In yesterday’s post, I reacted to Paul Graham’s much talked about essay on inequality by suggesting that the premise — entrepreneurship causes inequality — is far from obvious. Indeed, I conjectured that if things were working as they should, entrepreneurship would tend to decrease inequality.

My argument was based on where the entrepreneur started in the income distribution, where they ended, what their innovation did to the incomes of others and what they ended up doing with the wealth they accrued. Suffice it to say, that’s alot of moving parts and I will admit that it was hard to see how it fit together.

It turns out that recently some economists have tackled this issue head-on and I want to review that work here today. But before I do, in the management literature, researchers have found a positive correlation between inequality and entrepreneurship. For instance, Jesper Sorensen and Olav Sorenson found that new firm starts in Denmark were associated with an increase in wage dispersion (a measure of inequality). However, this differs from what I had in mind in two respects. First, I believe there is a fundamental difference between ‘growth’ entrepreneurship that is associated with start-ups that intend to grow and other entrepreneurship that is associated with the launch of new business establishments. Research has borne out a clear distinction; for example, if you define entrepreneurship widely, the entrepreneurial centre of the US is Montana whereas if you focus on growth entrepreneurship it is Silicon Valley. Second, wage dispersion is, in my reading of the Piketty et al literature, really not the main part of the story — broader measures of income and wealth distribution are what is driving the debate. This is not to say wage dispersion is unimportant but that the whole story needs that broader perspective.

My post yesterday predicted that Silicon Valley would have a lower income distribution than the rest of the US. Well, between 2005 and 2009, that simple prediction is mixed. According to the US census data, the San Francisco-Oakland-Fremont area has a Gini index of 0.473 while San Jose-Sunnyvale-Santa Clara has a coefficient of 0.448. The US has a Gini index of 0.467 over that period. This tells us little though. There are other drivers of income inequality than innovation so just looking at raw numbers at a window of time is a limited perspective.

What happens when a broader analysis is conducted? Two recent papers do this and present conflicting outcomes. Both papers focus not on measures of overall inequality (like Gini coefficients) but instead on inequality in top incomes; that is, changes in the share of income going to the 1 percent or 0.1 percent. Nonetheless, as Paul Graham himself is in the latter, I think that is a good starting place to look for evidence.

The first paper is by Philippe Aghion, Ufuk Akcigit, Antonin Bergeaud, Richard Blundell and David Hemous. They examine the relationship between innovation (not simply entrepreneurship) and top income inequality across different US states. Their theoretical framework is based on Schumpeter’s theory of creative destruction. This is the theory of innovation whereby incumbents and entrants compete to innovate where the incumbent has different motives from entrants as they seek to protect what they already have whereas entrants are not encumberecd by such concerns. In their model, innovation by either type of firm increases top income inequality but innovation by entrants comes with another effect — an increase in social mobility. If incumbents have entry barriers, however, the impact of entrant innovation on top income shares and social mobility is reduced. Their empirical analysis bears out these predictions. States with higher quality-adjusted patents tend to have higher top income shares but also higher social mobility. They also argue this relationship is causal with an increase in patents per capita explaining 17 percent of the total increase in top 1% income share between 1975 and 2010. In states where there appear to be entry barriers (specifically politically driven entry barriers) this correlation is weaker. Interestingly, if they look at broader measures of inequality such as the Gini coefficient, the positive correlation either falls to insignificance or becomes negative.

The second paper comes from Chad Jones and Jihee Kim. They too take a Schumpeterian perspective and, in particular, focus on a view of entrepreneurship whereby entrepreneurs expend effort and if they succeed earn growing income for a while until someone new comes along and displaces them. Like Aghion et al, destruction plays a critical role in their framework. Put simply, innovation by entrepreneurs has the effect of increasing their income but also decreasing or, indeed, removing, the income earned by successful entrepreneurs of the past. Thus, at a broad level, a higher rate of entrepreneurial activity could increase or decrease inequality.

Jones and Kim don’t stop there and, indeed, sharpen their prediction. They do so by, figuratively, adding Paul Graham into the model. Yes, seriously, he is added as a dude named Phi. Phi is something that makes it more productive for entrepreneurs to innovate. That sounds to me precisely how Graham sees himself. And from this there is good news and bad news. The good news is that if Phi is doing their job better, income per capita rises. The bad news is that the growth rate in income per capita also eventually is lower compared to the situation where Phi was not doing their job. Moreover, just as Graham suspected of himself, income inequality is higher. If Graham sees himself as part of the problem, he is at the same time not part of the solution.

Why does this happen? Growth is driven by the number of people who choose to become entrepreneurs and look for new ideas. So Phi makes it easier for them to grow their profits and so makes it more lucrative to be an entrepreneur. But for our would be entrepreneurs this isn’t all. A higher Phi boosts the reward from being successful but at the same time reduces the probability that any given would be entrepreneur is successful. If would-be entrepreneurs are risk-averse, riskier prospects drive them away and it turns out that effect dominates. The end result is that growth and inequality are negatively correlated.

That theory could raise lots of objections. Are entrepreneurs risk-neutral or loving? Is it really the case that Paul Graham is reducing the pool of would-be entrepreneurs? I don’t know at the micro level but Jones and Kim take their data to the macro level and find that it matches their theory. Between 1980 and 2007 they find that Phi did more of its job and at the same time, the US growth rate fell while inequality rose. This, of course, excludes the main period of impact of Y-combinator so Graham is not in the data even if he is in the model.

What to make of this? I am not sure. Both models emphasize something that is important: that innovation by new entrepreneurs, if it results in creative destruction (which is not a given if incumbents tend to acquire entrants), can lead to displacement in the Top 1% rather than an increase in its share per se. But each story focusses on the pool of talent becoming entrepreneurs and appear to neglect the role of capital in this process. What happens to capital is surely critical in the top incomes story. More work surely has to be done yet. But hopefully this convinces you that the relationship between entrepreneurship and inequality is not as simple as many have thought.