The mortality of companies

Abstract

The firm is a fundamental economic unit of contemporary human societies. Studies on the general quantitative and statistical character of firms have produced mixed results regarding their lifespans and mortality. We examine a comprehensive database of more than 25 000 publicly traded North American companies, from 1950 to 2009, to derive the statistics of firm lifespans. Based on detailed survival analysis, we show that the mortality of publicly traded companies manifests an approximately constant hazard rate over long periods of observation. This regularity indicates that mortality rates are independent of a company's age. We show that the typical half-life of a publicly traded company is about a decade, regardless of business sector. Our results shed new light on the dynamics of births and deaths of publicly traded companies and identify some of the necessary ingredients of a general theory of firms.

Keywords: firm longevity; mergers and acquisitions; stock markets; survival analysis.

Figure 1.

Number of firm births and deaths in each year. We observe that the number of firms entering (births, circles) and exiting (deaths, triangles) North American stock markets varies significantly over time, reflecting in part economic cycles. Note that before 1975 very few firms die, reflecting a survival bias in the Compustat dataset. Similarly, there are two spikes in births in 1960 and in 1974 that may be reflective of changes in the Compustat database or the conditions of market entry, not in the patterns we seek to analyse. We limited much of our analysis to the period after 1975 to control for this bias.

Figure 2.

Frequency distribution of firm lifespans. The frequency distribution of firm lifespans is approximately exponential, independent of business sector. Colours denote firms from different economic sectors (a) and with different reasons of death (b) for the period 1950–2009. Insets show the lifespan frequency distributions before normalization by sector size. In (b), the reasons ‘other’ and privatization were omitted; in (a), the telecommunications, utilities and transportation sectors were omitted based on small sample size. The aggregate distributions are fit by a simple exponential function shown in (c). For the full window, the fit is N(t, T) = 2226e^−λt with λ = 0.098 and 95% confidence interval . For the constrained window, the fit is N(t, T) = 2279e^−λt with λ = 0.131 and 95% confidence interval .

Figure 3.

Exponential fit to firm mortality. An exponential mortality curve (dashed line), with appropriate boundary conditions, is fit to sets of firms that are born and die within an observation window, T (solid line). The exponential curve is a good fit across observation windows from a few years to several decades. The half-life estimated from each curve increases with T as shown in the inset. Its limiting value for large observation windows, T → ∞, is approximately 7.02 years.

Figure 4.

Non-parametric estimators of firm mortality versus lifespan. The mortality function M(t) = 1 − S(t) obtained from both the Kaplan–Meier and Nelson–Aalen non-parametric estimators for the full and restricted (inset) datasets is well fit by an exponential curve with constant hazard rate. Note however that the curves obtained via both non-parametric estimators deviate from the maximum-likelihood estimate for λ, especially for long lifespans.