Size filters

To implement size filters, we first take a look at the distribution of a large number of transactions in private equity markets. Below are the histograms of raw observed prices in USD $ millions and the log-transformed prices. We can observe that both the distributions are truncated at the left due to prices being strictly positive. Also, the raw prices resemble an exponentially decaying distribution, whereas log-transformed prices resemble somewhat of a normal distribution. 

^{Histogram of transaction prices in private markets}

To understand whether the distribution in estimated shadow prices is drastically different, we replicate such plots with all the priced companies, dropping outliers at the top and bottom 1 percentile. Note that these are estimated shadow prices in the universe of private companies put together in the privateMetrics® database, where the estimation is based on factor prices that sufficiently explain the variation in transactions projected onto the financials of the companies in the privateMetrics® database. The plots reflect a similar distribution. However, the log scale shows a bimodal distribution, which is unsurprising given the variation in priced companies across countries. The notable takeaway from this exercise is that there exists a large proportion of priced companies in the privateMetrics® database that are smaller than the typically observed/modeled transaction in PE markets, i.e., the mass of firms below 0 in the log scale. Thus, any size treatment should ensure that these “small” companies are excluded.

^{Histogram of estimated shadow prices}

To achieve that, we filter out the prices in the shadow universe based on the distribution characteristics of transaction prices. Specifically, using the mean and standard deviation of the log of transacted prices, we compute the range to be within μ ± 2.58σ, which roughly spans 99.5% of transactions. In terms of raw prices, these filters result in excluding private companies with prices approximately below USD 2 million and above USD 14 billion.