Michael Ewens

Yesterday I posted a graph of the implied distribution of returns as an entrepreneurial firm increases its capital stock.  Today I present one important piece of that picture: the probabilities of return “regimes.”  First, the mixture model with mixing probabilities as a function of capital stock results in the following set of returns pdfs.

It is clear from the figure that the return regimes separate nicely into the outcomes “high,” “medium” and “low.”  Venture capitalists like to call the outcomes in their portfolios “home runs,” “singles” or “strikeouts” and they typically set goals for proportions of each in their portfolio.  The mean log returns and volatilities for each regime show extreme separation between the two tails.

Distribution of Returns by Regime

Regime			Probability
Home run	231%	123%	20%
Break-even	-1%	80%	60%
Bankruptcy	-273%	137%	20%
Full Model	-9%	112%	N/A

Includes all returns observations.  Estimated with sample selection and endogeneity corrections.

The mixing probabilities are a function of lagged capital stock, so I can plot the probability of each outcome for a range of dollars invested.  Figure 2 below shows that the bankruptcy risk is constant across capital stock while the probability of a home-run is highest for small firms.  Similarly, as firms raise more capital (and thus avoid bankruptcy) the most likely outcome becomes the “break-even” state with a 0% return.

Tomorrow I will discuss the motivation — theoretical and statistical — for the mixture model and parameterization of the mixing probabilities.

For our paper on apartment rental discrimination, I maintain a database of apartment rents across 30 US cities for 1 bedrooms or studios.  Once it is in mysql (easy), I can access it with PHP and send the data to a javascript file to make simple interactive graphs.

Average 1 Bedroom and Studio Rents in Major Cities (x-axis is week number since Feb 15th)

Here is how it was done:

1. PHP script to look through city names (I assume the database exists)

2. SQL statement:

SELECT WEEKOFYEAR( DATE ) AS woy, AVG( rent ) , COUNT( * ) FROM city_counts WHERE city = CITYNAME GROUP BY woy

3. For each city create a simple javascript-friendly string in PHP that looks like this:

{"LA": { label: "LA", data: [[8,1194.9206349206],[9,1261.7650969529]]},

4. Put it all together with Flot (this example) + jQuery.

I know very little (if any) Javascript, but got this up in 15 minutes.