Revisiting the Determinants of Entrepreneurship

Abstract

Entrepreneurship has long been seen as an important instrument in stimulating and generating economic growth. The amount of research trying to identify key factors that drive entrepreneurship is considerable; yet, little consensus has been achieved. We argue that this lack of consensus could be on account of model uncertainty as empirical studies often tend to be selective on what variables are included in the final model. Drawing on recent literature, we demonstrate the benefits of Bayesian model averaging (BMA) in reducing the impact of model uncertainty on empirical research in entrepreneurship. Additionally, BMA provides measures of variable importance and can be seen as a complementary approach to dominance/relative importance analysis. We show that when model uncertainty is corrected for, gross domestic product per capita, unemployment, the marginal tax rate, and the volatility of inflation are the only macro variables significantly and universally associated with aggregate entrepreneurship. Furthermore, the emphasis on inflation and taxation suggests that governments have the power to influence the quantity and distribution of entrepreneurial activity by setting incentives that are not entrepreneurship specific but overlap significantly with general and fundamental principles of economic stability.

Keywords

macro policy and entrepreneurial activity model uncertainty model averaging variable selection

Recent years have seen an increased focus on entrepreneurship as a major engine of economic change and growth (Baumol & Strom, 2007; Minniti & Lévesque, 2010). As a result, the macrolevel determinants of entrepreneurial activity have attracted considerable interest (e.g., Parker, 2009, chap. 4, for a review of the literature). Existing research suggests the drivers of entrepreneurship are manifold and span a wide spectrum of theories and explanations (e.g., Levie, Autio, Acs, & Hart, 2014; Zahra & Wright, 2011). Also, given the relatively large set of potential factors that may influence entrepreneurial activity, it is not surprising that the literature provides evidence of a wide range of empirical modeling possibilities, often leading to conflicting findings with respect to the statistical significance, sign, and relative importance of predictors (e.g., Dean, Shook, & Payne, 2007; Terjesen, Hessels, & Li, 2014).

For example, findings on the relationship between formal education and aggregate entrepreneurship provide conflicting results (Sobel & King, 2008; van der Sluis, van Praag, & Vijverberg, 2005). Similarly, some studies on the relationship between financial development and aggregate entrepreneurship have found a positive and significant linkage (Klapper, Amit, Mauro, & Delgado, 2007), while others have found no significant effects (Hurst & Lusardi, 2004). The result of these inconsistencies is that although the number of puzzle pieces is increasing, no coherent picture is emerging. This, of course, has important theoretical and policy implications for entrepreneurship research.

To address this gap in the literature, we suggest that the conflicting evidence may be attributed, in large part, to discretionary choices by researchers, for instance, in the context of deciding which variables to include in the empirical specification. Such discretionary choices across studies are a reflection of what is known in the empirical literature as “model” or “specification” uncertainty (see Simmons, Nelson, & Simohnson, 2011; Young, 2009). Revisiting a large set of potential macrolevel drivers of entrepreneurship, we seek to probe the robustness of individual predictors and demonstrate the possible effects of ignoring model uncertainty by applying “traditional methods” and Bayesian model averaging (BMA) to the data.

The issue of model uncertainty, while critically examined in the broader domain of the social sciences (e.g., Leamer, 1983), has not attracted significant attention in the field of entrepreneurship or management in general. Empirical entrepreneurship research regularly acknowledges and accounts for sampling uncertainty, which arises when dealing with samples from a larger population. Traditional measures of statistical uncertainty, such as t statistics and p values, help reduce concerns about the robustness of the empirical results with respect to alternative samples from the same population. Model uncertainty, instead, derives from uncertainty over which variables to include in the empirical specifications used to draw inference. It is reflected in researchers’ experiments with different specifications in the estimation process by adding or dropping variables from an empirical model. A robust empirical design should in theory account for total uncertainty (sampling + model uncertainty). However, traditional tests of statistical significance and model selection do not capture total uncertainty and may have unintended consequences in terms of overstating or understating the impact of key variables on the phenomenon being examined (e.g., Raftery, 1995; Young, 2009).

The dangers of ignoring model uncertainty can be averted through the application of BMA (e.g., Fernandez, Ley, & Steel, 2001; Young, 2009). BMA formally integrates researchers’ experimentation with different specifications into the estimation process such that both sampling and model uncertainty are accounted for. Inference is drawn based on a weighted average of all possible model specifications as opposed to a particular specification. Hence, BMA produces coefficient estimates and associated measures of dispersion (standard errors) reflecting total uncertainty. Beyond that, BMA provides posterior model and inclusion probabilities for particular regressors, which shed light on the importance of specific variables being examined. As a consequence, BMA may be seen as a complementary approach to relative importance/dominance analysis (Budescu, 1993; Johnson & Lebreton, 2004).

This study contributes to the advancement of the entrepreneurship literature in several ways. First, BMA analysis suggests that there is little or no evidence for the robustness of the statistical association of many of the macrolevel variables routinely used in predicting entrepreneurship rates across countries. Hence, it raises important concerns with respect to model uncertainty, which researchers need to consider when assessing the contributions of research. Second, through our analyses, we show that when model uncertainty is corrected for, gross domestic product (GDP) per capita, unemployment, the marginal tax rate, and the volatility of inflation are the only macro variables to emerge as being significantly and universally correlated with aggregate entrepreneurship. This is notable since the volatility of inflation, as a predictor of entrepreneurial activity, has captured surprisingly little attention in prior literature. Third, and perhaps most importantly, our results on inflation and taxation suggest that via monetary and fiscal policy, governments may influence the aggregate level of entrepreneurship more effectively by setting policy targets that emphasize the importance of general macroeconomic stability than by focusing on entrepreneurship-specific targets.

The Macrolevel Determinants of Entrepreneurship

We build on classic works in entrepreneurship to propose a theoretical framework that can accommodate logically and organically the broad and diverse body of extant empirical research on cross-country entrepreneurship. Specifically, consistent with Baumol (1990) and Kirzner (1997), we suggest that the aggregate level of entrepreneurial activity in a country may be understood as the unintended consequence of a multifaceted interplay between human capital, level of development, and institutions.

Human Capital

Human capital encompasses the productive capacities that individuals possess and allows individuals to exploit profit opportunities. The actions of alert entrepreneurs, in turn, produce unintended consequences at the market level and across markets (Kirzner, 1997). If the entrepreneur were not alert, change in economic life would be impossible. Human capital determines the quality of those changes. Thus, entrepreneurship scholars have studied the relationship between entrepreneurial activity and various aspects of human capital (Shane, 2003). Among those, population, education, and employment status have emerged as being particularly pertinent.

Population

Lévesque and Minniti (2011) developed a model showing that although population size and growth rate increase the future demand for goods and services, the distribution by age cohorts may have a negative effect on entrepreneurship if it creates excessive competition for resources. As a result, the nature of the linkage between population and entrepreneurship cannot be generalized theoretically. From an empirical point of view, however, results seem to converge on positive effects of population growth and density on the level of entrepreneurship. Brüderl and Preisendörfer (1998) and Florida (2003), for example, found that urban areas with high population densities provide appropriate infrastructure for business start-ups and development. Plummer and Pe’er (2010) describe a similar ecology to explain the geographical agglomeration of new ventures.

Education

Formal education improves individuals’ decision-making skills and their understanding of markets (Casson, 1995). Yet, many entrepreneurs tend to be jacks-of-all-trades, and their skills do not necessarily align with formal education (Lazear, 2005). Empirically, the majority of studies report a positive relationship between formal education and the probability of becoming an entrepreneur. Results, however, are far from consistent. Sobel and King (2008) found a positive relationship when accounting for education quality, whereas after conducting a meta-analysis of published research, van der Sluis et al. (2005) found a negative relationship especially for women, urban residents, and inhabitants of poor countries. As a result, no convergence is emerging. In fact, Parker (2009) reports that at the time of publication, 69 studies had found a positive relationship, 21 had found a negative relationship, and 27 had found no significant relationship at all.

Unemployment

Unemployment reduces the opportunity to generate income through paid labor and, therefore, may push individuals into self-employment out of necessity. On the other hand, when unemployment increases, entrepreneurs face a decline of markets for their products. Thus, like in the case of population, the nature of the relationship between unemployment and aggregate entrepreneurship cannot be determined theoretically and becomes an empirical question with many nuances. Evans and Leighton (1990), for example, found that unemployment is positively associated with the propensity to start new firms, but Audretsch and Fritsch (1994) as well as Garofoli (1994) found that unemployment is negatively related to starting new firms. Also, Thurik, Carree, van Stel, and Audretsch (2008) note that causality is a tricky issue in this context and provide evidence that an increase in unemployment may produce a lagged increase in entrepreneurship, which, in turn, will produce an improvement in economic condition and, as a result, a shift back into wage labor. Again, no convergence is emerging, with results being significantly different depending on whether cross-section or longitudinal data are used (Parker, 2009).

Level of Development

A significant amount of entrepreneurship research has shown that the economic context within which opportunities are discovered and exploited, in other words, the level of economic development of a country, strongly influences aggregate entrepreneurship (Baumol, 1990; Boettke & Coyne, 2009; Wennekers, van Stel, Carree, and Thurik, 2010). Within this context, the relationships between entrepreneurial activity and GDP per capita, technological development, and financial development have captured considerable attention.

GDP per capita

Several studies have shown that the relationship between aggregate entrepreneurship and GDP per capita is highly significant (Audretsch, 2007; Baumol & Strom, 2007). Moreover, there exists a significant amount of empirical evidence showing that the relationship is negative for all but the richest countries, where the relation turns positive though less significant (Amoros & Bosma, 2014). The rationale behind this finding is that at low levels of GDP, starting a business provides a path to circumvent the lack of employment opportunities and often is seen as an effective source of poverty alleviation. However, as GDP per capita increases, labor markets develop to provide more stable jobs and cause a switch from self-employment to paid employment (Wennekers et al., 2010). In other words, the negative relationship observed for many of the poorer countries captures the wide phenomenon of necessity entrepreneurship in which individuals who would prefer being employed are forced to start their own businesses due to the lack of employment alternatives (Hessels, Gelderen, & Thurik, 2008). The negative trend continues all the way up to a threshold level of per capita income where the combination of technological progress, developed financial markets, and human capital renders self-employment again attractive, especially for the wealthiest and most educated strata of population (Amoros & Bosma, 2014; Wennekers et al., 2010). Although Audretsch and Acs (1994) and Carrasco (1999) proposed a risk-based theory according to which entrepreneurship would behave in a procyclical way as entrepreneurship becomes more profitable with productivity increases and market growth, general consensus has emerged on the negative nature of the relationship when all types of entrepreneurship are taken into account.

Financial development

Much of the literature on the relationship between financing and entrepreneurship examines the role that various types of investors play in mitigating agency conflicts and asymmetric information surrounding entrepreneurial firms (Gompers, Lerner, Scharfstein, & Kovner, 2010). In other words, most of the analysis is predicated on the idea that entrepreneurship is systematically hindered by liquidity constraints (Evans & Jovanovic, 1989). While some empirical evidence supports this view, findings are highly contingent on the way in which financial variables are operationalized and on the industries considered. On the one hand, Klapper et al. (2007) found that financial development as measured by the ratio of domestic credit to the private sector as a percentage of GDP is positively correlated with entry rates and business density, suggesting that greater business opportunities and better access to finance are related to a more robust entrepreneurial sector. On the other hand, Hurst and Lusardi (2004) found that financial constraints do not really pose a problem for most early-stages businesses since the vast majority of them require very little capital.

Technological progress

By influencing productivity, technological progress is a primary driver of growth (Acs & Audretsch, 2005; Romer, 1990). In turn, increased productivity creates new profit opportunities and, therefore, should encourage self-employment. Indeed, Anokhin and Wincent (2011); Casson (1995); and Wennekers, Uhlaner, and Thurik (2002) all have shown that small firms play an important role in the development as well as diffusion of innovation. In contrast, it has also been argued that technological developments may create barriers to entry for new firms due to high research and development (R&D) costs (EIM/ENSR, 1996). In an attempt to reconcile these empirical findings, Acs, Audretsch, and Evans (1994) have suggested that the relationship between entrepreneurship and technological change may be U shaped and contingent on a country’s level of development. Unfortunately, notwithstanding existing research efforts, empirical findings are inconclusive, and as Parker (2009) reports, up to the date of publication, four studies had found a positive relationship, four showed a negative relationship, and two showed no significant connection.

Institutions

While the connections between human capital, level of development, and entrepreneurial activities have received substantial attention, research into the effects of institutions on aggregate entrepreneurship has burgeoned in recent years. Institutions set the rules of the game and have the power to influence the allocation of activity between productive, unproductive, and destructive entrepreneurship (Baumol, 1990; Boettke & Coyne, 2009; Murphy, Shleifer, & Vishny, 1991). Within this context, the relationship between entrepreneurial activity and taxes, inflation, administrative complexity, and globalization has received particular attention.

Administrative complexity

The theory of regulation suggests that administrative complexity, by increasing the costs of entry, is negatively associated to entrepreneurship (Gurley-Calvez & Bruce, 2008). Bjørnskov and Foss (2008) and Fogel, Morck, and Yeung (2008) contend that administrative complexity as manifested through institutional features, such as the amount of bureaucracy, the intellectual property rights regime, and the level of corruption, all can affect the level of entrepreneurship in a country. They also argue that a larger government is associated with higher levels of publicly financed provision of various services (such as health and education), which decreases the incentives for individual wealth formation. Empirical evidence largely supports the theoretical suggestions (Ciccone & Papaioannou, 2007; Fonseca, Lopez-Garcia, & Pissarides, 2001; Ho & Wong, 2007). On the other hand, Brock and Evans (1986) found little evidence that regulation had disproportionately harmed smaller firms in the United States. Moreover, van Stel, Storey, and Thurik (2007) found no significant effects in a large cross-country study.

Globalization

Trade theory argues that the integration of world markets creates new entrepreneurial opportunities (Acs, Morck, & Yeung, 2001). Indeed, a sizeable amount of literature suggests that market openness stimulates competition and entrepreneurial activity (Sobel, 2008). Empirical results support the idea that increased trade flows not only allow entrepreneurs to take advantage of international opportunities but also give them access to international capital markets (Alhorr, Moore, & Payne, 2008). However, increasing competition in international markets may have a negative impact on the survival rates of small businesses, thus dampening the interest in entrepreneurship (Keupp & Gaussmann, 2009). Finally, the relationship between market openness and entrepreneurship has been shown to be mediated by a country’s religion and postcommunism transition status (Ireland, Tihanyi, & Webb, 2008). As the integration of global markets increases, the literature on international entrepreneurship is providing increasing insights on the entrepreneurial drivers. Yet, in an insightful and comprehensive review of extant literature on internalization, Terjesen et al. (2014) document a wide array of inconsistent and divergent results.

Taxes

Because of its obvious political dimensions, the relationship between taxes and aggregate entrepreneurship has received a surprisingly large amount of attention (Parker, 2009). The theoretical literature states that taxation may influence entrepreneurship positively or negatively depending on changes in its absolute, relative, evasion, and insurance channels (Henrekson & Stenkula, 2010). Overall, although taxation has a negative influence on entry rates as an added production cost, its net effect depends on the way in which taxes are manipulated and on their nature. It is, in other words, an empirical question. Lee and Gordon (2005), for example, contend that the single most important channel by which high statutory corporate tax rates retard economic growth is the entrepreneurship channel. Henrekson (2005), more specifically, suggests that higher rates of personal taxation discourage the market provision of household-related products. Finally, Adam and Bevan (2005) highlighted the importance of nonlinearities in the way taxation influences the economy. Similarly, Gentry and Hubbard (2000) showed that the progressivity of the tax system matters. Given the range of taxes and taxation regimes, it is not surprising that no general agreement has yet emerged.

Inflation

Inflation and its volatility in particular discourage entrepreneurship because they render the business environment riskier and make it harder for entrepreneurs to recuperate the value of their investments and to form accurate expectations about the market (Parker, 2009). Similarly, McMillan and Woodruff (2002) suggest that volatility in macroeconomic policies discourages long-term contracts and relations necessary for successful entrepreneurship, as it is hard to distinguish whether or not the transaction partner is behaving honestly. This is consistent with empirical findings by Robbins, Pantuosco, Parker, and Fuller (2000), who report a significant negative correlation between inflation rates and percentages of employment in small businesses in the United States.

Summary

In spite of the tension inherent in the complex interplay of theory and empirical findings existing in entrepreneurship research up to date, the literature we reviewed provides us with the components of an organic framework in which aggregate entrepreneurship emerges at the intersection of human capital, level of development, and institutions. Importantly, this framework is consistent with Kirzner’s (1997) view of entrepreneurship as a universal form of human action and Baumol’s (1990) argument that the aggregate quantity and quality of entrepreneurship emerge at the intersection of economic development and institutions. Of course, while relatively broad, the list of variables we consider is far from complete. Indeed, the goal of our review was not to list all possible macroeconomic variables but, rather, to discuss well-established, theory-grounded drivers of aggregate entrepreneurial activity and to show that while our theoretical framework justifies the choice and inclusion of specific variables, it does not explain why findings have been often inconsistent with respect to significance and signs. This problem is widespread in the entrepreneurship literature, and it is compounded by the fact that several proxies have been used in the literature to measure theoretical constructs although little evidence exists on the reliability of some of these measures. Importantly, the contradictory evidence renders decision making tricky and places a considerable burden on policy makers. As mentioned in the introduction, we believe that the answer to this question is largely empirical and that a BMA approach can significantly contribute to the entrepreneurship literature by establishing which among those variables have a universal linkage to aggregate entrepreneurship and what the nature of that linkage is.

Data and Method

Data

A significant amount of past research has considered self-employment as a proxy measure of entrepreneurial activities (Grilo & Irigoyen, 2006). To track individual activity in venture creation and management, as well as ventures as the units of analysis (using the respondent as the informant for the venture), we use the Global Entrepreneurship Monitor (GEM) data—total early-stage entrepreneurial activity (TEA)—as a proxy of the dependent variable, that is, the level of entrepreneurial activities. The GEM project, which is the only globally harmonized data set dedicated to the study of individual-level entrepreneurial behavior across countries, provides an indicator of a country’s entrepreneurial activity by measuring the TEA rate. The TEA rate is calculated from surveys of the adult population in each country. The surveys register, among other things, the percentage of entrepreneurial initiatives carried out in a 1-year period. On this basis, the TEA rate measures the percentage of the adult population of a country (18 to 64 years old) that either is actively involved in starting a new venture or is the owner/manager of a business that is less than 42 months old (Reynolds, Bygrave, Autio, Cox, & Hay, 2002). The TEA data in this paper are obtained from the GEM database (available data set from 1999 to 2005).

Data for the independent variables are collated from various databases. To be included as a candidate predictor for explaining entrepreneurship rates across countries, variables were drawn from the wider entrepreneurship literature as discussed in the previous section. We should note that many of these variables are also standard variables used in the empirical macroeconomics literature. There are 32 variables, each with 80 observations. Given the number of variables, we chose to summarize them in a table rather than discuss them in the text. Table 1 defines the variables and provides information on the exact data sources.

Table 1

Variable Description and Sources

Variable	Description	Source
Dependent variable
Entrepreneurship rate	Overall total entrepreneurial activity (TEA)	Global Entrepreneurship Monitor consortium
Independent variables
Human capital
Population	Population growth rate, urbanization rate	World Development Indicators
Education	Gross secondary school enrollment rate, gross tertiary school enrollment rate	World Development Indicators
Unemployment	Unemployment rate as a percentage of labor force	World Development Indicators
Level of development
GDP per capita	Growth in real per capita GDP, log of real GDP per capita	World Development Indicators
Financial development	Lending interest rate, domestic credit to private sector as a percentage of GDP	IMF International Financial Statistics
Technological progress	R&D as a percentage of GDP, log of researchers per 1 million inhabitants	World Telecommunication Indicators
Institutions
Administrative complexity	Corruption perception index, administrative requirements index, bureaucracy costs, protection of IPR	Freedom House
Globalization	Imports as a percentage of GDP, exports as a percentage of GDP, trade (imports + exports) as a percentage of GDP, net FDI inflows as a percentage of GDP, net FDI outflows as a percentage of GDP, religion, net migration as a percentage of population	World Development Indicators
Taxes	Indirect taxes, indirect taxes squared, direct taxes, direct taxes squared, corporate marginal tax, corporate marginal tax squared, individual marginal tax, individual marginal tax squared	Freedom House
Inflation	Annual inflation, standard deviation of annual inflation	World Development Indicators

Note: FDI = foreign direct investment; GDP = gross domestic product; IMF = International Monetary Fund; IPR = intellectual property rights; R&D = research and development; TEA = total early-stage entrepreneurial activity.

Method

Model uncertainty raises an important question: How should researchers select the appropriate statistical model? Raftery (1995) suggests that researchers have three possible options to choose from. The first is to select few models based on the personal discretion of the researcher. However this strategy suffers from possible overconfidence in inference. An alternative is the presentation of all possible model combinations. Although unsystematic, doing so is preferable to the first option but poses substantial logistical issues. For instance, a model with, say, 10 explanatory variables requires reports on 2¹⁰ = 1,024 possible models, which is rather impractical. The third option is to explicitly account for model uncertainty through model averaging, where researchers can remove any impending uncertainty on account of erroneous model specification due to doubts about the inclusion of variables by creating a single unified model (e.g., Shou & Smithson, 2013; Young, 2009).

An intuitive approach towards model averaging

To illustrate the conceptual ideas behind BMA, we use a simple and intuitive example drawn from Chatfield (1995). Suppose that a researcher is interested in explaining the variation in a variable y with a potential explanatory variable x. Assuming no prior knowledge on the specification, there exist two possible models, enumerated as follows:

y = α_{1} + ε_{1} .

y = α_{2} + β x + ε_{2} .

Model 1 (M1) is an intercept-only model, where the data-generating process assumes that x has no impact on y, and Model 2 (M2) includes the variable x. Either of the above models can be estimated using traditional ordinary least squares (OLS). Estimating M2 via OLS implies the estimated regression equation

y = {\hat{α}}_{2} + \hat{β x} .

Given the estimate $\hat{β}$ , the coefficient’s standard error and the implied t statistic and p value, a statistically significant relationship between x and y may be supported or rejected in favor of M1. In the former case, $\hat{β}$ measures the unit effect of x on y. Note that in the process of testing for statistical significance of $\hat{β}$ , we have hypothesized that M2 is the “correct” specification; that is, we have set the prior probability of M1 being the “correct” specification equal to zero.

In this framework, it is important to understand that t statistics and p values account for uncertainty associated with repeated sampling of the data only (sampling uncertainty). To clarify, the obtained t statistics for variables may change if other variables are included/dropped from a specification. However, the t statistic is expected to remain consistent across repeated samples using the same specification. Interpreting the tests in the presence of alternate models is not the same (e.g., Young, 2009, among others). One possible remedy could be model selection tests. Model selection tests inherently compare two models at a time and assume that between the two models, one is “correct.” When the model space is large (e.g., with possible 1,024 models), the total model comparisons required would run into millions, making this approach difficult and impractical. In practice, most researchers tend to estimate and compare a few models, a procedure often motivated to ensure “robustness” of the findings. Though well intentioned and considered good practice, inference drawn in this manner may often reach wrong conclusions as it is a possibility that none of the estimated models is representative of the true underlying process that generated the data.

The BMA approach addresses and solves many of the problems discussed above. BMA works by assuming from the start that each of the models is “probabilistically correct” with probabilities p₁ and p₂ = 1 – p₁, the prior probabilities for M1 and M2, and generates posterior model probabilities ${\hat{p}}_{1}$ and ${\hat{p}}_{2}$ , where the posterior probabilities are obtained from updating the prior probabilities using the evidence given by the observed data. Taking account of the posterior model probabilities, the averaged regression equation and prediction is therefore

y = {\hat{p}}_{1} {\hat{α}}_{1} + {\hat{p}}_{2} {\hat{α}}_{2} + {\hat{p}}_{2} \hat{β} x .

It follows that the predicted unit effect of x on y is now ${\hat{p}}_{2} \hat{β}$ ; that is, the posterior weighted impact of x on y. Hence, the BMA approach reflects model uncertainty in prediction. Analogously, it reflects model uncertainty in inference, which is based on averaged coefficient distributions and averaged standard deviations. Note that if the researcher’s forced prior belief, “M2 is the correct specification,” in the context of traditional OLS estimation of M2 were true, then ${\hat{p}}_{2}$ should converge toward unity.

BMA in practice

The above intuitive explanation suggests that to implement BMA in practice, researchers should be able to estimate two quantities, namely, the parameters α and β, and the posterior probabilities for each model as captured by ${\hat{p}}_{1}$ and ${\hat{p}}_{2}$ in our example. To fix ideas, we consider multiple linear regression models, where an outcome variable Y is regressed on subsets of k = 32 potential explanatory variables that in turn can give rise to 2³² different models. We may denote a representative model of these models by M_j, which is identified by a typical OLS regression model

Y = α + β_{j} X_{j} + ε .

Estimating the coefficient of interest β after model averaging

Estimating the coefficients β in the Bayesian framework requires estimation of the posterior model probabilities. Mathematically, we can derive the posterior model probabilities of P(M_j | D) of each model M_j conditional (|) on the observed data D by applying Bayes’ law:

P (M_{j} | D) \propto P (D | M_{j}) P (M_{j}), \dots j = 1, \dots, 2^{k} .

Note that the quantity P(D | M_j) is known as the likelihood, which is an object familiar from maximum likelihood estimation in traditional frequentist statistics. The posterior model probabilities P(M_j | D) are used to calculate the posterior inclusion probabilities (PIP) of the 32 potential explanatory variables. In particular, the PIP of regressor Z_i is equal to the sum of the posterior model probabilities of those models containing regressor Z_i. Evidently, the larger an explanatory variable’s PIP, the stronger is the evidence that the variable is important for predicting the outcome variable Y. A Bayesian point estimator E(β | D) for the coefficients β, the analogue to the standard coefficient estimate in OLS, may now be obtained by taking a weighted average over the mean coefficients E(β | M_j, D) with the weights being the corresponding posterior model probabilities.

E (β | D) = \sum_{j = 1}^{2^{k}} E (β | M_{j}, D) P (M_{j} | D) .

Integral to the BMA approach is the specification of prior distributions for the coefficients β to be estimated as well as the set of candidate models {M₁, M₂, . . ., M_j} making up the model space. Turning to the prior distribution for the coefficients first, observe that we report BMA results based on three different prior distributions for the coefficients. All of these prior distributions are variants on Zellner’s g prior and can be implemented easily in the statistical program R (see appendix). The prior distributions of the coefficients are thereby assumed normalwith a prior mean of zero and a variance consistent with Zellner’s g prior $σ^{2} {(\frac{1}{g} X_{j}^{’} X_{j})}^{- 1}$ . Our three different choices in modeling g are grounded in the current state of the literature (e.g., Fernandez et al., 2001). While the choice of g may seem arbitrary, values of g = n and g = k², where n equals the number of observations and k equals the number of explanatory variables, have been shown to provide consistent estimators of the coefficients. The common approach with g = n is known as the unit information prior (UIP), since the choice contributes approximately as much importance to the prior as is embodied in one observation (Kass & Wasserman, 1995). The approach with g = k² is based on work by Foster and George (1994) and is referred to as risk inflation criterion (RIC). It tends to lead to smaller mean model sizes, that is, more parsimonious model specifications (Ley & Steel, 2009). The third approach follows Liang, Paulo, Molina, Clyde, and Berger (2008) and places a hyper prior on g (hyper-g), thereby abandoning the fixed-g assumption of the previous two choices. The hyper-g prior structure is suggested to be more robust to possible misspecifications due to a fixed-g assumption, an argument also advanced by Feldkircher and Zeugner (2009).

Two remarks shall round off this description of our coefficient prior choice. First, note that the wider literature on BMA, as well as the articles referred to in this paragraph, provides evidence that the results can be sensitive to the choice of g. Dispelling such concerns is the purpose of choosing alternative prior structures. Second, note that all three prior structures, in conjunction with the prior model probabilities to be specified below, belong to the class of uninformative priors. Common to uninformative prior structures is that the posterior determination is predominantly driven by the data via the likelihood as opposed to depending more heavily on the prior specification (see Zyphur & Oswald, 2013).

We conclude the discussion on prior choices in specifying a prior distribution for the model space {M₁, M₂, . . ., M_j}. The specification of prior model probabilities P(M_j) has been an area of active research interest (Ley & Steel, 2009). We follow the approach recommended by Ley and Steel (2009) and implement a fully random prior for the model space to allow for minimum interference with posterior inference. The advantage of their prior structure over the previously more common structure implying a binomially distributed model size (Fernandez et al., 2001, among others) is that it allows the researcher to impose less prior information. This completes our model set up.

Results

In the following subsections, we shall illustrate the potential arbitrariness of common frequentist model selection methods in the context of identifying the macrolevel determinants of entrepreneurship before moving to the findings of the BMA approach.

Multiple Linear Regression

Most empirical research employs some form of a regression-based approach (e.g., linear regression, probit/logit, panel data methods, structural equation models) to test relationships between variables. The goal of the enterprise would be to use statistical significance, as judged by a standard t test or F test at a particular level of significance (e.g., 5% or 10%), as evidence to support/disprove a particular theoretical proposition. Consistent with this approach, we regress TEA on various sets of independent variables drawn from the list presented in Table 2. While we have identified 32 variables as potentially important determinants of entrepreneurship, our objective is to show what happens when researchers base their inference on various subsets of the entire set of candidate regressors. The results for Models 1 through 4 are presented in Table 2.

Table 2

Economic Determinants of Entrepreneurial Activity

Variable	Model 1	Model 2	Model 3	Model 4
Log GDP	−7.02***	−8.57***	−8.04***	−7.84***
GDP growth	0.02	−0.07	−0.05	0.03
R&D expenditure	−0.54***	−0.22	−0.08	1.02**
Log researchers	2.03**	0.08	0.36	0.48
Exports	0.10***	25.48	17.07	23.56
Imports	−0.14***	25.31	16.93	23.59
Unemployment		−0.10***	−0.10***	0.00
Trade		−25.41	−17.01	−23.58
Secondary school enroll		−0.01	−0.01*	−0.01
Tertiary school enroll		0.02*	0.00	0.03
FDI inflows		−0.01	−0.04	−0.01
FDI outflows		0.03	0.02	0.04
Population growth		0.36	0.48	0.27
Total urban population			0.02*	0.02
Credit to private sector			−0.98	2.53
Indirect taxes				0.25
Indirect taxes squared				−0.01**
Direct taxes				−0.14
Direct taxes squared				0.01
Protecting IPR				−0.43**
Standard deviation of annual inflation				−0.04
Annual inflation				−0.13**
Administrative requirements				0.21
Bureaucracy cost				−0.19
Corruption index				0.10
Net migration rate				0.12
Religion				0.68
Interest rate				−0.05
Corporate marginal tax				−0.20
Corporate marginal tax squared				0.00
Individual marginal tax				0.50***
Individual marginal tax squared				−0.005**
Constant	27.49***	40.46***	38.62***	35.52***
Number of observations	80	80	80	80
Adjusted R²	.62	.69	.70	.81
Likelihood ratio tests		23.19	7.47	60.9
Chi-square p value		.00	.02	.00

Note: FDI = foreign direct investment; GDP = gross domestic product; IPR = intellectual property rights; R&D = research and development.

p < .10.

p < .05.

***

p < .01.

At this stage, we refrain from attributing interpretations to particular regressors and shall comment on the findings in the Discussion. For the first specification (Model 1), we find that five out of the six variables included are statistically significant. In Model 2, we add seven additional relevant variables and find that only two out of the 13 variables included are statistically significant. Adding two more variables in Model 3, four explanatory variables turn out statistically significant. Finally, we run the fully saturated regression model including all 32 regressors and find that six of the variables are statistically significant at conventional levels. Thus, depending on which specification is chosen, the number of significant variables changes.

Looking beyond this rather aggregate information, we find that only one among the 32 variables, log GDP, is statistically significant across all four specifications. The significance of several other variables, in contrast, changes depending on the specification. For instance, unemployment, while significant in Models 2 and 3, is insignificant in Model 4. Similarly for R&D, while negative and significant in Model 1, the variable turns positive and significant in Model 4. Clearly, this indicates that the sign and statistical significance of variables of interest may change depending on the specification used, thus implying a considerable burden on inference.

Next we seek the help of traditional model selection tools. For instance, on the basis of explanatory power, we find that Model 4 has the highest adjusted R² of around 89%. This is not surprising, as it is well known that increasing variables in a regression model will lead to larger R²s. The F statistic is also not very helpful in our case as for each of the models, the joint hypothesis test of all coefficients being equal to zero is rejected. Finally, we look at the Bayesian information criterion (BIC) to help aid model selection. Selection using the BIC statistic is based on identifying the model with the lowest possible BIC value. In this context, we find that BIC recommends Model 1. This recommendation is expected, because the BIC statistic includes a penalty term for additional parameters in a model. Inference based on this result, however, is likely erroneous as it suffers from several omitted correlated variables. Up to this point, our analysis indicates the dangers of ad hoc model selection and the limitations of standard model selection methods in use. In fact, the purpose of this exercise was to show that many of the inconsistencies found in existing cross-country studies of aggregate entrepreneurship may be attributed to model uncertainty and specification biases. Next, we discuss results from BMA.

BMA

We begin our BMA analysis by studying aggregate information on the implementation of the estimation process. In data sets with a large number of potential regressors, not every single model is estimated. An algorithm combs the model space (Markov Chain Monte Carlo [MCMC] sampler) and approximates the posterior model distribution. With the BMA results being based on MCMC simulations, the number of model draws needs to be specified by the researcher. In line with the literature, we chose 500,000 draws and dropped the first 50,000 as the burn-in sample. Final inference was based on the remaining 450,000 draws. We set the number of draws to be fairly high to ensure better convergence of the algorithm exploring the model space. Convergence in the case of BMA is indicated when the correlations of the posterior model probabilities are closer to unity (e.g., Fernandez et al., 2001). In our application, we find that model convergence was fairly high across all prior specifications (with the lowest being around 99.5% under the hyper-g prior), which allows us to turn to the presentation of the BMA findings.

One of our goals from using BMA is to identify the most relevant of the 32 candidate macrolevel regressors for predicting entrepreneurial activity. In the social sciences, a commonly used approach to assess variable importance is dominance analysis (Budescu, 1993) and relative importance (Lebreton & Tonidandel, 2011). Recent research suggests that when predicting mean effects, both BMA and dominance analysis tend to perform equally well, thus offering stronger evidence of complementarity between the two methods (Shou & Smithson, 2013). We shall briefly return to these methods in the Discussion section. Predictor relevance in the BMA context can be inferred from PIPs, which indicate the regressors’ probabilities of being included in the unknown specification having generated the data. Table 3 provides the PIPs across the three prior specifications.

Table 3

Posterior Inclusion Probabilities Across Different Coefficient Priors

Variable	UIP	BRIC	Hyper-g
(Intercept)	1.00	1.00	1.00
Log of GDP per capita	1.00	1.00	1.00
Annual GDP per capita growth	.07	.02	.10
R&D expenses as % of GDP	.11	.02	.21
Log of researchers per 1 million inhabitants	.05	.01	.10
Exports as % of GDP	.14	.02	.19
Imports as % of GDP	.18	.06	.25
Trade as % of GDP	.15	.03	.21
Gross secondary school enrollment	.03	.00	.07
Gross tertiary school enrollment	.04	.01	.09
FDI inflows as % of GDP	.06	.02	.09
FDI outflows as % of GDP	.04	.01	.07
Annual population growth	.20	.08	.25
Unemployment as % of total labor force	.99	.99	.97
Total urban population	.04	.01	.10
Domestic credit to private sector as % of GDP	.10	.03	.16
Indirect taxes	.59	.57	.57
Indirect taxes squared	.38	.40	.42
Direct taxes	.04	.01	.09
Direct taxes squared	.04	.01	.08
Protection of IPR	.04	.01	.09
Standard deviation of annual inflation	.92	.97	.89
Annual inflation	.12	.03	.20
Administrative requirements	.08	.02	.11
Bureaucracy cost	.03	.01	.06
Corruption index	.04	.01	.09
Net migration rate	.04	.01	.08
Religion	.04	.01	.09
Interest rate	.04	.01	.10
Corporate marginal tax	.06	.01	.12
Corporate marginal tax squared	.06	.01	.12
Individual marginal tax	.13	.02	.25
Individual marginal tax squared	.10	.01	.20

Note: BRIC = benchmark prior (from Hernandez, et al., 2001); FDI = foreign direct investment; GDP = gross domestic product; IPR = intellectual property rights; R&D = research and development ; UIP = unit information prior.

The differences in results between the BMA findings and the linear regression models are striking. First, we find that once we account for model uncertainty and average across the model space, only three variables, log of GDP per capita, unemployment as a percentage of the workforce, and the standard deviation of annual inflation, are suggested as key determinants of entrepreneurial activity. As can be seen from the table, these three variables have PIPs exceeding 90% across all three prior specifications. None of the other variables consistently finds its way into model specifications. Based on the order of importance, the next most important variable is the indirect tax rate, with an average probability of around 59%.

Beyond variable and model selection, most management scholars want to draw inference in terms of the size, sign, and statistical significance of the coefficients. BMA provides researchers with the posterior distributions for the coefficients, which can be used to compute a variety of statistics. In Table 4, we chose to report standardized estimates of the posterior mean coefficients as well as the associated posterior standard deviations (allows for easier comparison across prior choices). Since the effect sizes and uncertainty were qualitatively consistent across the different prior distributions, which indicates minimal influence on account of the prior coefficient distributions on the posterior means, we chose to report the results based on the benchmark prior (BRIC), suggested by Fernandez et al. (2001), only (other results are available from the authors upon request).

Table 4

Posterior Estimates (BRIC Prior)

Variable	Posterior M	Posterior SD
Log of GDP per capita	−6.35	.68
Annual GDP per capita growth	−.00	.01
R&D expenses as % of GDP	.00	.04
Log of researchers per 1 million inhabitants	.01	.10
Exports as % of GDP	.00	.24
Imports as % of GDP	−.00	.24
Trade as % of GDP	−.00	.24
Gross secondary school enrollment	.00	.00
Gross tertiary school enrollment	.00	.00
FDI inflows as % of GDP	−.00	.02
FDI outflows as % of GDP	.00	.00
Annual population growth	.04	.15
Unemployment as % of total labor force	−.09	.02
Total urban population	.00	.00
Domestic credit to private sector as % of GDP	.04	.27
Indirect taxes	−.07	.07
Indirect taxes squared	−.00	.00
Direct taxes	.00	.00
Direct taxes squared	.00	.00
Protection of IPR	.00	.01
Standard deviation of annual inflation	−.06	.02
Annual inflation	−.00	.01
Administrative requirements	.00	.03
Bureaucracy cost	.00	.01
Corruption index	.00	.01
Net migration rate	.00	.01
Religion	−.00	.02
Interest rate	.00	.00
Corporate marginal tax	.00	.00
Corporate marginal tax squared	.00	.00
Individual marginal tax	.00	.02
Individual marginal tax squared	.00	.00

Note: FDI = foreign direct investment; GDP = gross domestic product; IPR = intellectual property rights; R&D = research and development.

In line with the long regression estimate shown in Table 1, the mean coefficient on GDP per capita is negative and statistically significant. In contrast to the long regression estimates, the other mean coefficients on the three variables identified as important according to PIPs, namely, unemployment, standard deviation of annual inflation, and indirect taxes, turn out statistically significant when accounting for model uncertainty. Moreover, the sign of the mean coefficient for indirect taxes is negative as opposed to positive in the long regression. Statistical significance of the mean coefficients may be illustrated with the help of high-posterior-density (HPD) plots, where the densities are model-weighted mixtures. Figures 1, 2, 3, and 4 plot the densities along with 95% HPD intervals (the vertical hyphenated lines to the left and the right of the mean of the distributions) for the four variables found to be most important. As is evident from visual inspection of the graph, zero is not within the 95% HPD interval in any of the four graphs, hence indicating statistical significance of the coefficients.

Figure 1

Marginal Density of Log Gross Domestic Product

Figure 2

Marginal Density of Unemployment

Figure 3

Marginal Density of Standard Deviation of Annual Inflation

Figure 4

Marginal Density of Indirect Taxes

Note finally that the standardized coefficients analysis sheds further light on the relative importance of the variables identified as important. In light of the PIPs, the variables Unemployment and Standard deviation of annual inflation seem almost as important as GDP per capita. While there is very strong evidence for the inclusion of GDP per capita, the evidence for the other two variables appears only slightly weaker. Yet, the standardized coefficients suggest otherwise, with the impact of the variables Unemployment and SD of inflation being clearly dominated in magnitude by the impact of GDP per capita. To a lesser extent, the same observation holds for the variable Indirect taxes.

Discussion

The study of macroeconomic factors influencing aggregate entrepreneurship is, of course, a complex phenomenon. On the basis of classic works by Kirzner and Baumol, we present a broad, theoretically grounded framework for the study of aggregate entrepreneurship. Results obtained from testing this framework with appropriate analytical techniques allow us to then identify a set of empirically grounded variables that are significantly and systematically linked to aggregate entrepreneurial activity across countries. Specifically, our BMA analysis based on 32 macrolevel predictors routinely used in empirical entrepreneurship research identified only four variables as being universally relevant in explaining the linkages between macroeconomic conditions and aggregate entrepreneurship.

First, GDP per capita emerges as a key factor driving aggregate entrepreneurship. Our results show the relationship between GDP per capita and aggregate entrepreneurship to be negative and significant in both our BMA and standard regressions. This confirms previous findings by Amoros and Bosma (2014) and Wennekers et al. (2010), among others. This negative relationship is in part the result of necessity entrepreneurship. In other words, it reflects the activity of people who choose to start microbusinesses due to the lack of better employment alternatives. While not new, the important lesson is that no credible study of macroeconomic determinants of entrepreneurship can abstract from considering the level of economic development.

Second, in our BMA analysis, unemployment emerges unequivocally as being negative and significant. This is a clearer result compared to existing literature, where, akin to our own standard regressions, different model specifications have shown the relationship to be alternatively positive (Evans & Leighton, 1990) and negative (Audretsch & Frisch, 1994). When model uncertainty is taken into account and corrected for, it appears that the reduction in entrepreneurship caused by markets’ decline outweighs necessity entry. Importantly, our models do not take into account long-term effects. Thus, our results do not deny the possibility of a positive long-term linkage (Thurik et al., 2008).

Third, we found the variability of inflation to be significantly and negatively correlated to aggregate entrepreneurship. The same variable, however, was found not significant in our standard regression estimate. Our result confirms that volatility in macroeconomic policies discourages long-term contracts and relations necessary for successful entrepreneurship (McMillan & Woodruff, 2002). More importantly, our result highlights that the linkage between monetary policy and aggregate entrepreneurship is universally important. Surprisingly, this relationship has been relatively neglected in the literature. In fact, only a few studies have considered monetary instability. Even in those cases, researchers have focused on interest rates as a way to gauge costs of financing (Parker, 2009) rather than on the implications of unchecked increases of the money supply. Importantly, conditioning on the stage of development, the negative correlations between entrepreneurship and inflation and between entrepreneurship and unemployment suggest that net venture creation declines as the state of the economy worsens. This result confirms existing literature showing that entrepreneurship may be procyclical (Rampini, 2004).

Last, we found the relationship between individual marginal taxes and aggregate level of entrepreneurial activity to be significant and negative, although the effect is not as strong as for the three previous variables. By comparison, our standard regression estimate showed a significant but positive relationship, whereas results from existing literature are inconclusive or show other types of taxes to be significant. This illustrates the importance of correcting for model uncertainty. Our result supports existing research showing that the progressivity of the tax system matters (Gentry & Hubbard, 2000) and that higher rates of personal taxation discourage the market provision of household products (Henrekson, 2005).

Overall, in addition to providing evidence for the universal importance of these four variables and possible explanations for inconsistencies found in previous empirical literature, our results force entrepreneurship researchers to cogitate the relationship between aggregate entrepreneurship and macroeconomic variables in a fundamentally different way. While much entrepreneurship literature focuses on the identification of entrepreneurship-specific factors and the creation of related incentives, our results suggest that aggregate entrepreneurship is universally and significantly linked to a small set of important macroeconomic indicators that are not entrepreneurship specific but, instead, play a fundamental role in the creation of systemwide economic incentives and stability. This, of course, does not imply that other variables may not be importantly linked to entrepreneurship in specific contexts.

The previous considerations lend themselves to important policy implications. Our results indicate that entrepreneurship is significantly and systematically linked to inflation and taxation, two variables directly connected to macroeconomic stability that the government has the power to control. For example, policy makers interested in promoting entrepreneurial activity will want to pay close attention to the trade-off produced by an expansionary monetary policy with lower interest rates but a higher risk of inflation. Similarly, a fiscal policy with a lower marginal tax burden may be more effective than business-related taxes or public expenditure in the form of support programs. Although very preliminary, our policy analysis is consistent with Baumol’s (1990) argument that governments have the power to influence the distribution of entrepreneurial types by setting the appropriate incentives. We expand on his argument by showing that those incentives are not entrepreneurship specific but overlap significantly with general and fundamental economic principles.

Of course, while our results make a significant contribution to entrepreneurship theory, our main contribution remains in the application of BMA to the empirical investigation of entrepreneurship at the aggregate level and in showing the importance of accounting for model uncertainty.

Notwithstanding our intention to make a case for BMA analysis as a research tool, we do not want to suggest that traditional approaches toward empirical research should be discarded or ignored. In fact, we recommend the opposite. There is no substitute to good theory. This principle applies even to BMA-based empirical work. Had we not adopted a theoretical framework based on Kirzner (1997) and Baumol (1990), we could have chosen a different set of variables and obtained different results. We acknowledge this possible limitation. However, we note that BMA is particularly well suited to be used in conjunction with traditional approaches, such as multiple linear regressions. For instance, on the basis of theoretical considerations, an entrepreneurship researcher may identify certain variables explaining a particular outcome, and traditional methods can be used to draw such inference. Within the purview of BMA, these variables should be included in every possible specification (researcher imposes a prior probability of inclusion to one based on theoretical knowledge). Model averaging can now be used to test the impact of including or deleting other variables on the key variable of interest, hence explicitly ensuring robustness to model uncertainty in theory confirmation.

In a similar vein, a researcher can also control for unobserved heterogeneity by forcing the inclusion of country-/firm-specific dummy variables (as the case may be) onto every specification. Thus, concerns related to endogeneity can be effectively addressed using model averaged fixed-effect estimators. Finally, endogeneity concerns typically plague much of research in the organizational sciences. A solution to this problem is the use of instrumental variable estimators. In cases where several possible candidates as instruments are available, a researcher may be forced to choose a smaller set of instruments from a larger universe of available instruments. BMA can reduce uncertainty in the choice of instruments by averaging over the entire universe of available instruments as shown by Lenkoski, Eicher, and Raftery (2014). This innovation, coupled with the ease of implementation of fixed-effects models in the model-averaging framework, not only allows entrepreneurship researchers to effectively address model uncertainty but also helps allay endogeneity concerns.

Conclusion

In this paper, our major contribution is to address and help to alleviate a thorny issue, namely, model uncertainty, concerning much of empirical research in entrepreneurship and management in general. Having discussed the implications of our findings with respect to the entrepreneurship literature in the previous section, we conclude with a methodological remark in the context of our empirical results. Specifically, we showed that variables that were not captured as being significant in the full model specification turn out to be critical in determining aggregate entrepreneurship, thus raising concerns on how specification/model uncertainty can taint empirical inference.

In light of this finding, we would like to note that one of the important outputs from the BMA process is information on variable importance, and as such, the method offers a complementary approach to the better-known importance and dominance analysis (Budescu, 1993). The key difference between dominance analysis and BMA is that any form of relative importance analysis does depend on model specifications as well. For instance, if we estimate four different models (with subsets of independent variables), the relative importance of variables may change depending on which variables are included in the specification being analyzed (see Lebreton & Tonidandel, 2011). Beyond that, BMA analysis offers additional insights in the form of model-averaged coefficients and standard errors, which are not offered by dominance analysis. Finally, dominance analysis becomes computationally infeasible as the number of independent variables increases, whereas BMA offers a computationally attractive and statistically rigorous approach toward identifying variable importance even when the universe of potential predictors is expansive.

Footnotes

Appendix

Acknowledgements

Authors are listed in alphabetical order. All authors contributed equally. The suggestions and thoughtful comments by Mike Zyphur and Fred Oswald, as well as two anonymous reviewers, have been invaluable throughout the development of this article. The authors are grateful to Dean Shepherd, Paul Reynolds, and Bill Schulze for their valuable advice at the Academy of Management 2014 annual meeting.

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