Entrepreneurship and income inequality in cities: differentiated impacts of new firm formation and self-employment

ABSTRACT This article examines the effects of two types of entrepreneurship – new firm formation versus self-employment – on income inequality within cities in the United States. Regression analysis based on metropolitan areas between 2005 and 2015 shows that an increase in new firm formation decreases household income inequality. In contrast, more self-employment increases inequality. These results are consistent across different measures of income inequality and model specifications. This study highlights the need for differentiating entrepreneurship in understanding its role in regional development. It further confirms vibrant start-up activity as a key strength of a regional economy.


INTRODUCTION
Supporting entrepreneurial activity is a popular economic development strategy in cities and regions, as both scholars and policymakers have recognized the importance of entrepreneurship to regional prosperity. Entrepreneurship has been found to drive economic development through job creation (Decker et al., 2014), efficient allocation of market resources (Kirzner, 1997), innovation (Acs et al., 2013) and cluster development (Klepper, 2011). However, the impact of entrepreneurship on income inequality, an equity dimension of economic development, has not been well studied.
The United States has witnessed rising income inequality over the past century (US Census Bureau, 2016). It would help to build a more sustainable development path by identifying the sources behind this trend. Scholars have reported the development paradox that economic growth often comes with increased income inequality, with the magnitude varying in different US regions and time periods (Frank, 2009;Partridge, 2005). However, it is not politically realistic to sacrifice growth for equality. Ideally, regional policymakers can adopt some development strategies that propel equitable economic growth. This article assesses whether fostering entrepreneurship can be one of these strategies. While the positive contribution of entrepreneurship to economic growth has been well documented in the literature, we focus on its impacts on income inequality.
Theoretically, entrepreneurship could both increase inequality by contributing to the wealth accumulation in the top-income group and alleviate it by helping those at the bottom (Halvarsson et al., 2018). For the former, for example, successful entrepreneurs may be rewarded with high returns to their risk-taking behaviour and, therefore, entrepreneurship raises the income level at the very top of the distribution (Jones & Kim, 2018). For the latter, entrepreneurship can be a source of upward mobility for the low-income group as it encourages self-employment when the labour market does not provide enough traditional employment opportunities (Lippmann et al., 2005). Also, entrepreneurs create jobs for others, leading to improvements in the middle or at the lower tail of the income distribution. At the national level in the United States the past few decades have witnessed a decline in start-up activity (Decker et al., 2014), in parallel with increasing income gaps between the rich and average wage earners (Burkhauser et al., 2010;Madden, 2000). This pattern seemingly suggests a negative association between entrepreneurship and income inequality. At the state level, evidence exists that entrepreneurship measured by self-employment is positively associated with income inequality (Atems & Shand, 2018). The relationship between entrepreneurship and inequality appears to vary by entrepreneurship types. Based on this observation, we study the impacts of variegated entrepreneurship on income inequality in economically functional cities.
Economic regions represent an appropriate geographical unit analysis for this relationship, as the economic impacts of entrepreneurship, such as through job creation and knowledge spillovers, are regionally bounded (Qian, 2017;Stuetzer et al., 2018).
We distinguish and assess the inequality impacts of two commonly used entrepreneurship proxies: new firm formation (also known as start-up activity) and selfemployment. According to Parker (2018), focusing on market opportunity recognition and new firm formation 'is now standard practice in the business studies approach to entrepreneurship' (p. 7), while economic studies (especially labour and microeconomics) typically adopt self-employment as a proxy for entrepreneurship. Their divergent trends of change shown in our descriptive analysis below clearly demonstrate that new firm formation and self-employment represent different types of entrepreneurial activity. By definition, new firm formation refers to starting new businesses. The self-employed are 'individuals who earn no regular wage or salary but who derive their income by exercising their profession or business on their own account and at their own risk' (Parker, 2018, p. 12). The self-employment level of a region reflects the stock of its business ownerships, while new firm formation adds new business ownerships.
We use US metropolitan statistical areas (MSAs) as the geographical unit for empirical analysis. MSAs represent cities in the form of economically functional regions and have been well adopted in regional entrepreneurship research (Qian, 2017;Stuetzer et al., 2018). Using a panel dataset of 289 MSAs from 2005 to 2015, we examine the relationships between these two types of entrepreneurship and income inequality within cities (interchangeably used with MSAs in this article). Alternative measures of income inequality are used, including the Gini coefficient, the Atkinson index and the Theil index, to assess the robustness of these relationships. Our regression analysis reveals that higher rates of new firm formation in cities lead to reduced income inequality, likely through both the bottom and the top of the income distribution; by contrast, higher self-employment rates lead to increased income inequality, especially by negatively affecting the bottom income groups. These results are consistent to both panel fixed-effects and instrumental variables (IV) estimates.
We build our work on a related study by Lee and Rodríguez-Pose (2021) who have analysed the impact of self-employment on poverty in US metropolitan areas. We add new firm formation as another measure of entrepreneurship and focus on income distribution instead of poverty. Our research makes at least two major contributions to the literature. First, we contribute to a better understanding of the sources of income inequality within cities. Variations in income disparities have been documented across MSAs over time (Florida & Mellander, 2016;Madden, 2000). However, very limited research has focused on the sources of income inequality across cities. Second, we distinguish and directly compare the impacts of two different types of entrepreneurship. The current literature often fails to distinguish different types of entrepreneurship and rushes to make general conclusions about the relationship between entrepreneurship and inequality. In this article we raise the awareness that entrepreneurship is multidimensional and its impacts on income inequality (and economic development in general) should be contextualized by the varieties of entrepreneurship.
The rest of the article is organized as follows. After this introduction, we review the literature on the possible impacts of entrepreneurship on income disparities. Next we analyse the regional trends of entrepreneurial activity and income inequality over time. We then discuss regression methods and subsequently present regression results. Lastly, we summarize the research and discuss policy implications.

Multidimensional entrepreneurship
Often with data available at the subnational level, new firm formation and self-employment are among the most important proxies for entrepreneurship in regional studies. However, they represent different forms of entrepreneurship. In this literature review section we summarize the literature regarding their possible impacts on income disparities separately. Before that, it is useful to conceptually discuss new firm formation versus self-employment as proxies for entrepreneurship. New firm formation, also known as start-up activity, is one widely used proxy for entrepreneurship in regional studies (Lee et al., 2004;Liu et al., 2021;Stuetzer et al., 2018). A practical definition of a start-up is proposed by Luger and Koo (2005, p. 19) as: a business entity which did not exist before during a given time period (new), which starts hiring at least one paid employee during the given time period (active), and which is neither a subsidiary nor a branch of an existing firm (independent). Self-employment is another widely used measure for entrepreneurship, especially when studying its relationship with inequality (Atems & Shand, 2018;Bruton et al., 2021;Halvarsson et al., 2018;Lippmann et al., 2005). According to the US Internal Revenue Service (IRS) definition, 1 self-employment generally refers to those who 'carry on a trade or business as a sole proprietor or an independent contractor', 'a member of a partnership' or 'in business for ownself including a part-time business'.
While both new firm formation and self-employment are important segments in the US economy, their economic impacts are perceived to be different. As Audretsch et al. (2008, p. 126) point out, self-employment reflects the change of individual entrepreneurial behaviour but 'very little of this change is projected onto the larger industry, nation or global market'. Business start-ups, by contrast, have significant impacts on economic development in terms of job creation (Decker et al., 2014), market Entrepreneurship and income inequality in cities: differentiated impacts of new firm formation and self-employment efficiency (Kirzner, 1997) and innovation (Acs et al., 2013). Start-up entrepreneurs often bear high risk, instability and barriers to entry, but ultimately contribute significantly to the economy and society.

New firm formation and income inequality
Theoretically, new firm formation could impact income inequality in both positive and negative ways. On the one hand, new firm formation could increase income inequality through wealth concentration and accumulation. Financial resources are critical during the process of creating a new firm. These resources can be acquired, for example, from large-scale ventures, wealth inherited from parents and individual savings. Already affluent entrepreneurs, such as those who inherit wealth from family or born into an entrepreneurial family, can accumulate more wealth over time (Bhide, 2000). When the rich get richer, income inequality is exacerbated. Jones and Kim (2018) find that high-growth entrepreneurs account for a substantial share of the top 1% or 0.1% of income earners because of high financial returns to their risk-taking behaviour.
On the other hand, new firm creation may decrease income inequality, primarily due to its profound positive development impacts on the regional economy, known as entrepreneurial multiplier or spillover effects. Broader development impacts of new firm formation include inducing economic growth (Audretsch & Keilbach, 2004), which further leads to poverty reduction and improved living standards for the poorest (Roemer & Gugerty, 1997). The existing literature has shown that start-ups play a key role in creating new jobs and employment opportunities that may benefit low-and middle-income households (Audretsch et al., 2008;Haltiwanger et al., 2013). Typically, these job-creation effects by start-ups are geographically bounded to the regional labour market. Qian (2020) also reports the start-up rate as a significant predictor of intergenerational upward mobility in US metropolitan areas. In addition, when high-income employees choose to create or work for start-ups, the top income share is likely to shrink. This is based on the evidence that entrepreneurs' average initial income is lower and more uncertain than wage employees, and start-ups tend to pay less than large existing firms (Van Praag & Versloot, 2007). A higher share of start-ups, therefore, could 'crowd out' high-paying jobs that would have existed in incumbent firms. All these mechanisms imply a negative relationship between new firm formation and income inequality.
A very limited number of prior studies have empirically examined the relationship between new firm formation and income inequality. Using Global Entrepreneurship Monitor (GEM) data, Lecuna (2020) finds no significant relationship between the level of newly registered firms and the Gini coefficient at the country level. Using the same GEM data but a different sample of countries, Ragoubi and El Harbi (2018) suggest inequality is likely to induce new business creation. The impact of new firm formation on income inequality remains unclear. To our best efforts, we find no prior study that directly examines the impact of new firm creation on inequality at the city level.

Self-employment and income inequality
Similarly, a mix of mechanisms have been used to explain the relationship between self-employment and inequality. Self-employment could influence income disparities by affecting both the top and bottom income levels depending on the characteristics of self-employed individuals in an economy. For example, the high-income self-employed can influence the upper end of the earning distribution (Hamilton, 2000;Lee & Rodríguez-Pose, 2021). Some other studies suggest that self-employed entrepreneurs often have fewer financial resources and lower earnings than the average wage workers (Åstebro & Chen, 2014;Hamilton, 2000;Rupasingha & Goetz, 2013). Evans and Leighton (1989, p. 532) examine the self-selection process into self-employment using longitudinal data from the National Longitudinal Survey of Young Men and the Current Population Survey, and their results show that people 'who were receiving relatively low wages, who have changed jobs frequently, and who experienced relatively frequent or long spells of unemployment as wage workers' are more likely to shift to self-employment. Similarly, Hamilton (2000) investigates the earnings between self-employment and paid employment and finds that self-employed workers often earn less than wage and salary workers. In addition, Alvarez and Barney (2014) distinguish self-employment opportunities from the creation and discovery of opportunities and argue that self-employment generally does not generate employment opportunities for others and often has limited wealth-creation potential. Self-employment overall (except for a small number of entrepreneurial stars) remains in relatively low income and thus is likely to push down the income level at bottom of the distribution. On the opposite side, self-employment could be an alternative source of employment and income for those otherwise unemployed. Some studies point out that self-employment is a possible source of upward mobility for the disadvantaged groups (Bates, 1997;Fairlie & Robb, 2007). This type of entrepreneurs, whose motivation to start their own businesses is driven by the lack of opportunities in the labour market, could be categorized as necessity entrepreneurs (Lippmann et al., 2005). Necessity-based self-employment is likely to alleviate income disparities or poverty by helping population at the very bottom of the income distribution.
Due to the two opposite effects discussed above, the extent to which self-employment could affect income inequality is unclear. Halvarsson et al. (2018) find an inverse 'U'-shape relationship between income inequality and selfemployment in Sweden, suggesting that self-employment disproportionately affects the top and the bottom income distributions. Atems and Shand (2018) find that selfemployment is positively associated with income inequality at the US state level from 1989 to 2013. The paradox of the impact of self-employment on the economy is also pointed out by Lee and Rodríguez-Pose (2021) in the context of poverty reduction. They find that self-employed entrepreneurs in traded sectors contribute to income growth and poverty reduction, while others in non-traded sectors may saturate regional labour markets and cost jobs. Table 1 summarizes the potential mechanisms for the relationships between the two types of entrepreneurship and inequality. Empirically, the impact of entrepreneurship on inequality is understudied in the US context, especially at the city level. As the literature has suggested, entrepreneurship could impact the income level through both direct changes in entrepreneurs' income at the individual level, and through the multiplier or spillover effects to non-entrepreneurs in the regional labour market. The overall economic impacts of entrepreneurship on income inequality at the regional level is unclear. Thus, a comprehensive investigation on this relationship considering various entrepreneurship types and inequality measurements is needed. The following empirical analysis estimates the overall impacts of two types of entrepreneurship, that is, new firm formation and self-employment, on income inequality in US metropolitan regions over time.

Household income inequality in US metropolitan areas
This study measures household income inequality using the three commonly used indexes, including the Gini coefficient, Atkinson index and Theil index, following existing inequality studies (Atems & Shand, 2018;Frank, 2009;Halvarsson et al., 2018;Ragoubi & El Harbi, 2018). The Gini coefficient represents the relative dispersion of income across the entire income distribution of a population (Gini, 1936). Its value ranges from 0 (perfect equality) and 1 (complete inequality). The Gini coefficient is the most used measure of overall income inequality and wealth concentration. The Atkinson and Theil indices are used as additional measures for inequality as robustness tests. The Atkinson index is a welfare-based measure of inequality that represents society's aversion to inequalitythe willingness to forego certain income for a more equal distribution of income among people in a societywith the values bounded between 0 and 1 (Bellù & Liberati, 2006). The sensitivity of this index depends on a given coefficient parameter, indicating the degree of societal aversion to inequality. In this study, we consider both a low-aversion Atkinson index with a coefficient parameter of 2 and a high-aversion Atkinson index with a parameter of 0.5. Unlike the Atkinson index, the Theil index has an inequality aversion parameter of 1 and is an unbounded measure of inequality (Frank, 2009). For both indexes, a higher value indicates greater inequality.
Household income 2 data are collected based on the American Community Survey (ACS) one-year estimates from the Integrated Public Use Microdata Series (IPUMS) USA (Ruggles et al., 2019), which provides Table 1. Potential mechanisms explaining the relationship between entrepreneurship and inequality.
New firm formation Self-employment

Increase income inequality (+)
High financial returns to entrepreneurs' risk-taking behaviour (Jones & Kim, 2018) High returns to opportunity-driven selfemployment (Hamilton, 2000;Lee & Rodríguez-Pose, 2021) Limited financial capital and earnings lower than the average wage workers for low-ability selfemployed (Åstebro & Chen, 2014;Hamilton, 2000;Rupasingha & Goetz, 2013) Wealth accumulation and concentration among already wealthy start-up owners (Bhide, 2000) Limited employment and wealth creation capacity (Alvarez & Barney, 2014) Self-employed in non-traded sector may saturate existing markets and reduce income for some (Lee & Rodríguez-Pose, 2021) Decrease income inequality (-) Job creation across the income distribution (Audretsch et al., 2008;Haltiwanger et al., 2013) A possible source of upward mobility (Bates, 1997;Fairlie & Robb, 2007) A source of intergenerational upward mobility in cities (Qian, 2020) An alternative employment opportunity for the unemployed who have no income otherwise (Lippmann et al., 2005) Broader positive impact on inducing economic growth (Audretsch & Keilbach, 2004) that reduces poverty (Roemer & Gugerty, 1997) Lower initial income and uncertain wages for entrepreneurs and start-up employees who could have much higher wage income if working for incumbent firms (Van Praag & Versloot, 2007) Productive self-employed in traded sector has positive spillover effects in terms of income growth and poverty reduction (Lee & Rodríguez-Pose, 2021) Entrepreneurship and income inequality in cities: differentiated impacts of new firm formation and self-employment harmonized individual-level population samples from US Census microdata across time and space. It allows us to retrieve rich household samples within US regions and to study changes of regional income distribution over time. According to the census, the ACS is preferred over the Current Population Survey for regional analysis due to its large sample size (US Census Bureau, 2019). However, not all metropolitan areas are identified in the ACS IPUMS, and the MSA definition changes over time. Our panel dataset covers the 289 MSAs (in 2013 definition by the US Office of Management and Budget -OMB) with data provided by the IPUMS 3 from 2005 to 2015 with at least 250 sampled households within each metro area across the time span. Since household income reported in the ACS represents income earned during the previous calendar year, we forward the income variable to reflect current-year income. Household income data are converted to 2015 US dollars based on the consumer price index (CPI). 4 All inequality measures are calculated with household weights provided within the sample. Figure 1 shows the trends of change in cross-metro average inequality levels based on the four indexes. Clearly, income inequality was growing during 2005-15.

Entrepreneurship as new firm formation and self-employment
It has been challenging to reconcile appropriate data to evaluate entrepreneurship at the regional level (Storey, 1991). New firm formation and self-employment are chosen as the two proxies for entrepreneurship in this study not only because data are available at the regional level, but also because they are among the most used in regional entrepreneurship studies, as noted above. Firm birth data are retrieved from the Business Information Tracking Series (BITS) at the US Census Bureau. We focus only on new single-unit establishments to distinguish them from the groups of new establishments that are under common ownership or controlled by an existing enterprise like chain stores.
According to Figure 2, new firm formation (the number of new firms standardized by total employment) among our sample MSAs, on average, experienced an increase between 2005 and 2007. However, the Great Recession severely discouraged start-up activity between 2007 and 2009. Despite that new firm formation was slowly recovering after the economic downturn, it declined again from 2012 to 2013 and then remained almost flat until 2015. The decline in new firm formation likely results from factors such as slowing population and labour supply growth, growing monopoly power of large businesses, and business consolidation (Hathaway & Litan, 2014;Karahan et al., 2019). Considering the increasing income disparities during the same period, we expect a negative relationship between new firm formation and income inequality.
We measure self-employment using the non-farm proprietors (NFPs) employment data from the US Bureau of Economic Analysis (BEA) because it captures the full accounting of self-employment as noted in several existing studies (Rupasingha & Goetz, 2013;Stephens et al., 2013). According to the BEA (2017), NFP employment covers the number of sole proprietorships and general partners 5 based on place of residence. Rupasingha and Goetz (2013, p. 147) pointed out that 'NFPs are full-time or part-time owners of small businesses who organize and operate a business, take risks, and earn profits or incur losses'. Therefore, it is an appropriate measure for entrepreneurship from the perspective of self-employment.
As shown in Figure 2, self-employment (NFPs standardized by total employment) experienced an overall upward trend from 2005 to 2015 among MSAs in our sample, which is noticeably different from new firm formation. Debbage and Bowen (2018, p. 147) attribute this growing pattern to various factors such as 'the deindustrialization of the national economy and the shrinking workforce in manufacturing, the increased popularity of part-time self-employment, the decline in the number of farm proprietorships and the disruptive impact of scalable information technologies'. Different from new firm formation, self-employment does not seem to vary with business cycles. As Hipple (2010) explains, though negatively affected by economic recessions, self-employment may also rise during recessions because laid-off workers are forced to become self-employed. Because of their similar trends of change, we expect a positive relationship between self-employment and income inequality.

Baseline fixed effects analysis
To further examine how entrepreneurship impacts household income inequality at the metropolitan level, we employ regression analysis using space-time panel data. The baseline specification of the empirical model can be described as: 2005, . . . , 2014, 2015 where Inequality it is household income inequality measured by three different indexes in metro i at year t. Entrepreneurship, the primary explanatory variable, is measured by new firm formation or self-employment. We also include a series of control variables that may impact inequality in cities based on existing literature. D represents demographic factors including population size, gender and racial/ethnic composition. These variables are known to be among the predictors of inequality in cities (Florida & Mellander, 2016;Nord, 1980;Wilson, 1987). E contains a vector of economic factors including the unemployment rate, average firm size gross domestic product (GDP) per capita and cluster strength. Unemployment and GDP per capita are indicators of a city's economic conditions associated with income disparities (Brueckner & Lederman, 2018;Castells-Quintana & Royuela Mora, 2012;Mocan, 1999). Mueller et al. (2017) find that rising wage inequality is positively associated with increases in firm size. Cluster strength is measured by the percentage of employment in the clusters of traded sectors (i.e., sectors exporting products or services to customers outside the region). This is an indicator proposed by the Cluster Mapping Project. 6 K represents a vector of knowledge factors including human capital and innovation. Both are critical parts of the regional knowledge capital that could affect income inequality (Aghion et al., 2019;Jones & Kim, 2018). The regression model also controls for metropolitan fixed effects (i) and year fixed effects (t) to account for the impacts of time-invariant factors and economic cycles. 1 it is the error term. All variables are log transformed to control for the impact of outliers and report the results based on elasticity. All independent variables are lagged for one year to establish temporal precedence. We report robust standard errors to mitigate potential heteroscedasticity issues. The measurements, data sources and descriptive statistics of all variables are shown in Table 2. 7

Instrumental variables (IV) analysis
Despite the efforts to address endogeneity, the baseline regression estimation may not be sufficient to identify the causal relationship between entrepreneurship and inequality. A reverse causality is theoretically possible. For instance, if cities experience high levels of income inequality during an economic downturn, individuals at the low end of the income distribution may feel discouraged from engaging in entrepreneurial activity due to financial constraints (Aceytuno et al., 2020). Other studies suggest economic inequality could foster necessity-based entrepreneurial activity (  To mitigate these concerns, we construct an IV that is correlated with an area's entrepreneurship level but not associated with its income distribution. Specifically, for new firm formation, we calculate the predicted shifts of new firm formation at the national rate employing the Bartik shock approach, 8 also known as the shift-share   instrument. The concept was first introduced by Bartik (1991) to isolate local labour demand shocks by the predicted local employment growth based on the national employment growth rates across industries. This type of instrument has been widely used in the field of regional economics to: isolate sources of exogenous variation in local labor demand. … The idea is to isolate shifts in local labor demand that only come from national shocks in each sector of the economy, thereby purging potentially endogenous local demand shocks driving variation in employment or wages. (Ferreira & Baum-Snow, 2014, p. 52) The use of the Bartik shock as a valid instrument has been discussed by Goldsmith-Pinkham et al. (2020). Although the Bartik instrument is typically used for employment dynamics, conceptually it can well apply to firm dynamics: the growth of new firms in an industry at the national level represents an exogenous shock on new firm formation in the local industry. For self-employment, lack of industry-level data, we follow the IV approach by Lee and Rodríguez-Pose (2021) who study the impact of self-employment on poverty reduction in US metropolitan areas. We employ historical self-employment measured by the percentage of selfemployment in 1960, collected from IPUMS ACS, as the instrument for the present-day self-employment. This is built upon a growing body of literature on persistence of regional entrepreneurship, which shows that the historical level of self-employment in a region reflects its persistent cultural attitudes towards entrepreneurship and therefore can predict the level of self-employment today (Fritsch et al., 2019). Similar to the compromise made by Lee and Rodríguez-Pose (2021), we can only estimate cross-sectional IV regression models (using 2015 data) even though the baseline models are panel data regressions. We use the 1960 self-employment rate as an instrument for the 2015 Entrepreneurship and income inequality in cities: differentiated impacts of new firm formation and self-employment self-employment rate. Because the boundaries of metropolitan areas cannot fully match between 1960 and 2015, the IV cross-sectional models have a smaller set of metros in the sample (N ¼ 182). Table 3 reports the fixed-effect estimation results on the impact of new firm formation on the four measures of income inequality, controlling for relevant regional factors.

The impact of new firm formation on income inequality
As is evident, the coefficients of new firm formation are consistently negative for all four measures of inequality indexes and are highly significant at the 0.01 level for three of the four. This reveals that an increase in new firm formation is likely to decrease income inequality across metropolitan households over the study period. For the Gini index, the highly significant coefficient of 0.0259 indicates that a 10% increase in the new firm formation rate is associated with a 0.259% decrease in the Gini income index, when holding control variables constant. New firm formation is also a negative and significant predictor for the high-aversion Atkinson index and the Note: Robust standard errors are shown in parentheses. Significance levels: *p < 0.10; **p < 0.05; ***p < 0.01. As additional robustness tests we use the stepwise regression approach that different groups of control variables are incrementally introduced in alternative models of all four income inequality measures. For the results for these additional robustness tests, see Table A2 in Appendix A in the supplemental data online.

Shiqin Liu and Haifeng Qian
Theil index. For the low-aversion Atkinson index, despite that we still observe a negative coefficient of new firm formation, it is not statistically significant. These results are robust and consistent when control variables are introduced in a stepwise approach (see Table A2 in Appendix A in the supplemental data online). Overall, the results suggest that an increase in start-up activity is likely to decrease income inequality. Next, we discuss the results of control variables that are statistically significant at least at the 0.05 level. The share of the Black population is a positive and significant predictor of the low-aversion Atkinson index. This suggests that an increase in the Black population in a city is associated with an increase in income inequality over time. Unemployment works in a similar way: its significant, positive association with income inequality is only observed for low-aversion Atkinson. Average firm size exhibits an interesting pattern, positively associated with low-aversion Atkinson but negatively associated with other measures, though only the former relationship is statistically significant. The coefficients of GDP per capita are always positive and are significant at the 0.05 level for Gini and at the 0.10 level for high-aversion Atkinson. This echoes the past finding that economic development drives inequality (Brueckner & Lederman, 2018;Castells-Quintana & Royuela Mora, 2012). Innovation, measured by the patenting capacity in the city, shows a positive and significant relationship with all four inequality indexes. The knowledge economy, therefore, is a reliable predictor of increased income inequality, consistent with the literature (Lemieux, 2006;Moretti, 2012). Human capital is not significant at the 0.05 level, likely due to its high correlation with innovation (coefficient ¼ 0.65; see Table A1 in Appendix A in the supplemental data online). Table 4 shows the results of the relationship between new firm formation and income inequality based on IV estimates. The under-identification test is performed to determine whether the instrument is correlated with the endogenous regressor. This test reports the Lagrange multiplier (LM) statistic of 95.7 with p < 0.001 for the new firm formation baseline IV estimator. Based on that, we reject the null hypotheses that the equation is under-identified and that the instrument may not be relevant to the endogenous regressor. The weak identification test is used to examine whether the instrument is only weakly correlated with the endogenous regressor. The Stock-Yogo critical values are used to determine whether the instrument is performed weakly (Stock & Yogo, 2002). The result reports the Cragg-Donald F-statistic of 99.5 for the baseline model, which is higher than the reported critical value of 16.38 at the 10% level for the maximum acceptable bias. These results provide evidence that the instrument is relevant and not weak. Additionally, we introduce different groups of control variables in alternative model specifications as robustness tests. Based on the results of IV estimates, we find that the estimated coefficients of new firm formation are negatively associated with all inequality indexes. It is notable that this relationship is consistently significant at the 0.05 level in all alternative specifications, except for the low-aversion Atkinson index when the economic factors or all control variables are introduced in the model. This may suggest that the impact of new firm formation on inequality might be interacted with local economic conditions measured by unemployment, average firm size, GDP per capita and/or cluster strength. These results are consistent with those from the fixed-effects estimates. Table 5 reports the fixed-effect estimation results on the impact of self-employment on the four measures of income inequality, all control variables included (also see Table A2 in Appendix A in the supplemental data online for more results using stepwise approach). We find that the estimated coefficients of self-employment are consistently positive regardless of the measures of inequality, and it is highly significant at the 0.01 level when groups of control variables are introduced separately using the stepwise Table 4. Instrumental variables (IV) estimates: the impact of new firm formation on income inequality. Significance levels: *p < 0.10; **p < 0.05; ***p < 0.01.

The impact of self-employment on income inequality
process (see Table A2 online). When holding all control variables constant, the results are still highly significant at the 0.01 level for low-aversion Atkinson; the coefficient of 0.0256 means that, for every 10% increase in the selfemployment rate, the low-aversion Atkinson index will increase by 0.256%. For the Gini index, the coefficient for self-employment is significant at the 0.10 level.
These results all point out that higher self-employment likely contributes to higher household income inequality in US cities. For control variables, the results are largely similar to Table 3 when new firm formation is used as the proxy for entrepreneurship.
In Table 6 we report the IV estimates on the relationship between self-employment and income inequality, replicating the analysis from new firm formation in Table 4. Identification tests again suggest that the instrument for self-employment based on historical self-employment is relevant and not weak in the baseline model specification, with an LM statistic of 10.8 and p < 0.001, and F-statistic of 11.4. The IV estimation reports an overall positive relationship between self-employment and inequality, and it is significant at the 0.05 level for Gini, high-aversion Atkinson index and Theil index when holding demographic or knowledge factors constant. Different Note: Robust standard errors are shown in parentheses. Significance levels: *p < 0.10; **p < 0.05; ***p < 0.01. As additional robustness tests we use the stepwise regression approach that different groups of control variables are incrementally introduced in alternative models of all four income inequality measures. For the results for these additional robustness tests, see Table A2 in Appendix A in the supplemental data online.
1328 Shiqin Liu and Haifeng Qian from the fixed-effects estimation, we observe an insignificant relationship between self-employment and low-aversion Atkinson index. Another notable pattern is when economic factors are controlled for, the results become insignificant for all models.

Entrepreneurship and household income at different percentiles
To gain more insights on how new firm formation and self-employment impact household income inequality, we further conduct fixed-effects analysis on their impacts on household income at different percentiles (10th, 20th, 80th and 90th). The results of the entrepreneurship variables are shown in Table 7. The full results, including coefficients for control variables, are shown in Tables A3  and A4 in Appendix A in the supplemental data online.
For new firm formation, we have two interesting findings. First, new firm formation is a positive and significant predictor of household income at the 10th or 20th percentile when economic factors are not controlled for; when economic factors (or more specifically, unemployment) are included in the regression models, the impact of new firm formation is no longer significant at the 0.05 level. This implies that new firm formation creates jobs that benefit low-income families, leading to less income inequality. Second, at the high-income level, the impact of new firm formation also changes, and even more dramatically, after controlling for economic factors. New firm formation is positively and significantly associated with household income at the 80th or 90th percentile; after controlling for economic factors, however, this relationship becomes negative and significant. This implies another mechanismthe crowd-out effectby which new firm formation reduces economic inequality. Under the same economic conditions, more start-ups lower the income of high-income groups when they work for lower-paid start-up jobs than higher paid jobs they would otherwise take in incumbent firms. Both of these two mechanisms have been discussed in the literature review section.
Self-employment is negative and significant predictor of household income both at the top and the bottom of the income distribution, with or without control variables. The magnitude of the coefficients is greater at the 10th or 20th percentile than at the 80th or 90th percentile. The mechanism by which more self-employment leads to greater inequality, therefore, lies in the decreased income at the bottom of the income distribution. The literature has been clear that self-employed individuals often have fewer financial resources and lower earnings, and tend to have limited employment and wealth generation capacity (Alvarez & Barney, 2014;Åstebro & Chen, 2014;Borjas & Bronars, 1989;Lin et al., 2000). Our analysis shows that when there is an increase in self-employment in a city, its impact is likely to carry a higher weight at the bottom of the income distribution, thus increasing income disparities.

SUMMARY AND DISCUSSION
Entrepreneurship is widely recognized as a positive driving force in economic development, but the benefits could be accompanied by unintended consequences such as inequality. Income inequality may harm economic growth in the long run and have direct impacts on regional prosperity and quality of life (Castells-Quintana & Royuela Mora, 2012). In this article we examined the impacts of entrepreneurship on household income inequality across US metropolitan areas from 2005 to 2015 using both fixed-effects and IV estimators. We distinguished two types of entrepreneurshipnew firm formation and selfemploymentboth of which are recognized proxies for entrepreneurial activity in cities. We addressed the important notion made by Lee and Rodríguez-Pose (2021, p. 48) that 'research on the economic geography of entrepreneurship has often simply focused on the quantity rather than the type of new firm starts … economic development efforts should focus on the type of entrepreneurship rather than on its overall levels'.   Significance levels: *p < 0.10; **p < 0.05; ***p < 0.01. The household income from the Integrated Public Use Microdata Series (IPUMS) is top/bottom-coded, where income at the top or bottom 0.5th percentile of the income distribution within a given state is rounded to the nearest US$1000. Thus, we winsorize the data at the 10th and 90th percentiles to avoid this top/bottom-coded issue.
Our empirical results show that a city with a higher new firm formation rate tends to have lower income inequality within the city. This is likely due to the job creation effect of new firm formation towards low-income groups and to its crowd-out effect on well-paid jobs in incumbent firms towards high-income groups. By contrast, a higher self-employment rate tends to increase income disparities, mainly by lowering the income at the bottom of the income distribution. Though not entirely comparable, this latter finding is consistent with Atems and Shand (2018) at the US state level.
As an important policy implication, our analysis suggests that supporting new firm formation will help reduce income inequality in cities. New firm formation is good not only for job creation and productivity growth, as widely demonstrated in the literature, but also for equality, as revealed in this article. Therefore, it should be a key direction of efforts in economic development policy. Additionally, given the positive contribution of selfemployment to inequality identified in our analysis, an even more effective approach would be to reduce selfemployment and meanwhile increase new firm formation. This can be realized through financial, consulting, networking and other types of assistance that support the transition of self-employment working on own account into start-up firms with employees. This article has its limitations. First, it only examines selected metropolitan areas with sufficient household income data from ACS. Second, underreporting is a potential problem in national household survey, which could lead to overestimation of income dispersion (Mok et al., 2009). Also, the ACS income data are top-coded, where household income greater than the 99.5th percentile of the income distribution within a given state is rounded to the nearest US$1000. These are inherent problems with the data that we cannot address but should be aware of. Third, due to limited space, we focus only on the relationships between overall entrepreneurship levels and income distributions in cities. More nuanced accounts of entrepreneurship could shed light on more targeted economic development efforts. For instance, future research may break down start-ups by sector and examine their impacts on income at different percentiles. Such efforts would provide clearer guidance to policymakers on where entrepreneurship support should start and which household groups are more directly impacted.