statistics in finance - m&a and gdp growth

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Specialist Masters Programme

Please list all names of group members:

(Surname, first name)

1. Wei Bo

2. Agrawal Minakshi

3. Lemercier Jean

GROUP NUMBER:

MSc in: Finance

Module Code: SMM 248

Module Title: STATISTICS IN FINANCE

Lecturer: Professor Ana-Maria Fuertes Submission Date: 09 DECEMBER 2013

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18

11/27/2013

Statistics in Finance

Mergers & Acquisition effects on

Economic Growth

Bo Wei – Minakshi Agrawal – Jean Lemercier

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Introduction

Mergers and Acquisition global volumes amount to USD2.1 trillion for the first nine months of 2013, representing a

17% increase from 2012 levels. If this USD2.1 trillion figure is far from the peak of 2007 M&A volumes which were in

excess of $4 trillion, many economists and experts forecast that these volumes will continue to increase over the

next few years. Variation in M&A volumes are observed to follow patterns or waves, where volumes increase

substantially (1990s, 2001, 2008 – see graph) and then suddenly drop. Consequently, various literary works have

been increasingly focusing on explaining the determinants of change in M&A volumes, may it be fundamental factors

such as industrial/economic/regulatory shocks explained in the article “What drives merger waves?” (Harford, 2004)

and/or papers such as “The Free Cash Flow Theory of Takeovers: A Financial Perspective on Mergers and

Acquisitions and the Economy” where other factors such as agency costs, excess free cash flows and attempts of

market timing (Jensen, 1987).

The research on consequences of M&A activity and post-merger results at the firm level shows that there is a

widespread argument whether M&A creates value after taking cost (bid-premium) into account – however the

consensus is often that targeted companies performance improves post-acquisition (M. Healy, 1990). The commonly

used reasoning for justifying acquired companies’ outperformance is that M&A activities create value by constricting

agency costs and creating synergies between companies.

If acquisitions lead to sustainable long-term productivity gains at the firm level, one could argue that acquisitions at

the aggregate level may have an impact on economic growth. Literature displays two different theories. The first one

explains why M&A activity can induce GDP growth, thanks to increased productivity created though synergies and

slashing agency costs. The second theory support the idea that M&A transaction are detrimental to the economy in

the sense that they mostly result in more market control for the acquiring company, which rules out smaller

companies who lack in scale and size to remain viable or give them an incentive to cut down on R&D to remain

competitive. If the relationship between these two variables is hard to define, it seems as though a correlation could

reasonably be expected.

The aim of this paper is to investigate whether changes in volumes of M&A activity are correlated with growth at the

aggregate level – i.e economic growth.

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Motivation It was reported that nine thousand billion dollars was spent by North American and Western European firms on

mergers and acquisitions (M&A’s) between 1995 and 1999. This is about seven times the GDP of the United Kingdom

by an incomprehensive comparison. There are numerous literatures talking about determinants and consequences

of merger and acquisition. However, the impact of M&A on economic growth is seldom explored. Monitoring the

relationship between M&A activity and economic growth could prove valuable to forecast economic growth or

recessions. In our model, we use the data from 2001 to 2013, including the periods of financial crisis. We also want

to know the performance of M&A after the financial crisis, emphasizing the relationship between M&A and

economic growth.

Data Description

Our model will feature the following variables

Y : Real GDP growth (QoQ, %, United Kingdom)

X1 M&A Volumes in the United Kingdom (% Change in sterling volume, QoQ)

X2 Deal count (% Change QoQ)

X3 Average premium paid over the period, (%, Quarterly)

X4 Bank of England base rate (%)

All the data has been taken from Bloomberg.

X1 X2 X3 X4 Y

Mean 0.174249 -0.002463 0.194067 3.029412 0.368627

Median -0.043002 0.001887 0.185500 4.000000 0.500000

Maximum 2.929415 0.269231 0.466800 5.750000 1.300000

Minimum -0.774920 -0.320059 0.068600 0.500000 -2.500000

Std. Dev. 0.733997 0.117647 0.076554 2.059519 0.790314

Skewness 1.305859 -0.257670 1.069145 -0.298630 -1.680696

Kurtosis 5.242891 3.496132 4.606199 1.319012 6.506831

Jarque-Bera 25.18472 1.087412 15.19833 6.762682 50.14324

Probability 0.000003 0.580593 0.000501 0.034002 0.000000

Sum 8.886678 -0.125589 9.897400 154.5000 18.80000

Sum Sq. Dev. 26.93761 0.692037 0.293024 212.0809 31.22980

Observations 51 51 51 51 51 Table 1 - Summary statistics

There are 51 observations in our model from the year 2001 to 2013.

Mean: The mean GDP growth over the period is 0.36%, which corresponds to an average yearly growth of

approximately 1.4%. The average premium paid over the 2001-13 period amounts to 19.4%, which is consistent with

the economic theory: on average market premium for listed stocks are positive and fluctuate between 20-50%

depending on markets and business cycles (On the role of acquisition premium in acquisition research, Tomi

LAAMANEN, 2007).

Jarque Bera: The Jarque-Bera can be used to test the hypothesis that the observations follow a normal distribution.

When the Jarque Bera test result is close to zero, it means that the sample is likely to follow a normal distribution. X2

has the lowest Jarque-Bera, which means it is very likely to follow a normal distribution, as opposed to other factors

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related to M&A (X3 and X1). This could potentially mean that the number of deal varies in a more “normal” manner,

with symmetrical number of positive and negative values and low tails, compared with the premium paid for

example (see Figure 1). It seems rational as many companies still need to acquire others in times of negative GDP

growth, but are indeed more reluctant to pay high premiums. However we have to take into account the small size

of our sample which could induce a bias (T=51) – the same test should be conducted on a larger time period to be

more conclusive.

Std.Deviation: X4 has the highest standard deviation which shows that the Bank of England base rate fluctuated

more than others during this period, whereas X3 (average premium paid over the period) with the lowest standard

deviation seems relevant constant. Perhaps this could be explained by the violent cut in rates due to the fact that

our sample features the 2007/08 crisis (in two quarters the rates have been cut from 5% to 0.5%).

X1 X2 X3 X4 Y

X1 1.000000 0.140336 0.024210 0.001954 -0.200199

X2 0.140336 1.000000 -0.084778 -0.058191 0.174809

X3 0.024210 -0.084778 1.000000 -0.286419 -0.438661

X4 0.001954 -0.058191 -0.286419 1.000000 0.304387

Y -0.200199 0.174809 -0.438661 0.304387 1.000000 Table 2 - Correlation matrix

The correlation matrix gives low numbers for our variables: this is quite positive for our model as we know that

having multicollinearity would induce a bias in our model. This means that we have been selecting variables that are

not too related between each other. However, even if the pairwise correlations are low (highest correlation (X3,

X4)=0.28) it is not enough to prove that there is no multicollinearity for a multiple linear regression model such as

ours as one of the variable could be poorly correlated with one other, but highly correlated when taking into account

2 or more other variables.

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Table 5 –Coefficients of Regression with less observations (51-6)

Table 6 –Coefficients of Regression with less regressors (3)

Model Specification Dependent Variable: Y

Method: Least Squares

Date: 12/03/13 Time: 13:47

Sample (adjusted): 1 51

Included observations: 51 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.878025 0.349749 2.510442 0.0156

X1 -0.235082 0.134480 -1.748077 0.0871

X2 1.260784 0.844930 1.492176 0.1425

X3 -3.677868 1.339949 -2.744783 0.0086

X4 0.082003 0.049681 1.650595 0.1056

R-squared 0.297841 Mean dependent var 0.368627

Adjusted R-squared 0.236783 S.D. dependent var 0.790314

S.E. of regression 0.690436 Akaike info criterion 2.189908

Sum squared resid 21.92830 Schwarz criterion 2.379303

Log likelihood -50.84265 Hannan-Quinn criter. 2.262281

F-statistic 4.878048 Durbin-Watson stat 0.931785

Prob(F-statistic) 0.002306

Table 3 - Linear regression

Is there a multicollinearity problem in your regression?

Multicollinearity overestimates the Standard Error (S.E) of the explanatory variables. As a result, the t-

statistic of the regressors is underestimated when there is multicollinearity (as T-statistic for the null

hypothesis equals Â /S.E (Â)) and as a direct consequence the null hypothesis for the regressors tends to not

be rejected, although the joint hypothesis (F-statistic) rejects the null hypothesis. In our case, two out of the

four regressors reject the null hypothesis at the 10% significance level (two-sided test) namely X1 & X3. In

addition, X4 is very close to not being rejected at the 10% level. Therefore the T statistic “symptom” does

not prove to be relevant in our case to detect whether our model suffers from multicollinearity or not.

In a model with multicollinearity, parameters estimates change notably when observations are

excluded/added. We tested by deleting 6 observations (Observation N°5,10,15,20,25,30) and running a new

regression, the coefficient did not change significantly (see below).

In a model with multicollinearity, the parameter estimates change significantly when one parameter is

dropped. In our model it is not the case (see below).

Variable Coefficient

C 0.878025

X1 -0.235082

X2 1.260784

X3 -3.677868

X4 0.082003


C 0.890713

X1MINUS6 -0.230501

X2MINUS6 1.292053

X3MINUS6 -3.757550

X4MINUS6 0.088370


C 0.932787

X1 -0.206127

X3 -3.899481

X4 0.075433

Table 4 – Linear Regression Coefficients

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After running an auxiliary regression with X4: C X1 X2 X3, the R^2 result it 0.08, which is lower than 0.8, meaning there is no apparent multicollinearity. In conclusion, our model does not seem to have any significant multicollinearity and therefore does not need to be corrected for this.

Significance of the R²

Let’s test the significance of our model’s R² (29%):

Ho: X1=X2=X3=X4=0 or R²=0 / H1: X1 or X2 or X3 or X4 > 0 (at least one of them) and R²>0

F-statistic = [(RSSr-RSSu)/J] / [RSSu/(T-K)] = 4.87 (p-value = 0.0029 or 0.29%)

We reject the null hypothesis at any significance level (10, 5, 1%), R² is significant (in other words, at least one of the

regressors is significant). We can therefore say that the “fit” of our model is 29% since the null hypothesis has been

rejected, this number is significant. This makes sense since three of our individual regressors pass the t statistic.

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Is the model well specified (correct functional form and no omitted variable?)

Testing the functional form

Let’s check whether the change in Y over each regressor appears to be constant or not. If it does not appear to be

constant, then a nonlinear model could potentially better capture their behaviour.

From the four scatterplots, it is quite hard to infer the validity of the functional form of our model. However, we can

see that for X2 and X3, namely the Deal Count and the Average premium paid over the period, a curve pattern seems

to appear for extreme values (see curves for the two scatterplots). The pattern remains however predominantly

linear (see line for Deal count).

Conclusion on the functional form: The “suspicion” of a wrong functional form seems quite low. We have cleared out

the possibility of an interaction model, but it is still possible that a non-linear model explain better our variable.

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Omitted variable(s)

It is indeed very hard to assess which variable we missed on which could induce biased coefficients and biased error

term (autocorrelation of Et).

Many different factors explain (at least) GDP, both quantitative (infrastructure level, commodity prices, productivity

gains…) and qualitative (education levels, consumer business confidence...) to the extent that it is nearly impossible

to know which variable could be missing in our model.

We will have to run the RAMSEY RESET test to make sure there is no functional form/omitted variable issue.

Ramsey RESET test

Ramsey RESET Test

Equation: LINEARREGRESSION1

Specification: Y C X1 X2 X3 X4

Omitted Variables: Powers of fitted values from 2 to 3 Value df Probability

F-statistic 6.721729 (2, 44) 0.0028

Likelihood ratio 13.59719 2 0.0011

The Ramsey Regression Specification Error Test is used to identify incorrect functional form or omitted variable. It

adds two new terms to the regression, one term is the previously estimated Y^2 and the other is the previously es-

timated Y^3. We then run an F-statistic, in order to check if the two new terms are all together significant or not. In

our case they are highly significant since the F statistic deliver a p value of 0.0028 (0.28%) – the test rejects the

“joint” null hypothesis. This means that our model is imperfect because the variables would better capture the de-

pendent variable in a non-linear model and/or there are omitted variables.

Before “correcting“ for this possible bias using either GLS (Generalised Least Squares) or Newey West robust stand-

ard errors (corrected Standard errors that take the possible bias into account), we will try to estimate some non-

linear models to see if they better capture the changes in our dependent variable (Y).

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Non Linear Regressions

1) y=c+β1X1^3+β2X2^3+β3X3^3+β4logX4

Variable Coefficient Std. Error t-Statistic Prob. C 0.551001 0.124268 4.433962 0.0001

X1^3 -0.085530 0.024040 -3.557864 0.0009

X2^3 16.57297 12.15265 1.363733 0.1793

X3^3 -19.69698 5.552571 -3.547363 0.0009

LOGX4 0.164905 0.081524 2.022776 0.0489








2) y=c+β1X1+β2X2+β3X3^3+β4logX4


X1 -0.284838 0.125149 -2.275991 0.0275

X2 1.411744 0.780537 1.808684 0.0770

X3^3 -23.29767 5.825209 -3.999456 0.0002

LOGX4 0.156002 0.086490 1.803695 0.0778 R-squared 0.393733 Mean dependent var 0.368627







3) y=c+β1X1^3+β2X2^3+β3X3^3+β4X4^3


X1^3 -0.080232 0.024765 -3.239687 0.0022

X2^3 16.47492 12.56506 1.311170 0.1963

X3^3 -20.58295 5.751660 -3.578611 0.0008

X4^3 0.001790 0.001535 1.165911 0.2497 R-squared 0.432910 Mean dependent var 0.368627







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In these three non-linear regressions, we have mostly used the cubic factor as it captures the difference between

negative and positive changes when the square power does not account for this. In addition, the log function has

been used on interest rate (X4). It seems as though or non-linear model better explain our dependent variable as the

adjusted R^2 (overall fit of our model, adjusted for degrees of freedom) is higher for these three regressions than it

is for our linear model.

The non-linear regression No1 (y=c+β1X1^3+β2X2^3+β3X3^3+β4logX4) seem to be more instructive, with the highest

adjusted R^2 (0.41) and the regressors seem to even explain more as they reject more clearly the null hypothesis

(except X2). As a result, the joint hypothesis (F-stats) rejects the null hypothesis, meaning our R-square of 0.46 is ac-

tually significant. This model shows significantly higher coefficient than the linear model; this can easily explained by

the nature itself of the model: the cube of a percentage (regressor X1, X2, X3) is significantly lower than the initial

percentage, which causes to increase the coefficient.

Perhaps this improvement in R^2 could be explained by the fact that the Ramsey RESET test used on the linear mod-

el indicated a possible wrong functional form (to be more specific, a nonlinear model presence), it would then make

sense to have a higher fit with a non-linear model.

However it is possible that there are still omitted variable in this nonlinear model, which would induce a bias in the

significance of our variables. In order to verify this, we will look at Error autocorrelation.

Auto Correlated Errors

Auto Correlation of errors breaks the assumption No3 of the regression model. The direct effect of this is that it

creates a bias in the Error term, making it appear artificially smaller which in turn improves the fit of our model

through lower Standard Error and higher t-statistic sometimes misleadingly rejecting the null hypothesis.

For all these reasons it is crucial to try and identify the presence of autocorrelation in this non-linear model

(y=c+β1X1^3+β2X2^3+β3X3^3+β4logX4). In order to do so, the first possible element that can give an indication of Error

autocorrelation is the scatterplot of the Error term against the previous (t-1) Error term:

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In addition to the scatterplot of E(t) and E(t-1), the scatterplot of E(t-4) against E(t) has been used as we are using

quarterly data (error terms using quarterly data are often correlated with past year error terms, Et-4, as a result of

seasonal effect). It appears that the errors seem to be auto correlated to a certain extent: this is more apparent for

the first graph E(t-1) as the points are clustered around the straight line.

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Y Residuals

The residual graph seem to confirm this possible autocorrelation; instead of having successively unrelated positive

and negative error terms, they tend to be correlated with the previous one (see graph).

Even if the scatterplot and the Error graph gave us a short insight of the possible incidence of auto-correlation, this

needs to be further checked through a test.

Successive negative

error terms

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Autocorrelation Function (ACF)

The Autocorrelation Function correlogram test for autocorrelation of residuals up to a given order. The two bands

represent the confidence interval, determining whether the autocorrelation is significant and reject the null

hypothesis for a given order (Ho: Autocorrelation of order X = 0).

Here we can clearly see that there is autocorrelation of order 1 and 2 as the autocorrelation exceed the confidence

interval for the two given level.

LM Test

In order to have a more precise idea of the significance of the autocorrelation, we have run the LM test. This test

runs a regression including the different “lagged” error terms, and give us the probability that each error term is

significant to explain the other or not.

Test Equation:

Dependent Variable: RESID


Date: 12/08/13 Time: 15:56

Sample: 1 51

Included observations: 51

Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C -0.037652 0.124674 -0.302006 0.7645

X1^3 0.010583 0.027250 0.388386 0.7002

X2^3 -17.19601 13.60013 -1.264400 0.2147

X3^3 1.803476 5.835312 0.309062 0.7592

LOG(X4) 0.001848 0.082724 0.022341 0.9823

RESID(-1) 0.406643 0.187369 2.170283 0.0371

RESID(-2) 0.347684 0.174126 1.996737 0.0539

RESID(-3) -0.161794 0.184243 -0.878158 0.3860

RESID(-4) -0.229345 0.189469 -1.210459 0.2345

RESID(-5) -0.006312 0.196980 -0.032042 0.9746

RESID(-6) 0.229713 0.199338 1.152380 0.2572

RESID(-7) -0.174142 0.194161 -0.896891 0.3761

RESID(-8) -0.099336 0.215218 -0.461559 0.6473

RESID(-9) 0.126907 0.200615 0.632590 0.5312

RESID(-10) 0.007037 0.202569 0.034741 0.9725

RESID(-11) -0.118916 0.194220 -0.612273 0.5444

RESID(-12) 0.080295 0.190656 0.421152 0.6763

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Resid (-1) or E(t-1) is highly significant as it rejects the null hypothesis at the 5 and 10% level – there is undoubtedly

an autocorrelation of order 1. The autocorrelation of order 2 is only significant at the 10% but still needs to be

corrected for in our model. It is quite interesting to note that the two lagged error terms are positively correlated

with the error term, with coefficients of 0.57 and 0.32 – this coincides with what we have seen in the scatterplot of

E(t) and E(t-1), with E(t-1) increasing as E(t) was aiming higher.

Possible causes of the spotted Autocorrelation

There are many possible reasons for the Autocorrelation: a wrong functional form of our model, omitted variables,

inertia, overlapping effects…

In our case, a positive correlation is not uncommon as our dependent variable Y is GDP growth; the general

consensus for these kind of macroeconomic variable is that there is often the presence of business cycles which

provokes inertia/errors autocorrelation. In addition, our data may be impacted by seasonality, which the facto would

create an auto correlation of errors even if there were no omitted variable, functional form issue and so forth.

Furthermore, it is likely that we solved (at least partially) our functional form issue as the fit of the nonlinear model is

better (see nonlinear regression chapter). This would imply that it is more likely that the autocorrelation comes

from omitted variables or true autocorrelation.

Correcting our model (Autocorrelation issue)

There are mainly two ways to account for autocorrelation in our model: use GLS (Generalised Least Squares) or

Newey West robust standard errors. In our case, taking into account the low number of observation we have in hand

(51) it is better to use the Generalised Least Square than to keep our model and adjust the standard error. This

means that the coefficient as well will be corrected for autocorrelation.

Before adjusting for autocorrelation Variable Coefficient Std. Error t-Statistic Prob.

C 0.551001 0.124268 4.433962 0.0001

X1^3 -0.085530 0.024040 -3.557864 0.0009

X2^3 16.57297 12.15265 1.363733 0.1793

X3^3 -19.69698 5.552571 -3.547363 0.0009

LOGX4 0.164905 0.081524 2.022776 0.0489








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After adjusting for autocorrelation (GLS) Dependent Variable: Y


Date: 12/08/13 Time: 16:45



Convergence achieved after 42 iterations Variable Coefficient Std. Error t-Statistic Prob. C 0.351675 0.280397 1.254204 0.2167

X1^3 -0.039173 0.018705 -2.094249 0.0423

X2^3 10.21791 12.45011 0.820708 0.4164

X3^3 -12.78975 4.693083 -2.725235 0.0093

LOG(X4) 0.206902 0.193196 1.070945 0.2903

AR(1) 0.490130 0.167984 2.917728 0.0056

AR(2) 0.146960 0.155062 0.947751 0.3487 R-squared 0.630049 Mean dependent var 0.353061







After using the GLS, the coefficient and the standard error of our variable changes: this is because our regressor t-

statistic was artificially inflated because of the autocorrelation of order 1 and 2. After taking this into account, we

can see that X1 is still significant at the 5 and 10% level, and X3 at any level. However interest rates are no longer

significant.

The most important insight the GLS model gives us is that in our model the UNITED KINGDOM base rate may not be

useful in our model. If we did not account for autocorrelation we could have been using this “irrelevant variable”.

Hence our final model will only feature X1 and X3 as irrelevant variable such as X2 and X4 may artificially increase

the t statistic of our other variable.

Final model chosen, adjusted for Auto Correlation (GLS)


C 0.536207 0.262746 2.040778 0.0473

X1^3 -0.035361 0.017981 -1.966591 0.0556

X3^3 -13.94418 4.366606 -3.193368 0.0026

AR(1) 0.536202 0.152236 3.522171 0.0010

AR(2) 0.176200 0.151127 1.165910 0.2499

The R-squared of the regression and the adjusted R-squared shoot higher with the autocorrelation adjusted (GLS)

regression. This is normal as the autocorrelation variables are added into the model – this does not mean that our

model really improved as we are only interested in the real impact of the X1 X2 X3 X4 to explain Y and not into the

explanatory power of the autocorrelation.

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Hypothesis Testing Interaction models

We have seen in the last paragraph that the interest rate factor seems to be insignificant after taking autocorrelation

into account. This is quite unexpected as literature shows that interest rates have a significant effect on M&A levels

(Factors affecting international mergers and acquisitions, Reed&Babool, 2003). Perhaps an interaction model could

be interesting to estimate taking into account the impact of interest rate on the average premium paid : The

regression would take the following form: Y: C X1^3 X3^3 (X4*X3^3) AR(1) AR(2) (with X3 being the average

premium paid and X4 the United Kingdom base rate).

Likewise, an interaction model taking into account the possible relationship between the premium paid and the

global M&A volumes could intuitively prove valuable : Y: C X1^3 X3^3 (X1^3)*(X3^3)


X4*X3^3 5.464 2.51 2.17 0.0353

X1^3*X3^3 2.30 3.15 0.73 0.46

It appears that the first interaction model, using the relationship between interest rates and average premium paid,

improves our model as the variable added (X4*X3^3) is significant at the 5 and 10% level. In turn it slightly improves

the adjusted R^2.

On the other side, the possible effect of the second interaction model proves to be insignificant after running the

relevant regression (the X1^3*X3^3 coefficient appear to be insignificant at the 5,10 and 1% levels).

Checking the normality of the Error term


X1^3 -0.085530 0.024040 -3.557864 0.0009

X2^3 16.57297 12.15265 1.363733 0.1793

X3^3 -19.69698 5.552571 -3.547363 0.0009

LOGX4 0.164905 0.081524 2.022776 0.0489 R-squared 0.463842 Mean dependent var 0.368627







~ 17 ~


0

2

4

6

8

10

12

14

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Series: ResidualsSample 1 51Observations 51

Mean 6.59e-17Median -0.004087Maximum 1.167325Minimum -2.024367Std. Dev. 0.578690Skewness -0.563006Kurtosis 4.529200

Jarque-Bera 7.663500Probability 0.021672

Non-normality of Ԑt poses no problem for large T because in that case t-statistic follows N (0, 1). However, we only have 52 observations which is a relatively small T. Let’s test the normality of Ԑt

H0: Ԑt follows a normal distribution

H1: Ԑt does not follow a normal distribution

From the histogram of Ԑt, we can see that it is not bell-shaped. Additionally, Jarque-Bera equals 7.66300 which is

much bigger than 0. Therefore, reject the null hypothesis. Ԑt does not follow a normal distribution because of a

relatively small T.

~ 18 ~


Dummy Variables

Binary variable in the explanatory variable

Before using any dummy variable, it is important to recall what the initial data used comprises:

Y : Real GDP growth (QoQ, %, UNITED KINGDOM)

X1 M&A Volumes in the United Kingdom (% Change in sterling volume, QoQ) Used in the final model

X2 Deal count (% Change QoQ)

X3 Average premium paid over the period, (%, Quarterly) Used in the final model

X4 Bank of England base rate (%)

Some interesting dummy variable we could have used could be a dummy variable reacting to a specific industry. For

example we could have used a dummy variable taking the value 1 if the average premium paid over the period in the

financial industry had increased or 0 if the average premium paid over the period in the financial industry had

increased (or any other industry). This way we could have measured if any industry has a higher correlation with GDP

growth than another. However we were unable to use any of this due to lack of data.

The dummy variable we have created (DummyCrisis) is a structural break dummy variable taking the value 1 if the

values recorded in the sample are after quarter 1 2007 (Observation 23, beginning of the Global financial crisis) and

0 if the values have been recorded before quarter 1 2007 (the remaining observations). This variable will be useful to

assess whether the relationship between M&A premiums/volumes and GDP growth in the United Kingdom has

significantly changed after the crisis (Q1 2007).

Dependent Variable: Y


Date: 12/08/13 Time: 20:03


Included observations: 51 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DUMMYCRISIS 0.187783 0.189022 0.993444 0.3257

X1^3 0.162804 0.131406 1.238943 0.2217

X3^3 -23.37007 8.561167 -2.729776 0.0090

X4*X3^3 11.62079 3.395521 3.422389 0.0013 DUMMYCRI-

SIS*(X1^3+X3^3+X4*X3^3) -0.253133 0.134286 -1.885030 0.0658 R-squared 0.176834 Mean dependent var 0.368627





Durbin-Watson stat 0.826232

In order to check whether the crisis changed the relationship between M&A and GDP growth in the UNITED

KINGDOM, we need to reject the joint hypothesis Ho: B (Dummy Crisis) = B (Dummy Crisis*X1^3+X3^3+X4*X3^3) = 0.

In our case, the second hand of the null hypothesis B (Dummy Crisis*X1^3+X3^3+X4*X3^3) = 0 rejects the null

hypothesis at the 10% level (p value = 0.658). We can therefore conclude that the global financial crisis starting in

2007 significantly changed the relationship between M&A volumes/acquisition premium and the GDP growth in the

United Kingdom.

~ 19 ~


Binary variable expressed in the dependent variable

The second dummy variable use is related to the original Y (Real GDP growth in the UNITED KINGDOM). It

takes the value 1 if there is positive GDP growth in the UNITED KINGDOM and 0 if there is negative GDP

growth. This way we are able to see if the model can explain for positive or negative GDP growth values.

Dependent Variable: DUMMY_GDP_GROWTH


Date: 12/08/13 Time: 19:33


Included observations: 51 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.853358 0.071067 12.00771 0.0000

X1^3 -0.027651 0.015500 -1.783992 0.0809

X3^3 -9.851929 4.031901 -2.443495 0.0184

X4*X3^3 2.417120 1.840633 1.313201 0.1955 R-squared 0.175018 Mean dependent var 0.784314







Dependent Variable: DUMMY_GDP_GROWTH

Method: ML - Binary Logit (Quadratic hill climbing)

Date: 12/08/13 Time: 19:35



Convergence achieved after 5 iterations

Covariance matrix computed using second derivatives Variable Coefficient Std. Error z-Statistic Prob. C 1.795447 0.530267 3.385928 0.0007

X1^3 -0.185624 0.226831 -0.818334 0.4132

X3^3 -64.68640 44.73894 -1.445864 0.1482

X4*X3^3 15.57773 14.18400 1.098260 0.2721 McFadden R-squared 0.144657 Mean dependent var 0.784314

S.D. dependent var 0.415390 S.E. of regression 0.389180

Akaike info criterion 1.048804 Sum squared resid 7.118656

Schwarz criterion 1.200320 Log likelihood -22.74451

Hannan-Quinn criter. 1.106703 Restr. log likelihood -26.59108

LR statistic 7.693147 Avg. log likelihood -0.445971

Prob(LR statistic) 0.052798

In this case the dummy variable is used as a dependent variable. In order to assess whether our model explains

well the period of positive or negative GDP growth, we use the Hit rat and Pseudo R^2 values for both the model

and the logit model :

Linear model

Pseudo R^2 = 0.175

HIT Rate = 0.807

~ 20 ~


Logit model

Pseudo R^2 = 0.174

HIT Rate = 0.807

The first observation we can have is that the hit rate and the pseudo R^2 are very different. This means that,

when both the estimated and the actual data indicate a positive (negative) GDP growth (i.e a value above

(below) 0.5), the gap between the actual data and the estimated one is quite large.

In other words, when there is actual positive (negative) growth, the estimated possibility of positive GDP growth

is slightly above (below) 0.5 and not close to 1 (0).

We can as well notice that the difference between the logit and the linear model is very small or even negligible.

This is because when regressing the linear model we only have one value outside of the 0;1 interval. This

means that in this respect the logit model will not be significantly different from our linear model.

~ 21 ~


Conclusion

The relationship between mergers & acquisition and GDP growth seem to be in accordance with literature as some

of the variables we have used (Average premium paid over the period & Change in M&A volumes) are significant to

explain the relationship with GDP growth. Interestingly enough, the most significant explanatory variable (Premium

of the M&A deals) is negatively correlated with GDP growth (the coefficient in our linear regression is -3.67). This

would mean that when the average paid premium over the period grows by 1%, the GDP growth reacts negatively

and decreases by 3.67%. This points in the direction that mergers and acquisition solely increases the market control

of the acquiring company and rules out smaller firm out of the industry, which in turn leads to reduced innovation

and spending in R&D, negatively impacting GDP growth.

This conclusion seem logical from our data, especially after having taken into account the possible bias impacting the

model, yet there are many other aspects which still have to been taken into account.

Even if there is an apparent relationship (R^2 or explanatory power of our model >0), we should not forget that this

only implies that the explanatory variables and the dependent variable behave (or change/move) in the same

direction over the period used in the sample. It does not mean that there is any causality between our explanatory

variable and the dependent variable, in other words, the explanatory power of our model does not mean in any way

that mergers and acquisition explain GDP growth.

In addition, it is possible that some biases remain in our analyses. As discussed earlier in the development of the

project, omitted variable could artificially reinforce our model and drive us to retain some irrelevant variables to

explain GDP growth.

statistics in finance - m&a and gdp growth

Business

volumes of ma activity

performance of ma

impact of ma

ma activities

ma transaction

consequences of ma activity

e economic growth

united kingdom x1 ma