Thus, we use panel data analysis in our research. Panel data permits us to analyze the factors of private equity activities (fundraising and investing) using both spatial and temporal features of the data. Ideally, only those regressors should be included that are robust to the inclusion or exclusion of other regressors. Hence, we use BMA to examine if the variables provided in the existing literature are truly robust drivers of private equity fundraising and investments.
Then, we apply regression models with fixed effects (FE) and random effects (RE). The fixed effects model implies that all panel members have the same variance and that there is no correlation over time, neither between nor among panel members. The random effects model implies that the unobserved effect is independent of the explanatory variables and that both the unobserved effect and the explanatory variables may fluctuate randomly over time and across countries. According to Jeng and Wells (2000), FE estimation provided a better explanation of the evolution of private equity across countries and RE estimation provides a better explanation of the evolution of PE over time.
We then apply a panel data analysis with both horizontal dimension (i) and temporal dimension (t) in this research paper. We can then construct the model as follows:
where i = 1...N represents the number of countries and t = 1...T represents the number of years for which empirical simulations are run.
As a quality check, we run the Hausman specification test to compare the consistency of FE and RE models in explaining the behaviour of the private equity market in the European countries.
3.1 Data Sources
Private equity activity (fundraising, investments, and divestments) data for this research was supplied by Invest Europe, a trade association representing private equity and venture capital firms and investors in Europe. However, the data comes from the European Data Cooperative (EDC). EDC is a joint initiative developed by Invest Europe and its national association partners to collect Europe-wide industry data on PE activity. The EDC platform acts as a central hub for private equity and venture capital groups across Europe.
Based on the provided data, a balanced panel dataset was constructed. Our dataset consists of annual data spanning from 2010 to 2020 from the following 16 WE countries: Austria, Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden, Norway, Switzerland, United Kingdom, and the following 13 CEE countries: Bulgaria, Croatia, Czech Republic, Estonia, Greece, Hungary, Latvia, Lithuania, Poland, Romania, Serbia, Slovakia, and Slovenia.1
All variables associated with the private equity industry are normalized by the GDP in order to make the data more comparable. This modification is necessary for at least two reasons. Firstly, as countries have varying economic levels and economic growth rates, the problem of heteroscedasticity may arise, which states that the higher the economic level, the larger the observed variability. Consequently, normalizing data by GDP permits us to address this issue. Secondly, because all variables are initially stated in nominal terms, an observed increase in a variable over time may be solely attributable to a change in price levels. So, varying inflation rates among countries could affect the estimation of parameters. Normalizing variables by GDP circumvents this issue because GDP includes the effect of inflation in each country.
The discrete nature of the PE industry poses a unique analysis issue. Because the database only contains information from private equity firms that opted to submit it willingly, the data may be skewed. A portion of the data may be missing, and its correctness and reliability are unclear; therefore, it may be biased.
In addition, the data for the independent variables were gathered from a wide range of sources, including Eurostat, the International Monetary Fund (IMF), the World Bank, the OECD National Accounts, and the Heritage Foundation.
It is essential to highlight the potential limitations of the Heritage Foundation’s index of economic freedom as a data source. Key criticisms include political bias, limited transparency, and subjectivity in measurement. Despite these limitations, the index's quantitative nature, wide coverage, clear methodology and standardized format makes it a useful tool for conducting comparative research and analysis. This paper addresses the aforementioned biases by combining data from the World Bank (worldwide governance indicators) with the data from the Heritage Foundation (index of economic freedom) to gain a more balanced perspective.
As the market capitalization data for several countries was missing in the above-mentioned data sources, it was manually collected by perusing the websites and monthly and annual reports of the respective stock exchanges. Among these are Nasdaq Nordic (Sweden, Finland, and Denmark), Nasdaq Baltic (Estonia, Latvia, and Lithuania), Belgrade Stock Exchange (Serbia), Zagreb Stock Exchange (Croatia), Prague Stock Exchange (Czech Republic), Bucharest Stock Exchange (Romania), Bratislava Stock Exchange (Slovakia), London Stock Exchange (United Kingdom), and Borsa Italiana (Italy).
3.2 Target Variables
Fundraising is the amount of money raised by PE funds as a percentage of GDP. And investments are the amount of money invested in private companies based in Europe as a percentage of GDP. Fundraising and investments are commonly used as key indicators of private equity activity because they are strong measures of the PE industry's health and growth.
As demonstrated by Balboa and Martí (2001), Schertler (2003), Kelly (2012), Bernoth and Colavecchio (2014), and Henchiri (2016), most of the research examining the determinants and drivers of PE activity uses funds raised and invested as the target variables. And thus, to study the drivers of private equity, we employ these two target variables as well: Fundraising & Investments. Fundraising represents investor confidence in PE firms. Investments, on the other hand, represent the PE firms’ strategies and decisions for the deployment of capital into private companies.
3.3 Explanatory Variables
Furthermore, we employ the following factors as explanatory variables:
Divestments: the amount of money divested as a percentage of GDP. This variable is directly related to the PE process2. The authors Balboa and Martí (2001) and Félix et al. (2007) standardize this variable to the corresponding GDP. And the research conducted by Jeng and Wells (2000) and Félix et al. (2007) indicates a positive relationship between investments and divestments.
The macroeconomic factors described below are defined in Appendix Table (7). Several authors, including Gompers and Lerner (1998), van Pottelsberghe de la Potterie and Romain (2004), Cherif and Gazdar (2011), and Félix et al. (2012), have concluded that GDP growth is indicative of economic expansion and thus has a positive impact on PE activity. The short-term interest rates, at which financial organizations can borrow funds from one another for a short period of time, are obtained from the OECD, with the exception of Serbia, Romania, Bulgaria, and Croatia due to a lack of availability. The money market rates for these countries are obtained from the IMF. Short-term interest rates are the rates at which short-term borrowings are affected between financial institutions or the rate at which short-term government paper is issued or traded in the market. Gompers and Lerner (1998) and van Pottelsberghe de la Potterie and Romain (2004) show that a higher interest rate results in higher fundraising and investment activity. Cherif and Gazdar (2011) and Félix et al. (2013) have shown a negative correlation between PE activity and unemployment rate. According to the findings of Félix et al. (2013), market capitalization acts as a proxy for the liquidity of the stock market, and a positive association between PE activity and fundraising and investment might be anticipated. This variable, however, has been shown to be statistically insignificant by Jeng and Wells (2000) and Balboa and Martí (2003). Research and development (R&D) expenditure acts as a proxy for innovation and technological advancement. According to research by Gompers and Lerner (1998), the demand and supply of venture capital investments in the United States increased during the 1990s as a result of the country's increased spending on research and development and the resulting technological advancements. It was also proven by Romain and de la Potterie (2004) that technological advancements have a beneficial effect on the development of venture capital investments.
The Heritage Foundation's index (Beach and Kane, 2007) reflects the degree of economic freedom annually in countries as a measure of institutional quality. The index takes into account the following aspects scored on a scale from 0 to 100 and weighted equally: (1) rule of law (property rights, judicial effectiveness, and government integrity); (2) government size (tax burden, government spending, and fiscal health); (3) regulatory efficiency (business freedom, labor freedom, and monetary freedom); and (4) market openness (trade freedom, investment freedom, and financial freedom). The 12 Economic Freedoms, defined by Beach and Kane (2007), are described in Appendix Table (8).
Worldwide governance indicators (WGI) indicators measure how well countries run their governments. It is a World Bank research initiative and is based on surveys of public and private sector specialists, non-governmental organizations, and other international organizations. WGI is composed of the following six indicators: (1) control of corruption; (2) government effectiveness; (3) political stability and absence of violence; (4) regulatory quality; (5) rule of law; and (6) voice and accountability. These indicators determine the effectiveness of governance systems in promoting economic growth, eliminating poverty, and promoting social welfare. They are described in Appendix Table (9).
3.4 Descriptive Statistics
The summary of the descriptive statistics for all the variables (target and explanatory) is presented in Table (1). Given that more than 60% of the data is missing for judicial effectiveness and fiscal health, we eliminated these institutional variables from our study. Similar data gaps exist for interest rates, market capitalization, and research and development expenditure (highlighted in gray). We impute these values using a predictive mean-matching algorithm.3
3.5 Stationarity Tests
The stationarity of the series data is analyzed using the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. The KPSS test is a unit root test that checks whether a certain series is stationary.
The outcomes of the stationarity tests are displayed in Appendix Table (10). According to the KPSS test, the variables market capitalization, R&D expenditure, and financial freedom are non-stationary. Therefore, using differencing, these variables are transformed into stationary series. The temporal component of the panel data is shortened from 11 years (2010–2020) to 10 years (2011–2020) due to differencing. Only stationary series are considered in this research.
3.6 Correlation
We examine correlations among potential private equity fundraising and investing determinants. Table (2) shows the correlation matrix. By observing the correlation matrix, we notice several strong correlations (greater than 0.7), which are highlighted in gray. And to account for multicollinearity, we exclude the following variables from our analysis: economic freedom index, property rights, government spending, control of corruption, government effectiveness, regulatory quality, rule of law, and voice and accountability.
3.7 Bayesian Model Averaging
We employ a Bayesian model averaging (BMA) approach to decrease the model uncertainty associated with the selection of variables. BMA is a robust statistical technique with a solid theoretical background. To account for model uncertainty, BMA performs a marginalization over models to derive posterior densities on model parameters (Hoeting et al., 1999).
However, the empirical outcomes of such processes might be highly sensitive to prior assumptions. Five macroeconomic factors and nineteen institutional variables are used as a starting point for our analysis. Because of the lack of data indicated in subsection 3.1, we eliminate two of the institutional variables (judicial effectiveness and fiscal health). Now we apply BMA to six subsets of our panel data to find the best explanatory variable for each region and PE activity combination: CEE fundraising, WE fundraising, Europe fundraising, CEE investments, WE investments, and Europe investments. In our research, we treat the combined CEE and WE regions as a single European one.
A summary of the BMA results is shown in Appendix Table (11), with X denoting the variables with a Posterior Inclusion Probability (PIP) of more than 0.8. The Appendix Tables (12) – (13) present the complete results of the BMA. And since the economic freedom index, property rights, and government spending, control of corruption, government effectiveness, regulatory quality, rule of law, and voice and accountability all have low PIP, removing them from our analysis to eliminate multicollinearity has no major effect on our results.