Exchange Market Pressure in Korea

1
Exchange Market Pressure in Korea

• Alycia McLarty
• Kristin McMahon
• Tyler OHagan

2
Exchange Market Pressure in Korea

• Exchange Market Pressure in Korea An
  Application of the Girton-Roper Monetary Model
  by Inchul Kim
• Examines the simultaneous adjustment of both
  exchange rates and the balance of payments in
  Korea
• Girton-Roper model states that an excess domestic
  supply of money will cause some combination of
  currency depreciation and an outflow of foreign
  reserves
• The following empirical equation was derived to
  assess Exchange Market Pressure on Korea
• R E -D P Y M

3

• R the change in foreign reserves as a proportion
  of the monetary base
• E the percentage appreciation of the exchange
  rate
• D the change in domestic credit as a proportion
  of the monetary base
• P the percentage change of the foreign price
  level
• Y the percentage change of real income
• M the percentage change of the money multiplier
• The data period considered begins with March
  1980, the first month after the adoption of the
  managed floating exchange rate system and ends
  July 1983

4

• Under a managed float system any excess supply of
  money can be relieved by some combination of an
  exchange depreciation and a loss in foreign
  reserves
• The magnitude of the market pressure is
  independent of whether the monetary authorities
  absorb the market pressure in the exchange rate
  or in foreign reserves

5
Exchange Market Pressure

• The result of excess demand or excess supply of
  the domestic currency
• This pressure on the exchange rate is relieved
  by
• (1) An exchange rate appreciation (excess
  demand) or depreciation (excess supply)
• (2) Government intervention buys (excess
  supply) or sells (excess demand) foreign
  reserves

6
Managed (Dirty) Float

• The Government (Central Bank) attempts to
  moderate exchange rate movements without keeping
  the exchange rate rigidly fixed
• The exchange rate does NOT fluctuate freely
• The Central Bank may buy or sell foreign reserves
  to prevent large changes in the exchange rate

7
R2 The coefficient of determination

• Proportion of the variation in DEP variable
  explained by INDEP variables through the sample
  line.
• Represents the total squared error that is
  represented by the model.
• Statistical measure of how well a regression line
  approximates real data points.
• Used in calculation of F-test statistic.

8
R2 and R2 Adjusted

• R2 RSS (residual sum of squared errors)
• TSS (total sum of squared
  errors)
• 1 ESS (estimated sum of squared errors)
• TSS (total sum of
  squared errors)
• R2 adjusted 1 Variance (e)
• Variance (Y)
• 1 ESS/n-k
• TSS/n-1
• R2 adjusted (R bar squared) is better because it
  does not change just because of a change in the
  number of variables.

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Question 1

• Estimate the following regression model
• LHVi a ß1Di ß2Pi ß3Yi ß4Mi ei
• OLS LHV D P Y M

• LHVi 0.0052498 0.78016Di 0.29007Pi
  0.056392Yi 0.63734Mi

(1.581) (-6.158) (0.5897)
(3.697) (-6.224)
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Question 1

• Test model for the existence of a regression at
  the 10 level of significance. F-Statistic
• OLS LHV D P Y M
• PRINT ANF

• F 12.11798 F0.05 2.23
• F gt F0.05 , therefore the model is significant at
  10 level.

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Question 1

• What is the coefficient of determination (R2) in
  estimated regression and what does this tell you?

• R2 0.5671, 56.71 of the variation in LHV is
  explained by the independent variables through
  the sample line.

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Hypothesis Testing

• Test the null hypothesis HO against the
  alternative hypothesis HA.
• Can only reject or not reject null hypothesis.
• T-test for significance is example of a
  hypothesis test testing the null hypothesis that
  a coefficient or constant should be equal to
  zero.
• Ex. HO a 0 t-stat a Sa St. Error for
  constant
• HA a ? 0 Sa
• Compare to t.05 for 10 level of significance or
  t.025 for 5 level of significance.
• If t-stat gt t.05(t.025) or t-stat lt - t.05(t.025)
  then reject HO at the 10 (5) level of
  significance.

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F-Test

• Two tailed hypothesis test to determine validity
  of restrictions.
• To estimate OLS with restrictions in Shazam
• OLS / NOCONSTANT
• TEST
• TEST Eqn 1
• TEST Eqn 2
• END

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• Example restrictions
• a 0, ß1 -1, ß2 1, ß3 1
• Shazam Code
• OLS / NOCONSTANT
• TEST
• TEST ß1 -1
• TEST ß2 1
• TEST ß3 1
• END

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F-Statistic

• F R2U R2R n k 1
• 1 R2U k 1
• n of observations U unrestricted
• k INDEP vars (DF) R restricted
• If F gt F(table) Reject Restricted Model
• Shazam code to print F-stat
• OLS
• PRINT ANF

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Question 2

• Test for model in question 1 the null hypothesis
  Ho that a 0 at the 10 level of significance.
• OLS LHV D P Y M
• TEST
• TEST CONSTANT 0
• END

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Question 2
t 1.581 Compare to t0.05 1.684 t lt t0.05 ,
therefore accept the null hypothesis that a is
not significant at the 10 level.
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Question 2

• On the basis of maximum adjusted coefficient of
  determination criterion, does the constant term
  belong in your model?
• OLS / NOCONSTANT
• R2(unrestricted model) 0.5203
• R2(no constant) 0.5014
• Therefore, because R2 is higher with the constant
  (a) included, the constant term belongs in our
  model.

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Question 2

• Are we going to drop or keep the constant term
  and why?
• By itself a is not significant but it seems to
  contribute to the model as a whole
• We keep the constant term because it increases
  the fit of the model (R2 R2).
• There is a risk of misspecification if a
  (constant term) is omitted.

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Question 3

• Note in basic equation of paper there is no
  constant and all coefficients are 1.
• Kims restrictive model r e -d p y m
• Perform F-test on restricted model, test null
  hypothesis (a 0, ß1 -1, ß2 1, ß3 1,
• ß4 -1)
• Should one reject Kims restrictive model for a
  more general G-R model?

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Question 3

• Test restricted model
• sample 2 43
• OLS LHV D P Y M / NOCONSTANT
• TEST
• TEST D -1
• TEST P 1
• TEST Y 1
• TEST M -1
• END

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Question 3

• OLS / NOCONSTANT

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Question 3

• Test/F-test output

• Results show an exaggerated F statistic
  (1109.8325). This happens when the constant term
  is omitted from the regression. Both R2 and F are
  biased and therefore we should reject the
  restricted model for the more general form (as in
  Q1).

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Question 4

• One of the key assumptions of the Kim model is
  the concept of Purchasing Power Parity (PPP).
  This states that the domestic price level P is
  equal to the exchange rate times the foreign
  price level. In dynamic form this converts to
  e p - p. Where p rate of domestic
  inflation, p rate of world inflation and e
  rate of appreciation of the local currency.

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• (A) In the constructed variable list, DIFF is
  comparable to p - p. For PPP to hold, e and
  DIFF should be highly correlated. Calculate the
  correlation coefficient of e and DIFF. Does this
  correlation test significantly different from
  zero at the 5 level of significance?

r 0.15746 t 0.15746v(43-2)/(1-0.157462)
1.021 t0.025 2.021 t lt t0.025 ? Cannot reject
the null hypothesis (r0) cannot confidently say
there is a correlation between E and DIFF
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• (B) More than being correlated, one should find
  that for PPP to hold that when one regresses E
  onto DIFF, the coefficient ß should equal 1. Run
  the regression E a ßDIFF e and test the
  null hypothesis that ß 1 at the 5 level of
  significance.

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• t0.025 2.021, compare to t -787.3113
• t lt -t0.025 Reject the null hypothesis
  therefore ß?1
• (C) Do the results of (A) and (B) support Kims
  strong assumption of PPP? Explain.
• No, the results of (A) and (B) do not support the
  purchasing power parity assumption. There is NOT
  a strong correlation between E and DIFF and the
  coefficient on DIFF does NOT equal 1.

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• GRAPH DIFF / TIME

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• GRAPH E / TIME

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Question 5

• Kim added the variable Q (e-1)/(r-1) to test
  the distribution of exchange market pressure
  between changes in the exchange rate (e) and
  changes in foreign reserve holdings (r).
• Reestimate regression with Q added.
• OLS LHV D P Y M Q
• Test the null hypothesis that ß5 0
• TEST Q 0

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Question 5

• With Q added to the regression all the
  significant variables remain significant (t gt
  1.684). The R2 improves from 0.5671 to 0.6514 and
  the R2 improves from 0.5203 to 0.6030.

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Question 5

• The t test shows the t statistic of 2.9505203 is
  greater than the t-table value of 1.684 therefore
  we reject the null hypothesis that Q0 Q is
  therefore significant at the 10 level
• Does it appear that distribution influences
  exchange market pressure? Explain.
• It does appear that distribution influences
  exchange market pressure because the presence of
  the variable Q increases the fit of the model and
  the variable itself is significant.

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Question 6

• It is easy to demonstrate that the estimated
  coefficients for the model are the sum of the
  estimated coefficients if one runs separate
  regressions of R and E onto D, Y, P, and M. Kim
  concludes that in the case of Korea, most
  exchange market pressure is absorbed by
  adjustments in foreign reserves. If Kims
  conclusions are correct then D, Y, P and M should
  not influence E alone.

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Regression using Foreign Reserves as the
Dependent Variable
Regression using Exchange Rate as the Dependent
Variable
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• (A) Estimate the following multiple regression
• E a ß1D ß2P ß3Y ß4M e

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• (B) Test the null hypothesis (ß1 ß2 ß3 ß40)
  at the 10 level of significance.

F0.10 2.84 F lt F0.10 Therefore Accept the
Null Hypothesis the variables together do not
explain a significant proportion of the model.
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• (C) Do your results in part (B) support Kims
  conclusion that most of the pressure is absorbed
  by changes in foreign reserve holdings? Explain.
• The result of (B) supports Kims conclusion that
  most of the pressure is absorbed by the change in
  foreign reserve holdings, as (B) indicates that
  there are other variables influencing E ( the
  exchange rate).

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Question 7

• Test for the existence of first order
  autocorrelation with 5 level of significance.
• If there is existence of first order
  autocorrelation, transform it and re-estimate it
  using the Cochrane-Orcutt procedure.

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Autocorrelation (Serial Correlation)

• Issue when working with time-series data
• Definition When successive values in the data
  are consistently correlated to each other.
• Two common ways to detect
• Plotting the residuals over time and looking for
  pattern
• The Durbin-Watson statistic

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Plotting of Residual over time

• Useful in detection of serial correlation
• Equation
• residt LHV (0.0052498) (0.78016D) -
  (0.29007P) - (0.05639Y) (0.63734M) ut
• ut ?ut-1 et
• Shazam Command for Plot
• plot resid

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Plot of Residual Output
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The Durbin-Watson Statistic

• More accurate and conclusive test
• Tests for first order autocorrelation
• Formula
• Compares the residual of time period t with time
  period t-1
• DW range 0 4 (2 being perfect no
  autocorrelation)
• Shazam command to calculate DW statistic
• OLS LHV D P Y M / DWPVALUE

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The Durbin-Watson Statistic
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The Durbin-Watson Statistic

• 43 Observations, 4 Independent Variables
• (n43, k4)
• Calculated DW 2.15501
• At the 5 level of Significance
• dL 1.38 (4- dL) 2.62
• dU 1.72 (4- du) 2.28
• Therefore, since our DW of 2.15501 lies in the
  range of dU to (4- du) 2.28, then there is no
  significant evidence of first- order
  autocorrelation.

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Serial Correlation Coefficient (rho, ?)

• ut ?ut-1 et
• Is a measure of the degree of correlation between
  consecutive residual values.
• Values range from
• -1 (perfect negative serial correlation)
• 0 (no serial correlation)
• 1 (perfect positive serial correlation).

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Methods of Calculating rho (?) (first order
serial correlation coefficient)

• Regress the residual against the lagged residual
  without a constant and the coefficient on the
  lagged residual is the estimated value for rho
  (?)

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Methods of Calculating rho (?) (first order
serial correlation coefficient)

• Use the /rstat command in Shazam to display the
  estimated value rho (? value)

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Methods of Calculating rho (?) (first order
serial correlation coefficient)

• t-ratio of correlation coefficient -0.6104
• Critical value of t-ratio from 5 level of
  significance with 41 degrees of freedom 2.021
• Coefficient significant if (t gt tcrit) or (-t lt
  -tcrit)
• Insignificant if (-tcrit lt t-ratio lt tcrit)
• Our t-ratio of the serial correlation coefficient
  is insignificant, and therefore there is no
  significant evidence of serial correlation.

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Question 8

• Test for the presence of higher order
  autocorrelation using the Lagrange multiplier
  test for higher order autocorrelation.
• Include the lag residuals for lags 1, 2, 3 and
  12.

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Question 8 The Lagrange Multiplier Test

• Can be used to test for the presence of first
  order autocorrelation, as well as higher order
  autocorrelation.
• Theory You take the residuals from the original
  regression and regress the current residual onto
  the explanatory variables within the model plus
  the lagged values of the residuals up the desired
  length.

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Question 8 Steps of the Lagrange Multiplier Test

• 1) Estimate the model by OLS, as usual, and
  calculate the residual for the original OLS
• OLS LHVt a ß1Dt ß2Pt ß3Yt ß4Mt et
• Residual e LHV - a - ß1Dt - ß2Pt - ß3Yt - ß4Mt
• 2) Run an auxiliary regression of the residual
  onto the explanatory variables PLUS the lagged
  values of the residuals.
• OLS et a ß1Dt ß2Pt ß3Yt ß4Mt et-1
  et-2 et-3 et-12

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Steps of the Lagrange Multiplier Test

• 3) Obtain the LM statistic by
• LM(?2) (n p)R2
• n number of observations
• p number of lagged variables (or d.f)
• Compare to critical value from the chi-square
  distribution at desired level of significance,
  and the degrees of freedom equal to the number of
  lagged variables (in our case d.f. 4)

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Question 8

• sample 2 43
• genr resid LHV - 0.0052498 (0.78016D) -
  (0.29007P) - (0.05639Y) (0.63734M)
• genr resid1 lag(resid, 1)
• genr resid2 lag(resid, 2)
• genr resid3 lag(resid, 3)
• genr resid12 lag(resid, 12)
• ols resid D P Y M resid1 resid2 resid3 resid12

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Question 8
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Question 8

• Results
• R2 0.3023
• n 43 observations
• P 4
• LM statistic (43-4) 0.3023 11.79
• Chi-square critical value (10 level of
  significance) 7.78
• Therefore, we can reject null hypothesis of
  uncorrelated error terms. Meaning, that at the
  12th degree of lag there exists evidence of
  autocorrelation.

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The Lagrange Multiplier Test

• Reasons for including the explanatory variables
  in the auxiliary regression
• To correct for any bias in the original OLS
  regression due to misspecification of the error
  term
• To keep the test consistent

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Question 8 Shazam Commands

• Shortcut to calculating lag variables
• The variable desired to lag is named resid
• Shazam command to calculate lag
• genr residalag(resid, a)
• where a is the degree of lag desired
• Example. For 4th degree of lag
• genr resid4 lag(resid, 4)

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Question 9

• Having discovered higher order autocorrelation in
  the model in question 8, you now need to
  transform the model by creating new variables of
  the form
• Yt Yt ?1Yt-1 - - ?pYt-p
• Xjt Xjt ?1Xjt-1 - - ?pXjt-p
• Then re-estimate the model using the new
  variables.

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• Only lag 12 is significant at a meaningful level
  with an estimate of ?12 0.257.
• In order to create variables with a 12 period
  lag, the command LAG(var,n) was used where var is
  the original variable and n is the number of lags
  required
• New variables were created using the GENR
  command
• LLHV LHV - (0.257)LAG(LHV,12)
• LD D - (0.257)LAG(D,12)
• LAP P - (0.257)LAG(P,12)
• LY Y - (0.257)LAG(Y,12)
• LM M - (0.257)LAG(M,12)

60

• Does correcting for autocorrelation significantly
  alter any of the coefficients? If so, which ones?
  Does the re-estimated model alter your
  conclusions about whether the Korean data
  supports or rejects the Girton-Roper model?
• Correcting for autocorrelation did not
  significantly alter the coefficients and the
  re-estimated model actually strengthens the
  support for the Girton-Roper model as the
  variables remained significant and the R2
  increased substantially.

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Question 10

• One can also test the null hypothesis in problem
  3 using the Lagrange multiplier test. This is
  done by creating the restricted residual
• RRESID LHV D P Y M
• and then regresses RRESID onto D, Y, P and M.
  The test statistic is a chi-squared random
  variable with k1 degrees of freedom (5). The
  chi-squared variable is calculated by the
  following equation
• ?2 nR2
• Where n the number of observations

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• (A) Using the Lagrange multiplier test, test the
  null hypothesis (ß1-1, ß21, ß31 and ß4-1)at
  the 5 level of significance.

?2 (43)(0.992) 42.656 ?20.05
11.07 42.656 gt ?20.05 therefore reject the Null
Hypothesis
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• (B) Does the data support the Kim version of the
  Girton-Roper model or a more general version?
  Explain.
• The data supports the more general Girton-Roper
  model, as indicated by part (A) which tells us to
  reject the null hypothesis (Kims version) that
  restricts the models coefficients.