Moreno - Final Examination

Jan Luziel D.
Moreno
Bachelor of Science in Economics
Environmental and Development Economics
Econ 148 - Final Examination
I. Identification.
1. A statistical property of a time series where characteristics, like the mean,
variance, and other moments, are constant over time. Stationary
2. A statistical property of two or more-time series variables where the linear
combination of said variables produces random errors. Non-stationary
3. A component of a time series which translates to having current values being
partly determined by its past values. Trend
4. The order of *********** tells us the number of differencing a time series must
go through in order to be stationary. Differences
5. A component of a time series contributing to regular ups and downs in the
value of the series. This component is persistent for a period, like for a year.
Seasonal Component
6. A **** **** process is characterized with having the coefficient of the AR (1)
component to be equal to 1. Unit Root
7. The A******** D*****-F***** test can be used to determine the stationarity of a
time series. Augmented Dickey-Fuller
8. A time series process that is stationary and unpredictable. It is a sequence of
random errors. White Noise
9. A time series process that is not stationary and hard to predict. Its current
value is dependent on previous values. Deviations of current and previous
values are random. Random Walk
10. A statistical hypothesis used to determine whether a time series is useful in
forecasting another time series. Granger Causality Test
II. Essay.
1. In a finite distributed lag model (FDL), we allow one or more variables to affect
y with a lag. For example, consider the model crimet = bo + b1unempt +
b2unempt-1 + b3policet + ut , suppose that unemp is constant equal to z, in all
time periods and increases by one unit z + 1 at current time t and reverts to its
previous level at other future time, show (i) that b1 is the immediate change in
crime due to the one-unit increase in unemployment at time t and (ii) that b2 is
the change in crime one period after the temporary change.
2. If we are interested in the permanent effect of unemployment on crime, show
that after one period crime has changed by b1 + b2. (Note that at before time
t, unemp is constant z, and at time t, unemp increases permanent to z + 1).
3. In an equation for annual data, suppose that intt = 1.6 + 0.48inft – 0.15inft-1 +
0.32inft-2 + ut, where int is an interest rate and inf is the inflation rate, what are
the impact propensity and long-run propensity?
The impact propensity is 0.48, while the long-run propensity is 0.48 −
0.15 + 0.32 = 0.65.
4. For an ADL(1,1) model, derive expressions for the effect of a permanent
change in Xt on to Yt, Yt+1, Yt+2, and Yt+3.
This says that for an ADL(1, 1) model, a temporary unit increase in Xt
results in a change in Yt , which decreases as t increases and returns to the
initial value of Yt. On the other hand, if the increase in Xt is permanent
(imposing Yt−1 = Yt = Yt+1... = Y , Xt−1 = Xt = Xt+1... = X), then the changes
in Xt , Xt+1 and so on will lead to the following cumulative marginal effects.
Imposing the stability condition allows us to determine the long-run
effect of a permanent increase in X. It is given by the long-run multiplier or
equilibrium multiplier.
If the unit change in Xt is permanent, the expected long-run permanent

cumulative change is Y is given by
5. Differentiate the difference in effect of a deterministic trend from a stochastic

trend when doing a regression analysis.
Time series with a deterministic trend always revert to the trend in the
long run meaning the effects of shocks are eventually eliminated. Forecast
intervals have constant width. Time series with a stochastic trend never
recover from shocks to the system which shows the effects of shocks are
permanent.
6. Outline the Engel-granger test for cointegration. How can we derive the
error-correction model from this exercise?
The Engle Granger step method is a single equation technique which is
conducted as follows, the first step is that make sure that all the individual
variables are I(1). Then estimate the cointegrating regression using OLS.
Followed by saving the residuals of the cointegrating regression, ûₜ.
Lastly, test these residuals to ensure that they are I(0). The second step is to
use the step 1 residuals as one variable in the error correction model.
It says that the change in Yt is due to the current change in Xt plus an
error-correction term: if Yt−1 is above the equilibrium value corresponding to
Xt−1, that is, if the ‘disequilibrium error’ in the square brackets is positive, then
a ‘go to equilibrium’ mechanism generates additional negative adjustment in
Yt. The speed of adjustment is determined by 1 − φ, which is the adjustment
parameter. Note that stability assumption ensures that 0 < 1 − φ < 1.
Therefore only a part of any disequilibrium is made up for in the current
period.
7. Outline the Granger causality test.

Granger causality is an econometric test used to verify the usefulness
of one variable to forecast another.
A variable is said to:
● Granger-cause another variable if it is helpful for forecasting the
other variable.
● Fail to Granger-cause if it is not helpful for forecasting the other
variable.
Granger causality only provides information about forecasting ability, it
does not provide insight into the true causal relationship between two
variables. In particular, we should use Granger causality testing when:
● We are interested in forecasting performance, not the theoretical
model behind the forecast.
● Our data is stationary.
When testing for Granger causality:
● We test the null hypothesis of non-causality
(H0:β2,1=β2,2=β2,3=0)
● The Wald test statistic follows a χ2 distribution.
● We are more likely to reject the null hypothesis of non-causality
as the test statistic gets larger.
● We should test both directions X⇒Y and X⇐Y.

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Jan Luziel D.

Econ 148 - Final Examination

If the unit change in Xt is permanent, the expected long-run permanent

5. Differentiate the difference in effect of a deterministic trend from a stochastic

7. Outline the Granger causality test.

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