Load and Tidy Data

debt <- read_csv("Corporate debt.csv") |>
  rename(date = DATE, debt = BCNSDODNS_PCH)

gdp_ff_cpi <- read_csv("GDP FF CPI2.csv") |>
  rename(date = DATE, fedfunds = FEDFUNDS, gdp = GDP_PCH, cpi = CORESTICKM159SFRBATL_PCH) 

macro_data <- left_join(gdp_ff_cpi, debt)

mna <- read_excel("X Mergers & Acquisitions (M&A) - United States (quaterly).xlsx") |>
  janitor::clean_names()

data <- cbind(macro_data, mna[, 2:3])

Question

What is the effect of broad macroeconomic factors (i.e GDP and interest rates) on the volume of M&A deals in the US?

This question is important for decision makers at investment banks and other institutions who have to choose when to pursue M&A deals and what is the condition of the economy best for that. For instance, I hypothesize that at times of rising GDP, M&A valuations tend to be higher as future growth appears more promising – this is something which should be kept in mind during risk assessment and valuation.

Model

One of the models I am trying to estimate is:

\[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + u_i\] Yes, there is certainly an issue of omitted variable bias here because M&A deals are not only explained by changes in GDP – this is why I am also going to model the # of M&A Deals using other metrics such as CPI, interest rates (FFR) and percent changes in corporate debt during the next phase of the project. I don’t believe selection bias is an issue in this data set seeing as it is simply a time series of economic metrics collected in the US.

Source

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 contains the percent Federal Funds Effective Rate, percent change in Gross Domestic Product, Corporate Debt and Sticky Price Consumer Price Index.

Data Visulazation

## 
## Regression Results
## ===============================================
##                         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

Analysis

The regression shows negative relationship between the percent change in GDP and the volume of M&A deals in the US. The y-intercept could be interpreted as when there is no change in GDP we can expect to have 2,719 M&A deals. The \(\hat{\beta}_1\) or the slope shows that for every percent increase in the change in GDP results in a loss of approximately 231 deals. It is worth noticing that there are six outliers in which the GDP growth is negative, those points could be affecting the data so if we remove them we would get this scatter plot:

Here our y-intercept is about 3007.8 and the \(\hat{\beta}_1\) is -435.9, showing a more drastic decrease in M&A deals per percentage point lost in GDP. This suggests that the outliers were contributing to a more positive relationship than in this model.

Classical Assumptions

1) Linearity

The population relationship is linear in parameters as well as it has an additive error term – the is model: \[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + u_i\] 2) Sample Variation There is variance in x between -1.95174 and 2.52713 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 is seasonal and follows certain trends which are not random and often dependent on each other.

4) Exogeneity \[ \widehat{\text{# of M&A Deals}} = \hat{\beta}_0 + \hat{\beta}_1 \widehat{\text{GDP % change}} + u_i\] 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 x variable (GDP % change) and y variable (# of M&A Deals). Other factors that effect our y variable are the interest rates, CPI and corporate debt levels all are which effected by changes in the GDP level.

5) Homoscedasticity Looking at the scatter plot showed above the error term is not stable throughout the x values and thus does not meet requirements for homoscedasticity. If we look at the M&A Deal Volume in Periods of Positive GDP Growth graph, between a 0% and 0.5% our error terms are much smaller (closer to the model estimate) than in 2% and 2.5% showing us that the error terms do not have the same variance.

BLUE

Based on the answers in my previous questions the coefficients in my model are not meeting requirements to be BLUE (best linear unbiased estimator). This is because the data does not meet the random sampling and exogenous assumptions of OLS.

Residuals

Confidence interval

##                 2.5 %      97.5 %
## (Intercept) 2401.2801 3037.299237
## gdp         -464.1512    2.484359

The confidence interval is between -464.15 and 2.48.

Testing Hypotheses

The two-sided hypothesis is testing whether \(H_0: \beta_1 = 0\) (null hypothesis) or \(H_1: \beta \neq 0\) (alternative hypothesis) is true. To test this we need the \(SE(\beta_1)\) and the t value.

##              Estimate Std. Error   t value     Pr(>|t|)
## (Intercept) 2719.2897   160.7307 16.918299 1.508689e-34
## gdp         -230.8334   117.9252 -1.957457 5.245287e-02

Looking at the table above, we can interpret the results for our GDP coefficient. The p-value is 0.0525 which is slightly above the typical significance level of 0.05 (probability of rejecting the null hypothesis when its actually true), this means that we fail to reject the null hypothesis. In other words, 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.

Conclusion

This analysis looks at how macroeconomic factors, specifically GDP growth, relate to the volume of mergers and acquisitions (M&A) deals in the US. The results from my regression show that there is a negative relationship between GDP growth and the number of M&A deals. As GDP grows, the number of M&A deals tends to go down – for every 1% increase in GDP growth, the number of M&A deals decreases by about 231. It’s also important to note that the p-value for GDP’s effect is slightly above the 0.05, meaning the evidence for this relationship isn’t strong enough to be considered statistically significant at the 5% confidence level.

Questions

In the next part of this project series I aim to complete a multiple regression analysis using the Federal Funds Rate (FFR), Consumer Price Index (CPI) and changes in US corporate debt levels. I hope to answer questions such as, is the M&A market supply or demand (sell side or buy side) driven? For example, lower interest rates in the economy may increase demand as cheaper borrowing enables more acquisitions. On the other hand, higher corporate debt levels could suggest a supply-driven pressure to restructure or diversify companies.