The Impact of Economic Growth on US M&A Activity
Part 2
Artemy Mukhin
2024-12-05
Prior work
The question of interest for this project is: What is the effect of broad macroeconomic factors on the volume of M&A deals in the US? In the previous section attempted to answer this question by building a regression of the volume of annual M&A deals on annual GDP percent change which can be expressed as such:
\[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + u_i\]
The M&A data was sourced from the Institute for Mergers, Acquisitions & Alliances and the macroeconomic data was sourced from FRED, Federal Reserve Economic Data. The variables in the M&A data are the volume and value of deals in a given quarter between Q1 of 1985 up to Q3 of 2017. The FRED data includes the annual percent change in the Federal Funds Effective Rate (FFR), Gross Domestic Product (GDP), Corporate Debt, and the Sticky Price Consumer Price Index (CPI) for the same time period.
The results I found showed that for every percent increase in the change of annual GDP resulted in a decrease of approximately 231 M&A deals. It is also important to note that at the 95% confidence level there is not enough evidence in the data to say that the GDP variable has a statistically significant effect on the number of M&A deals. Knowing this, I aim to run a multiple regression with the other macroeconomic variables, such as the federal funds rate, consumer price index and corporate debt levels in order to get a more statistically significant result and improve my inference.
Multiple regression model
The final model I am attempting to estimate uses all the following macroeconomic variables:
\[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + \hat{\beta}_2 \widehat{\text{FFR}} + \hat{\beta}_3 \widehat{\text{Debt % change}}+ \hat{\beta}_4 \widehat{\text{CPI}}+ u_i\] One potential issue is collinearity between predictor variables, although this is something I will test for in the following step. I will also add the variables one by one is order to see how the model changes with each additional variable – this will also allow me to track the significance of each predictor. By adding all these macroeconomic variables I am attempting to increase the accuracy and predictive power of my previous simple regression.
Collinearity
Collinearity is the correlation between predictor variables in such a way that it forms a linear relationship. If the predictor variables are perfectly correlated, running a multiple regression is not possible because the design matrix cannot be inverted. If there is imperfect collinearity, meaning the predictor variables are nearly correlated there is a risk of poor estimates and large standard errors.
| gdp | cpi | debt | fedfunds | |
| gdp | NA | -0.004 | 0.343 | 0.395 |
| cpi | -0.004 | NA | 0.231 | 0.075 |
| debt | 0.343 | 0.231 | NA | 0.238 |
| fedfunds | 0.395 | 0.075 | 0.238 | NA |
As we see from the table above, the largest correlation between variables is 0.395 which suggest a moderate, positive relationship between the Federal Funds Rate (FFR) and GDP as well as a correlation of 0.343 between GDP and Corporate Debt*. Due to this number being quite low, I would say that there is minimal concern for collinearity.
*Please note that all variables are measured in annual percent change.
Classical Assumptions
1) Linearity
The population relationship is linear in parameters as well as it has an additive error term – the is model: \[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + \hat{\beta}_2 \widehat{\text{FFR}} + \hat{\beta}_3 \widehat{\text{Debt % change}}+ \hat{\beta}_4 \widehat{\text{CPI}}+ u_i\]
2) Sample Variation
There is variance in x between 1727.6923747 and 3135.176861 as seen in the first scatter plot.
3) Random Sampling This data does not mean random sampling requirements seeing as it is time series data, or data collected over a specific period of time. Additionally, macroeconomic data such as GDP, FFR, CPI and Corporate Debt are seasonal and follow certain trends which are not random and often interdependent on each other.
4) Exogeneity \[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + \hat{\beta}_2 \widehat{\text{FFR}} + \hat{\beta}_3 \widehat{\text{Debt % change}}+ \hat{\beta}_4 \widehat{\text{CPI}}+ u_i\] The model above does not meet the exogeneity requirements of classical OLS assumptions because seeing as factors which impact our residual, \(u_i\) also impact our dependent variables and the y variable (# of M&A Deals). Other factors in the residual which impact our independent and dependent variables could be any number of macroeconomic factors such as inflation expectations, global trade policies and geopolitical events. It would be impossible to include all the variables and perfectly predict the volume of US M&A deals in a given year.
5) Homoscedasticity
Looking at the residuals vs. fitted values plot above for our model we can see that the residuals appear to be randomly scattered and no clear pattern is present (seeing as the line of best fit has a slope of almost 0), thus I can say this model meets the homoscedasticity requirement. There are more error terms around the fitted value of 2400 but this is simply because the fitted values are typically closer to the mean.
Linear regressions
| Dependent variable: | |
| Number of M&A Deals | |
| GDP | -230.833* |
| (117.925) | |
| Constant | 2,719.290*** |
| (160.731) | |
| Observations | 131 |
| R2 | 0.029 |
| Adjusted R2 | 0.021 |
| Residual Std. Error | 877.071 (df = 129) |
| F Statistic | 3.832* (df = 1; 129) |
| Note: | p<0.1; p<0.05; p<0.01 |
| Dependent variable: | |
| Number of M&A Deals | |
| GDP | -384.285*** |
| (124.185) | |
| FFR | 574.111*** |
| (183.419) | |
| Constant | 2,938.699*** |
| (170.584) | |
| Observations | 131 |
| R2 | 0.098 |
| Adjusted R2 | 0.084 |
| Residual Std. Error | 848.612 (df = 128) |
| F Statistic | 6.945*** (df = 2; 128) |
| Note: | p<0.1; p<0.05; p<0.01 |
| Dependent variable: | |
| Number of M&A Deals | |
| GDP | -380.481*** |
| (124.424) | |
| FFR | 561.340*** |
| (184.294) | |
| CPI | 7.250 |
| (8.764) | |
| Constant | 2,935.580*** |
| (170.836) | |
| Observations | 131 |
| R2 | 0.103 |
| Adjusted R2 | 0.082 |
| Residual Std. Error | 849.660 (df = 127) |
| F Statistic | 4.847*** (df = 3; 127) |
| Note: | p<0.1; p<0.05; p<0.01 |
| Dependent variable: | |
| Number of M&A Deals | |
| GDP | -390.307*** |
| (130.709) | |
| FFR | 556.560*** |
| (185.925) | |
| CPI | 6.697 |
| (9.061) | |
| Corporate Debt | 17.432 |
| (68.449) | |
| Constant | 2,921.822*** |
| (179.777) | |
| Observations | 131 |
| R2 | 0.103 |
| Adjusted R2 | 0.075 |
| Residual Std. Error | 852.805 (df = 126) |
| F Statistic | 3.625*** (df = 4; 126) |
| Note: | p<0.1; p<0.05; p<0.01 |
Interpretaion
I gradually added the variables to each consecutive model in order to see the impact which each brought – specially on the \(R^2\). The first model, which I ran in the previous section of this project shows that a 1 percent increase of percent annual change in GDP resulted in a decrease of approximately 231 M&A deals. The \(R^2\) is 0.029 (or adjusted 0.021), meaning that GDP only explains 2.9% of the variability in the data and the significance code tells us the coefficient is significant at a 5% level.
In the second model, I added the annual change in interest rates (FFR) which resulted in a more negative coefficient of -384, suggesting that a 1% increase in annual GDP change results in a decrease of 384 M&A deals, while holding FFR constant. The FFR coefficient of 574 tells us that a 1% increase in the annual change of interest rates results in an increase of 574 M&A deals. In the first model, the FFR was an omitted variable causing an upward (or positive) bias. In the second model, the \(R^2\) increased to 0.098 (or adjusted 0.084) suggesting that FFR helped explain much more of the variability in the data than just GDP. Finally, both variables in the second model are significant at the 1% level indicating that our standard error and p-vales decreased.
Both the third and the fourth models represent a decrease in the adjusted \(R^2\) and a minimal increase in th normal \(R^2\) suggesting that the predictor variables of CPI and Corporate Debt have very little statistic significance on changes of the volume of M&A Deals. Neither CPI or Corporate Debt are significant at a level under 10% indicating that the coefficients are not statistically distinguishable from zero.
Confidence Interval
Model 1 (GDP)
## 2.5 % 97.5 %
## (Intercept) 2401.2801 3037.299237
## gdp -464.1512 2.484359Model 2 (GDP, FFR)
## 2.5 % 97.5 %
## (Intercept) 2601.1704 3276.2277
## gdp -630.0073 -138.5631
## fedfunds 211.1850 937.0379Model 3 (GDP, FFR, CPI)
## 2.5 % 97.5 %
## (Intercept) 2597.5270 3273.6333
## gdp -626.6932 -134.2688
## fedfunds 196.6561 926.0233
## cpi -10.0914 24.5923Model 4 (GDP, FFR, CPI, Corporate Debt)
## 2.5 % 97.5 %
## (Intercept) 2566.04754 3277.59551
## gdp -648.97654 -131.63839
## fedfunds 188.61951 924.50098
## cpi -11.23368 24.62773
## debt -118.02597 152.89091If we look at model 4, which contains all the predictors we will notice that GDP and the FFR do not include 0 in their confidence intervals which are -648.98 to -131.64 and 188.62 to 924.50 respectively. This indicates that we can reject the null hypothesis and thus the coefficients are statistically significant. This however is not the case for the variables CPI and Corporate Debt which have the confidence intervals of -11.23 to 24.63 and -118.03 to 152.89 respectively, both of which contain 0 which means these variables could possibly have no effect on the outcome variable.
Joint hypothesis testing: F-test
Model 1 (GDP)
##
## Linear hypothesis test:
## gdp = 0
##
## Model 1: restricted model
## Model 2: number ~ gdp
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 130 102181104
## 2 129 99233605 1 2947499 3.8316 0.05245 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model 2 (GDP, FFR)
##
## Linear hypothesis test:
## gdp = 0
## fedfunds = 0
##
## Model 1: restricted model
## Model 2: number ~ gdp + fedfunds
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 130 102181104
## 2 128 92178223 2 10002881 6.9451 0.001369 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model 3 (GDP, FFR, CPI)
##
## Linear hypothesis test:
## gdp = 0
## fedfunds = 0
## cpi = 0
##
## Model 1: restricted model
## Model 2: number ~ gdp + fedfunds + cpi
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 130 102181104
## 2 127 91684092 3 10497012 4.8468 0.003161 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Model 4 (GDP, FFR, CPI, Corporate Debt)
##
## Linear hypothesis test:
## gdp = 0
## fedfunds = 0
## cpi = 0
## debt = 0
##
## Model 1: restricted model
## Model 2: number ~ gdp + fedfunds + cpi + debt
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 130 102181104
## 2 126 91636920 4 10544184 3.6245 0.007856 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The F-test allows us to see if a group of variables are jointly significant. In this scenario we will be using the F-static to support or reject a null hypothesis which can be expressed as \(H_0: \beta_1 = 0\). We will also be using the p-value which represents the likelihood of obtaining the observed result (or something more extreme) assuming the null hypothesis is true – meaning the lower it is, the less probability that our results occurred by chance. We aim to have a p-value of 0.05 or less in order to reject the null hypothesis.
The first model (not a multiple regression) just barely fails the null hypothesis test with a F-statistic of 3.8316 and a p-value of 0.05245 – this means that at the 95% confidence level there is not enough evidence to say the GDP variable has a statistically significant effect on the number of M&A deals. In model 2 the variables GDP and FFR can be said to be jointly significant at a 1% level seeing as their p-value is 0.001369. The increased F-statistic in model 2 of 6.94 indicates that the predictors explain a larger proportion of the variation in the dependent variable (# of M&A deals) relative to the residual variation. The following models 3 and 4 both are significant at the 1% level but also feature decreased F-statistic indicating that the additional variables (CPI and Corporate Debt) did not significantly improve the models explanatory power.
Plotting residuals
The first density plot shows us the distribution of residuals for a
simple regression where the only predictor is GDP. It is slightly left
skewed and has a small peak around -1000. The second density plot is the
distribution of residuals for a multiple regression with the predictors
of GDP, FFR, CPI, Corporate Debt. It is also slightly left skewed
(although a little less than the simple regression) and the error terms
are more normally distributed. I would also note that the small peak
around -1000 which we observed in the simple regression flattens out
suggesting an improvement in the model’s fit.
Inferences
Based on the multiple regression analysis, there is a statistically significant relationship at the 95% confidence level between both GDP and FFR variables on the volume of M&A deals. This level of significance is only observed when FFR is included in the multiple regression model. Annual percent change of GDP has a negative relationship on the volume of M&A deals with a decrease of 384 deals for every 1% increase in change in GDP. Meanwhile FFR has a positive relationship with the volume of M&A deals, with an increase of 574 deals for every 1% increase in change in FFR.
Both CPI and Corporate Debt are not statistically significant at the 95% confidence level and have little impact on the predictive power of the model when added – thus I would look for other variables which may help explain variability more. Looking at our simple regression, there was not enough evidence to say that at the 95% confidence level there was a significant relationship between the GDP and the volume of M&A deals. However, this changed when we added the FFR which drastically improved the predictive power of the model by increasing the \(R^2\) as well as the significance of each variable. This may have occurred because interest rates are a key macroeconomics variable which help explain how broader monetary policy effects M&A volume in the US. It’s also worth noting that in the first model the FFR was an omitted variable causing a upward bias in the coefficient estimation.
Next steps
Having reached this point I would be interested to do more qualitative research on the effect of macroeconomic variables on the volume of US M&A deals – specifically why rising changes in annual interest rates cause an increase in M&A activity. Rising interest rates correlate with times of rising inflation and borrowing costs so perhaps companies may seek to finalize these deals before rates further increase. Additionally, these macroeconomic conditions may put pressure on already struggling companies with weak balance sheets causing a rise of M&A volume.