Hypothesis and empirical methods

The model in equation 1 is proposed to explain the stock of entrepreneurs and underlies some hypothesis on the grounds of the theoretical and empirical research presented.

Where N is the number of entrepreneurs; Y is a measure of economic activity and w is wage, both related to the macroeconomic context. Variable y is a measure of economic development representing some variables associated to the states' context conditions

Assuming a Cobb-Douglass function, equation 1 turns to 2

Where β is the neutral component of the function not dependent upon the right-hand side variables Y, w, or y. The parameters β _Y , β _w, and β _y are the corresponding parameters of the argument. It is expected β _y to be positive and the size of the parameter depending on the type of venture. On the one hand, entrepreneurship may be pro-cyclical: expansions generate opportunities, make individuals more willing to bear risk and make credit more likely. This will increase the number of entrepreneurs of higher ability who foresee opportunities. However, expansions may also induce lower ability entrepreneurs to search for jobs given improved labor opportunities. In addition, ß _w is expected to be negative: given that w represents the opportunity costs of entrepreneurship, high level of wages ceteris paribus will induce individuals to search for jobs rather than venturing; but if wages are low, lower-ability marginal type will enter entrepreneurship expecting better gains as compared to salaried employment. Finally, the parameter ß _y is expected to affect the number of entrepreneurs differentially depending on the entrepreneur type. Development entails certain economical and institutional context which may induce or hinder entrepreneurs to undertake investments and create jobs. These may include the working of financial markets, the level of efficiency of the rule of law and contract enforcement, the quality of the government performance, policy support and regulations, the level of conduciveness of the knowledge context, among other factors. These factors may be related, although partially, to the concept of EE, which involves, in addition, more entrepreneurship-specific contextual factors, interactions and policies. In general, higher development would be consistent with relatively larger and more sophisticated ventures, whereas lower development induces self-employment and more rudimentary ventures.

An unbalanced panel data is estimated tracking 30 of the 32 states during the period 2005-2019. Campeche and Tabasco were dropped given the GDPp bias from the oil industry. The empirical work is based on the log-transformation of equation 2.

Where lNitn represents the natural log of the number of entrepreneurs of type n; the sub-indexes i and i refer to the individual states and years included in the regressions. The parameter β^ is the intercept and the parameters β^Y and β^w are associated to the natural log of the variable of economic activity (Y _it ) and wage (w _it ) correspondingly.

The type of entrepreneurs (n) considered in the study are the total number of entrepreneurs (Inentr), the self-employed individuals (Inse) and the employers (Inemp). Data on the stock of entrepreneurs were obtained from the National Survey of Occupation and Employment (ENOE, by its acronym in Spanish) elaborated by INEGI, which surveys individuals aged 15 or more and tracks the independent workers divided into self-employees and employers by state on a quarterly basis. INEGI defines an independent worker as an individual who runs his own enterprise or business and does not have a boss or superior to whom he is accountable for his performance or outcomes. A self-employee is an individual who works alone or with the support of family members at his own house or somebody else's without any commitment to pay them for their services. An employer is an independent worker who uses the services of one or more workers in exchange for an economic remuneration in monetary or kind.

A relevant characterization of the types of enterprises and entrepreneurs, which may be implicit in INEGI data, is provided in ^{Acs et al. (2017}), who propose the necessity, opportunity and innovation driven entrepreneurship types. The former includes those individuals who have no other option to make money in the labor market and undertake self-employment activities to survive; the second group includes those entrepreneurs who see opportunities to bring a good or service to the market, have serious expectations of job creation and growth, and whose returns will be higher than engaging in salaried work. The third group is the innovation-driven entrepreneurship which, like opportunity entrepreneurship, have serious expectations of job creation and growth from bringing an innovation to the market. Likewise, the authors also make a distinction between the small business owner who replicates what others do, and the entrepreneur who innovates. The former includes many forms of self-employment and small businesses in the streets, corners or shopping centers whose owners manage, operate or run routine business activities as they exhibit a known production function and operate in a well and clearly defined way. The later includes high-impact ventures, which conduct the necessary activities to create an innovative, high-growth company where not all markets are well established or clearly defined. The former involves activities that generate employment and income for their families; the second ensures that innovation facilitates increased productivity and contributes to economic growth. The relative presence of these types of entrepreneurs in INEGI data is unknown, but certainly it biases to the former case.

The proxies used to represent Y _it and w _it are the GDP per state in real terms at 2013-prices and the workers' average income by working hour obtained from the Economic Information System (BIE, by its acronym in Spanish) and the ENOE, both elaborated by INEGI. The level of development is included as dummy variables controlling for the lower developed states (y _l ) and the higher developed states (y _h ) with the associated parameters β^yl and β^yh correspondingly. The use of dummies instead of the direct measures of GDPp per state avoids specification concerns arising from the potential correlation with other right-hand variables specially Y _it and wage w _it . In addition, it allows considering the long-term nature of development, thus avoiding the short-term volatility of the GDPp not necessarily related to a structural economic, social and institutional change.

The dummy variable y _l takes the value of 1 if the states have an average GDPp during the 2005-2019 period lower than the mean minus 0.5 standard deviation and 0 otherwise and includes Chiapas, Guerrero, Hidalgo, Mexico, Nayarit, Oaxaca, Puebla, Tlaxcala, Veracruz, and Zacatecas. The variable y _h equals 1 if the state has an average GDPp greater than the states mean plus 0.5 standard deviation and 0 otherwise and includes Aguascalientes, Baja California, Baja California Sur, Chihuahua, Ciudad de Mexico, Coahuila, Colima, Jalisco, Nuevo Leon, Queretaro, Quintana Roo and Sonora. The rest of the states are considered as average developed. The variables IS _P , IS _S and lS _T are the natural logs of the shares of the primary, secondary and tertiary sectors of the economy computed as the proportion of the value added of the sector in the total value added and β^sP, β^ss and β^sT are the corresponding parameters. Finally, the period of the 2008 crisis is also controlled through the inclusion of three dummy variables t _c such as t _c = 2008, 2009 and 2010 which take the value of 1 for those years correspondingly and 0 otherwise and β^tc=08 , β^tc=09 and β^tc=10 are the associated parameters. The parameters β^Y,β^w,β^SP,β^SS and β^ST represent the slopes -a degree of responsiveness of the stock of entrepreneurs of any type n- and turn out to be the elasticities of the number of entrepreneurs to 1% changes in their corresponding variables: e^Y=β^Y,e^w=β^w,e^SP=β^SP,e^SS=β^SS and e^ST=β^ST The parameters associated to the dummy variables β^yl,β^yh and β^yh are instead intercept changes -deviations from the intercept β^ associated to the groups and specific years entailed in the dummy variables.

The error term is given by ϵit=αi+nit integrated by an individual time invariant component α _i and an error term n _it which vary randomly across individuals and time periods. An ample discussion on the empirical issues analyzing entrepreneurship and small business is provided in ^{Parker (2018}), who emphasizes the specification problems associated to the possible omitted variable bias and simultaneity, which may apply in estimating 3, affecting the assumptions regarding the component a _i capturing the individual states effects. This issue requires selecting the estimation method between Random Effects (RE) or Fixed Effects (FE) in order to control for this possible bias. Endogeneity caused by the simultaneous determination of the entrepreneurship outcomes, GDP and w may also be an issue. Entrepreneurship is considered as, both determined by, and a determinant of economic performance (^{Audretsch and Keilbach, 2004}; ^{Hartog et al., 2010}; ^{Thurik et al., 2008}), though the later effect will be dependent upon the type of venture; besides, entrepreneurship and w may also be determined in conjunction with the level of production. This issue is addressed by comparing the FE and the Fixed Effects Instrumental Variables (FE IV) models. Finally, there is also a potentially unstable, long-run relation caused by non-stationarity of some panels' time series, which requires testing for cointegration.

Estimation of the effects on local entrepreneurship and employment

The estimates derived from equation 3 will be used to obtain the impact on the entrepreneurial outcomes by type and state derived from the changes in the macroeconomic context and their employment implications, assuming the level of development and the sector structure invariant. Consequently, the change of the number of entrepreneurs of any type ΔNin provided that GDP _i and wage changes cetiris paribus is given by 4

This change will be dependent on the production and wage elasticities of the entrepreneurial outcomes e^Y and e^w correspondingly. A measure of the relative impact per state would be given in terms of employment (E _i ) by the ratio ΔNin∕Ei, which represents the entrepreneurial effect -this is the change in entrepreneurial outcomes with respect E _i . Assuming that E _i is the sum of entrepreneurs of all types (N _i ) and the number of salaried workers (L _i ), equation 5 follows:

Where Sin is the share of entrepreneurs of any type in employment, which affects the size of the impact ∆NinEi. However, entrepreneurs employ other people so the total -absolute- impact on employment ∆Ein is given by 6

Where Lin is the number of workers employed by the entrepreneurs, specified by θi∆Ni so equation 6 turns to 7

Where θi∆Ni is the employment impact derived from the change in the number of entrepreneurs, and θi is the average number of workers employed by the entrepreneurs. The employment relative effect is given by the quotient in equation 8

The relative employment effects across the states will not only depend on Sin, like the entrepreneurial effect of equation 5, but additionally on θ _i which is measured as the total number of dependent, salaried employees working with the entrepreneurs divided by the total number of entrepreneurs.

The relative entrepreneurial and employment effects of equations 5 and 8, and the absolute entrepreneurial and employment effects of equation 6 are estimated by type of venture and state. The factor θ _i applies to the number of employers and to a fraction of the total entrepreneurs given by the ratio employers-total entrepreneurs. The self-employed individuals are assumed not to have salaried workers so they are not affected by θ _i . In addition, it will be assumed ∆GDP _i =1% w¡ = 0, as they seem more neutral and do not divert from the focus of this research. Besides, this implies that ∆GDP _i and ∆w _i will be the same for all states so the impact on the state employment derived from entrepreneurship will depend mostly on Sin,θi and the GDP _i elasticity ê _Y , which are linked to the long run patterns of development of the local economies.

Econometric outcomes

The econometric results of equation 3 are reported for the three entrepreneurial outcomes (n) in Table 7. The models are estimated using 413 observations as Mexico City missed seven observations; except for three, which include 383 observations given the inclusion of lGDPt-1 and lwt-1 as instruments. The regressions' statistics suggest the global significance of the econometric estimations and that most of their variance are due to differences across states (rho). The explanation capacity of the models is acceptable. Estimations also bias to the acceptance of RE model according to the Hausman test in regression 1 and 2. This implies that individual states characteristics are not correlated with the time-varying characteristics of the independent variables, evading the endogeneity issues. Regression 3 rejects the RE model indicating an endogeneity problem, which is solved partly by the FE estimation. However, the possible simultaneity involving the entrepreneurship outcome, GDP and w required comparing the FE and FE IV using lY _t-1 and lw _t-1 as instruments, which turned out to be a preferable model according to the Hausman test exhibited in Table 7. This result indicates that employers, as opposed to the total number of entrepreneurs and the self-employees, are simultaneously determined with output and wages, which suggest the effects of employers on performance, stressing the more opportunity-driven nature of these ventures. This may be explained by the fact that employers are larger and possible more sophisticated ventures as compared to the other two measures of entrepreneurs. Although not necessarily innovative, these ventures may be run by more educated entrepreneurs possessing general training and some specific skills, allowing them to deal with larger ventures.

The variable Y _it , representing the level of economic activity, turned out to be significant at 5% with a positive effect over the entrepreneurial outcomes lnempr, lnese, lnemp but different in size. These results concur with the previous research arguing the importance of the level of economic activity as a determinant of the number of entrepreneurs and the pro-cyclical nature of entrepreneurship (^{Lucas, 1978}; ^{Aghion and Bolton, 1997}; ^{Sutton, 1991}; ^{Rampini, 2004}). The parameter estimates ß _Y yield 0.42, 0.32 and 0.90 correspondingly, suggesting that 1% change in GDP brings a 0.42% change in the overall entrepreneurship, 0.32% change in the number of self-employed individuals and 0.90% in the number of employers. This implies that the employers would receive a larger impact from economic downturns, than the self-employment ones, given that the corresponding elasticities ê _Y turns out to be higher. In sum, the responsiveness of the entrepreneurial outcomes to changes in economic activity diverge between the types of ventures, possibly reflecting their differential characteristics in terms of the type of good/service, market segments targeted, business models, education, among other; which determine their responsiveness to market variations and the exploitation of opportunities. On the one hand, the self-employed individuals produce traditional income-inelastic goods and services oriented to low-income markets or to satisfy basic consumption, which are consistent with necessity entre-preneurship. The employers, on the other, produce goods which are more income-elastic oriented to higher income markets, and possible more opportunity driven.

The effects of the labor markets dynamics, as measured by the wage level (w), over the entrepreneurial outcomes reveal also important divergences: Wages do not seem to affect entrepreneurship in general- wages are statistically insignificant as shown in regressions 1. However, they turn out to be significant at 5% though contrary in signs for the group of self-employees and employers of the regressions 2 and 3 correspondingly. On the one hand, the elasticities ê _w associated to the self-employed individuals Inse turn out to be -0.19 and for the employers lnemp 0.79; this means that 1% change in wages generates a negative 0.19% impact in the former and a positive 0.79% impact in the later. These results may reflect the necessity-opportunity dichotomy of entrepreneurship by which the hardships of the labor markets characterized by depressing wages and the lack of labor opportunities, encourage self-employment and discourage the employers to venture, due to the lack of market opportunities associated to the deficient demand. These processes are consistent with the "recession-push" and "prosperity-pull" hypothesis emphasized in ^{Georgellis et al. (2005}), ^{Parker (2009}), ^{Schuetze (2000}), ^{Ghatak et al. (2007}), ^{González et al. (2018}) and ^{Texis et al. (2019}).

The binary variables y _i and y _h and their associated parameters β^yl and β^yh provide diverse results regarding the effects of the level of development on entrepreneurship. At 5% significance, the less developed states (yl = 1) tend to experience an upward shift in all types of entrepreneurs as suggested by the regressions 1, 2, and 3. Conversely, the most developed states (yh =1) tend to exhibit a statistically significant downward shift in the total number of entrepreneurs and the self-employed individuals as illustrated in regressions 1 and 2, but not in the number of employers inemp. These results share consistencies with ^{Wennekers et al. (2005}), ^{Acs et al. (2008}), and ^{Ramírez-Urquidy et al. (2013}) on the entrepreneurship divergences along the stages of economic development. These results connect indirectly with the differing contexts accompanying those development stages, and the related economical and institutional divergences influencing the entrepreneurial outcomesas well as, argued in ^{Alvarez and Urbano (2011}), ^{Baumol and Strom (2007}), ^{Liñán and Fernandez-Serrano (2014}), ^{Aparicio et al. (2016}), ^{Dvoulety (2018)}, and ^{Brás and Soukiazis (2018}). Under this framework, better context conditions allow relatively stronger labor markets and higher rewards from salaried work, promoting a bias toward fewer and larger enterprises, consistent with opportunity entrepreneurship. Conversely, less conducive context conditions, characterizing the low-income states, are associated to depressing labor markets and individuals finding a way to improve by self-employing, imposing a bias toward necessity entrepreneurship. It is relevant to underline, however, that there is a gap between the economic and institutional context as advocated in this research, which is a subset of the general conditions, and the entrepreneurial ecosystem concept, involving more entrepreneurial specific dimensions, in encouraging or constraining types, quantity and quality of entrepreneurial activity.

The sector structure of the states as measured by ISp, ISs and IS _T and the associated elasticities e^SP=β^SP,e^SS=β^SS and e^ST=β^ST , are mostly insignificant across the entrepreneurial outcomes. These results suggest that, generally, the entrepreneurial outcomes are independent of the sector structure of the states, and that the sector variations regarding their underlying technologies and minimum efficient scales are not reflected in these types of entrepreneurs.

Besides, the dummy variables t _c = 08, t _c = 09 and t _c = 10 and the associated parameters β^tc=08,β^tc=09 and β^tc=10 are foundmostly significant at 5% but alternating in signs: whereas the parameter β^tc=08 and β^tc=10 which control for the initial and the final year of the crisis, turned out to be negative at 5% significance level in the complete set of regressions; the toughest year of the crisis in Mexico controlled by β^tc=09 resulted positive and significant at 5% for the total number of entrepreneurs and the self-employed individuals; however, this parameter was not significant for the employers. These results reflect the enduring instabilities associated to those years and the dynamic entrepreneurial processes of entry-exit, the salaried employment-self-employment two-way transiting, and the pull-push effects.

The effects of economic downturns over entrepreneurship and employment in the Mexican states

The estimation of the relative (% of employment) and absolute (Total quantity) entrepreneurial and employment effects derived from equations 5, 8, and 6 are reported in Appendix 4 and 5 for the three types of entrepreneurial outcomes under the premises displayed in Table 8. The distribution of these effects is exhibited in the Figures 1 through 4, where the darkest color depicts those states displaying the highest negative impact and the lightest the lowest negative impact.

The big picture suggests that the per-state relative, entrepreneurial impact derived from a 1% decline in GDP _i cetiris paribus averages -0.113% for the total number of entrepreneurs, -0.069% for the self-employees and 0.047% for the employers; the estimated per state employment effects average -0.161, -0.069 and -0.102% correspondingly (see Appendix 4). In general, the relative entrepreneurial impacts (see Figure 1) are largest in some southeastern states such as Oaxaca, Guerrero, Chiapas, which are shaded darkest in the figure, followed by Veracruz, Puebla, Michoacan, Nayarit, Hidalgo and Yucatan. Separating by type of venture, the relative effect in self-employment is largest in Oaxaca, Guerrero and Chiapas followed by Puebla, Veracruz and Mexico. It is apparent that the strongest entrepreneurs relative impact hit the southern states, particularly the self-employees, given their relatively large population and occupation trends biased toward this type of ventures.

Source: own elaboration using ArcMap.

Figure 1 Distribution of the relative entrepreneurial effects 

The employers' entrepreneurial relative effects turn out to be largest in Sinaloa, Guerrero, Chiapas, Puebla, Jalisco, Nayarit, Durango and Colima, which may be explained by the interaction of a relatively higher share of the employers in employment and the higher GDP _i elasticity of such ventures, as compared to the total entrepreneurs and the self-employees. The effects in the northeastern states are rather more modest (except for Baja California), which is explained possibly by the relatively stronger labor markets and job opportunities associated to the location of large manufacturing industries, discouraging selecting entrepreneurship as an occupation.

The relative total employment effects (see Figure 2) are felt strongest in some southeastern and pacific states such as Guerrero, Oaxaca and Chiapas, followed by Puebla, Michoacan, Jalisco, Hidalgo, Sinaloa, Durango and Baja California Sur. The relative entrepreneurial and employment effects converge in the self-employment case so these are not included in the Figure 2. As for the relative employment effects associated to the employers, they tend to affect the northern and northwestern states more, and some central and pacific states. These effects are largest in Baja California Sur, Sinaloa, and Jalisco, followed by Baja California, Sonora, Chihuahua, Coahuila, and Durango. Despite the modest relative, total-employment effects in the northern states, when considering the employers' relative employment effects separately, they become among the most affected states due the interaction of the relatively higher GDP _i elasticity of such ventures and the average venture size in those states.

Source: own elaboration using ArcMap.

Figure 2 Distribution of the relative employment effects 

The entrepreneurial and employment per state absolute effects are exhibited in Appendix 5. In gross terms, 1% decline in GDP _i is expected to produce an overall reduction in the number of entrepreneurs by venture type and the related employees distributed heterogeneously across the different states.

The impact in the number of entrepreneurs is largest in Mexico, followed by Puebla, Oaxaca, Jalisco, Veracruz and Mexico City. Discomposing into types of ventures, the self-employees' absolute effects are highest in Mexico, Oaxaca, Puebla, Jalisco, Guerrero and Chiapas, whereas the strongest effects derived from the decline in the number of employers are located in Jalisco, Puebla, Mexico, Mexico City, Veracruz and Chiapas (see Figure 3). The size of these effects is related to the population size of these states, which correlates with the number of entrepreneurs, along with the GDP _i elasticity of the ventures.

Source: own elaboration using ArcMap.

Figure 3 Distribution of the absolute entrepreneurial effects 

As for the absolute impact in the employment (see Figure 4) produced by the entrepreneurs' decline, the strongest effects turned out to be in some central and eastern states, such as Mexico and Mexico City, and also in Veracruz and Puebla; followed by the southern and eastern states Michoacan, Guerrero, Oaxaca, Chiapas, Guanajuato; and the northern state of Nuevo Leon. These states are the most populated in the country which is reflected certainly in the absolute values. As before, the absolute entrepreneurial and employment effects converge in the self-employment case, so they are not included in the Figure 4. The employment absolute impact related to the employers is strongest in Jalisco and Mexico, followed by the neighboring states Michoacan, Guanajuato, and Puebla, and the northern states of Baja California, Chihuahua and Nuevo Leon (see figure 4). Some less populated states in the north facing also a significant absolute effect are Sonora, Coahuila and Tamaulipas. Despite the importance of the size of the states' population to determine the dimension of these effects, the results also exhibit the role played by the interplay between the higher GDP _i elasticity of the employers, and the average venture size characteristic of the northern states.

Source: own elaboration using ArcMap.

Figure 4 Distribution of the absolute employment effects