Assignment Fisher 1

Testing the Existence

and Forecasting the

Fisher Effect in Malaysia

and Canada

BSc Banking and Finance

073604149

073604149Testing the Existence and Forecasting the Fisher Effect in Malaysia and Canada

1.0 Introduction

For my project, I wish to test, forecast and compare to see if there is a fisher

effect in both Canada and Malaysia between the years of 1995 to 2009 with

quarterly seasonally adjusted data which I think will give me a good span of data to

build a model and so I can have a good comparison of the two countries. It is not as

much as I wanted, but I think it is enough for this project. My project is structured as

follows;

Section 2.0 is the economic and econometrics background theory of the

fisher effect.

Section 3.0 I will talk about previous published papers on the fisher effect and

its existence.

In section 4.0 I will explain my data, my variables and how I got them and

what I did to them.

Section 5.0 will be all my results from the tests I used from econometric

models and graphs.

Section 6.0 I will then finally evaluate my results and then compare my

results in the conclusion.

The reason I choose the two countries, that I thought I might get results that

differ due to continental reasons, which may affect the factors that affect the fisher

effect, and also I think that Malaysia is not such a well developed country in terms of

its economy as Canada is.

2.0 Economics Theory

The fisher effect was introduced in 1930, and it shows the relationship

between interest rates and inflation, and it shows that the nominal interest rate at a

given time is equal to the sum of the real interest and the expected rate of inflation.

There are three variables in the fisher equation, they are nominal inflation rate

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which is denoted by ‘p’, which is the change in price level, the nominal interest rate

’i’ which is the actual interest rate without any adjustments in the economy and the

real interest rates ‘r’ which is the interest rate that has been adjusted to remove the

effects of inflation. This relationship can be denoted by:

r=i- π

The purchasing power can be found by finding the difference between the nominal

interest rate and the rate of inflation, and the above can be rearranged to give:

i=r+ π

the more accurate fisher effect equation is written as:

it=rt+ π et

where π et is the expected inflation rate. Once the nominal interest rate has been set,

the inflation rate is known, therefore only adjust to the expected inflation.

There are two types of Real interest rates, ex ante and ex post. Ex ante is when for

example the interest rate that the borrower and the lender expect to receive when

the take out a loan, the actual real interest rate realised is the ex post real interest

rate.

The fisher effect hypothesis says that the efficient capital markets

compensate for changes in the purchasing power of money in the long run will not

have an effect on a countries relative prices. For example, if the rate of expected

inflation increased by 2%, this should change the nominal interest rate and increase

that by 2%. This movement together of the expected inflation and nominal interest

rate is what the fisher effect is.

2.1 Econometric Theory

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The nominal interest rate can be divided into two parts, the ex ante real

interest rate ret, and the expected inflation π e

t. This was proposed by Fisher (1930).

Using this, the fisher effect can be written as it= ret + πt

e . It is possible that the

expected inflation may be different from actual inflation. The errors are said to be

stationary, both types of interest rates have similar properties when they differ by a

stationary factor, therefore:

it= πte+rt+e where rt=it- πt

e

Changes in expected rate of inflation are shown by nominal interest rate which can

be shown by It= πte

This means that it+(it- πte)+( πt

e- πt)= πt+et, where E(et)=0 and is stationary.

The international fisher effect says that the difference in two countries

interest rate should be equal to the difference in its expected inflation. This means

that if a country has a high nominal interest rate then it will have a high expected

inflation.

3.0 Literature review

In the paper ‘Is there really the Fisher effect’ written by Paul A. Johnson,

Johnson writes about how the cointegration of the inflation and nominal interest

rates is constant with any theory implying a stationary interest rate and therefore is

not a sufficient condition for the fisher effect to hold.

Mishkin also wrote a paper ‘Is the Fisher effect for real’ where he found

support for the long-run fisher relationship where inflation and interest rates are

cointegrated. In his later paper he found that both interest rate and inflation

contained unit roots and the rest indicated that there was evidence of long run fisher

effect but none for short run fisher effect. His paper solves the problem of why

strong fisher effect occurs only in some periods and not others by re-examining the

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relationship between inflation and interest rates with modern techniques. Mishkin

was one of the first to use the Engle-Granger concept of Cointegration successfully.

In another paper, ‘the fisher effect: new evidence and implications’ written

by Fahmy and M.Kandil, the results that they achieved did not support the short run

fisher effect because short-term interest rates are associated with small changes in

expected inflation. The results also did not favour the long run fisher effect and the

correlation between nominal interest rates and inflation rates until they move

together in relation. They use the Johansen test for cointegration.

Perez, S.J and M.V Siegler (2003) performed similar studies where they

explore the field of potential non linearity’s data sets.

A paper published by Arusha Cooray ‘THE FISHER EFFECT: A REVIEW OF THE

LITERATURE’ showed that by using the Johansen cointegration approach, there was a

presence of a relationship between nominal interest rates and inflation for some

developing countries, which were Malaysia, Sri Lanka and Pakistan, while no

evdidence of the fisher effect for other developing countries like Fiji, India and

Thailand.

4.0 Description of my data.

Below is a list of my data that I have used, and the abbreviated name for that

variable that has been used in eviews. The abbreviation is in italics.

Cpi_mly: CPI Malaysia

Nominal_mly: nominal interest rate of Malaysia

Logcpi_mly: log CPI Malaysia (inflation rate Malaysia)

Lognominal_mly: log nominal Malaysia

5


dlogcpi_mly: first differential inflation Malaysia

dlognominal_mly: first differential nominal interest rate Malaysia

resid_mly: Residual Malaysia

Cpi_can: CPI Canada

Nominal_can: nominal interest rate of Canada

Logcpi_can: log CPI Canada (inflation rate Canada)

Lognominal_can: log nominal Canada

dlogcpi_can: first differential inflation Canada

dlognominal_can: first differential nominal interest rate Canada

resid_can: Residual Canada

I collected my data from two different sources; I got data from the ESDS

website and from the Bank of Canada website. I have quarterly data from 1999 to

2009, which is not as much as I would have liked but I still think the number of

observations I have will give enough evidence to see if there is an existence of the

fisher effect in Canada and Malaysia. It was difficult to get data for a longer time

because there was data missing and the earliest data I did find was starting from

1999. To get the inflation rate of the two countries I had to get the CPI data then log

it to get the inflation rate.

5.0 Analysis

First I will show a comparison of my regular data and my logged data, then I

will do a test for normality using histograms, then I will test my data for stationarity,

to do this I will have to use the augmented dickey fuller test to test the presence of a

unit root. The Dickey fuller test is one of the most used tests, it tests whether a unit

root is present in an autoregressive model. Then I will test my variables for

cointegration using engle granger test, I will test for heteroskedasticity, then with

this I will run the regression of the model and test for stationarity of my residuals.

Then I will compare my results of the two countries. I will perform a unit root test to

6


test if a time series variable is stationary or non stationary using an autoregressive

model. I will also do a forecasting test, by using the Chow forecast test.

5.1 Comparison of original data and transformed data.

In the appendix the plotted variables are against their logged values. The

reason for logging the values is to convert the data into a smaller range which makes

the data to work with and to create a model with. The graphs show what I expected,

showing a smaller version of the normal variable for the respected variables. The

graphs show that there isn’t a structural break, and it follows a trend, this is good for

the tests that I want to implement.

5.2 Histograms, Test for normality.

There are many tests that you could do to check if the data is normally

distributed, one test is to plot your data into a histogram and to see if is normally

distributed with this graphical method. The results are summerised in the table

below and the histograms are in the appendix.

Skewness Kurtosis Jarque-Bera Probability

Log Cpi Canada -2.366404 9.155652 150.7288 0.000000

Dlog Cpi Canada -2.802828 12.97633 321.9201 0.000000

Log Cpi Malaysia -0.028557 2.23713 1.438698 0.487069

Dlog Cpi Malaysia 1.350618 9.752628 127.8287 0.000000

Log nominal Canada 0.041422 1.62081 4.772571 0.091971

Dlog nominal

Canada -0.479133 3.348232 2.555537 0.278658

Log nominal

Malaysia 0.66748 2.178807 6.038844 0.048829

Dlog nominal

Malaysia -1.255697 10.05003 135.3577 0.000000

7


As you can see my histograms in the appendix for all of my log variables they are not

normally distributed, therefore the variables are not normal. But when I differenced

the log of the variables, there is a slightly more consistency, but it is not normally

distributed, just there is a bit more of a left skweness. Dlogcpi Canada is left skewed,

I did this by eye by looking at the histogram itself, but as you can see on the right of

every histogram is a table of numbers, and at the skewness there is a number, for it

to be normally distributed, the number should be zero, the number should be as

close to zero as possible for it to be normally distributed. The range at which the

skewness is is from -1 which is left skewed to 1 which is right skewed. Also if you look

at the Kurtosis, this number should ranged between -2 and 2, if it is between this it is

normally distributed, and again as you can see most of the data is outside this range.

So as you can see my data has a non-normal distribution. Also if you look at the

Jarque-Bera statistic and the corresponding probability, if that probability is less than

0.05 then again the data is not normal.

5.3 Stationary properties of variables

To test whether my data for stationarity, I used the ADF test at both level

and first difference to test for a unit root of all my logged variables and I achieved

the following results:

Variable DF Used Level (H0)

1st

Difference

(H1)

t-statistic

Critical

value t-statistic

Critical

value

lognominal_mly

Trend and

intercept -1.97244 -3.495295 -3.66315 -3.495295

lognominal_can

Trend and

intercept -2.73596 -3.489228 -5.25478 -3.493692

logcpi_mly

Trend and

intercept -2.61554 -3.490662 -5.85026 -3.492149

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logcpi_can

Trend and

intercept -1.75387 -3.489228 -4.34684 -3.489228

And as you can see in 1st difference the t-statistic is smaller than the critical value of

5% which shows that the data is stationary. Stationary is when the statistical

properties of a time series’ data, such as mean and variance, are all constant over

time. We are given an idea for finding appropriate forecasting models whilst making

data stationary. Having stationary data makes extrapolation more valid when using

statistical findings. I could have also used the Phillips Perron test, which would have

done the same thing.

5.4 Autocorrelation function of the variables.

The autocorrelation function (ACF) of a variable expresses the correlation

between the two variables at different points in time and this is displayed graphically

in the appendix. When the autocorrelation function moves in a steady pattern it

means that the variables are non stationary.

In the appendix are the auto correlation and partial correlation function of the

inflation and interest rates for both Canada and Malaysia. There are two sets of

graphs per variable of log and dlog, which is the level and 1st difference part, and this

is done because at level the variables my not be stationary, so doing it at 1st

difference makes the variables stationary. The reason for using difference log on my

logged variables is because for my logged variables there is negative inflation values,

so I had to difference them.

5.5 Cointegration

Cointegration is and econometric property for time series variables. It is a

way of testing the hypothesis of the relationship between variables that have a unit

root. This is used to help describe the movement of data that is measured over a

period of time. If two or more series are individually integrated but some linear

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combinations of them have a lower order of integration then the series are said to

be cointegrated.

Engle and Granger introduced the notion of Cointegration. They showed that

a linear combination of integrated variables can possibly be stationary. This process

tries to determine whether or not the residuals of the equilibrium relationship are

stationary. Engle and Granger (1997) found that if Cointegration exists between two

variables in the long-run, then there must exist either unidirectional or bi-directional

Granger causality between the two variables. They also found that the cointegrated

variables must have an error correction model representation.

What I expect to find is that there is a relationship between the inflation and

nominal interest rates for Canada. However not such an obvious relationship in

Malaysia. To test for the existence of Cointegration, I have to use Engel Granger. I

have to run a regression and test it for unit root using ADF test. If at level it is

stationary and at 1st difference it is stationary, then I will have to run an error

correction model. But before this I will first run my regression, then I will check for

heteroskedasticity, using the white test, it basically means that a series of random

variances that are different, there is also series of data which have the same

variances which is called homoskedasticity. And the white test tests to see whether

the variance of residuals is constant. My results are summerised below and the full

output is in my appendix:

White test

Obs*R-

squared Prob Chi2 value

Canada 21.2838 0.0000

11.0704976

9

Malaysia 8.064592 0.0000

11.0704976

9

So if the R2 value is less than or equal to the Chi squared then you can not reject the

null hypothesis, therefore it is heteroskedasticity.

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Now I will do the engel granger method for Cointegration. The output for my

regression for Canada gives the regression:

πt=22.67175-4.678007it+et

The output for my regression for Malaysia gives:

πt=4.775677-0.181368it+et

The two regression tables shown in the appendix shows the regressions of

linear relationships between interest rates and inflation. Also if you look at the prob

(F-statistic) value on the two regressions, the regression for Canada and the

regression for Malaysia are 0.000001 and 0.000000 respectively. The two regression

outputs show the regressions of linear relationships between interest rates and

inflation.

The coefficients are estimated by OLS and to check if there are any unit

roots present in the residuals I will test my them for unit roots, with the

Augmented dickey fuller test, my results are summerised as followed and the

tables are output is in the appendix:

Residual Level

1st

Difference

t-statistic

Critical

value t-statistic

Critical

value

Residual Canada -1.969410 -3.489228 -4.350184 -3.490662

Residual Malaysia -2.166312 -3.490662 -6.192455 -3.490662

So as you can see, for my critical value which is 5% is larger than the t-statistic figure,

therefore the unit root test confirms that the residuals are stationary at 1st

difference, and are non stationary at level, therefore my variables are not

cointegrated, so there is no need to do an error correction model. If I was to do an

error correction model, then I would use two step engel granger procedures, to

correct my model then I would have to redo the ADF test again and then the

amended residuals would be stationary at 1st difference.

5.6 Chow Forecasting

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The Chow test was invented by economist Gregory Chow. In econometrics,

the Chow test is most commonly used in time series analysis. The chow forecast test

estimates the model for a subsample. The estimated model is then used to predict

the values of the dependent variable. A large difference between the actual and

predicted values casts doubt on the stability of the estimated relation over the two

subsamples. The Chow forecast test can be used with least squares and two-stage

least squares regressions.

My chow forecasting output is summerised below:

F-

statistic

F-

statistics(Chow) Prob.F

Canada

from

2005 Q1

39.21799

12.85481 0.0000

Malaysia

from

2005Q1

87.97009

9.423081 0.0000

So if you look at the ‘prob f’ number, for both the output for the chow test says its

0.0000 for both regression then this means that there is a high margin of error, so in

other words the regression will be very inaccurate in forecasting future figures. The

figure closest to one means it will be a better forecaster. I have tried various

different years, and I get the same results, the errors could have occurred from a

number of things, this could be because in inaccurate data, or because I tried to

forecast before the financial crisis and the data I have for that period may have been

impaired.

6 Conclusion

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http://en.wikipedia.org/w/index.php?title=Gregory_Chow&action=edit&redlink=1

http://en.wikipedia.org/wiki/Time_series_analysis


After analysing both countries by carrying out a number of tests I found that

both countries generated very similar results for unit root and Cointegration, I have

found that because the residuals at level are stationary and at 1st difference are non

stationary shows that they are not cointegrated, which shows that fisher effect holds

for both countries. For Canada I did expect the fisher effect to hold, because being a

well developed country and for having a good economy. However for Malaysia I had

my doubts because it is still a developing country in some sense. There is a negative

relationship between nominal interest rates, and inflation. And because they are not

cointegrated at this point, then I do not have to run an error correction model.

Another test for Cointegration I could have used is Johansen test, but I could have

only used this test if I had more variables which would make it multivariate, but it

was not, it was univariate. However I have seen papers and journals that used the

Johansen test for the fisher effect and with univariable data. And an alternative unit

root test I could have done is the Phillips Perron. And I would have done another

forecasting test to just verify the forecasting accuracy of my regression, and to

compare the two forecasters. I would do this because for the chow forecasting I saw

that both of the regressions are very poor forecasters to predict future values.

If I were to make changes to this project, I would pick more variables to make

my model multivariate and try the Johnsen test, because I have heard that it is more

sophisticated to use than the Engle Granger, and gives more of an accurate result.

And I would have chosen two very different countries, for example a developing

country, for example India and a well developed country like the United Kingdom to

see and compare them. Also what would be interesting to see in these very different

countries, that in quarterly data, how the holidays for the countries may affect the

results. For example in the UK it is a highly Christian populated country so in the final

quarter when Christmas and in the second quarter when Easter takes place, to see if

this has any significance on the results, and India is a high number of Hindus, and to

see whether the results change in corresponding to their holidays and festivals.

I would have also changed the CPI data, and find another source to show

inflation, because I read that even though I can find out inflation from calculating the

log of CPI, I could get slightly different results from another source for example if I

13


found the inflation from the countries GDP data then I might have got different

results, for example my data may not have been stationary at any point, or may

result into the regression being a better forecaster with a low probability of errors.

Also I think if I had more practice and experience in using eviews or any other

econometrics software, I could execute and interpret more tests and to get better

results and more accurate results.

Appendix of raw data

TimeNominal MLY CPI MLY Nominal Can CPI Can

1995q01 5.03 77.8749

86.93333333 7.99

1995q02 5.41067 78.3058 87.6 7.343331995q03 5.557 78.8379

87.76666667 6.47333

1995q04 6.01733 79.5222

87.86666667 5.76333

1996q01 6.276 80.4851 88.2 5.106671996q02 6.32333 81.1694

88.83333333 4.68667

1996q03 6.535 81.6762 89 4.141996q04 6.51367 82.183

89.66666667 2.89333

1997q01 6.29133 83.0446 90.1 2.963331997q02 6.433 83.1714

90.23333333 3

1997q03 6.20267 83.5515

90.53333333 3.18333

1997q04 6.70133 84.4131

90.56666667 3.88667

1998q01 5.94867 86.6178 91.1 4.439671998q02 8.879 87.9356 91.1 4.819

14


1998q03 6.93067 88.2904 91.2 4.912671998q04 5.698 88.9493 91.6 4.7521999q01 5.427 90.0643

91.86666667 4.74733

1999q02 3.10433 90.267

92.56666667 4.54767

1999q03 2.837 90.343

93.16666667 4.719

1999q04 2.73467 90.7739

93.76666667 4.865

2000q01 2.74733 91.5118

94.36666667 5.13467

2000q02 2.75733 91.5424 94.8 5.583672000q03 2.989 91.6648

95.66666667 5.60367

2000q04 2.951 92.2765 96.7 5.637332001q01 2.85 92.9188

96.93333333 4.85

2001q02 2.80733 92.9799 98.2 4.3512001q03 2.79 92.9188

98.23333333 3.62433

2001q04 2.72133 93.3776

97.73333333 2.24767

2002q01 2.72967 94.2645

98.43333333 2.12633

2002q02 2.72467 94.7845 99.5 2.592002q03 2.725 94.8457 100.6 2.890332002q04 2.749 95.0292

101.4666667 2.736

2003q01 2.79633 95.488

102.7666667 2.93867

2003q02 2.78133 95.6409

102.2333333 3.18833

2003q03 2.80333 95.7938

102.7666667 2.70167

2003q04 2.77233 95.7632 103.2 2.651672004q0 2.53 96.3749 103.7 2.12767

15


12004q02 2.54667 96.742 104.5 2.001332004q03 2.457 97.2007

104.7666667 2.212

2004q04 2.0495 98.1795

105.5666667 2.53867

2005q01 2.3475 98.6913

105.9666667 2.48233

2005q02 2.32 99.5249

106.4333333 2.46167

2005q03 2.42067 100.458

107.4666667 2.71733

2005q04 2.84883 101.325 108 3.241332006q01 2.94667 102.392

108.6666667 3.66333

2006q02 3.102 103.626

109.1333333 4.14967

2006q03 3.409 104.026 109.2 4.150332006q04 3.45133 104.393 109.5 4.1692007q01 3.41733 105.093

110.6666667 4.171

2007q02 3.38967 105.16

111.4333333 4.29067

2007q03 3.48967 105.893

111.4666667 4.22533

2007q04 3.438 106.693

112.2333333 3.916

2008q01 3.374 107.794

112.7333333 2.91

2008q02 3.439 110.261 114 2.706672008q03 3.433 114.795 115.3 2.273332008q04 3.314 112.995

114.3666667 1.67

2009q01 2.377 111.795

114.0666667 0.716667

2009q02 1.898 111.695 114.1 0.232009q03 1.96267 112.161

114.2666667 0.233333

16


Appendix of outputsComparison of original data and transformed data.

70

80

90

100

110

120

1996 1998 2000 2002 2004 2006 2008

CPI MLYLOGCPI_MLY

-2

0

2

4

6

8

10

12

1996 1998 2000 2002 2004 2006 2008

CPI CanLOGCPI_CAN

17


0

20

40

60

80

100

120

140

1996 1998 2000 2002 2004 2006 2008

Nominal CanLOGNOMINAL_CAN

0

2

4

6

8

10

12

1996 1998 2000 2002 2004 2006 2008

Nominal MLYLOGNOMINAL_MLY

Histograms, test for normality.

Log CPI Canada

0

2

4

6

8

10

12

14

16

-1 0 1 2

Series: LOGCPI_CANSample 1995Q1 2009Q4Observations 60

Mean 1.124237Median 1.293021Maximum 2.078191Minimum -1.514128Std. Dev. 0.723547Skewness -2.366404Kurtosis 9.155652

Jarque-Bera 150.7288Probability 0.000000

Dlogcpi Canada

18


0

4

8

12

16

20

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 -0.0 0.2

Series: DLOGCPI_CANSample 1995Q1 2009Q4Observations 59

Mean -0.060887Median -0.008358Maximum 0.199625Minimum -1.136532Std. Dev. 0.221683Skewness -2.802828Kurtosis 12.97633


Log CPI malaysia

0

2

4

6

8

10

4.4 4.5 4.6 4.7

Series: LOGCPI_MLYSample 1995Q1 2009Q4Observations 59

Mean 4.546965Median 4.551606Maximum 4.743148Minimum 4.355104Std. Dev. 0.103172Skewness -0.028557Kurtosis 2.237130


Dlogcpi malaysia

0

2

4

6

8

10

12

14

-0.01 0.00 0.01 0.02 0.03 0.04

Series: DLOGCPI_MLYSample 1995Q1 2009Q4Observations 58

Mean 0.006290Median 0.005852Maximum 0.040298Minimum -0.015804Std. Dev. 0.007680Skewness 1.350618Kurtosis 9.752628


19


Log nominal can

0

2

4

6

8

10

4.45 4.50 4.55 4.60 4.65 4.70 4.75

Series: LOGNOMINAL_CANSample 1995Q1 2009Q4Observations 60

Mean 4.606131Median 4.605655Maximum 4.747537Minimum 4.465142Std. Dev. 0.090665Skewness 0.041422Kurtosis 1.620810


Dlog nominal Canada

0

2

4

6

8

10

-0.005 0.000 0.005 0.010

Series: DLOGNOMINAL_CANSample 1995Q1 2009Q4Observations 59

Mean 0.004786Median 0.004821Maximum 0.012983Minimum -0.008128Std. Dev. 0.004417Skewness -0.479133Kurtosis 3.348232


log nominal malaysia

20


0

4

8

12

16

20

24

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

Series: LOGNOMINAL_MLYSample 1995Q1 2009Q4Observations 59

Mean 1.261041Median 1.094939Maximum 2.183689Minimum 0.640801Std. Dev. 0.389120Skewness 0.667480Kurtosis 2.178807


Dlognominal malaysia

0

4

8

12

16

20

24

-0.6 -0.4 -0.2 -0.0 0.2 0.4

Series: DLOGNOMINAL_MLYSample 1995Q1 2009Q4Observations 58

Mean -0.016226Median -0.001790Maximum 0.400521Minimum -0.558589Std. Dev. 0.124558Skewness -1.255697Kurtosis 10.05003


Autocorrelation function of the variables.

Log and dlog of CPI of Canada at level

log and dlog of CPI Canada at 1st difference

21


log and dlog of CPI malaysia level

log and dlog of CPI malaysia at 1st difference

log and dlog of nominal interest in Canada level

22


log and dlog of nominal interest rates in Canada 1st difference

log and dlog of nominal interest rates in malaysia level

log and dlog of nominal interest rates in malaysia 1st difference

23


CointegrationWhite TestWhite test for Canada:

Heteroskedasticity Test: White

F-statistic 15.66755 Prob. F(2,57) 0.0000Obs*R-squared 21.28380 Prob. Chi-Square(2) 0.0000Scaled explained SS 61.36587 Prob. Chi-Square(2) 0.0000

Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 04/17/10 Time: 23:30Sample: 1995Q1 2009Q4Included observations: 60

VariableCoefficien

t Std. Error t-Statistic Prob.

C 1091.274 298.0955 3.660821 0.0006LOGNOMINAL_CAN -477.8290 129.4198 -3.692087 0.0005LOGNOMINAL_CAN

^2 52.29830 14.04255 3.724274 0.0005

R-squared 0.354730 Mean dependent var 0.337905Adjusted R-squared 0.332089 S.D. dependent var 0.846490S.E. of regression 0.691801 Akaike info criterion 2.149670Sum squared resid 27.27957 Schwarz criterion 2.254388Log likelihood -61.49011 Hannan-Quinn criter. 2.190631F-statistic 15.66755 Durbin-Watson stat 0.423025Prob(F-statistic) 0.000004

White Test for Malaysia

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RegressionRegression for Canada:

Dependent Variable: LOGCPI_CANMethod: Least SquaresDate: 04/17/10 Time: 23:10Sample: 1995Q1 2009Q4Included observations: 60

VariableCoefficien


C 22.67175 3.911218 5.796597 0.0000LOGNOMINAL_CAN -4.678007 0.848971 -5.510207 0.0000


Regression for malaysia:

Dependent Variable: LOGCPI_MLYMethod: Least SquaresDate: 04/17/10 Time: 23:14Sample (adjusted): 1995Q1 2009Q3Included observations: 59 after adjustments

VariableCoefficien


C 4.775677 0.033783 141.3643 0.0000LOGNOMINAL_ML

Y -0.181368 0.025617 -7.079841 0.0000

R-squared 0.467907 Mean dependent var 4.546965Adjusted R-squared 0.458572 S.D. dependent var 0.103172S.E. of regression 0.075916 Akaike info criterion -

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Heteroskedasticity Test: White

F-statistic 4.433234 Prob. F(2,56) 0.0163Obs*R-squared 8.064592 Prob. Chi-Square(2) 0.0177Scaled explained SS 5.959772 Prob. Chi-Square(2) 0.0508

Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 04/17/10 Time: 23:32Sample: 1995Q1 2009Q3Included observations: 59

VariableCoefficien


C -0.030538 0.012416 -2.459677 0.0170LOGNOMINAL_ML

Y 0.056650 0.019105 2.965162 0.0044LOGNOMINAL_ML

Y^2 -0.020316 0.006825 -2.976605 0.0043

R-squared 0.136688 Mean dependent var 0.005568Adjusted R-squared 0.105855 S.D. dependent var 0.007067

S.E. of regression 0.006682 Akaike info criterion-

7.129215

Sum squared resid 0.002501 Schwarz criterion-

7.023578

Log likelihood 213.3118 Hannan-Quinn criter.-

7.087979F-statistic 4.433234 Durbin-Watson stat 0.497435Prob(F-statistic) 0.016319


2.285065

Sum squared resid 0.328506 Schwarz criterion-

2.214640

Log likelihood 69.40941 Hannan-Quinn criter.-

2.257574F-statistic 50.12415 Durbin-Watson stat 0.114388Prob(F-statistic) 0.000000

Augmented dickey fuller tests on residualsFor Canada at level:Null Hypothesis: RESIDCAN has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on AIC, MAXLAG=10)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -1.969410 0.6053Test critical values: 1% level -4.124265

5% level -3.48922810% level -3.173114

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test EquationDependent Variable: D(RESIDCAN)Method: Least SquaresDate: 04/17/10 Time: 23:47Sample (adjusted): 1995Q3 2009Q4Included observations: 58 after adjustments

Canada at 1st difference:Null Hypothesis: D(RESIDCAN) has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on AIC, MAXLAG=10)

t-Statistic Prob.*


5% level -3.49066210% level -3.173943


Augmented Dickey-Fuller Test Equation

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Dependent Variable: D(RESIDCAN,2)Method: Least SquaresDate: 04/17/10 Time: 23:47Sample (adjusted): 1995Q4 2009Q4Included observations: 57 after adjustments

And my results for Malaysia at level is:

Null Hypothesis: RESID01 has a unit rootExogenous: Constant, Linear TrendLag Length: 1 (Automatic based on AIC, MAXLAG=10)

t-Statistic Prob.*


5% level -3.49066210% level -3.173943


Augmented Dickey-Fuller Test EquationDependent Variable: D(RESID01)Method: Least SquaresDate: 04/17/10 Time: 23:41Sample (adjusted): 1995Q3 2009Q3Included observations: 57 after adjustments

And at 1st difference:Null Hypothesis: D(RESID01) has a unit rootExogenous: Constant, Linear TrendLag Length: 0 (Automatic based on AIC, MAXLAG=10)

t-Statistic Prob.*


5% level -3.49066210% level -3.173943


Augmented Dickey-Fuller Test EquationDependent Variable: D(RESID01,2)Method: Least SquaresDate: 04/17/10 Time: 23:41

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Sample (adjusted): 1995Q3 2009Q3Included observations: 57 after adjustments

Chow Forecasting

Chow forecaseting from 2005Q1 for Canada:

Chow Forecast Test: Forecast from 2005Q1 to 2009Q4

F-statistic 12.85481 Prob. F(20,38) 0.0000Log likelihood ratio 122.9829 Prob. Chi-Square(20) 0.0000

Test Equation:Dependent Variable: LOGCPI_CANMethod: Least SquaresDate: 04/30/10 Time: 14:28Sample: 1995Q1 2004Q4Included observations: 40

Variable Coefficient Std. Error t-Statistic Prob.

C 21.29822 3.187329 6.682154 0.0000LOGNOMINAL_CAN -4.383027 0.699893 -6.262427 0.0000


Chow forecaseting from 2005Q1 for Malaysia:

Chow Forecast Test: Forecast from 2005Q1 to 2009Q3

F-statistic 9.423081 Prob. F(19,38) 0.0000Log likelihood ratio 102.8068 Prob. Chi-Square(19) 0.0000

Test Equation:Dependent Variable: LOGCPI_MLYMethod: Least SquaresDate: 04/30/10 Time: 14:26Sample: 1995Q1 2004Q4Included observations: 40

Variable Coefficient Std. Error t-Statistic Prob.

C 4.677912 0.020858 224.2786 0.0000LOGNOMINAL_MLY -0.138210 0.014736 -9.379237 0.0000

R-squared 0.698341 Mean dependent var 4.490985

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Adjusted R-squared 0.690403 S.D. dependent var 0.069920S.E. of regression 0.038905 Akaike info criterion -3.606692Sum squared resid 0.057516 Schwarz criterion -3.522248Log likelihood 74.13384 Hannan-Quinn criter. -3.576160F-statistic 87.97009 Durbin-Watson stat 0.255183Prob(F-statistic) 0.000000

Bibliography

Johnson, P.A. (2006), ‘Is there really the Fisher effect?’, Applied Economics Letters 13, pp. 201-203.

Perez, S.J. and M.V. Siegler (2003), ‘Inflationary expectations and the Fisher effect prior to World War I’, Journal of Money, Credit and Banking 35, pp. 947-965.

Fahmy, Y.A.F. and M. Kandil (2003), ‘The Fisher effect: new evidence and implications’, International Review of Economics and Finance 12, pp. 451-465.

Gujarati D.N. (1995), Basic Econometrics, 3rd edition, McGraw-Hill International Editions.

Mankiw,N.G. (2000), Macroeconomics, 4th edition, Worth Publishers, chapters 7 and 18.

Arusha Cooray (2002), ‘THE FISHER EFFECT: A REVIEW OF THE LITERATURE’ . (http://www.econ.mq.edu.au/research/2002/6-2002Cooray.PDF)

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Assignment Fisher 1

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