2. BE333 Spring 2016 Coursework - Option 2 – Sina Erdal
The coursework option consists of data manipulation and estimation in EViews,
analysis and interpretation. The coursework must be written up individually.
In your answers to the questions below, you should present your EViews equation
estimation output as it would be in published academic papers. (Examine several
such papers, the approaches to presentation are fairly standard.) Raw EViews
regression output should be included only in an Appendix. You should also
include the studies/books you have utilised in the analyses in a “References” section.
The principle of purchasing power parity (PPP) states that the exchange rate
between two countries will, at least in the long-run, fully reflect the changes in the
price levels of the two countries. Even if it does not hold exactly, the PPP model
provides a benchmark to suggest the levels that exchange rates should achieve.
This can be examined using a simple regression model:
Percentage changes in the exchange rate = + β1 × difference in inflation rates + ut
The PPP implies that = 0 and β1 = 1. That is, the currency of the country with the
higher inflation rate will in the long run depreciate at a rate that is equal to the
difference in inflation rates.
In the file “be333 coursework 2 spring 2016.xlsx” on Moodle you will find monthly
data from 1/1975 to 12/2010 for the following variables:
USDJPY: the USD – Japanese yen exchange rate in yen per USD
US CPI: the US consumer price index
JP CPI: the Japanese consumer price index
Question 1) (25 points) Import the file into Eviews as monthly data. Form the
percentage monthly return series (RET) for the exchange rate and monthly inflation
rates (USINF and JPINF) for the two economies and report and comment on their
descriptive statistics.
jpinf = jpcpi/jpcpi(-1) – 1
usinf = uscpi/uscpi(-1) – 1
ret = usdjpy/usdjpy(-1) - 1
The descriptive statistics shows a greater central tendency of the distribution under
USINF (0.33%) and JPINF (0.14%). This means that the US inflation rate has
increased more than Japanese inflation rate over time. RET (-0.25%) has a lower
central tendency which is also negatively signed, therefore the US dollar has
weakened against the Japanese Yen over time.
3. It is also evident that RET has the most amount of outliers, followed by JPINF and
then USINF. (Mean – Median) JPINF 3.96X10-4 USINF 3.38X10-4 RET 24.56X10-4.
Standard deviation shows the deviation from the mean. Therefore the higher the
standard deviation, the more dispersed the data is from the mean. It gives us a
(95%) confidence level that the mean falls within a certain range if the test output
was repeated. RET (3.33%) has the highest standard deviation which is reflected by
the amount of outliers present in its distribution. JPINF (0.57%) has a lower standard
deviation and USINF (0.37%) has the lowest. Therefore RET and JPINF has more
probability of being away from its mean value than USINF.
JPINF has positive skewness therefore the mass of the data is concentrated to the
left of the distribution. RET and USINF are both negatively skewed, meaning the
mass of the data are concentrated to the right of the distribution.
Kurtosis is a measure of the peak of a distribution. The data shows that RET, JPINF
and USINF have kurtosis above 3 therefore they are leptokurtic. Meaning they have
a higher peak in comparison to a normal distribution.
JPINF USINF RET
Mean 0.001374 0.003346 -0.002456
Median 0.000978 0.003008 0.000000
Maximum 0.027157 0.015209 0.121059
Minimum -0.012950 -0.019153 -0.143560
Std.Dev 0.005732 0.003684 0.033272
Skewness 0.991608 -0.331324 -0.176195
Kurtosis 5.017866 6.899647 4.222720
Jarque-Bera 143.7552 280.9823 29.07854
Probability 0.000000 0.000000 0.000000
Observations 431 431 431
Question 2) (25 points) Estimate the following model using OLS in Eviews:
RETt β1 * (JPINFt – USINFt) + ut
Comment in detail on your regression output. State/interpret the signs, magnitudes,
and statistical significances of the coefficients and the statistical significance and fit
of the overall regression. Test the joint hypothesis = 0 and β1 = 1 using the Wald
test. Does PPP appear to hold in this dataset?
The following statistics are found in ‘Appendix 1’. The coefficient expresses the
relationship between the independent variables and the dependant variable. As the
differential between inflation rates increase by 1 unit (usinf-jpinf), the Japanese yen
exchange rate in yen per USD will increase by 0.4 units. As a result the value of the
yen against the dollar increases. This means an appreciation in the yen or a
depreciation of the dollar.
4. The R-square shows 0.48% of the percentage monthly return series can be
explained by the regression line. This means 0.48% of the dependant variable is
explained by independent variables. Therefore R-square has low explanatory power.
In this case the R-square is not a very good fit to the data. It can be increased if we
included more factors into the right hand side of the equation.
As the residual sum of squares is quite high, it means the data set fits poorly. This is
reflected by the low R-squared figure. The regression shows us that there is
0.473734 variation in the data set that is not explained by the regression model.
The P-value in ‘appendix 1’ for (usinf-jpinf) is 0.1515, as this is above the 5%
significance level, it means the slope coefficient is not significant. The intercept slope
coefficient 0.056 is almost equal to 5% significance level, therefore it is significant.
The significance of both variables are backed up by the standards errors. As shown,
the standard error of the differentials in inflation rates is high 28%. The standard
deviation is lower for the intercept at 0.11%.
The p-value for the F-test is 0.15 which is above the 5% significance level. Therefore
the overall regression is statistically not significant.
Least Squares Regression Output
(Dependant variable: RET)
Observations
431
Sample
1975-2010
Variables Coefficient Std.Error t-statistic Prob
C -0.003250 0.001693 -1.919257 0.0556
USINF-JPINF 0.402409 0.280062 1.436857 0.1515
R-squared 0.004789
Adjusted R-
squared
0.002470
Sum squared
resid
0.473734
Durbin-Watson
stat
1.962761
F-statistic 2.064558
Prob(F-statistic) 0.151488
The Wald test in ‘appendix 2’ with joint hypothesis, α = 0 and β1 = 1, shows that the
PPP does not hold. This is because the F-statistic 0.0024 and Chi-square 0.0022 are
below the 5% significance level.
Wald Test
Null Hypothesis: C(1)=0, C(2)=1
Observations
431
Sample
1975-2010
Test Statistic Value df Probability
F-statistic 6.102976 (2,429) 0.0024
Chi-square 12.20595 2 0.0022
5. Question 3) (25 points) In an essay of less than 250 words, define and critically
discuss the problem of autocorrelation in an estimation setting. Be sure to mention
the consequences of autocorrelation on the properties of OLS estimators.
Autocorrelation/serial correlation is a time series problem in an estimation setting. It
violates one of the Gauss-Markov conditions that is the covariance of error terms is
equal to zero [cov (ut, ut-1) = 0] Ұt≠t-1. Therefore the error covariance when
autocorrelation is present is no longer equal to zero. This means the error terms are
dependent from one another. The effect on todays ‘Ut-1’ error term will effect
tomorrows ‘Ut’ error term. Any error term should have no correlation with any other
error term in the data. There should be no predictability or patterns in results.
Positive autocorrelation causes positive values to be followed by positive values and
negative followed by negative. Alternatively negative autocorrelation causes positive
to follow negative and negative to follow positive values. There is no theory behind
autocorrelation, it is created by error. Autocorrelation is usually a result of a variable
being omitted that ought to be included in the regression output. The omitted variable
is included in the error term as autocorrelation. Another reason can be because the
model has the wrong functional form, for example, a linear-in-variable was included
instead of a log-linear model which should have been fitted. The consequences of
autocorrelation include linear biased estimators when there is a lagged dependant
variable on the RHS of the equation. Bias variances and standard errors are caused
by the equations underestimating. As a result coefficients may appear statistically
significantly different from zero, whereas this should not be the case. This also
means the R square; F and T tests are not reliable. (Gujarati and Porter, 2010).
Question 4) (25 points) Test the model given in Q2 for autocorrelation using the
Durbin-Watson test and comment on your results.
The Durbin Watson (DW) test is used to identify autocorrelation in data. The DW
statistic is equal to 2-2ê. ê is the parameter in the AR(1) autocorrelation relationship
Ut = ê Ut-1+Ɛt. When ê is equal to 0 and DW is equal to 2, then there is no
autocorrelation. DW equal to 0 means there is severe positive autocorrelation. DW
equal to 4 means severe negative autocorrelation.
1.96271=2-2 ê
1.96271−2
−2
= ê
ê = 0.018645
As ê is positive and close to 0, this implies no autocorrelation. ê can be between -1
and 1.
6. We must now test the null hypothesis that autocorrelation does not exist in the data
against the alternative hypothesis of autocorrelation. The Durbin Watson statistic as
given by the data in appendix 1 is 1.962761. The upper and lower bounds, dU and dL,
of the DW statistics are 1.84636 and 1.83704 respectively. These critical values are
found under the Durbin Watson 5% significance table with 430 observations and 2
parameters (k=2). As the Durbin Watson statistic 1.962761 is above the upper bound
1.844636 and below 2, we can comfortably accept the null hypothesis that
autocorrelation does not exist in the data between the residuals. dU<DW<2.If the DW
statistic was between dL and dU it would be in the region known as the grey area and
we would need to test further for autocorrelation. Lastly if the DW was between dL
and 0 then it will be evident there is positive autocorrelation present. This test can
also be repeated by reflecting the statistics into the region between 2 and 4; that is if
DW from the regression output is above 2. In the region between 2 and 4, dU and dL,
are 2.15364 and 2.16296 respectively.
