Macro Eco No Metrics 4

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VEC model the influence of export on

economic growth

Katarzyna Lada, Piotr Wjcik

19.04.2007/26.04.2007

This classes are based on:

E. Anoruo (2001) Exports and economic growth: an error correction

model

You can find link to this article as well as the data for the classes on the web

pages www.wne.uw.edu.pl/~krosiak or www.wne.uw.edu.pl/~pwojcik. You

should copy basics4.wf1 and vec anoruo.wf1 into chosen folder.

basics4.wf1

Data description: quarterly Danish data 1974q1 1987q3, downloaded from

johansens website http://www.math.ku.dk/~sjo/data/data.html

Variables: described in the workfile

VEC anoruo.wf1

Data description: quarterly Polish data 1996q4 2006q3

Variables: GDP Gross domestic product (in real terms), exportsexports

(in real terms), M2 money supply (under the M2 definition), rerreal

exchange rate (zloty/euro)

1 Macroeconomic background

The purpose of the cited paper is to investigate whether the export-led

growth hypothesis holds for five emerging economies of Asia . Authors

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Macroeconometrics 2007, handout4

use cointegration concept to analyse long-run relationship between exports and

GDP growth. To estimate short-run relationships, they use VEC model.

For most countries they have found evidence for the export-led growth hy-

pothesis.

Questions to the paper:

1. Characterise shortly the import substitution and exports promotion stra-

tegies.

2. List some different methods used in the literature to investigate the export-

led growth hypothesis?

3. What econometric tools and procedures are used in the paper (in order as

they appear in the text)?

2 Econometric analysis in Eviews

Vector Error Correction (VEC) model is multivariate generalization of ECM

model known from the previous classes. You can see it also as VAR model desi-

gned for use with nonstationary time series that are known to be cointegrated.

The specification of VEC models contains the cointegration relations, so it as-

sumes that the economy converges to the long-run relationships. On the other

hand, it allows also for the short-run adjustment dynamics.

The very simple example of VEC model is the one below, with one cointe-

grating equation (y = x) and one lag of difference terms:

xt = 1(yt1 xt1) + 11xt1 + 12yt1 + 1t

yt = 2(yt1 xt1) + 21xt1 + 22yt1 + 2t

2.1 Cointegration test

Remember, the cointegration test is only valid if you have non-stationary series!

Task: Find out if the series: ibo, ide, lrm, lry are non-stationary. Check the

intergration order. Can they be cointegrated?The purpose of the cointegration test is to determine whether several non-

stationary time series are cointegrated or not. The presence of a cointegrating

relation forms the basis of the VEC specification. EViews implements VAR-

based Johansen tests.

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In empirical studies you work with series with the seasonality, so you can

include seasonal dummies to get rid of the seasonality. However, you should

bear in mind that standard 0-1 seasonal dummies affect both the mean and the

trend of the level series. To handle this problem, Johansen suggests using cen-

tered (orthogonalized) seasonal dummy variables, which shift the mean without

contributing to the trend. Centered seasonal dummy variables for quarterly and

monthly series can be generated by the commands:

series dq = @seas(q) - 1/4

series dm = @seas(m) - 1/12

for quarter q and month m, respectively.

Task: Create centered seasonal dummies: d1, d2, d3.

To perform Johansen cointegration test, first open the series: ibo, ide, lrm,

lry, as group

or

Task: Estimate simple VAR model of four variables: ibo, ide, lrm, lry, and

one lag. To get rid of seasonality include, as exogenous variables, three seasonal

dummies: d1, d2, d3.

and then select View/Cointegration Test...

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and provide the required information.

Deterministic trend assumption of test

Practical guides:

use case 1 only if you know that all series have zero mean (unusual in

empirical studies);

case 5 may provide a good fit in-sample but will produce implausible

forecasts out-of-sample.;

use case 2 if none of the series appear to have a trend;

use case 3 if series are trending and you believe all trends are stochastic;

use case 4 if series are trending and you believe some of them are trend

stationary;

use case 6 if you are not certain which trend assumption to use (Eviews

will help you determine the choice of the trend assumption).

Exogenous Variables

You may also provide some exogenous variables (but not trend or constant

since they are specified in the trend assumption of test).

Lag interval

Specify the lags of the test VAR as pairs of intervals. Note that the lags are

specified as lags of the first differenced terms used in the auxiliary regression,

not in terms of the levels!

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Results interpretation

Number of cointegrating vectors

The first two tables report results for testing the number of cointegrating

relations. Two types of test statistics are reported: trace statistics and the ma-

ximum eigenvalue statistics. For each table, the first column is the number of

cointegrating relations under the null hypothesis, the second column is the or-

dered eigenvalues of the matrix , the third column is the test statistic, and the

last two columns are the 5% critical values.

Coefficients of cointegrating vectors

The second part of the output provides estimates of the cointegrating rela-

tions and the adjustment parameters . As is well known, the cointegrating

vector is not identified unless we impose some arbitrary normalization.

The remaining tables report estimates from a different normalization for

each possible number of cointegrating relations.

2.2 Imposing identifying restrictions

To impose restrictions in a cointegration test, select View/Cointegration Test...

and bring up the VEC Restrictions tab. You will enter your restrictions in the

edit box that appears when you check the Impose Restrictions box:

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Restrictions on the Cointegrating Vector

To impose restrictions on the cointegrating vector , you must refer to the (i,

j)-th element of the transpose of the matrix by

B(i,j)the j-th element of in the i-th cointegrating relation.

Restrictions on the Adjustment Coefficients

To impose restrictions on the adjustment coefficients, you must refer to the

(i, j)-th elements of the matrix by A(i,j) the j-th element of in the i-th VEC

equation.

Example:

A(3,1)=0

The first two tables are as before. The second part of the output begins by

displaying the results of the LR test for binding restrictions:

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If the restrictions are not binding for a particular rank, the corresponding

rows will be filled with NAs.

Interpretation of the results: Conditional on there being only one co-

integrating relation, the LR test does not reject the imposed restriction at co-

nventional levels.

2.3 Estimation of VEC model

In the VAR toolbar click on Estimate and choose Vector Error Correction fromthe VAR Type tab. Remember that now, lag interval refers to first differences of

the variables in the VEC. Do not include constant and trend in the Exogenous

Variables tab, they should be specified in the Cointegration tab. In that tab

you decide on the number of cointegrating equations (less than the number

of endogenous variables!) and the trend specification. If you want to impose

restrictions on the cointegrating relations and/or the adjustment coefficients,

use the Restrictions tab.

Then click OK to estimate the VEC. Estimation of a VEC model is carried

out in two steps. First, using the Johansen procedure, the cointegrating rela-

tions are estimated. Then the error correction terms is constructed from theestimated cointegrating relations and a VAR in first differences including the

error correction terms as regressors is estimated.

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Output

In the first table you see results from the first step Johansen procedure

(estimates of cointegrating relations). If you did not impose restrictions, EViews

will use a default normalization that identifies all cointegrating relations.

The second table shows results from the second step VAR in first diffe-

rences, including the error correction terms (denoted CointEq1, CointEq2, ...)

estimated from the first step.

Task: Explore some views from VEC and compare them with those for VAR

Diagnostic Views

View/Cointegration Graph...

Graph of the estimated cointegrating relations.

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Proc

Procs/Make Cointegration Group...

This proc will create and display an untitled group object containing the

estimated cointegrating relations (COINTEQ01, COINTEQ02, ... )

PLEASE, LEARN MORE ABOUT THE ABOVE MENTIONED TOPICS

READING CHAPTER 24 OF Eviews 5 Users Guide.

3 Assisted work

Open the workfile vec anoruo.wf1. We will analyse Polish data series: exports

(exports), gross domestic product (gdp), money supply (m2) and exchange rate

100 ECU/100 Euro (rer).

1. Provide description of the time series into the workfile:

Open the series, View/Label... and add the description from above.

2. Generate the annualised growth rates (ith quarter of a current year over

ith quarter of the previous year) of the following time series: GDP, exports

and M2

series ggrow=100*(gdp-gdp(-4))/gdp

series egrow=100*(exports-exports(-4))/exports

series mgrow=100*(m2-m2(-4))/m2

3. Test for a unit root in each variable: ggrow, egrow, mgrow and rer = apply

appropriate ADF test.

Conclusion: test suggests the presence of I(1) for all variables.

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4. Test for cointegration using Johansen procedure.

Open the series as a group, View/Cointegration test...

Try to interpret the results analogously as in the paper on page 12.

5. Specify and estimate VEC consisting of four variables: egrow, ggrow, mgrow

and rer, with 4 lags and the cointegrating relations (the number of the co-

integrating relation should be taken from the resul)

(a) Perform and interpret the Granger Causality Test

(b) Estimate and interpret Impulse Response Functions

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