Theories on firm mortality


The mortality of companies


Investigating the exponential age distribution of firms


The mortality of companies

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.)

A. Public companies and lifespan

Publicly traded companies are among the most important economic units of contemporary human societies. (Alchian 1972Coase 1988Hannan and Carroll 1992, 2000Jovanovic 2001


<- As of 2011, the total market capitalization of firms in the New York Stock Exchange was 14.24 trillion dollars, comparable to the entire gross domestic product of the USA.

While researchers have devoted considerable attention to the distribution of firm size (Simon and Bonini 1958; Stanley, Amaral, Buldyrev, Maass, Leschhorn, Salinger and Havlin 1996, 1997a, 1997b; Axtell 2001), the distribution of firm lifespan has been the subject of far fewer studies (Coad 2010). Thus, despite the availability of much quantitative information, our understanding of the way public companies live and die remains limited.

B. Datasets, Definitions, and Survival biases

Arguments addressing the statistics of company lifespans hinge on the interpretation of the meaning of the death event for a company. In this paper, definitions of ‘birth’ and ‘death’ are based on the sales reports available in the Compustat database. 

-> firms may ‘die’ through a variety of processes: they may split, merge or liquidate as economic and technological conditions change.

i) Datasets

Data on publicly traded companies were obtained from the Compustat North America and Compustat Historical databases,  covering the period of 1950–2009 and contain most financial information for North American and overseas American Depositary Receipt firms reported in their income statements and balance sheets, filed to the US Securities and Exchange Commission. A total of 28 853 publicly traded companies are included in the database. From these, we excluded 2292 that did not report any sales over the 60-year timespan. We also noted that 6868 companies were listed (alive) either in 1950 or in 2009, with 160 of those companies reporting sales for the full 60-year span of the dataset.

ii) Definitions

We define ‘birth’ to occur not at a company’s founding, but rather when it first reports sales in the Compustat database. We take ‘death’ to occur in the year when a company stops reporting sales. For each company, we define lifespan to be the total number of years for which the company reports non-zero sales.

<- There are a number of companies that fail to report for several years between years of activity. Such cases of re-entry are not counted as additional new births or deaths; the additional years are simply added to the total lifespan.

-> This definition is similar to the Bureau of Labor Statistics Business Employment Dynamics measures of entries, which include mergers, takeovers and industrial reclassification

-> This broad definition of death will affect the conclusions we can draw from our data, as an instance of firm death does not necessarily connote failure (Carroll & Delacroix 1982).

* As a metric of mortality that is closely related to lifespan, we use the term half-life, defined as the time it takes for half of the firms in a given cohort to die (following the above definition of death).

* For survival analysis, this half-life corresponds to the age t by which the cumulative mortality fraction M(t) = 0.5 (50%).

iii. Survival biases and subsampling

The historical data on Compustat database do have problems of survival bias (Ball & Watts 1979): almost no firms die in the first 20 years of the dataset. To account for the effects of this bias, we ran our analysis both on the entire dataset and on a set limited to firms reporting sales between 1975 and 2009. A comparison between analysis of the entire sample and this reduced set suggests that the effect of survival bias is limited. This is likely because the first 20 years comprise a very small proportion of the entire dataset.


C. Theory of the firm

There is a great diversity of perspectives on a theory of the firm, focusing on different aspects of their costs, organization and evolution. 

Economists such as Coase [1988, 1937, 1960] and Williamson [1991; 1985] proposed that firms exist in order to minimize (positive) market transaction costs involved in the production of goods and services. In situations when there is particular specificity of goods and services exchanged between two economic agents, such transactions may be best organized internally to an organization rather than negotiated in the open market (Alchian 1972, Williamson 1985 ).

-> As such, firms may split, merge or liquidate in response to economic agents evolving new and better ways of dealing with the various costs and revenues of production and exchange (Arrow 1969; Grossman and Hart 1986; Hart and Moore 1990; Tadelis 2002). 

-> Therefore, at least on the average, the merger of existing companies should be approximately neutral in terms of the balance between costs and benefits. ??

(However, this relatively simple picture becomes more complex in the light of behavioural studies of the impact of decision-making and management practices on the growth and viability of actual firms.)

D. Organizational ecology

In the framework of organizational ecology, companies are seen as units of selection in markets and their longevity is the result of their successes of learning and adaptation in these environments (McPherson 1981, 1983).

Organizational ecology has often suggested that the mortality rates of firms are age-dependent (Hannan and Carroll 2000).

liability of newness (Stinchcombe 1965): young establishments experience higher mortality rates, supported by observation of US manufacturing plants (Dunne, Roberts and Samuelson 1989), Argentinian and Irish newspaper companies and other types of businesses (Carroll & Delacroix 1982).

<- Theoretical grounding draws from the adaptive requirements of market entry; it takes time for young companies to gain the competencies and build relationships that will ensure their ability to survive (Hannan 1998; Freeman, Carroll and Hannan 1983). + New companies are likely to be smaller and less experienced and thus more susceptible to market shocks (Hannan 1998). Knott & Posen [2005] stress the evolutionary character of these arguments by suggesting that liability of newness is evidence for market-based selection.

However, liability of adolescence is also seen. In a study of West German business enterprises, Bruderl & Schussler [1990] find that companies are, in fact, protected from mortality in the immediate period after founding.

<- This liability of adolescence likely results from the buffer a firm acquires via its capital endowment at birth [Hannan 1998], which is also a characteristic of firms that have recently entered financial markets. <- As their initial capital stock is expended, less profitable companies become more vulnerable to environmental changes in market conditions.

And liability of senescence or obsolescence: mortality rates increase as companies age.
1) liability of senescence: as companies age, they accumulate rules and stagnating relationships with consumers and input markets that render them less agile and that re-configuration is increasingly expensive (Henderson & Clark 1990);
2) liability of obsolescence: environmental requirements change over time and that, although firms may improve in competence and efficiency with age by becoming more specialized, these specific adaptations also increase the companies’ risk to new kinds of external shocks that will inevitably beset them.

** Coad [2010a] has argued that these assorted liabilities constitute small deviations, at the tails, from an aggregate lifespan distribution that is generally well approximated by an exponential distribution. <- This proposition has been confirmed in Italian, Spanish and French firms (Navaretti, Castellani & Pieri 2014

<<- the statistical patterns of firm entry and exit will affect the distribution of firm sizes in any given year and set its form and temporal stability (Coad 2010bAmaral et al. 1997a).  <<- thus a better understanding of the mortality risk of firms is necessary to generate new insights on the empirically observed scaling regularities in firm size frequency distributions??? (Amaral et al. 1996; Axtell 2001)

(the existing literature on firm survival has often focused on tracking small samples of firms in specific industries. )


We confirm the hypothesis of an approximately constant mortality rate, finding that the exponential distribution of firm lifespans holds across business sectors and causes of mortality. We apply survival analysis to estimate in a variety of ways that the firms in our dataset have a half-life of approximately 10 years, regardless of age.





A. 新しさの不利益(liability of newness):古い企業に比べて、若い組織は、多様な困難に遭遇することにより、消滅率が高い。

Stinchcombe 1965 によれば、理論的に四つの事由に起因する:1)教え込む前任者がいない;2)有効かつ能率的な役割やルーチンを構築精錬するには時間を要する;3)成員間信頼を構築する時間;4)他の組織との安定した関係がいない

Freeman, Carroll and Hannan 1983の実証が裏つける:1800-1980における476のアメリカの労働組合、1800-19807大都市の地方新聞社2768社、1951-1979アメリカ半導体産業企業1159社 → 組織の年齢が若いほど、消滅率が有意に高かった。

Carroll 1983 は組織の消滅率を扱った52の先行研究のデータを分析した結果、46において年齢との負の関係を示していた。


Carroll & Delacroix 1982Swaminathan 1996: 1800-1900アルゼンチンの新聞社

Singh, Tucker, House 1986:1970-1982トロントのボランタリーソーシャルサービス

Amburgey, Kelly, and Barnett 1993: 1771-1963フィンランドの新聞社

Halliday, Powell,, and Granfors 1987: 1870-1920アメリカの州立法律事務所

B. 若年期の不利益(liability of adolescence):組織の創成期には消滅率は低く、年齢をたるに従い徐々に上昇し、再び下降する

Bruderl and Schussler 1990: 1980-1989西ドイツの企業

Mahood 2000: 1976-1986アメリカの中小企業

Kale and David 1998: 1985-1994アメリカの建設業界

基本負の関係が予期されるため、新しさの不利益を否定するではない、初期に一時的に消滅率が低い状態が発生する論拠、組織の創成期において保有されている資源に求める(組織が有する創業時の財務的資本や人的資源が有意に消滅率を下げる (Bruderl, Preisendorfer, and Ziegler 1992))(外部組織との関係の欠如やルーチンや役割の構築の費用という生存に対する負の影響を緩和する (Fichman and Levinthal 1991))。→ しかしその資源が枯渇する

C. 加齢の不利益(liability of aging):新しい組織ほど生存に有利、年齢と消滅率が正の関係

-> 新しさの不利益は年齢とともに変化する組織の規模をコントロールしないという統計処理の不備により生じた小ささの不利益(liablility of smallness)(Barron, West, and Hannan 1994)

Barron et al. 1994: 1914-1990ニューヨークの信用組合、時間依存変数として各年の総資産額を採用するとこにより、年齢と消滅率の正の関係を実証

Ranger-Moore 1997: 1813-1985ニューヨークの生命保険会社、年齢とともに変化する総資産額を規模の変数としてコントロールした

Barnett 1997; Barnett and Amburgey 1990: 1877-1933ペンシルブァニア州の電話会社

Baum and Mezias 1992: マンハッタンのホテル

Carroll and Swaminathan 1992: 1975-1990アメリカの醸造業者

i) 時代後れの不利益(liability of obsolescence)

環境の変化により、組織の有する能力が環境の求める能力と一致しないこと <- 組織には経路依存性があるため、創成期の環境に適合した組織能力を一度獲得すると、以後引き続いて、新しい環境に対応するように自身の能力を変化させることが困難である (Hannan and Freeman 1984)

ii) 老年の不利益(liability of senescence)(Carroll and Hannan, 2000)

組織の加齢に伴い増加する、組織内の様々な規則、ルーチン、組織構造の堆積により不利益 <- 規則やルーチンは一過性ではなく耐性を持つもの、古いの上に新しいものが積み重なる。その結果、複雑に絡み合った規則、ルーチン、組織構造は組織有効性や能率性を阻害し、安定した環境であろうとも、変化の激しい環境であろうとも、組織に対して費用を発生させる (Barron et al. 1994)

D. ABCの矛盾

Barron et al. 1994の規模コントロール説 <- しても、依然として、新しさと若年期を示している研究が存在


Hannan et al. 1998 先行研究において年齢と規模は過度に単純な変数として扱われており、該当個体群への参入方法と個体の規模の分布を考慮していない <- (その解釈は先行研究の結果を必ずしも十分に説明していない)

** 年齢は、正と負の両者の影響も代替している

<- Thornhill and Amit 2003 はカナダの倒産した企業について調査、古い企業は環境の変化による知識の陳腐化が原因、新しい企業は経営上の知識や財務管理能力の欠如が原因


つながり+知識 -> 新しさの不利益 

他の組織との安定した関係は、資源獲得において有利に動き (Pfeffer and Salancik 1978) + 役割やルーチンは組織の問題解決能力のストックとして、組織能力を形成する (Nelson and Winter 1982)

摩擦 -> 老年の不利益

liability of senescence (Barron et al. 1994; Inkson, Pugh, and Hickson 1970)


資源賦存量 -> 創成期の不利益を緩和 

(Fichman and Levinthal 1991)

環境変化 -> 時代後れの不利益

liability of obsolescence

** 加齢の不利益を示している研究対象は、すべて、多額の資本を必要とする業種(銀行、保険、て電話会社、ホテル)/ 新しさの不利益を示しているは設立に際し、比較的大規模な資本を必要としない組織

前者は慎重である、生存を担保するの知識とつながりを出来るだけ入手しようとする -> 十分なを確保できなかったは、設立を思いとどまる可能性高い -> 新しさの不利益を蒙ることが結果的に少ない、主に摩擦の影響のみが作用している

E. 実証の方向




Investigating the Exponential Age Distribution of Firms

The age distribution to be an interesting feature of industrial structure. The age distribution may be of direct interest in theoretical models of the firm size distribution, as well as providing indirect information on a number of phenomena such as entry rates, survival rates, and possibly even the age of technology used in production.

However age distribution of a population of firms has barely been investigated in empirical work (only Coad and Tamvada 2008 focus on census data covering around 700’000 small scale firms in India & Segarra et al. 2008)focus on a sample of about 85’000 firms taken from the Spanish Mercantile Register).


Figure 2 shows that, even in a sample of small businesses, these firms have very different ages. Most firms are relatively young, but some are extremely old.

The shape of the distribution appears to follow an approximately straight line with negative slope over most of the support. Given that the y-axis is expressed in logarithms, this straight line of negative slope suggests that an exponential distribution would be a valid approximation of the empirical age distribution.

In later sections of the paper, however, we focused on situations in which the exponential gave only an imperfect representation. In contrast to the exponential benchmark, we observed that young establishments seem to be especially numerous, the oldest firms seem to be exceptionally long-lived, and at the disaggregated level of certain specific sectors we can observe a particularly irregular age structure

<- i) Concerning the large number of young establishments, it could be that this excess weight in the age distribution corresponds to over-entry by inefficient establishments who exit shortly afterwards (the case of ‘hopeful monsters’); excess entrepreneurship undertaken by overoptimistic entrepreneurs. (Santarelli and Vivarelli 2007) ->> To the extent that departures from the exponential benchmark among young establishments represent over-entry, then the exponential age distribution could be used to gauge the magnitude of this phenomenon.

<- ii) Departures from the exponential benchmark in the case of the oldest firms also have a ready economic explanation, in that certain long-lived firms, and especially family firms, do not pursue economic rationality in the sense of maximization of expected profits, but instead they may seek to maximize their chances of survival (e.g. by pursuing risk-averse strategies).

<- iii) the exponential distribution may not always be a valid heuristic at the disaggregated level of individual sectors, e.g. the international airline industry. In contrast to the smooth shape observed at the aggregate level, the age distribution of this particular sector is much messier and displayed conspicuous multimodality.

** The exponential is still a useful benchmark for understanding the age structure of industries. For example, we suggest that theoretical models of firm entry, exit, and industry evolution would do well to generate an exponential age distribution as part of their output, even though the empirical data is not exactly exponentially distributed.

(other candidate distributions such as the Pareto, or intermediate cases (between the exponential and the Pareto) could also be fruitfully investigated.)



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s