The Initial Trade Impact of Brexit: Exchange Rate Volatility Analysis

This report provides a statistical analysis of the initial trade impact of Brexit, specifically examining the effect of exchange rate volatility on UK trade. The analysis employs panel data and regression methods to determine the relationship between Gross Domestic Product Index (GDPI) and Exchange Index System (EIS). The report explains the types of data required, the reasons for using panel data, and the methods employed, including regression and Panel Least Square. The results section presents the regression analysis outcomes, including coefficients, standard deviations, t-statistics, and probabilities, offering insights into the relationship between the variables from 2012 to 2018. The findings indicate a negative relationship between EIS and GDPI, with a low R-squared value, suggesting the data set might not be entirely reliable for measuring outcomes. The report concludes with an interpretation of the results and a discussion of the statistical significance of the findings.

The Initial Trade Impact of Brexit:
Effect of Exchange Rate Volatility on
UK’s Trade

TABLE OF CONTENTS
Statistical analysis:.................................................................................................................1
Panel data................................................................................................................................1
Type of data required for panel analysis................................................................................1
Reason for application of Panel data......................................................................................2
Description of methods...........................................................................................................5
Results....................................................................................................................................6
REFERENCES................................................................................................................................9

Statistical analysis:
Regression is referred as statistical measurement implied in finance, investing along with
other disciplines which attempts for determining strength of relationship among single dependent
variable along with series of other altering variables which are replicated as independent
variables. It helps financial and investment managers for valuing asset and understanding
relationship among variables like commodity prices along with stock of business with deal with
particular commodities. Generally, it is used for examining relationship among one dependent
and independent variable (Anderson, James and Eric van Wincoop, 2003). After performing this
analysis, regression statistics could be used for purpose of predicting dependent variable when
independent variable is known.
Panel data
Panel data is considered as type on longitudinal data or data gathered at different point of
time. There are three main types of longitudinal data such as Time series data, polled cross
sections and panel data. Time series data comprise many observations as few as single unit such
as trends of stock price and aggregate national statistics. The pooled cross sections is two or
more independent samples of various units which are drawn through same population at various
other time periods. Simultaneously, two of more observations on many units are referred as panel
data (Tinbergen, 1962). The panel data could be analyzed when there is requirement of
describing changes over time or for estimating superior trends in social phenomena along with
estimation of causal models. Panel data is useful because with observations which span both
individuals and time in cross sections with availability of more information and gives more
efficient estimates. Its use allows for empirical test for broad range of hypothesis. On basis of
panel data, one can control unmeasurable and unobserved sources of individual heterogeneity
which vary across individuals but it does not vary over time. Simultaneously, this will lead to
omit variable bias.
Type of data required for panel analysis
The basic panel method is in need of at least 2 waves of measurement as in this data set
there is presence of GDP and EIG where panel datasets includes time invariant and time varying
variables. There is presence of alternative method for structuring data to keep every measures in
single record. Sometimes, it is referred as wide format.
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The estimation techniques for panel models as General linear model is referred as
foundation of estimation of linear panel model such as ordinary least squares, Weighted least
squares and Generalised least squares (Dell’Aricca, Giovanni, 1999). The least squares
estimation of panel models entails with three steps where first is data transformation of with
estimation of first stage, secondly, estimation of parameters with application of ordinary Least
squares and at last estimation of variance and covariance matrix of estimates.
Reason for application of Panel data
Panel data could undertake explicit amount of individual particular heterogeneity as
individual is denoted as micro unit. With combination of data in two dimensions, panel data
provides various data variation, more degree of freedom along with less collinearity. In the
similar aspect, panel data is better suited comparatively to cross sectional data for understanding
dynamics of alteration. For instance, it is best appropriate for understanding behavior of
transition. It is better for measuring and detecting effects which could not be observed in time
series or cross section data. It helps in enabling study of models which comprises complex
behavior models such as effect of economic cycles or technological change. Conversely, it
minimizes effects of aggregation bias and from aggregating firms in broad groups. In case, all
cross sectional units have similar number of observations in time series, then panel is balanced
and vice versa.
For instance:
Estimation of (1) is dependent on assumption what are undertaken related to intercept
(a0), a1 as slope coefficient along with error term. There is presence of several assumptions
could be made in order for estimating such as follows:
In the first assumption, slope and intercept coefficients are constant across firms and time
along with error term which captures variation over firms and time. In the same series, slope
coefficient is constant but in this context intercept varies over time and firms. Henceforth, all
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intercept and slope (coefficient) vary over firms and then intercept along with slope vary over
time and firms. In this aspect, pooled regression through OLS as this is estimation but pooled
regression might give outcome in heterogeneity bias (Dell’Aricca, Giovanni, 1999).
Panel method will lead to fixed effects estimation and random effects estimation which is
described as follows:
Fixed Effects estimation: The above estimate is suggesting about better aspect to model data
which would allow every firm for having its own intercept such as:
It is also replicated as one way or fixed effects models and simplest way for estimating
and to allow every firm with presence of its own intercept or for creating set of dummy (binary
variable), one for every firm and inclusion as regerssor.
Conversely, this estimation form is replicates as Least squares Dummy variables as there
is no constant with this regression. On the contrary, there are various groups and they become
highly tedious for purpose of creating all required dummy variables. Some of economic software
with ability for automating. Thus, the method used is replicated as covariance estimator and it
operates on differencing with fixed impact through expressing variables about deviations through
group means.
So,
The further extension is allowing intercepts for varying across different time duration as
it is replicated as two ways fixed effects:
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The time dummy coefficients could allow the function of regression for shifting over
time for purpose of capturing alterations in government regulation, technology, external
influences and tax policy etc. It allows slope coefficients and intercept for varying across groups.
Random Effects Estimation:
The fixed effects model has assumed that every group has presence of non stochastic group
which is specific component to y. There is inclusion of dummy variables is a method of
controlling for unobservable impact on y (Ethier, 1973). On the contrary, unobservable effects
might be random as random effects model which attempts to deal with this:
In the above equation, is treated as component with random error term as it is element of
error which directly varies among group but not within particular groups. Along with this
element of error which varies over time and group. There is presence of assumptions such as:
There is introduction of error component which directly varies across time duration but
not across groups such as two way random effects. Estimation os random effect model could not
be performed through OLS, rather than technique replicated as generalised least square method
should be used.
Demerits of fixed test:
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 It wipes out explanatory variables which does not vary within individual. (time invariant
like gender and race)
 One is often interested in effects which separate sources of individual heterogeneity.
Hausman Test: The test with context of statistical significance of variation among
coefficient estimates about getting FE and through RE, in null hypothesis which is estimated
with RE which is consistent and efficient and estimates of FE is not inefficient. In the similar
aspect, test has form of Wald test and directly reported in Chi2form with k-1 degree of freedom.
In case W is smaller than critical value then random effect is replicated as preferred estimator.
Advantages of panel data:
 High accurate inference of model parameters as it comprises more degree of freedom and
sample variability comparatively to cross sectional data.
 Great capacity to capture complexity of human behavioural hypotheses.
 It simplifies computation along with statistical inference.
Description of methods
Regression method: In accordance with analysing the outcomes on which determinants
have been set on the dependents as well as independent variables. There has been analysis over
variation which results the relationship between GDP and another variable. However, using this
technique will be effective with reference to address the relationship between GDP and EIG.
This is the most reliable and adequate techniques which in turn will be effective for addressing
the outcomes and determining the relationship between the variables.
Panel Least Square: In this statistical method there have been analysis made by
researchers over the economic as well as epidemiological data set. It will use the two-
dimensional panel data to address the data set. Therefore, the data is required to be collected over
time and same individual and a regression is run over these two dimensions. However, in relation
with analysing the GDP, POP and other variables with the panel least square method on which it
can be said that this technique is very helpful and effective in terms of analysing the data set as
well as making the adequate interpretation of the outcomes. The data from various regions have
been gathered over the period of 2012 and 2018. Thus, to analyse it which will be helpful in
bringing the correct information regarding the outcomes.
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Results
GDPI: In relation with analysing the regression analysis between GDPI and EIS on which
it can be said that, this will be effective and adequate analysis over the data set. To addresses the
relation between these variables on which making better observation. However, this method will
be accurate and reliable to determine the relationship and estimate the dependency of a variables
on another. To analyse the validity as well as defining the relationship between the variable will
be effective in relation with drafting the reliable observation. There will be use of Panel Least
Square method as well as regression analysis method to address the outcomes.
Dependent Variable: LOG(EIG)
Method: Panel Least Squares
Date: 03/05/19 Time: 12:31
Sample: 2012Q1 2018Q2
Periods included: 26
Cross-sections included: 19
Total panel (balanced) observations: 494
Variable Coefficient Std. Error t-Statistic Prob.
C 12.89419 27.46941 0.469402 0.6390
LOG(GDPI) -0.520026 2.091060 -0.248690 0.8037
R-squared 0.000126 Mean dependent var 6.062844
Adjusted R-squared -0.001907 S.D. dependent var 1.857069
S.E. of regression 1.858838 Akaike info criterion 4.081821
Sum squared resid 1699.998 Schwarz criterion 4.098835
Log likelihood -1006.210 Hannan-Quinn criter. 4.088501
F-statistic 0.061847 Durbin-Watson stat 0.071228
Prob(F-statistic) 0.803704
Interpretation: On the basis of above listed table on which regression analysis have been
made on the data set. It has defined the relationship between EIS and GDPI over the period of
2012 to 2018. It has been analysed by considering the Panel least square method for regression
analysis have presented the outcomes as coefficient, standard deviation, T-statistics and
probability of the data base. Thus, the Coefficient of the data base is -0.52 as per LOG(GDP)
standard error as 2.09, T-statistics as -0.248 and probability as 0.803. However, in analysing such
outcomes on which it can be said that there has been negative relationship between the variables.
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As per considering R value of the data set on which it has presented the value as -0.0019 which
defines -0.019% of relationship among the variables.
Thus, the data set is not being reliable and adequate for measuring the outcomes and
answering the data base. The R square have been gathered by researcher which is being denoted
as 0.00012. Similarly, in accordance with the F- statistics of the data base on which there have
been ascertainment of result as 0.061. Thus, in accordance with such outcomes on which it can
be said that the data is required to be between 0.60 to 0.70 thus, more than 70% is being denoted
as the most reliable in addressing the outcomes. Moreover, in relation with the presented
outcomes on which it can be said that there has been negative relationship between the variables
which is not dependent on each other. Moreover, the changes incurred in one variable would not
affect another variable in context with developing the effective observation.
GDPJ: In accordance with analysing the effective panel least square regression with the
help of considering the outcomes. However, in relation with such aspects there have been
consideration over the GDPJ and EIG from the data set of 2012 to 2018. Therefore, with
reference to analyse the relationship between this variable the below listed results will be helpful
in justifying the analysis such as:
Dependent Variable: LOG(EIG)
Method: Panel Least Squares
Date: 03/05/19 Time: 12:44
Sample: 2012Q1 2018Q2
Periods included: 26
Cross-sections included: 19
Total panel (balanced) observations: 494
Variable Coefficient Std. Error t-Statistic Prob.
C -4.058472 0.236647 -17.14992 0.0000
LOG(GDPJ) 0.960155 0.022156 43.33530 0.0000
R-squared 0.792401 Mean dependent var 6.062844
Adjusted R-squared 0.791979 S.D. dependent var 1.857069
S.E. of regression 0.846997 Akaike info criterion 2.509802
Sum squared resid 352.9629 Schwarz criterion 2.526816
Log likelihood -617.9210 Hannan-Quinn criter. 2.516482
F-statistic 1877.949 Durbin-Watson stat 0.123425
Prob(F-statistic) 0.000000
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Interpretation: On the basis of above presented outcomes in which it can be said that,
there have been determination over the results that have been presented by implicating the
regression analysis through Panel Least Square method. However, in accordance with this, on
which it can be said that their analysis through determining the coefficient, standard error, T-
statistics and probability of the data base. As per analyzing the co-efficiency of LOG(GDPJ)
which is 0.960, Standard errors as 0.022, T-statistics as 43.33 and probability as 0.000. thus, as
per the outcome it can be said that there is a positive relationship among the variables. Thus, the
changes or fluctuations incurred in one4 variable would affect another variable. It states that,
there will be acceptance to the alternative hypothesis.
Similarly, in accordance with the outcomes on which the model summary of the data base
has been presented the R square have bene determined as 0.792 and R value as 0.791. thus, is
states that there is 79.19% of relation has been set between the variables. The F-statistics have
been analyzed by considering the outcomes on which it has presented as 1877.949. therefore, it
defines that the variables which reference outcomes more than 70% than they are more reliable
to analyze and determining the results. However, as per considering such outcomes on which it
can be aid that there is appositive relationship among the variables which defines that the
changes incurred in the one covariable would affect the another one.
Moreover, in accordance with such outcomes on which it can be said that there have been
positive relationship between GDP and EIG as per 2012 to 2018. Thus, analyzing such outcomes
defines that there has been acceptance to the alternative hypothesis of the data set. The changes
incurred in GDP of a country would affects its EIG rate. It will be suggested to the government
that, improving the employment rate in the country which will be effective to balance the
employment rate. Thus, for the economic growth perspective this method will be effective to
address the social issues. the dependency of a nation on another nation will be reduced as there
will be effective control over the number of imports in the nations. Thus, the raise in GDP level
will effectively makes raise in the level of exports form the nations. On the other side, it will be
profitable for the economy to have better balance of payment and balance of trade.
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REFERENCES
Books and Journals
Dell’Aricca, Giovanni (1999) Exchange Rate Fluctuations and Trade Flows: Evidence from
European Union. IMF Staff Papers. 46(3). 315 -334
Ethier, W. (1973) International Trade and the Forward Exchange Market. American Economic
Review. 63. 494-503.
Tinbergen, J. (1962). Shaping the World Economy; Suggestions for an International Economic.
Twentieth Century Fund, New York. Retrieved from http://hdl.handle.net/1765/16826
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