HANDOUT 1

Question 1

How do we get a de-trended GDP series? What does it show?

Answer 1

Plot the residuals - what’s left in GDP having extracted the time trend. Shows business cycles.

Question 2

seasonality =

Answer 2

fluctuations in the data with a regular period

Question 3

If we extract the time trend and seasonal trend from a series, what are we left with?

Answer 3

Economic series - cyclical elements = explained by economics e.g. income, prices. We’ve extracted the deterministic elements.

Question 4

Adjustment to equilibrium if NO lags

Answer 4

If X1 increases by 1 unit, Y adjusts immediately to the new equilibrium.

Question 5

If we only have lags on X variable, how does a change in income today affect the model?

Answer 5

In each period, there’s a direct effect of the change in income on consumption in that period (no indirect). smooth consumption over time. Eventually the shock dissipates out the system

Question 6

2 methods of finding LR effect

Answer 6

1. sum up SR marginal responses

2. solve for LR equilibrium equation

Question 7

A lagged dependent variable picks up…

Answer 7

Persistence of habits.
Today’s consumption choice affects tomorrow’s consumption choice. Suppose we find £1 today and buy a Mars bar, affects tomorrow’s consumption as now addicted to mars bars.

Question 8

What is dYt-1 / dX1t if the shock is unexpected?

Answer 8

If the shock is unexpected, a change in income today has NO effect on yesterday’s consumption.

Question 9

Sum of geometric series =

Answer 9

a / (1 - r)

Question 10

The LR effect of an increase in income today tells us

Answer 10

The total additional increase in consumption over an individual’s lifetime from finding £1 today over what it would’ve been without the income shock.

Question 11

What do we implicitly assume about the coefficient on the lagged dependent variable? Why?

Answer 11

We assume the coefficient on the lagged dependent variable is < 1 in absolute magnitude. Condition for stability. We need the indirect effects to get smaller over time so that the shock eventually dissipates out of the system.

Question 12

Therefore, the persistence of shocks over time is determined by…

Answer 12

The coefficient on the lagged dependent variable. Large coefficient = more persistent shocks.

Question 13

If the coefficient on the lagged dependent variable is positive (but < 1), what do the dynamics of returning to equilibrium look like?

Answer 13

Smooth decay back to 0 at rate 0.5. Shock eventually dissipates out of the system.

Question 14

If the coefficient on the lagged dependent variable is negative (but > -1), what do the dynamics of returning to equilibrium look like?

Answer 14

Oscillations between +VE and -VE - but the shock will eventually dissipate out of the system as long as the coefficient on the lagged dependent variable is not more negative that -1.

Question 15

Therefore, the adjustment back to equilibrium is determined by (2)…

Answer 15

1. The sign of the lagged dependent variable

2. The magnitude “

Question 16

How do we estimate models with only lagged X variables?

Answer 16

STANDARD OLS

Question 17

Which CLRM assumption is violated when we have a lagged dependent variable?

Answer 17

E(€t I explanatory variables) = 0
Since COV(Yt, €t) ≠ 0
And COV(Yt, Yt-1) ≠ 0
So COV(Yt-1, €t) ≠ 0 - Yt-1 is an explanatory variable here = CLRM assumption 1 violated.

Question 18

When we have a lagged dependent variable, what do we replace CLRM assumption 1 with?

Answer 18

CLRM assumption 1 = strict exogeneity
Replace with Contemporaneous exogeneity
E(€t I Y1, Y2,...,Yt-1) = 0
Error term is uncorrelated with PAST values of Y. But it can be correlated with Yt.
Still assume E(€t I Xts) = 0

Question 19

Is OLS unbiased for lagged dependent variables?

Answer 19

NO - but it IS CONSISTENT

As t–> infinity, E(b1)–>B1

Question 20

When we have a lagged dependent variable model, how do we test single and multiple restrictions?

Answer 20

Single = approx Z test via CLT
Multiple = Chi-squared test

Question 21

What assumption that we had for cross-sectional data do we get rid of? Why?

Answer 21

Get rid of assumption of random sampling, because with time-series data observations are related across time.

Question 22

What 2 conditions do we replace the random sampling assumption with?

Answer 22

1. Stationarity

2. Weak dependence

Question 23

3 conditions for stationarity

Answer 23

1. E(Yt) = M - mean constant over time
2. V(Yt) = sigma^2 Y - variance constant over time
3. COV(Yt, Yt-h) = gamma h - covariance of the variable between 2 points in time depends only on how far apart, not location in space.

Question 24

Weak dependence condition

Answer 24

COV(Yt, Yt-h) –> 0 as h–> infinity

A variable today is NOT really driven by what it was at some infinite point in the past.

Question 25

We can do some time-series analysis only if…

Answer 25

We are prepared to assume stationarity & weak dependence (even though they’re very unrealistic for most series)