3290a diploma economics project

Diploma in Economics: Econometrics Project, May 2011 Candidate Number: 3290A

(Clive) Xuli Xiao

1

Using monthly data on the spot exchange rate

and the short term interest rate for 10 countries,

test whether uncovered interest parity holds.

Word Count: 1915 (including tables, graphs and equations)


(Clive) Xuli Xiao

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[1] Introduction

The foreign exchange market has a huge trading volume compared to other asset classes and

its trading activity is recession proof. The Triennial FX survey by Bank of International

Settlements (BIS, 2010) shows that between April 2007 and April 2010, trading volume of

global foreign exchange market increased by 20 percent to $4.0 trillion. A large number of

researchers have tried to find the determinants of the Exchange rate changes. We also intuitively

believe that, there must be some relationship between Spot Exchange rate, Future Exchange rate

and Interest rate movements. Uncovered Interest Parity (UIP) is one of the most notable

assumptions. In essence, UIP describes that due to arbitrage opportunities are exploited

instantaneously in international finance market (exchange market) and bonds market by market

participants such that the appreciation/depreciation of Country A’s currency against Country B is

the expected result from the decrease/increase of Country A’s interest rate relative to Country B.

Ross, et al., (2008), revisited this famous assumption by linking the CIP (Covered Interest

Parity) and UFR (Unbiased Forward Rate) conditions. By assuming that there is no arbitrage

opportunity in a sense that market participant is locked in the profit and loss once he/she enters

the Forward exchange contract, then CIP states:

𝐹𝑡+1

𝑆𝑡=

1 + 𝑖𝑡∗

1 + 𝑖𝑡 [Covered Interest Parity]

Where F denotes the Forward exchange rate at time t+1, S denotes Spot exchange rate at time t.

𝑖𝑡∗ is the interest rate in foreign country and 𝑖𝑡 is the interest rate in home/base country at time t.

In addition to the CIP condition, if agents are risk neutral, then investors are happy to take either

the Forward contract with certain payoff or the Spot exchange rate in the future with uncertain

payoff today. In this case, UFR (Unbiased Forward Rate) should hold:

𝐹𝑡+1 = 𝐸 𝑆𝑡+1 [Unbiased Forward Rate]

It suggests that Forward exchange rate is equal to expected future Spot rate. Therefore

combining CIP and UFR, we can get the UIP:

𝐸(𝑆𝑡+1)

𝑆𝑡=

1 + 𝑖𝑡∗

1 + 𝑖𝑡 [Uncovered Interest Parity]

Moreover, if market participants have rational expectation, we would have:𝑆𝑡+1 = 𝐸(𝑆𝑡+1) + ∈ ,

where ∈ is white noise. We would have 𝑆𝑡+1

𝑆𝑡=

1+𝑖𝑡∗

1+𝑖𝑡 , if we take natural logs from both sides, we

would get Equation (1) (UIP Condition), as log(1 + 𝑖) ≈ 𝑖, which is tested in this paper.


(Clive) Xuli Xiao

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[2] Empirical Framework and Analysis

[2.a. Data Description]

We estimate the UIP assumption by setting the US as the home/base country, i.e. 𝑖𝑡 denotes

the one-month interest rate (as a percentage rate per year) in the US at time t, whereas, 𝑖𝑡 denotes

the one-month interest rate in the foreign country.

In this paper, we estimate exchange rates 𝑆𝑡 from 9 different countries/regions against the

USD: Australia(AUD), Canada(CAD), Switzerland(CHF), Europe(EUR), UK(GBP), Japan(JPY),

Norway(NOK), New Zealand(NZD) and Sweden(SEK). Graph 1 and 2 below plots the monthly

Spot rates changes from the 9 countries across the whole time horizon from Jan 1976 to June

2010 and the one-month interest rates movements in 10 countries (including the US) during the

same period.

Graph 1 Graph 2

[2.b. Time Series Regression Equation]

𝑆𝑡+1 − 𝑆𝑡 = 𝑎 + 𝑏 𝑖𝑡 − 𝑖𝑡∗ + 𝜖𝑡+1 Equation (1)

The main regression equation in this paper is displayed above, in which S from Equation (1) is

expressed in natural log terms. If UIP holds, we should be able to find intercept a to be 0 and

coefficient b to be 1 statistically significant and a high R-squared.

0.0

0.5

1.0

1.5

2.0

2.5

1980 1985 1990 1995 2000 2005 2010

S_AUD S_CAD S_CHF

S_EUR S_GBP S_JPY

S_NOK S_NZD S_SEK

0

5

10

15

20

25

30

1980 1985 1990 1995 2000 2005 2010

I_AUD I_CAD I_CHFI_EUR I_GBP I_JPY

I_NOK I_NZD I_SEK

I_USD


(Clive) Xuli Xiao

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Stationary Test

To avoid spurious regression results, we first test for stationary (See Appendix [1.1]) of the

data in 9 countries. Augmented Dickey-Fuller test shows that, at 1% significant level, all

dependent variables (𝑆𝑡+1 − 𝑆𝑡 ) pass the stationary test, i.e. I(0). However, for explanatory

variables 𝑖𝑡 − 𝑖𝑡∗ , we find 7 out of 9 countries are I(0), but series CHF and EUR cannot pass the

test at 5% significant level (with P-value 0.4313 and 0.2859 respectively). ADF shows that these

two series CHF and EUR are I(1) (significant at 1% level), i.e. it is difference-stationary process

(See Appendix [1.2]).

Hence, we use Equation (3) to examine the validity of UIP for countries CHF and EUR.

Equation (3) is derived from differencing Equation (2) from (1). Using this transformation, we

can run regression on stationary data and are able to achieve the same goal (test for the validity

of UIP). If UIP holds, we would find coefficient b to be 1 and ∝ be 0 in Equation (4) below.

𝑆𝑡 − 𝑆𝑡−1 = 𝑎 + 𝑏 𝑖𝑡−1 − 𝑖𝑡−1∗ + 𝜖𝑡 Equation (2)

𝑆𝑡+1 − 𝑆𝑡 − 𝑆𝑡 − 𝑆𝑡−1 = 0 + 𝑏 𝑖𝑡 − 𝑖𝑡∗ − 𝑖𝑡−1 − 𝑖𝑡−1

∗ + 𝜖𝑡+1 − 𝜖𝑡 Equation (3)

∆ 𝑆𝑡+1 − 𝑆𝑡 =∝ +𝑏 ∆ 𝑖𝑡 − 𝑖𝑡∗ + 𝑢𝑡+1, where 𝑢𝑡+1 = 𝜖𝑡+1 − 𝜖𝑡 Equation (4)

[2.c. Time Series Regression Results]

Seven countries/regions are estimated by OLS using Equation (1). The remaining two (EUR

and CHF) are estimated using Equation (4).

Heteroscedasticity Test – White

Heteroscedastic is found significant in CHF, GBP and SEK at 1% significance level, which we

use White Robust process to correct the variance for Heteroscedasticity (See Appendix [2.1]).

For all other countries, the standard errors of the regressions residulas are found to be

Homosdecatistic at 5% sig. level.

OLS regression results of the 9 countries (with robust standard errors) can be found in

Appendix [2.2].


(Clive) Xuli Xiao

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Serial Correlation Test

Breusch-Godfrey Serial Correlation LM Test is used to test for serial correlation in the

residuals of the regressions (with 10 lags). We notice that, at 5% significance level, they all pass

the Serial Correlation LM test except for CHF and EUR, which we know from Equation (4) that

serial correlation in residuals of these two regressions 𝑢𝑡+1 = 𝜖𝑡+1 − 𝜖𝑡 is expected. The

correlogram of residuls and squared residuals exhibit the same results (see Appendix [2.3] and

[2.3.1]).

Summary

In addition, Wald Test for joint significance of H0: a = 0 and b = 1 are estimated. At 5%

significance level, H0 is rejected in all countries. Table1 below summarize the results from the

OLS estimation.

Table 1:

OLS using Equation (1) [UIP Hypothesis]

Countries a p-value b p-value R-squared Wald joint test

Η0:a =0, b=1

AUD -0.00171 0.3598 -0.00039 0.4003 0.001722 Rejected

CAD -0.00046 0.6579 -0.00049 0.3796 0.001879 Rejected

GBP -0.00335 0.0659 -0.00125 0.0730 0.011457 Rejected

JPY 0.010405** 0.0000 -0.00251** 0.0001 0.039237 Rejected

NOK -0.0018 0.3025 -0.00066 0.1347 0.005437 Rejected

NZD -0.00422 0.0511 -0.00093** 0.0186 0.013399 Rejected

SEK -0.00171 0.3111 -0.00019 0.77 0.000385 Rejected

α OLS using Equation (4) Η0: α =0, b=1

CHF 3.18E-05 0.9895 -0.00782 0.0712 0.012307 Rejected

EUR -6.89E-05 0.9749 -0.00928** 0.0007 0.027541 Rejected

** Rejects the null a equals 0, b equals 0, respectively, at 1% significance level

Intercepts a are insignificant at 5% sig. level with a negative absolute value except for JPY. Most

coefficients b are also insignificant at 5% sig. level and have small negative values except for


(Clive) Xuli Xiao

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JPY, NZD and EUR which are significant at 1% sig. level and have values of -0.00251, -0.00093

and -0.00928 respectively. For CHF and EUR, intercept α is very close to 0 and insignificant

which can be explained from Equation (3) that the intercept is cancelled out when we transform

Equation (4) by differencing Equation (1) from its lagged series Equation (2).

When Wald Test for joint significance of H0: a = 0 and b = 1; H0: ∝ = 0 and b = 1 (UIP

Hypothesis) are estimated, UIP Hypothesis are all rejected in 9 countries at 1% sig. level. The R-

squared values are very small as well. This empirical finding could be possibly due to the

“exchange rate disconnect puzzle” introduced by Obsteld and Rogoff (2000), who mention that

nominal exchange rate is disconnected from real economic variables.

[2.d. Panel Data Estimation]

It is intuitive to estimate the UIP in a panel data set that has both a cross-sectional (9 countries)

and a time series (monthly) dimension.

𝑆𝑡+1𝑗

− 𝑆𝑡𝑗

= 𝑎 + 𝑏 𝑖𝑡𝑗− 𝑖𝑡

𝑗 ∗ + 𝜖𝑡+1

𝑗 Equation (5)

Accordingly, similarly to Equation (4) we can write:

∆ 𝑆𝑡+1𝑗

− 𝑆𝑡𝑗 =∝ +𝑏 ∆ 𝑖𝑡

𝑗− 𝑖𝑡

𝑗 ∗ + 𝑢𝑡+1

𝑗, where 𝑢𝑡+1

𝑗= 𝜖𝑡+1

𝑗− 𝜖𝑡

𝑗 Equation (6)

j denotes the 9 individual country we estimated. We obtain a balanced panel data set from

Equation (6) accordingly. Hence, UIP would hold, if ∝ = 0 and b = 1 are statistically significant.

Stationary Test

Levin-Lin-Chu unit-root test and Im-Pesaran-Shin unit-root test are used to test for stationary

of the panel data set. As expected, the cross sectional time series we measure according to

Equation (6) are stationary which we cannot reject at 1% significant level (see Appendix [3.1]).

Results are summarized in Table 2 below.


(Clive) Xuli Xiao

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Table 2

Levin-Lin-Chu P-value Im-Pesaran-Shin P-value

∆ 𝑆𝑡+1𝑗

− 𝑆𝑡𝑗 -78.4911** 0.000 -57.4518** 0.000

∆ 𝑖𝑡𝑗− 𝑖𝑡

𝑗 ∗ -45.0690** 0.000 -45.3678** 0.000

** Rejects the null that the series is non-stationary, at 1% significance level

Pooled OLS

We proceed to estimate Pooled OLS after non-stationary of the panel data set is strongly

rejected. We use robust standard errors clustered by individual (see Appendix [3.2]) when we

regress the Pooled OLS, outputs can be summarized below in Table 3.

Table 3 - Pooled OLS - robust standard errors

∝ p-value b p-value R-squared [UIP Hypothesis]

0.0000355 0.074 -0.0029506* 0.022 0.0048 Rejected

* Rejects the null a equals 0, b equals 0, respectively, at 5% significance level

Pooled OLS estimate does not indicate the validity of UIP. b is significantly different from 0,

but has a negative value, again fails the UIP assumption. Our finding is consistent with findings

from other literatures, for example, Maynard and Philips (2001), pp.673, argues that “UIP

condition must be reversed in sign.”

Fixed Effect and Random Effect models

Furthermore, Fixed Effect model (allows individual effect) and Random Effect model (does

not allow individual effect) are estimated. We run the pooled OLS regression first and test for

AR(1) serial correlation in residual as expected from Equation (6). By using Wooldridge test for

autocorrelation in panel data (in Stata, written by Drukker(2003) according to

Wooldridge(2002)), we strongly reject no AR(1) serial correlation at 5% significant level (See

Appendix [3.1]). Therefore, we correct for the presence of AR(1) serial correlation by running

the regression taking into account the AR(1) disturbances in the two models we estimate (See

Appendix [3.3]), which are summarized in below:


(Clive) Xuli Xiao

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Table 4

Fixed Effect Estimation [UIP Hypothesis]

α p-value b p-value α =0, b=1

0.0001006 0.915 -0.0031456** 0.000 Rejected

Random Effect Estimation

α p-value b p-value α =0, b=1

0.0001881 0.920 -0.0031054** 0.000 Rejected

** Rejects the null that the estimate is 0 at 1% level

Empirical findings from Fixed Effect and Random Effect estimations suggest statistical

insignificant intercepts a and significant slope coefficients b (very small negative value) at 1%

sig. level. UIP Hypothesis is again rejected in both models. We notice that both models show

similar results and intuitively we use Hausman test (see Appendix [3.5]) to distinguish which

model is superior in our panel data estimation. According to Hausman (1978) test, we cannot

reject (P-value: 0.6219) the null that unobserved effect (individual effect) is uncorrelated with

every explanatory variable in both cross-sectional (9 countries) and time series (monthly)

dimensions (at 5% sig level). So Hausman test recommends Random Effect model. However,

Johnston and DiNardo (2007) mention that it is common in applied research that two estimators

are not significantly different from each other. One possible reason is that the variance in the

change in explanatory variables is not large enough to distinguish the two estimators.

[3] Conclusion

Empirical findings in our paper fail to accept the validity of the Uncovered Interest

Parity (UIP) in individual OLS on time series data including 9 countries (Australia,

Canada, Switzerland, Europe, Great Britain, Japan, Norway, New Zealand and

Sweden) and pooled OLS, Random Effect model and Fixed Effect model on panel

data. We conclude that all models we use cannot resolve the UIP puzzle. All results

show that the coefficient b has a negative value across different significance level

which is consistent with findings from voluminous empirical literatures.


(Clive) Xuli Xiao

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Appendix (complete version of Eviews output is available on request)

(Eviews outputs and outputs summary)

[1] Stationary Test – ADF test Augmented Dickey-Fuller test statistic

(5% ADF test stat: -2.868; 1%: -3.446 𝑆𝑡+1 − 𝑆𝑡 p-value 𝑖𝑡 − 𝑖𝑡

∗ p-value

Null Hypothesis: unit root exists

Exogenous: Constant; Lag Length: 0

(Automatic - based on SIC, maxlag=17)

AUD -19.12886** 0.000 -3.010237* 0.0348

CAD -20.94159** 0.000 -3.426791* 0.0106

CHF -19.93280** 0.000 -1.698397 0.4313

EUR -19.76744** 0.000 -2.002378 0.2859

GBP -18.43164** 0.000 -4.187651* 0.0008

JPY -19.46875** 0.000 -3.585440* 0.0065

NOK -18.93116** 0.000 -3.761899* 0.0036

NZD -9.399106** 0.000 -3.003397* 0.0354

SEK -18.23383** 0.000 -3.651351* 0.0052

**Rejects the null that series is non-stationary, at 1% sig. level; *at 5% sig level

[1.1 ADF test – I (1)] CHF I(1)

Null Hypothesis: DDI_CHF has a unit root

Exogenous: Constant

Lag Length: 4 (Automatic - based on SIC, maxlag=17) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -13.01161 0.0000

Test critical values: 1% level -3.446162

5% level -2.868405

10% level -2.570492

EUR I(1)

Null Hypothesis: DDI_EUR has a unit root

Exogenous: Constant

Lag Length: 8 (Automatic - based on SIC, maxlag=17) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -6.832881 0.0000

Test critical values: 1% level -3.446321

5% level -2.868475

10% level -2.570530


(Clive) Xuli Xiao

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[2]Regression and residuals tests [2.1] Heteroskedasticity Test - White

Countries F-statistic Prob. F(2,410)

AUD 2.413461 0.0908

CAD 0.361601 0.6968

CHF 5.743049** 0.0035

EUR 2.004996 0.1360

GBP 5.607478** 0.0040

JPY 1.652777 0.1928

NOK 1.325663 0.2668

NZD 2.479638 0.0850

SEK 9.614281** 0.0001

**Rejects the null that residuals exhibit Homosdecasity, at 1% sig. level e.g. CHF

Heteroskedasticity Test: White F-statistic 5.743049 Prob. F(2,409) 0.0035

Obs*R-squared 11.25429 Prob. Chi-Square(2) 0.0036

Scaled explained SS 23.13748 Prob. Chi-Square(2) 0.0000

Test Equation:

Dependent Variable: RESID^2

Method: Least Squares

Date: 05/17/11 Time: 04:34

Sample: 1976M03 2010M06

Included observations: 412 Variable Coefficient Std. Error t-Statistic Prob. C 0.002248 0.000249 9.043456 0.0000

DDI_CHF -0.000491 0.000311 -1.580557 0.1148

DDI_CHF^2 0.000236 0.000102 2.316651 0.0210 R-squared 0.027316 Mean dependent var 0.002409

Adjusted R-squared 0.022560 S.D. dependent var 0.004914

S.E. of regression 0.004858 Akaike info criterion -7.808966

Sum squared resid 0.009654 Schwarz criterion -7.779687

Log likelihood 1611.647 Hannan-Quinn criter. -7.797385

F-statistic 5.743049 Durbin-Watson stat 1.091168

Prob(F-statistic) 0.003469


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[2.2] OLS Regression with robust Standard Error Dependent Variable: S

Method: Least Squares; Date: 05/15/11 Time: 22:54

Sample (adjusted): 1976M02 2010M06

Included observations: 413 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C -0.001708 0.001863 -0.916781 0.3598

DI_AUD -0.000386 0.000459 -0.841928 0.4003

C -0.000456 0.001029 -0.443195 0.6579

DI_CAD -0.000494 0.000562 -0.879512 0.3796

C 3.18E-05 0.002418 0.013151 0.9895

DDI_CHF -0.007815 0.004320 -1.809115 0.0712

White heteroskedasticity-consistent standard errors & covariance;


C -6.89E-05 0.002190 -0.031490 0.9749

DDI_EUR -0.009280 0.002723 -3.407567 0.0007


C -0.003346 0.001815 -1.843925 0.0659

DI_GBP -0.001245 0.000693 -1.797630 0.0730

White heteroskedasticity-consistent standard errors & covariance

C 0.010405 0.002436 4.271105 0.0000

DI_JPY -0.002509 0.000612 -4.096947 0.0001

C -0.001797 0.001741 -1.032304 0.3025

DI_NOK -0.000658 0.000439 -1.498905 0.1347

C -0.004219 0.002157 -1.956014 0.0511

DI_NZD -0.000927 0.000392 -2.362622 0.0186

C -0.001712 0.001689 -1.014115 0.3111

DI_SEK -0.000188 0.000643 -0.292572 0.7700

White heteroskedasticity-consistent standard errors & covariance


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e.g. CHF:

Dependent Variable: DDLOGS_CHF


Date: 05/15/11 Time: 23:36

Sample (adjusted): 1976M03 2010M06


White heteroskedasticity-consistent standard errors & covariance Variable Coefficient Std. Error t-Statistic Prob. C 3.18E-05 0.002418 0.013151 0.9895

DDI_CHF -0.007815 0.004320 -1.809115 0.0712 R-squared 0.016554 Mean dependent var 9.76E-05







[2.3] Breusch-Godfrey Serial Correlation LM Test: Countries F-statistic Prob. F(10,401)

AUD 0.424557 0.9346

CAD 1.683549 0.0824

CHF 37.67349** 0.0000 EUR 31.20954** 0.0000

GBP 0.915795 0.5184 JPY 1.464996 0.1501

NOK 1.068878 0.3851 NZD 1.795441 0.0595

SEK 1.545964 0.1208

**Rejects the null that residual has no Serial Correlation, at 1% sig. level e.g. CHF

Breusch-Godfrey Serial Correlation LM Test: F-statistic 37.67349 Prob. F(10,400) 0.0000

Obs*R-squared 199.8298 Prob. Chi-Square(10) 0.0000

Test Equation:

Dependent Variable: RESID


Date: 05/17/11 Time: 04:36

Sample: 1976M03 2010M06

Included observations: 412

Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C -0.000899 0.001763 -0.510207 0.6102

DDI_CHF 0.000583 0.002189 0.266377 0.7901


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RESID(-1) -0.904699 0.049616 -18.23409 0.0000

RESID(-2) -0.787641 0.066626 -11.82176 0.0000

RESID(-3) -0.665453 0.075609 -8.801223 0.0000

RESID(-4) -0.668714 0.080348 -8.322710 0.0000

RESID(-5) -0.544315 0.082494 -6.598249 0.0000

RESID(-6) -0.554731 0.082742 -6.704386 0.0000

RESID(-7) -0.391971 0.080494 -4.869554 0.0000

RESID(-8) -0.344374 0.076005 -4.530970 0.0000

RESID(-9) -0.173158 0.067479 -2.566114 0.0106

RESID(-10) -0.149579 0.050057 -2.988164 0.0030 R-squared 0.485024 Mean dependent var -2.02E-19







[2.3.1] Correlogram of residuals and squared rediduals

CHF

Sample: 1976M03 2010M06

Included observations: 412

Autocorrelation Partial Correlation AC PAC Q-Stat Prob ****|. | ****|. | 1 -0.529 -0.529 116.12 0.000

.|. | **|. | 2 0.049 -0.320 117.14 0.000 .|. | *|. | 3 0.024 -0.171 117.38 0.000 *|. | **|. | 4 -0.090 -0.223 120.73 0.000 .|* | *|. | 5 0.106 -0.089 125.44 0.000 *|. | **|. | 6 -0.137 -0.211 133.29 0.000 .|* | *|. | 7 0.127 -0.089 140.09 0.000 *|. | *|. | 8 -0.111 -0.187 145.31 0.000 .|* | .|. | 9 0.125 -0.029 151.88 0.000 *|. | *|. | 10 -0.111 -0.138 157.10 0.000

Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|*** | .|*** | 1 0.449 0.449 83.575 0.000 .|. | **|. | 2 0.036 -0.207 84.123 0.000 .|. | .|. | 3 -0.026 0.061 84.410 0.000 .|. | .|. | 4 -0.020 -0.032 84.580 0.000 .|. | .|. | 5 0.027 0.057 84.893 0.000 .|. | .|. | 6 0.045 0.005 85.751 0.000 .|. | .|. | 7 0.029 0.009 86.104 0.000 .|. | .|. | 8 0.035 0.032 86.632 0.000 .|* | .|* | 9 0.113 0.112 92.021 0.000 .|* | .|. | 10 0.106 0.004 96.829 0.000


(Clive) Xuli Xiao

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EUR

Date: 05/16/11 Time: 05:21 Sample: 1976M03 2010M06 Included observations: 412

Autocorrelation Partial Correlation AC PAC Q-Stat Prob ****|. | ****|. | 1 -0.522 -0.522 112.98 0.000

.|. | **|. | 2 0.050 -0.305 114.04 0.000 .|. | *|. | 3 0.019 -0.160 114.19 0.000 *|. | **|. | 4 -0.084 -0.206 117.13 0.000 .|* | *|. | 5 0.084 -0.101 120.10 0.000 *|. | *|. | 6 -0.097 -0.175 124.03 0.000 .|. | *|. | 7 0.065 -0.121 125.79 0.000 .|. | *|. | 8 -0.032 -0.134 126.23 0.000 .|. | .|. | 9 0.046 -0.053 127.14 0.000 .|. | *|. | 10 -0.052 -0.107 128.30 0.000

Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|*** | .|*** | 1 0.473 0.473 92.818 0.000 .|* | *|. | 2 0.163 -0.078 103.85 0.000 .|. | .|. | 3 0.028 -0.024 104.17 0.000 .|. | .|. | 4 -0.024 -0.021 104.41 0.000 .|. | .|. | 5 -0.004 0.028 104.42 0.000 .|. | .|. | 6 0.010 0.004 104.46 0.000 .|. | .|. | 7 -0.000 -0.014 104.46 0.000 .|. | .|. | 8 -0.012 -0.010 104.52 0.000 .|. | .|. | 9 0.021 0.044 104.71 0.000 .|. | .|. | 10 0.032 0.007 105.13 0.000

[2.4] Wald Test C(1)=0, C(2)=1 F- Test Statistic df Probability

AUD 3249498** (2, 411) 0.0000

CAD 1905624** (2, 411) 0.0000

CHF 27879.24** (2, 410) 0.0000 EUR 68669.04** (2, 410) 0.0000

GBP 1621953** (2, 411) 0.0000 JPY 3005953** (2, 411) 0.0000

NOK 3715154** (2, 411) 0.0000

NZD 5576160** (2, 411) 0.0000 SEK 1493832** (2, 411) 0.0000

**Rejects the null that a=0, b=1 at 1% sig. level


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e.g. CHF

Wald Test:

Equation: EQ_CHF Test Statistic Value df Probability F-statistic NA (2, 410) NA

Chi-square NA 2 NA Restriction variance cannot be computed. Restrictions may

not be unique.

Null Hypothesis: C(1)=0, C(1)=1

Null Hypothesis Summary: Normalized Restriction (= 0) Value Std. Err. C(1) 3.18E-05 0.002418

-1 + C(1) -0.999968 0.002418

Restrictions are linear in coefficients.


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[3 Panel Data]

(Stata output)

[3.1] Stationary Unit Root Test

Adjusted t* -78.4911 0.0000 Unadjusted t -74.3863 Statistic p-value LR variance: Bartlett kernel, 23.00 lags average (chosen by LLC)ADF regressions: 1 lag

Time trend: Not includedPanel means: IncludedAR parameter: Common Asymptotics: N/T -> 0

Ha: Panels are stationary Number of periods = 412Ho: Panels contain unit roots Number of panels = 9 Levin-Lin-Chu unit-root test for FX

Adjusted t* -45.0690 0.0000 Unadjusted t -44.3663 Statistic p-value LR variance: Bartlett kernel, 23.00 lags average (chosen by LLC)ADF regressions: 1 lag

Time trend: Not includedPanel means: IncludedAR parameter: Common Asymptotics: N/T -> 0

Ha: Panels are stationary Number of periods = 412Ho: Panels contain unit roots Number of panels = 9 Levin-Lin-Chu unit-root test for IntDif

Z-t-tilde-bar -57.4518 0.0000 t-tilde-bar -17.5366 t-bar -35.0699 -2.150 -1.970 -1.880 Statistic p-value 1% 5% 10% Fixed-N exact critical values ADF regressions: No lags included

Time trend: Not includedPanel means: Included sequentiallyAR parameter: Panel-specific Asymptotics: T,N -> Infinity

Ha: Some panels are stationary Number of periods = 412Ho: All panels contain unit roots Number of panels = 9 Im-Pesaran-Shin unit-root test for FX


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[3.2] Pooled OLS with robust standard errors clustered by individual

[3.3] Autocorrelation test for Panel Data

Z-t-tilde-bar -45.3678 0.0000 t-tilde-bar -14.1680 t-bar -19.9820 -2.150 -1.970 -1.880 Statistic p-value 1% 5% 10% Fixed-N exact critical values ADF regressions: No lags included

Time trend: Not includedPanel means: Included sequentiallyAR parameter: Panel-specific Asymptotics: T,N -> Infinity

Ha: Some panels are stationary Number of periods = 412Ho: All panels contain unit roots Number of panels = 9 Im-Pesaran-Shin unit-root test for IntDif

_cons .0000355 .0000173 2.05 0.074 -4.40e-06 .0000753 IntDif -.0029506 .0010451 -2.82 0.022 -.0053607 -.0005405 FX Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust (Std. Err. adjusted for 9 clusters in Countries)

Root MSE = .043 R-squared = 0.0048 Prob > F = 0.0224 F( 1, 8) = 7.97Linear regression Number of obs = 3708

Prob > F = 0.0000 F( 1, 8) = 437.025H0: no first-order autocorrelationWooldridge test for autocorrelation in panel data


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[3.4] Fixed Effect and Random Effect with corrected AR(1) Residuals

F test that all u_i=0: F(8,3689) = 0.00 Prob > F = 1.0000 rho_fov 2.462e-06 (fraction of variance because of u_i) sigma_e .05703201 sigma_u .00008949 rho_ar -.50135856 _cons .0001006 .0009377 0.11 0.915 -.0017379 .0019391 IntDif -.0031456 .0008365 -3.76 0.000 -.0047857 -.0015056 FX Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = -0.0028 Prob > F = 0.0002 F(1,3689) = 14.14

overall = 0.0049 max = 411 between = 0.0218 avg = 411.0R-sq: within = 0.0038 Obs per group: min = 411

Group variable: Countries Number of groups = 9FE (within) regression with AR(1) disturbances Number of obs = 3699

theta 0 rho_fov 0 (fraction of variance due to u_i) sigma_e .056964 sigma_u 0 rho_ar -.50135856 (estimated autocorrelation coefficient) _cons .0001881 .0018697 0.10 0.920 -.0034765 .0038527 IntDif -.0031054 .0008324 -3.73 0.000 -.004737 -.0014739 FX Coef. Std. Err. z P>|z| [95% Conf. Interval]

corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0010 Wald chi2(2) = 13.92

overall = 0.0048 max = 412 between = 0.0126 avg = 412.0R-sq: within = 0.0048 Obs per group: min = 412

Group variable: Countries Number of groups = 9RE GLS regression with AR(1) disturbances Number of obs = 3708


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[3.5] Hausman Test

(Without robust standard error but corrected for AR (1) in residuals)

Prob>chi2 = 0.6219 = 0.24 chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)

Test: Ho: difference in coefficients not systematic

B = inconsistent under Ha, efficient under Ho; obtained from xtregar b = consistent under Ho and Ha; obtained from xtregar IntDif -.0031449 -.0031042 -.0000407 .0000824 FE1 RE1 Difference S.E. (b) (B) (b-B) sqrt(diag(V_b-V_B)) Coefficients


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Bibliography

Drukker, D. M. (2003). Testing for serial correlation in linear panel-data models. Stata

Journal 3: 168–177.

Hausman, J.A. (1978). "Specification Tests in Econometrics", Econometrica, 46 (6), 1251–1271.

Johnston, J, DiNARDO, D. (2007). Modern Financial Management. 4th ed. Singapore: McGraw-Hill.pp. 404

Maynard A, Phillips, P. (2001). Rethinking an old empirical puzzle: Econometric evidence on

the forward discount anomaly. Journal of Applied Econometrics 2001; 16; pp. 673

Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data.

Cambridge, MA: MIT Press. Obstfeld, M; Rogoff, K (2000), "The Six Major Puzzles in International Macroeconomics: Is

There a Common Cause?", in Bernanke, Ben; Rogoff, Kenneth,NBER Macroeconomics

Annual 2000, 15, The MIT Press, pp. 339–390

Ross, S R, Westerfield, R. W, Jaffe, J.J, Jordan , B.J., (2008). Modern Financial

Management. 5th ed. New York: McGraw-Hill, pp. 880 - 881

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http://www.bis.org/publ/rpfx10.htm

3290a diploma economics project

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