving average form.
What does the moving average of VAR(1) show?
That it is fully characterised by the infinite past realizations of the process.
What does the moving average of VAR(1) imply about shocks?
That: (I) the process is nothing more than the joint effect of shocks to it; & (II) that recent shocks matter more.
What is the unconditional expectation of x(t) [in VAR(1) MA form]?
E[x(t)] = pi = (I-A)^(-1) c
The stochastic term is cancelled as all the u’s have means of 0.
What is Matrix sum(u)?
It tells us by how much the shocks co-move.
What is true if the time subscripts of two U(t) terms don’t match?
The expectations are zero.
They must be uncorrelated over time.
What is are expectations of two u(t) terms?
The corresponding value in Matrix sum(u).
How do you obtain the MA form of VAR(p)?
By forcing it into a VAR(1) form and using an extractor matrix.
Which variable tranforms the VAR(1)?
A(1)
When do we consider a modelled IRF function to be true?
When the predicted IRF is equal to the IRF from actual data.
Can you use coefficients to estimate the impact of one variable on another in a VAR?
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).
How do you estimate the impact of a shock in one period on a variable of interest?
By looking at the variable’s moving average coefficients at the relevant time period.
The impulse response function is contained in MA coefficent matrices.
Can you use OLS to estimate a systems of equations?
Yes, but only when all the regressors are the same. Otherwise you must use GLS.
What is the IS curve?
The combination of interest rates and GDP that is consistent with the goods market equilibrium.
After a positive demand shock, how is the steady state achieved again?
Households take notice of higer prices and revise their expectations, shifting SRAS left.
Under neoclasiccal theory, what drives economic growth?
Technology
What do square matrices do to a vector space?
They deform it.
What is the scaling factor of a matrix?
It’s eigenvalues
Why do VARs explode?
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
How do you force a VAR(p) into a VAR(1)?
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.
What does stationarity refer to?
The rules of a particular stochastic process’ evolution and there resistence to change.
Under the Wold Decomposition Theorem, what represents the trend compenent?
The deterministic process y(t)
Under the Wold Decomposition Theorem, what is true about the relationship between y(t) and x(t)?
They are uncorrelated.
Mathematically, how does the moving average of VAR(1) show that recent shocks matter more?
The increasingly higher powers of A(1) make the coefficent smaller, as it is less than one.
Why does the MA’s second term cancelled upon deriving the unconditional expectation?
The u terms have means of zero.
What is the main assumption underlying the shock process?
That it is IID with variance-covaraince matrix sum(u).
What is always true about shocks under our assumptions?
They are uncorrelated over time.
What period do we start at when applying OLS to a VAR?
(- p) + 1
