From a Drunkard's Walk to a Pile of Drunks

This morning Paul wrote a very insightful post about job creation by new companies, trying to put things in a larger economic and mathematical context. (I am one of those (blessed? unfortunate?) people who thinks the game of baseball explains everything in life, including the economy, so it helps me to think of Paul's post in terms of the never-ending debate between sabermetricians and those who prefer a non-statistical view of baseball. In this view, Paul's post is the equivalent of putting a 5-hit game on Opening Day in a larger context of probability, rather than imbuing it with deeper meaning.)

I want to try to round out Paul's point by discussing the accumulating universe of firms over time (or, the accumulating pile of drunks in Paul's illustration). In an economy with a more or less steady influx of new firms and more or less consistent survival rates, we will have an accumulating number of firms as an economy moves through time. And, in any given year, "young" firms (5 years old and younger, including brand new startups) will constitute the largest percentage of the overall number of firms. By sheer arithmetic, then, shouldn't we expect that we will see a large number of new jobs from the largest cohort of firms? Maybe, maybe not.

Here is how it might work. Let's start with an economy with zero firms. In Year 1, we have 700,000 new businesses started (firms plus establishments; my thanks, by the way, to Mike Horrell for research assistance). Using survival rates calculated from the Business Dynamics Statistics database, we know that the average survival line for firms founded each year since 1977 looks like this:

So twenty percent of new firms survive to age one, two-thirds to age two, and so on to age 5. For age 6 and up, Mike used imputed survival lines extrapolated out from age 5. The real-world will be lumpier, but from what research I've seen from the SBA and others, the survival line post-age 5 is mostly a smooth downward slope. At some point, it likely becomes a near-asymptote, although some organizational research does suggest that survival for several decades, say to age 40 and beyond, is quite rare--conceivably, all firms die at some point.

Using these survival rates we can construct a chart showing the birth, death, and survival of firms as an economy moves forward from Year 1. In the first year, there are the 700,000 new firms. In Year 2, the initial batch of startups now consists of 552,440 firms, joined by the second year's round of incoming startups, another 700,000. So there are now 1,252,440 firms in this economy. If we continue this process out to, say, year 25, the process looks something like this:

 By year 10, firms ages 5 and younger account for nearly two-thirds of all firms. By the end of the series, in year 25, firms ages 5 and younger account for one-third of all firms. With assumed constancy of startups and survival rates, the absolute number of firms younger than age 5 remains the same but constitutes a decreasing proportion of the entire universe of firms. It remains true, however, that in any given year, young firms make up the largest cohort of companies. This would be reinforced if we added a constraint that no firm survives past, say, age 20. The point is that if the level of firm formation is steady (which it has been in the United States), and if survival rates for new firms have been consistent (ditto), than this is what an economy's population of firms would look like over 25 years.

What does this mean for job creation? It means we should expect the largest number of new jobs from the largest cohort of firms. I don't think is purely a function of the numbers, however--data from economists at the Census Bureau indicate that young firms add, on average, 3.7 (net) jobs per year. Firms ages 6 to 28, meanwhile, add (net) about one job per year. The oldest firms (age 29 plus) add nearly two and a half (net) jobs per year--still fewer than young firms. So it's true that young firms are adding one to two more (net) jobs per year than older firms, but this might be where Paul's drunkard's walk comes in.

So if young firms add 4 jobs per year, that means they add, in net terms, about eight million per year. In year 25, for the other 5 million firms in the economy, they will add about five million jobs; in year 10, they will add four million. (Note that in year 25 we haven't yet reached a point with any 29-year-old plus companies.) Many of those older firms will of course be larger than young companies, but we're talking about their net incremental contribution to American employment. 

None of this changes the fact that young firms account for most net job creation in the United States over time. What I'm wondering about is the why of this. Is it a subjective or normative comparison: young firms are "better" than all other companies? Or is it (partly) a function of mathematics and probability? What, if anything, does this mean for policy? It's never a bad thing when commentators and policymakers begin to realize the importance of new and young companies and stop seeing the economy solely in terms of our behemoth firms, but it's not clear what policies fall out of this if what we're talking about is a natural accumulation of firms and the ensuing natural distribution of net job creation. There is still plenty of dynamism to be worked in here--job creation, job destruction, the outstanding growth of certain companies--but this is (I think) an important point to make. 

It parallels something else I've been working on with regard to high-growth or top-performing firms. When we say that young firms create X% of jobs, or high-growth firms account for X% of job creation, should we be surprised that reality looks this way? Or, should we be more surprised if the economy did not look like this? In the case of high-growth firms, the question is: are we surprised that we find something resembling a Pareto distribution? Don't get me wrong--this does not belittle the importance of new and young firms and what they contribute in terms of jobs and innovations. Far from it. But it is important to keep things in perspective, mathematical and economic. Kind of like an Opening Day performance.

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The tax problems facing young business today should be factored in to your formula with respect to their survival rate and job growth potential, don't you think?

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