# MODEL on KOREAN EXCHANGE RATE DETERMINATION by cmz65105

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```									ERROR CORRECTION MODEL on KOREAN EXCHANGE RATES

General Form

Yt 0 1X t  1 X t 1 2Yt 1ut or

Yt 0 1X t  1( X t 1Yt 1 )ut when we assume equality between  1   2

(NOTE: This way we can call         ( X t 1Yt 1 )SRADJ t . We can first test for the
above restriction before we impose this restriction using Wald).

In our case, in PPP model, Yt  log NEXCt and hence, Yt   log NEXCt  d log NEXCt

Similarly, Yt [ log NEXCt ]  X t [log p h t  log pf t ]

Hence, I call X t  DIFPt  log p h t  log pf t and create it accordingly (see below).

We need X t  dX t  dDIFPt to generate the first regressor in our model on the RHS.
I create dDIFPt by using the Eviews command below.

I call   SRADJ DIFPt 1 LogNEXCt 1 and create it as below.

Once these variables are created, it is easy to check whether PPP really holds and whether Short-
run disequilibrium (adjustment towards long-run stable cointegrated relationship exists).

Below, the coefficient of SRADJ is significant and positive, hence there is deviation from the
PPF in the short-run, but in the long-run, because of the existence of cointegration between
exchange rate and price ratio, this disequilibrium disappears and a long-run stability is achieved.

However, a number of diagnostic checks are needed, for instance, see if AR(4) is present in your
quarterly data (use B-Godfrey test). If so, add ar(1) ar(2) ar(3) ar(4) to your model along with
dummy variables to capture structural changes. Graphing lognexc is a first step towards identifying
Error Correction Model: Initial Model

Source |        SS        df      MS           Number of obs =    62
-------------+------------------------------        F( 2, 59) = 11.54
Model | .006916984 2 .003458492               Prob > F    = 0.0001
Residual | .017684147 59 .000299731               R-squared = 0.2812
Total | .024601131 61 .000403297              Root MSE     = .01731

------------------------------------------------------------------------------
D.lexrate |          Coef. Std. Err.           t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ldifp       |
D1 | .5356129 .1585586 3.38 0.001 .2183378 .8528879
sradj         | .0700736 .0305932 2.29 0.026 .0088567 .1312904
_cons          | .464791 .2018968 2.30 0.025 .0607964 .8687857

After performing LM test on SC with lags=4, there is evidence for even 12th order,
AR(12) serial correlation. I added a time trend t and lagged dependent variable to correct
for serial correlation. But time trend turned out to be insignificant so I dropped it but
kept the lagged dependent variable. Next, I again tested for AR (4). No serial correlation
was found with the inclusion of the lagged dependent variable-which is significant! (See
the log file for tests and alternative specifications). The result is below:

Source |      SS      df      MS                       Number of obs = 61
-------------+------------------------------                F( 3, 57) = 32.22
Model | .01469796 3 .00489932                          Prob > F = 0.0000
Residual | .008668251 57 .000152075                       R-squared = 0.6290
Total | .02336621 60 .000389437                        Root MSE     = .01233

------------------------------------------------------------------------------
D.lexrate | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lexrate       |
LD | .670811 .0890901 7.53 0.000 .4924113 .8492108
ldifp       |
D1 | .1503346 .1693271 0.89 0.378 -.1887372 .4894064
sradj       | .0500136 .0219468 2.28 0.026 .0060658 .0939613
_cons          | .3304593 .1448661 2.28 0.026 .0403701 .6205486
------------------------------------------------------------------------------
Note adjusted Rsq improved considerably! But ddifp turned insignificant. We need to add
some dummies to capture structural breaks to improve on this model. When we graph
lexrate against time for Korea, we see that the won depreciated consistently since 1984
till the early 1988, and then appreciated from 1988 till 1992, and depreciated again
against the dollar, so creating two time dummies for these periods, we can actually fit a
better model as it is currently misspecified.

reg d.lexrate l.d.lexrate d.ldifp sradj d88 d92

Source |        SS        df      MS                   Number of obs =   61
-------------+------------------------------                F( 5, 55) = 22.53
Model | .015699627 5 .003139925                       Prob > F   = 0.0000
Residual | .007666584 55 .000139392                      R-squared = 0.6719
Total | .02336621 60 .000389437                       Root MSE    = .01181

------------------------------------------------------------------------------
D.lexrate |          Coef. Std. Err.           t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lexrate        |
LD | .4576171 .1166871 3.92 0.000 .2237709 .6914634
ldifp       |
D1 | .1767859 .1634987 1.08 0.284 -.1508727 .5044445
sradj         | .0370291 .0216026 1.71 0.092 -.0062634 .0803216
d88           | -.0154306 .0057571 -2.68 0.010 -.026968 -.0038931
d92           | .0095217 .0047104 2.02 0.048 .0000818 .0189616
_cons           | .2520502 .1420857 1.77 0.082 -.0326959 .5367963
------------------------------------------------------------------------------

UNIT Root and Cointegration Tests

Before you specify your model, do unit root and cointegration tests on your dependent
and independent variable(s) as follows.

If unit root exists on lognexc and difp variables, then you can (should) difference these
variables and see next whether a cointegrating (long-term) relationship exists between
lognexc and difp (in level terms, not in first differences as in ECM)(as PPP implies)

Unit Root Test: dfuller lexrate (Augmented DF test). This test searches for a unit root in
level lexrate variable. Repeat it for difp variable. If there is a unit root, the series is non-
stationary (does not have a constant variance over time, and there is growth in these
series!) and first-differencing should be applied for use in models.

Based on the p-value (MacKinnon p>alpha), we can not reject the null! There exists a
unit root! Alternatively, d-f test statistics in absolute value is less than the absolute value
of the criticals at 1, 5 and 10% significance-again, can not reject the null of a unit root.
There exists unit root in level terms of lexrate!
dfuller lexrate, lag(4) trend regress

Augmented Dickey-Fuller test for unit root                 Number of obs =              58

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical          5% Critical        10% Critical
Statistic          Value              Value             Value
------------------------------------------------------------------------------
Z(t)           -2.384             -4.132             -3.492            -3.175
------------------------------------------------------------------------------
* MacKinnon approximate p-value for Z(t) = 0.3895

------------------------------------------------------------------------------
D.lexrate |          Coef. Std. Err.           t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lexrate       |
L1 | -.0468462 .0196505 -2.38 0.021 -.0862963 -.0073962
LD | .6755657 .1354887 4.99 0.000 .4035607 .9475707
L2D | -.0117261 .1581486 -0.07 0.941 -.3292226 .3057703
L3D | .1231394 .1551363 0.79 0.431 -.1883097 .4345885
L4D | -.0124157 .1286154 -0.10 0.923 -.2706218 .2457904
_trend        | -7.26e-06 .0000997 -0.07 0.942 -.0002075 .0001929
_cons          | .3115659 .1301214 2.39 0.020 .0503363 .5727954
------------------------------------------------------------------------------

. dfuller lexrate, trend regress

Dickey-Fuller test for unit root                    Number of obs =                62

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical          5% Critical        10% Critical
Statistic          Value              Value             Value
------------------------------------------------------------------------------
Z(t)           -2.949             -4.124             -3.488            -3.173
------------------------------------------------------------------------------
* MacKinnon approximate p-value for Z(t) = 0.1468

------------------------------------------------------------------------------
D.lexrate |          Coef. Std. Err.           t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lexrate       |
L1 | -.0699019 .0236998 -2.95 0.005 -.1173251 -.0224786
_trend        | -.0003136 .0001309 -2.40 0.020 -.0005755 -.0000516
_cons          | .4780376 .1559378 3.07 0.003 .1660067 .7900684

Repeat the same procedure for first differences: dfuller d.lexrate, trend regress

dfuller d.lexrate, trend regress

Dickey-Fuller test for unit root                          Number of obs =               61

---------- Interpolated Dickey-Fuller ---------
Test         1% Critical       5% Critical   10% Critical
Statistic         Value            Value            Value
------------------------------------------------------------------------------
Z(t)          -3.124           -4.126           -3.489           -3.173
------------------------------------------------------------------------------
* MacKinnon approximate p-value for Z(t) = 0.1007

------------------------------------------------------------------------------
D2.lexrate | Coef. Std. Err.               t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
D.lexrate |
L1 | -.2790501 .0893358 -3.12 0.003 -.4578752 -.100225
_trend       | -.0000708 .0001019 -0.70 0.490 -.0002748 .0001331
_cons        | .0029275 .0037329 0.78 0.436 -.0045448 .0103997
------------------------------------------------------------------------------
We get a better result, p-value is significant at 10%, hence we barely reject the Null at 10%:
There is no unit root in first differences. We don’t need further differencing of the data. Repeat the
same for difp variable. I could not find unit root in these series.

Johansen Cointegration Test:, we have found no evidence of cointegration between
log(excrate) and diffp.

Date: 11/21/05 Time: 19:00
Trend assumption: Linear deterministic trend
Series: LOG(EXRATE) DIFFP
Lags interval (in first differences): 1 to 2

Unrestricted Cointegration Rank Test (Trace)

Hypothesized                              Trace               0.05
No. of CE(s)         Eigenvalue          Statistic       Critical Value     Prob.**

None             0.188672           14.90303          15.49471             0.0612
At most 1 *         0.074585           4.030692          3.841466             0.0447

Trace test indicates no cointegration at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue)

Hypothesized                            Max-Eigen             0.05
No. of CE(s)         Eigenvalue          Statistic       Critical Value     Prob.**

None             0.188672           10.87234          14.26460             0.1607
At most 1 *       0.074585         4.030692         3.841466          0.0447

Max-eigenvalue test indicates no cointegration at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

LOG(EXRATE)          DIFFP
-5.198721         48.70651
14.96714        -17.65585

D(LOG(EXRAT
E))           -0.000398        -0.002972
D(DIFFP)         -0.003969         5.80E-05

1 Cointegrating Equation(s):       Log likelihood     336.9849

Normalized cointegrating coefficients (standard error in parentheses)
LOG(EXRATE)         DIFFP
1.000000       -9.368940
(2.36525)

Adjustment coefficients (standard error in parentheses)
D(LOG(EXRAT
E))           0.002071
(0.00837)
D(DIFFP)         0.020636
(0.00631)

```
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