samlet årgang - Økonomisk Institut - Københavns Universitet

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Table 2. Parameter estimates of the ARDL models.
NATIONALØKONOMISK TIDSSKRIFT 2005. NR. 1
Denmark Norway Sweden
-0.019 * (-2.78) -0.030 * (-2.68) -0.034 * (-3.07)
0 0.806 * (5.37) 1.480 * (5.06) 1.444 * (5.46)
1 – – – – 0.321 * (4.87)
2 0.252 * (3.01) – – -0.512 * (-7.80)
R – 2 0.25 0.15 0.44
DW 1.82 2.20 1.93
LM(2) 1.29 [0.52] 2.08 [0.35] 3.57 [0.17]
LMARCH(2) 0.35 [0.84] 5.41 [0.07] 39.72 [0.00]
Note: t-values of the parameter estimates in parenthesis and with a * indicating significance at least at the 5 per cent
level. LM(2) and LMARCH(2) are Lagrange Multiplier tests for second order residual autocorrelation and second order
autoregressive conditional heteroscedasticity, respectively, with p-values in parenthesis [ ].
4. Alcohol consumption in the long run: a mean reversion process or a random
walk?
When evaluating the data for alcohol consumption from figure 1 these variables seem
very much to exhibit random walk behaviour, i.e. be non-stationary I(1)-variables.
Testing for unit root behaviour by the Dickey-Fuller test statistic is reported in table 3.
The conclusion from the DF/ADF-tests is in all three cases non-stationarity as the
critical value is -2.88 at the 5% level of significance according to MacKinnon (1991).
When taking a closer look at figure 1 an alternative interpretation of the unit root
hypothesis – especially for Norway and Sweden – might be an asymmetric adjustment
process towards a long-run level of alcohol consumption that is non-zero. Such an
alternative hypothesis to the random walk behaviour as tested for in table 3 might be
the so-called threshold autoregressive model (TAR-model) as presented in Enders and
Granger (1998), see also Enders and Siklos (2001). In the present case of alcohol
consumption levels the most obvious version of these models will be the TAR model
with a linear attractor – the latter being the average long-run level of alcohol consumption.
The threshold model (TAR) with a linear attractor is defined by (2) and (3), see
Enders and Granger for further details:
ln At =It1 (ln At-1 –A – )+(1 –It )2 (ln At-1 –A – )+∑iln At-i + t i=1
where the linear attractor (A – ) is the average value of A t in logs and t is a white noise
disturbance term. The indicator function, I t , is defined as:
p
(2)