Final Exam Flashcards
What is an eigenfactor?
The degree to which eigenvectors are blown up or squashed.
What happens to the AR(1) model when |B(1)| = 1?
The process drift off with infinite variance.
The so-called “random walk”.
When the eigenvalues of A(1) are less than 1, what is true of VAR(1)?
It is stable.
What is a stationary process?
One that’s autocovariances do not depend on time.
Mathematically, how does the MA(1) process show that older shocks matter less?
The A(1) coefficients, which are necessarily less than one, are raised to increasingly higher powers.
So they approach zero.
The autocorrelations of the stochastic process can be reformulated to create a (…)
VAR
When can you use OLS on a systems of equations?
When all the regressors are the same.
How do you estimate the betas of a VAR?
(i) Force in the form: X = BZ + U; (i) use the formula: Bhat = XZ’(ZZ’)^(-1).
What does a correlation between a shock to inflation and GDP mean in the real world?
That the shock to GDP is also a shock to inflation in that % of cases.
What does theory say an IRF should measure?
The isolated effect of a shock to one variable on another.
If we don’t orthogonalize, what does the IRF actually measure?
The cumulative effect of a shock to one variable on all other variables in the system.
What do all positive definite matrices have?
A Choleski Decomposition
When is a matrix positive definite?
When: z’A(z) > 0
or: all eigenvalues > 0
What does positive defintieness mean, intuitively?
That matrix A will not reflect vector x in the opposite direction.
What is true of the variance-covariance matrix of w(t-i)?
It is diagonal.
What is the orthogonal representation of our VAR?
x(t) = Mu + Sum(O(i)w(t-i))
How does one caculate the effect of a shock post-orthogonalization?
IRF: x(t) = Mu + o(i)P
What is the decomposition of w(t-i)?
w(t-i) = P^(-1)u(t-i)
What is the decomposition of O(i)?
O(i) = o(i)P
What does the orthogonalized shock w(1, t) depend on?
The unorthogonalized shock u(1, t)
What does the orthogonalized shock w(k, t) depend on?
All of the unorthogonalized shocks u(1,t), u(2,t), … ,u(k,t)
What is the heirarchical structure of assumptions?
That the order of the variables in an orthogonalized VAR matters, with the first being most important and affected by no other variables.
What are the two main identification strategies for dealing with the heirarchical structure of assumptions?
(i) Argue that the order of the variables is jusfied by economic thoery; or (ii) caculate the orthogonalized VAR for every possible ordering and show that the answer does no depend on it.
What is L^(2)x(t)?
x(t-2)
What is the equation for the theorectical VAR?
x(t) = M(1)x(t-1) + psi(t)
Why can we remove the constant from the theorectical VAR?
Because we only need to cnsider data as deviations from the mean.
At least as far as identification is concerned.
How can the theorectical VAR model be modified to allow for simultaneous effects to the variables?
M(0)x(t) = M(1)x(t-1) + psi(t)
This also allows shocks to be identified seperately as Sum(psi) = I.
Why can’t we allow for theorectical shocks to be correlated?
Because it leads to models that don’t make any definite predictions.
How do we identify the theorectical VAR with the empirical one?
Solve u(t) = M(o)^(-1)psi(t)
What does var[u(t)] equal?
E[u(t)u(t)’] = Sum(u)
What does u(t) = M(o)^(-1)psi(t) solve to?
Sum(psi) = M(o)Sum(u(t))[M(o)]’
What matrix contains our known quantities?
Sum(u)
What matrix term contains our unknown quantities?
M(0)Sum(psi)[M(0)]’
Post-identification, how many unknown quantities are there?
#unknowns = K^2 + K(K+1)/2
The K^2 is the # in M & K(K+1)/2 is the # above the Sum(psi) diagonal.
Post-identification, how many known quantities are there?
#knowns = K(K+1)/2
What is #unknowns - #knowns?
K^(2)
How many addtional knowns do we need to identify a VAR (that we don’t have)?
K^(2)
What are the two innocuous restrictions we can impose to reduce the number of additional knowns needed?
(i) that Sum(psi) is diagonal (decreasing unknowns by K(K+1)/2); and (ii) that the diagonal elements of M(0) are all 1.
Result: only K(K+1)/2 unknowns
What is the case-specific restriction we can impose to identify VARs?
If two variables are known to be unrelated, set their (contemporaneous) model coefficents to zero.
e.g. Taxes in year one will not depend on GDP in year one.
What is the trade-off we face when choosing the order of a VAR model?
The one between in-sample fit and out-of-sample accuracy.
How many degress of freedom does y = x + z have?
2
What are the degrees of freedom for n=5, mu=1.
4
What happens to a model’s fit when you increase the number of parameters?
It goes up.
What happens to a model’s degrees of freedom when you increase the number of parameters?
They go down.
What is parismony?
Using the fewest parameters possible that result in a statisfactory compromise between fitting the data and keeping the analysis simple.
How do we assess the likelihood that a model is true?
By comparing them to a model with a variance of sigma^2.
What is the step-by-step procedure for assessing whether a model is true?
(i) Obtain the residuals; (ii) caculate each residual’s probability by comparing with a normal distribution; and (iii) multiply the probability to obtain the model’s likelihood.
What two concepts does VAR specification rely on?
Degrees of freedom and model likelihood
What is true of complex models?
They consume more degrees of freedom and are therefore less likely to be correct.
What is the Akaike criteria for specifying VARs?
AIC = -2[log(L) - k/T]
Where L is likelihood, k is the # of paramters, and T is the # of obs.
What is the Hannan-Quinn criteria for specifying VARs?
HQ = -2[log(L) - k*log(log(T))]
Where L is likelihood, k is the # of paramters, and T is the # of obs.
What is the Schwartz criteria for specifying VARs?
SC = -2[log(L) - K*log(T)/T]
Where L is likelihood, k is the # of paramters, and T is the # of obs.
What is real investment?
The aggregate level of investment from a macroeconomic point of view.
What is the formula for expenditure?
E = I + C +G
How do you derive the IS curve?
Set Y = E
If an investment has a return of 6% and inflation is -2%, what is my real return?
8%
How does inflation alter investment decisions?
It causes people to choose high risk, high return endeavours.
What is the consumption function?
C = c(0) + c(1)[Y-T]
Where c(0) is autonomous consumption and c(1) is MPC.
What is the LM curve?
M = P*L(i-r, Y)
What is the investment function?
I = v(0) - v(r)
Where v is the elasticity of investment.
How is “crowding out” due to government spending represented in the IS-LM model?
It causes the IS-LM model to reach a new equailibirum at a higher interest rate and slightly higher output.
Without it, Y would be higher and r would be unchanged.
How is an increase in output automatically dampened by other variables?
An increase in Y causes an increase in M(d), which in turn increases r and thereby reduces I. The reduction in I reduces E and therefore Y.
But not enough to fully erase the gain to Y (need stage 2 for that)
What is aggregate demand?
The relationship between the price level and output that is consistent with both the goods and money market equilibrium.
What is the one shift in the IS-LM model that will not also shift AD?
When LM shifts due to prices.
What two things do Type I Firms use to set their prices?
(i) The general price level (P); & (ii) the phase of the business cycle (Y-Ybar).
Given: p(1) = P + a(Y-Ybar)
What do Type II Firms use to set their prices?
Forecasts of the price level and growth.
Given: p(2) = P(e) + a(Y(e)-Ybar)
How can the pricing decisions of Type II firms be simplified?
If the firms set their prices in the long-run, then Y(e)-Ybar = 0 and p(2) = P(e).
What is true of firms in the long-run?
They are all Type I.
What is a recession mathematically?
Y < Ybar
What are adaptive expectations?
P(e) = P(t-1)
What is the steady state mathematically?
Where Y = Ybar & P = P(e)
Why do we reframe the IS-LM-AS model as changes to output and price level?
To simplify it by removing regular and predictable increases in growth and expectations.
What is NIPA
National Income and Production Accounts
Consistent of 7 accounts showing the distribution of income.
What is double-entry accounting?
That each data term is entered twice, once on each side of the table.
What is GDI?
Measure of the incomes and costs incurred in the production of GDP.
It should be equal to GDP.
When should durables be considered an investment?
For reference, PCE is divided in durables, non-durables, and services.
Over shorter time spans
What is Gross Private Domestic Investment?
All investment in fixed assets by firms and non-profit organizations
How do you caculate NDP?
NDP = GDP - CFC
CFC: Consumption of Fixed Capital
When estimating a VAR, what time do we start at?
-p + 1
What is orthogonalization, exactly?
Forcing the residuals to have a diagonal variance-covariance matrix.
What is true about the economy when there are no Type II firms?
There are no recessions as Y = Ybar.
