A dependent variable can be defined as the factor that changes resulting from changes in the independent variable (Geweke, 2010, p. 310). For example, in a controlled experiment, this can be described as what tends to be tested for result (Hendry, 2009, p. 60). In this assignment, I decided to analyze the number of mergers and acquisitions (M&A) in Britain, among companies in the United Kingdom between 1969 and 2011. I find the variable of interest since it exhibits considerable variability and would, therefore, be challenging to model. The variable (Mergers & Acquisitions) exhibits high year to year variability, and hence can be of considerable interest for modeling and forecasting purposes.
A Merger takes place when two firms of the same size agree to join into one single company (Donald W. K. Andrews, 2005, p. 132). It increases the power and value of the two companies or organizations into one large organization (Vuong, 1998, p. 56). On the other hand, acquisitions occur when one company that is more established, takes over another company, and, therefore, the bought company seizes to exist (Tonkin, 2011).acquisitions lead to loss of brand name for the bought company (Raymong Thomas, 2001, p. 29).
I obtained the data (both the dependent and independent variables) from the office of national statistics website. From the data, the dependent variable exhibits unpredictable fluctuations and using the independent variables (Appendix: Table 1.1) it can be interesting to find the possible outcomes.
The X-axis-axis represents the number of years from 1969-2011, and the Y-axis-axis represents the number of companies acquired (UK Mergers and Acquisitions). Beginning 1969, the number of UK mergers and acquisitions was slightly above 800. From the graph, the data seems to be having irregular occurrences causing larger increase at times and lower increases at times. There is a sudden increase between the years 1986 and 1987 from approximately 400 to 1500. The number of companies acquired then reached its peak in 1988, where it began decreasing gradually averaging 500 for the next 11 years. That is between 1991 and 2002. From the graph, it is evident that the dependent variable has some fluctuations with some patterns and trends. The fluctuations may have resulted from sudden changes in cash expenditures on M & A of subsidiaries or sudden changes in Total expenditure-(initial plus deferred payments), which are the two independent variables affecting the number of companies acquired. In this assignment, an investigation is conducted to determine to what extent these independent variables affect the dependent variable (Number of companies acquired).
Since I have more than one independent variable. The single equation econometric model to be used shall be a multiple regression model which can be estimated using the ordinary least square method, which entails minimizing the summation of square (vertical) deviations of points from the line. The multiple regression model allows for analysis of two relationships between variables and leads to a linear equation (Vuong, 1998, p. 74). From the data collected, the variables (independent variables) that affect the UK mergers and acquisitions (number of companies acquired) are [cash expenditures on M & A of subsidiaries] and [Total expenditure-(initial plus deferred payments)].
The independent variables impact on the dependent variable. The extent to which these independent variables affect M&A can be investigated.
Therefore, after performing the regression, the single equation becomes:
The coefficient of determination (R2) is just among the tools that can be used to determine the quality of the model. Since this method automatically gives the p-values, we can use the statistics thumb rule to determine if the model can be termed as statistically significant. According to the thumb rule, we reject (H0) null hypothesis if p<0.005, meaning the variables are crucial in explaining the changes in the dependent variable. From the results obtained, the p values for the coefficients are 0.940 and 0.719. Both values exceed 0.005; hence we do not reject the null hypothesis, this means that the independent variables are not necessary in explaining the changes in the dependent variable.
I collected sample data on proxy independent variables that I had identified under part 2. Cash expenditure on M&A of independent companies, which is measured in monetary terms, is a proxy for Cash expenditure on M&A of subsidiaries, while Percentage of M&A in cash is a proxy for Total expenditure-(initial plus deferred payments). The figures for the new independent variable are appropriate because they exhibit similar variability to the variables discussed in part 2. These data is represented in (Appendix: Table 1.2)
Data is not available for the full 42-year period corresponding to the dependent variable. Data for the independent variables lacked for the years 1969-1971 and 2006(which have been marked with blue). But, I assumed that during specific times the changes in the independent variables were related. For example, examining Table 1.2, the change in independent variable X2 is lower around 1972-1978 but exceptionally high around 2000-2005 hence I used this procedure to estimate for the values of the missing years. An example: if in 1972 X2=373, X1=19, and Y=1210 then through estimation in 1971 where Y=884, X1 will be equal to 14, and X2 273, through estimation. The same procedure is used for 2006. I repeated the regression of my initial data, but dropped the last five years (which would later be used for forecasting), and the following results were obtained.
When I drop the last five years the single equation from data in becomes
The coefficient of determination R2 falls to 0.41%, which is even less compared to the initial R2 of 0.78. This means that lesser of the variations in the independent variables are expressed in the dependent variable. In terms of significance level, using the thumb rule whereby we reject the null hypothesis if the p value is <0.005, the p values are 0.92 and 0.84 for the coefficients, meaning we do not reject the null, implying the data is statistically insignificant, and; therefore, the two independent variables are not necessary in determining the dependent variable.
Both the coefficients are positive; hence there is a positive relationship between the independent and dependent variable.
In the light of my regression output, my R2 is too low, and the data is statistically insignificant. I decided to amend the model in terms of re-specifying the form in which my independent variables enters the model. Since the dependent variable keeps fluctuating, I decided to distribute the values of the independent variable in a constant manner. Variables become related if their values systematically correspond to each other. Therefore, I arranged the data in each column of the dependent (number of companies acquired) and the independent variables in ascending order. I performed another regression, and obtained the following results.
After the re-estimation, our new R2 became 0.881, meaning the regression equation explains about 88.1% of the total variation in number of companies acquired. This implies that there is a strong relationship between the independent and the dependent variable.
When we look at the coefficients, the coefficient for X1 has a p value of 0.003, this value is < than 0.005 hence the variable is significant in explaining the variations in the number of companies acquired. This is the finally selected model because there is a strong relationship between the independent and the dependent variable.
QUESTION 5. CRITICAL EVALUATION.
In establishing a reliable multiple regression model, several factors should be taken into consideration in order to produce the expected forecasts, which tends to be closer to the actual value. It can be crucial to use relevant independent variables which eliminate the chances of obtaining a wrong estimation equation. The independent variables should be carefully examined hand in hand with their proxy variables in case of absent data for some independent variable. The researcher can also use other ways to establish data, as long as the methods are justifiable.
In order to ensure that the variations in the dependent variable come from the model, we should ensure a systematic relationship between the dependent and independent variables. In addition to ensuring that the coefficient of determination increases, we have to add the number of observations. When we use fluctuating data for both variables in constructing the model, there is a higher chance of the model becoming statistically significant. The error term tends to be crucial since it caters for the errors of omission, measurement and variables; therefore, it caters for all the other factors that miss out in the model.
Before establishing an economic theory, we should first state the theory or hypothesis to understand the relationships. The next process should involve specification of the mathematical model of the relationship between the dependent and independent variable. Here, we just see the relationship, but we have to add the error term to make it an econometric model. Data collection can be extremely crucial, in the process of model building. The data gives us the actual results of the dependent variable resulting from the independent variable.
Considering that we have obtained data, our next agenda should be estimation of the model that involves estimating the parameters. We have to develop suitable criteria to establish whether the estimates obtained agree with the expectations of the theory; hence this calls for hypothesis testing. If the chosen model does not refute the hypothesis or theory, we may use it to predict future values of the dependent variable.
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Geweke, J., 2010. Complete and Incomplete Econometric Models. 4th ed. Philadelphia: Princeton University Press.
Hendry, D. F., 2009. Dynamic Econometrics. 7th ed. New York: Oxford University Press.
ONS, 2009. Labour Market Statistics. [Online] Available at: http://www.ons.gov.uk/ons/datasets-and- tables/index.html?pageSize=50&sortBy=none&sortDirection=none&newquery=mergers &content-type=Reference+table&content-type=Dataset [Accessed 20 December 2012].
Raymong Thomas, A. W., 2001. Modern Econometrics. 3rd ed. United Kingdom: Addison Wesley Longman Ltd.
Reuben Morrison, R. R., 1991. Econometrics Models and Economic Forecasts. 3rd ed. Singapore: Mc Graw-Hill Books co.
Tonkin, R., 2011. Mergers and Acquisitions including UK companies. [Online] Available at: http://www.ons.gov.uk/ons/rel/international-transactions/mergers-and- acquisitions-involving-uk-companies/q3-2011/dd-am-dataset.html. [Accessed 20 December 2012].
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