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Determinants of Small firm survival and growth

Abstract and Keywords

Many excellent surveys of the literature on business growth and survival have appeared in the last decade. This article focuses on small firm literature on survival and growth, drawing on largely non-size-specific surveys only when the intersection between their subject matter and that of small firm growth and survival is significant. The focus is moreover primarily on testable or tested theories, implying a neglect of theory, however intrinsically interesting, which offers no (immediately) testable or tested implications. It is important to note at the outset that the industrial economics literature in general has a rather disparate definition of the term ‘small firm’ from the small business literature as located in the small business journals.

Keywords: business growth, business survival, small firms, tested theories, industrial economics, business journals

7.1 Introduction

Several excellent surveys of the literature on business growth and survival have appeared in the last decade. These include Caves (1998) who surveys over 80 theoretical and empirical papers relating to the turnover and mobility of firms (both small and large); Sutton (1997), who summarizes the results of a number of papers on Gibrat's Law of proportionate firm growth and its relationship to industrial concentration; and Geroski (1995), who identifies a number of ‘stylized facts’ and ‘results’ in the area of industrial entry. A text by Storey (1994) also summarizes the research on (very) small firms’ survival and growth (among other things) until about 1993. In this chapter we shall however focus on the small firm literature on survival and growth, drawing on these largely non-size-specific surveys only when the intersection between their subject matter and that of small firm growth and survival is significant. Our focus (mainly for reasons of space) is moreover primarily on testable or tested theories, implying a neglect of theory, however intrinsically interesting, which offers no (immediately) testable or tested implications.

It is important to note at the outset that the industrial economics literature in general has a rather disparate definition of the term ‘small firm’ from the small (p. 162) business literature as located in the small business journals. This definition ranges from Hall (1987) who uses quoted companies in her analysis of growth and survival and defines small in terms of sub-median employment size in the US quoted sector in which the median firm has 2,300 employees, down to Cressy (1996b) whose start-up sample from the UK has a mean employment size of 1.5 full-time employees (with about the same number of part-timers) and whose typical firm is much more likely to be unincorporated rather than simply unquoted.

7.2 Definitions

Small firm

There are many definitions of a small firm, but most rely on the numbers of employees of the firm falling below a certain threshold (Bank of England, 2003), sometimes combining this threshold with one on sales (Berger and Udell, 1998).1 The UK's Bolton Committee report (Bolton, 1971), one of the earliest studies of small firms, attempted to define small in terms of the classically perfectly competitive firm, including reference to absolute employment size. A firm was small if it satisfied four criteria:

  1. 1 It was an independent entity, i.e. not a subsidiary of a larger firm

  2. 2 It constituted a small proportion of the total market (measured by sales) and so had no power to influence price

  3. 3 Its owners and managers were the same people

  4. 4 It had less than 100 employees

Bolton was well aware that the definition of small might well depend on the characteristics of the industry in which the firm was located and that an employment measure might be more appropriate for service industries where output would be likely to be a function of the number of sales assistants, consultants, service personnel and so on, and less appropriate for highly capital-intensive industries where output would be very much a function of the equipment with which labour worked. Despite these qualifications, most researchers and government departments now work with definitions based on employment.

(p. 163) Growth

If one is to adopt a definition of growth consistent with the classical theory of the firm, growth should be measured in terms of the change in (discounted) cash flow profits. Firms in the classical model, be they competitive, oligopolistic or monopolistic in nature were profit-, or more exactly, wealth- maximizers.2 However, small businesses in practice are notorious for concealing their true profits from the tax authorities for income or corporation tax avoidance reasons. Even sales measures of growth often fall into the same ‘errors in variables’ problem, as firms seek in practice to minimize their reported sales, to avoid VAT. Thus, despairing of the true economic measures, researchers have sought after alternatives that are robust to manipulations. These generally boil down in practice to measures of employment or asset change and only occasionally sales change.

Of course change can be absolute or proportionate, and for different purposes one might (in theory) use either measure. However, the literature almost exclusively concentrates on the former. Hence the term ‘growth’ in this chapter will refer to a proportionate change in some firm-level variable like employment, sales or assets expressed as a rate per annum.3, 4

Firm failure/survival

The following definitions apply to incorporated businesses, small or large. We distinguish first between exit and failure. A firm exits an industry when it ceases to trade in that industry.5 It may cease to trade either voluntarily or involuntarily. Voluntary cessation occurs when the firm is sold, merged or closed by its owners. Involuntary cessation or bankruptcy6 occurs when it is closed by its creditors. The latter happens when the firm fails to meet debt obligations as they fall due or violates covenants in the loan agreement. The classical firm, operating in a world of certainty, would always exit voluntarily. Once uncertainty is introduced, however, expected profits and equity maximization is consistent with involuntary exit as the uncertainty is resolved.7 As pointed out by (p. 164) Schary (1991), the determinants of these different forms of exit are in principle different. Hence any study of exit should ideally distinguish the alternatives discussed.

What in theory determines whether a firm voluntarily exits? Traditionally, firms were assumed to be profit or equity maximizers and the firm would voluntarily exit the industry if the (known) value of continuing were less than the (known) value of exiting, both being measured in terms of the present discounted value (PDV) of profits or net cash flow from so doing.8 This kind of exit is a decision made by the firm's equity holders, which in the case of small firms, are its owner-managers. For the definition to be plausible in an applied research context we need to assume a very specific objective on the part of the owner-managers, namely that of wealth maximisation.9 Exit under this definition does not imply that the firm did not meet its owners' objectives, since during its lifetime it may have yielded a handsome income to its owners. It merely means that ‘at this point in time’, the value to the entrepreneur of continuing is less than the value to him/her of stopping or of switching.10

Finally, this model of closure (for it is a model) is embedded not only in an environment of certain knowledge (e.g. of prices, technology and so on) but also one of perfectly functioning capital markets. Once we allow for Knightian uncertainty, or for capital market imperfections, then it becomes possible that a firm may, despite acting optimally with respect to the relevant decision variables, find that it is unable to pay its debt obligations as they fall due and thereby falls into bankruptcy. This event would now be an example of involuntary closure since by definition, the shareholders' wishes would be ignored by creditors (notably the bank) in their desire to recover debts.11 This outcome is consistent also with low entrepreneurial ability reflected in poor judgement.12

(p. 165)

So, in summary, expected wealth maximization under uncertainty is a possible objective for the entrepreneur and bankruptcy or closure is consistent with this objective. Failure, now due to ‘bad luck’, and consistent with the entrepreneur's objective, may be the outcome, and is (for borrowers) defined by the event of bankruptcy. In practice, however, for small businesses, particularly unincorporated small businesses, the classical objective of wealth maximization cannot always, and perhaps even in a majority of cases, be assumed to hold. Thus, for example, a Sole Trader may be in business to avoid unemployment or ‘to be their own boss’, or ‘to gain independence’ or to achieve a target income. Failure in this case might be defined as the negation of any of these objectives, none of which is necessary or sufficient for wealth maximisation.13 The concept of firm failure, then, is necessarily relative to the objectives of ‘the’ entrepreneur. Failure of the firm might in fact therefore simply be defined as ‘the inability of the entrepreneurial team to meet the objectives they have set themselves’.14

Much of the empirical literature on small business closure, apparently due in the large to data limitations, unfortunately ignores the fine distinctions of definition we have emphasized.15 In this chapter, we shall therefore define failure pragmatically as either solvent or insolvent closure unless otherwise specified, and use the term closure in instances where there is no way to distinguish voluntary and involuntary closure in the data.

Preamble to the survey

It will soon become clear that the issues of growth and survival are intimately related. Not only is survival an obvious necessary condition for continued growth, but also in the discussion of the empirical work on survival and growth we shall find that estimates of growth, and its relation to size and age of firm, will be influenced by estimates of the survival rates of firms. From an empirical perspective the two are therefore inextricably linked.

The structure of the remaining part of the chapter is as follows. We begin with a discussion of what started as a purely statistical regularity accounting for the observed growth patterns of large firms, namely Gibrat's Law of Proportionate Growth. This alleged law relies on chance to explain a substantial part of the firm's observed growth pattern. However, it also presupposes a constant population of firms and cannot therefore deal with exits, which among small firms are high. Still retaining the role of chance in firm growth we then show that the literature has introduced models attempting to provide theoretical underpinnings for the (p. 166) systematic part of growth and examine their empirical validity. We show that these models still ignore systematic influences on growth that have been identified, namely, age and size effects. This leads on to optimizing theories of firm growth which attempt to explain the stylized facts of growth the previous literature had identified.

7.3 Gibrat's law and its variants

The distribution of firm sizes in an industry is generally positively skewed with large numbers of small firms and a small numbers of large firms. The exact form of the distribution has been variously identified as Lognormal16 (Hart and Prais, 1956), Pareto (Simon and Bonini, 1958), and Yule (Ijiri and Simon, 1964). While these early studies were based on samples of large quoted companies they recognized that a substantial part of firm growth (and decline) was random in nature. They therefore attempted to provide an underlying parametric stochastic model of firm growth that would ‘explain’ the observed size distribution and which could in principle be applied to the whole size distribution of firms, quoted and unquoted.17 The most famous of these models is Gibrat's Law of Proportional Growth (Gibrat, 1931). This alleged law can be written in the following form:

Determinants of Small firm survival and growth (1)

where x is the log of firm size at time t, and ε a white noise error term. The tildes indicate random variables. This ‘law’, as the eponymous author saw it, implies that the expected (log) size of a firm in t is simply its size in t−1.18 By successive substitutions into equation 1 we find that the current size under this law is simply the initial size plus a series of random shocks to the firm over subsequent periods:

Determinants of Small firm survival and growth (2)

The law can be shown to result from taking a fixed population of firms of identical initial sizes but each subject to random shocks.19 It is also clear from equation 2 that, viewed from the present, Gibrat's law implies a constant expected or average firm size in t periods' time given by the initial size x 0. More generally, the expected size of the firm viewed from period t is its current size, i.e. its size in t−1.

(p. 167)

Empirically speaking, Gibrat produced evidence from French large firms' behaviour to support his hypothesis. A seminal later study by Hart and Prais(1956) on quoted companies in the UK appeared to confirm Gibrat's own finding and to establish a convincing fit to the data. However, whether the law would apply to unquoted firms was left open to later researchers to investigate.

The Gibrat model can be generalized in a very simple and instructive way. Rewrite equation 1 in the following form:

Determinants of Small firm survival and growth (3)

Where β is a constant. To get an idea of the effect of beta on growth we can rewrite 3 in the form of a growth equation

Determinants of Small firm survival and growth (4)

We can now see that for β a positive fraction this period's expected growth is negatively related to last period's firm size. This implies that small firms grow faster than large:

Determinants of Small firm survival and growth (5)

By contrast, for beta equal to one the effect of size on growth is zero and for beta greater than one it is positive. Another implication of Gibrat's law (β = 1) in addition to the constancy of the unconditional mean is that the unconditional variance increases without limit.20 By contrast, for β < 1 the unconditional mean tends to zero, while the unconditional variance tends to a finite limiting value,21 and for β < 1 the variance increases even faster over time than under Gibrat's law.

Prais (1981) estimated the relationship (3) for UK manufacturing firms with more than 25 employees firms in three periods: 1885–1939, 1939–50 and 1951–58. He found that in fact Gibrat's law failed to hold in any of these periods, producing betas of 0.98, 0.77 and 1.12. Pre-WW II and during WW II, beta was therefore less than one implying that small (quoted) firms grew faster than large ones. Post-WW II (at least until 1958) beta was greater than one and therefore large (quoted) firms grew faster.22 Prais was particularly concerned about the effects of such (p. 168) increasing concentration on the market power of the large companies. Fortunately, however, these trends appear to have been substantially reversed in the post-1971 period. For example, see Hart and Oulton (1997) who examined a very large sample23 of UK firms in the period 1989–93, including firms with fewer than 17 employees.

Simon and Bonini (1958) argued that one reason why Gibrat's law did not fit the data perfectly (the tail of the distribution was too fat) was that there was no allowance for the effects of birth of firms into the lowest size class: the total number of firms was assumed fixed. They argued that taking births into consideration, Gibrat's law might be resurrected by allowing it to operate above the minimum efficient scale (MES) for the industry. This generated another appropriately skewed distribution of firm sizes but this time described by the parameters of the Yule distribution rather than those of the Lognormal. They did not however, examine the effect of deaths among firms in the initial cohort.

A major variant on the Gibrat process, along with an optimizing model of firm and market behaviour, arrived in 1982 with the publication of what was to be a highly influential24 article by Jovanovic (Jovanovic, 1982). This paper provided the first stochastic model of firm survival and growth based on individual optimization and market equilibrium.25 It generates a rich set of predictions about the relationships between firm age and size, survival and growth and about the mean and variance of the size distribution. It also generates Gibrat's law as a special case.26 Finally, while the model does not account for some aspects of industrial shakeouts27 and a number of other well-known influences on growth,28 it is nonetheless a better description of, and explanation for, the process of survival (p. 169) and growth than any of its forebears. We therefore devote some time to an exposition of it.29, 30

Jovanovic imagines an economy in which entrepreneurial ability is dispersed in the population of potential entrepreneurs. This ability is not known to an individual who has no business experience. All individuals know by contrast the distribution of talent in the population. Entrepreneurship itself, however, is a ‘learning experiment’: you find out just how good (talented) you are at it only by entering the industry and progressively getting feedback from the market. This may lead to higher or lower output than that produced initially, as the estimate of one's ability randomly rises above or falls below the initial value. So the process of learning starts with some prior belief about one's costs or equivalently about one's productivity as an entrepreneur. These beliefs evolve over time. There is a critical level of (estimated) returns as a function of ability defined by the value of an outside alternative to entrepreneurship W, which might be the present discounted value (PDV) of wage employment. Individuals look indefinitely far ahead in their plans (i.e. operate with an infinite time horizon). A cohort of entrepreneurs enters in each period t. Time in the model is identical to the tenure of a continuing entrepreneur.

To understand the optimization procedure and how it impacts on output, growth and exit, note that in period t each entrepreneur behaves as a competitive firm taking the sequence of market prices {p t} as given and choosing an output q t based on a cost function which depends on his imperfectly known costs (inverse of ability) θ t. He chooses output to maximize current expected profits π t (conditional on making subsequent decisions optimally) given by

Determinants of Small firm survival and growth (6)

Determinants of Small firm survival and growth is the expected value of the cost parameter for period t, updated according to Bayes' rule, and c(q) is convex in q.31 This output will be positive if the value of staying in, V(t), exceeds the value of quitting entrepreneurship, W. Optimization generates an output

Determinants of Small firm survival and growth (7)

which is decreasing in 
Determinants of Small firm survival and growth the current estimate of costs. This implies that there is a derived distribution of output conditional on the current estimate of costs. Hence, once we know the distribution of theta in any period we know also that of q.

(p. 170)

All potential entrepreneurs start with the same estimate of their costs, 
Determinants of Small firm survival and growth.32 If the price is high enough they will all enter. Subsequent updating of their beliefs will lead some to revise them upwards and to contract and others to revise them downwards and to expand, even if price is constant. The density of costs evolves over time as ERs update according to Bayes' rule. This rule for a Normal distribution takes the form

Determinants of Small firm survival and growth (8)

where ≥t is the current observation on costs and w(t) and θ t are weights attached to last year's mean estimate 
Determinants of Small firm survival and growth and this year's observation. Bayes' rule implies that as t goes to infinity the weight to last period's mean estimate of costs, w(t), goes to one.

Let the density of expected costs in t+1 given expected costs in t be written

Determinants of Small firm survival and growth (9)

This density has the property that the best estimate of next year's cost is simply today's costs:

Determinants of Small firm survival and growth (10)


Thus, standing in period t viewing his decision for t+1 the entrepreneur is faced with a distribution of costs centred on 
Determinants of Small firm survival and growth and a distribution of q, centred on 
Determinants of Small firm survival and growth (θ̄t) (see Figure 7.1).

Jovanovic shows that there exists a failure boundary defined in terms of ability, or equivalently, output or growth such that once the firm's costs rise above the boundary the entrepreneur exits. In Figure 7.1, this is denoted by 
Determinants of Small firm survival and growth If current costs are estimated to be above 
Determinants of Small firm survival and growth then the ER exits; if below he stays at least one more period. In output terms this implies that for exiting firms, next period's output is zero and growth between this period and next is −100%:

Determinants of Small firm survival and growth (11)

Determinants of Small firm survival and growthClick to view larger

Figure 7.1 Entrepreneurial talent and output in Jovanovic (1982)

Several predictions follow from the Jovanovic model and can be seen from a manipulation of Figure 7.1. First, smaller firms fail more frequently as a higher q(t) implies a smaller chance of q(t+1) falling below q*(t + 1). Secondly, younger firms are more likely to fail than older ones as younger firms have fewer observations of costs on which to base their judgement of their true costs. The greater variability of their estimates means that finding that their current output is low (i.e. their current costs (p. 171) are high) they are more likely to quit.34, 35 Thirdly, larger non-failing firms of a given age grow more slowly. This follows from the fact that for fixed t the firm's cost parameter must lie in the interval [
Determinants of Small firm survival and growth], implying that, output must lie in the interval 
Determinants of Small firm survival and growth. (See Figure 7.1.) Now, while subsequent output may lie above or below the initial level, it is clear that expected growth 
Determinants of Small firm survival and growth must therefore be a decreasing function of q(t).36 In other words, larger businesses grow more slowly. Finally, the Jovanovic model implies older firms have a smaller variance of growth rates for the same reasons that older firms are less likely to fail: the variance of the ER's estimate of costs is lower for ERs with longer tenure.37

(p. 172)

7.3.1 Tests of the Jovanovic model

What of the tests of this rich set of predictions? Jovanovic himself provides some evidence for their validity, but many subsequent studies, some of which cover really small firms (defined as those with fewer than five employees), have demonstrated the power of the model.

Hall (1987) while still using quoted company data, with very large ‘small’ firms, was the first study to examine the potentially important issues of selection out of the sample (by deaths of firms) and unobserved heterogeneity in the estimation of relationship (3), the generalized Gibrat process.38 Her sample consisted of 1,778 US manufacturing firms in the year 1976. Her sample consisted of two panels selected from this set with employment data for the periods 1972–79 and 1976–83 respectively. Hall identified two types of selection bias that may arise in a panel of firms. The first occurs because selection out of the sample by death is not random; the second occurs because the selection into the sample by births is not random.39 However, despite the theoretical possibilities she identified, after adjusting for the first of these two effects she found that growth was still negatively related to size as predicted by the Jovanovic model: the ‘small firm effect’ could not be accounted for either by unobserved heterogeneity or by selection bias. Hall also confirmed Hymer and Pashigans' finding that the variance of growth rates declined with size of firm, again as predicted by the Jovanovic theory.40, 41

While Hall's study is a landmark in the empirical analysis of growth and survival, her sample, as noted, consisted entirely of quoted companies and her ‘small’ still means in most people's terminology ‘very large’. Evans (1987a, b) by contrast was the first economist to use a panel dataset with seriously small firms included. Evans (1987a) data, was able to remedy some of the defects of her dataset. His sample, again for US manufacturing, and covering the five-year period 1976–80 consisted of a sample of some 20–30,000 firms in 100 industries classified at a rather detailed (p. 173) level (the two-digit level). His size grouping was furthermore defined to include firms with as few as five employees. Evans' data in a second paper (Evans, 1987b) (See Table 7.1) included firms with as few as one employee. In both of these papers Evans was interested in testing Jovanovic's predictions regarding the relationship between firm size and growth, and that between firm age and growth and the variance of growth. His data also allowed him to examine the effects of failure on both these relationships. Evans found that controlling for selection bias smaller and younger firms grew faster and died more frequently than larger, older firms. The variability of growth also decreased with age. In Evans (1987a), these results held both in aggregate and for upwards of 75 percent of the industries studied.

Table 7.1 Failure rates by size and age of firm (from Evans, 1987b)

Age (years)

Mean no. employees






Row average

















































Evans (1987a) provides a useful conceptual framework to analyse some of the empirical tests of Jovanovic's theory which generates Gibrat's law as a special case.

Write the firm's log size in period t in the form

Determinants of Small firm survival and growth (12)

where γ(x t−1, a t−1) is a deterministic function of log size x and log age a of the firm and u is a white noise error term. Evans actually writes this model in growth form (derived by re-arranging equation 6):

Determinants of Small firm survival and growth (13)

The partial derivatives of the growth function with respect to x and a can then be written as γx, γa and show (conveniently) the elasticity of the expected change in size42 (or equivalently of the logarithmic growth rate) with respect to the change in the size and age of the firm.43 Gibrat's law says that gamma and u are independent (p. 174) of x and a or equivalently that these derivatives are identically zero. Evans found from his empirical work on US manufacturing firms between 1976 and 1982 that γx, γa < 0 consistently with Jovanovic's theory. However, he also found contrary to a Jovanovic special case, that under the assumption of a Cobb-Douglas firm production function with decreasing returns to scale, firm growth was not independent of size for mature firms. Finally, Evans reported that deviations from Gibrat's law were less marked the larger and the older the firm.

7.4 Survival of small businesses

An aspect of the studies reported above is that by and large they deal with small firms of five employees and above and with ages less than six years. However, it is possible to argue that most of the interesting features of firm failure occur within the first six years of trading. The issue of early survival is particularly poignant for the self-employed as most self-employed people in an economy do not have employees and most firms die within the first two to three years of trading (Cressy, 1993). Moreover, researchers in the 1990s inspired by Evans and Jovanovic made some interesting discoveries regarding the survival and closure patterns of seriously small and young firms based on datasets often covering predominantly service industries.

Survival among a random cohort of start-up businesses is remarkably low and varies a great deal in the first two or three years of the firm's life. For example, Brüederl et al. (1992) found that in a cohort of German startups, 24 percent went out of business in the first two years of trading and 37 percent exited in the first five years; Cressy (1996b) found that in a cohort of UK start-ups, 45 percent died in the first two and a half years of trading and 80 percent in the first six years; Mata and Portugal (1994) (as we have seen) found that in a cohort of Portuguese start-ups 20 percent died in the first year and 50 percent in the first four years.44

Given the dramatic propensity to demise in the very early stages we might well ask at this point whether the Jovanovic model accounts for the facts of small firm (p. 175) survival. A number of European studies have found that it does. Mata and Portugal (1994), show that in Portuguese manufacturing firms, between one and 100 employees survival rates (failure rates) start at 78 percent (22%) after one year for the new entrants, falling to 52 percent (48%) after four years. But the variation of failure rates with size is also remarkable: after four years, 75 percent of the large firms are still in operation (implying a 25% failure rate) whereas only 44 percent of the smallest (one–two employees) are still around (a 56% failure rate). Likewise, a four-year size transition matrix45 of these firms shows that among survivors the tendency is to grow rather than to shrink (a finding also echoed in Cressy (1993) and elsewhere), but that post-entry mobility46 tends to decrease with size. This evidence is consistent with Jovanovic's prediction that growth rates decline with size.47, 48, 49 The two key findings of the empirical literature—that small firms are less likely to survive and tend to grow faster than large (controlling for survivorship bias)—have been confirmed in many different country studies. For example, among European countries, we find the two propositions validated in Scotland (Reid, 1991), Germany (Harhoff and Waywode, 1998), the Netherlands (Van Praag, 2003), England (Storey et al., 1987; Cressy, 1996a), Italy (Audretsch et al., 1999) and Austria (Weiss, 1998). By and large, the findings for service industries tend to mirror those for manufacturing.

(p. 176)

Determinants of Small firm survival and growthClick to view larger

Figure 7.2 Simulation: Young firm failure and capitalization (Cressy, 2005)

These findings have been given a more systematic underpinning in empirical studies of closure rates over the firm life cycle—see Ganguly (1985) and Cressy (1997, 2005) for the UK; Brüederl et al. (1992) for Germany; Van Praag (2003) for Holland and Audretsch and Argarwal (2001) for the US. This research examines the structure and determinants of the failure rate of a given cohort of firms over the first six to ten years of trading. The general finding is that the firm failure distribution over time trading is positively skewed with most firms dying50 in the first two and a half years of life. However, if a firm survives the first two years (‘the valley of death’) its long run survival chances are high: the remainder often live to a ripe old age—see Figure 7.2.51 There are empirically identifiable factors causing the curve to shift. Cressy (1997, 2005) develops a theoretical model which simulates the empirical failure curve and he argues that there are three principal factors influencing the position of the curve: (p. 177) initial capitalization, growth and risk. He shows that in the case of initial capitalization the curve shifts downwards and to the right as the firm gets more money at start-up. The honeymoon period for the entrepreneur and his business (during which the firm ‘cannot’ fail) is also lengthened by money (see Figure 7.2). A roughly similar effect is predicted from higher mean growth rate and lower risk associated with it. What is clear from the Cressy model is that in the long run the initial conditions (e.g. start-up size) don't matter: closure rates for initially small and large firms converge.

Extant empirical work, moreover, confirms these predictions. For example, firm exit rates have been found significantly related to both the firm and industry life cycle and to calendar time.52 Moreover, the advantages to size are short-lived: over time they disappear. The theory is as follows.

Industries are characterized in the early stages of a technology by experimentation with short production runs of experimental designs until in the mature stage a dominant design emerges. In the early, or formative, stage the motivation of entry is innovative skill in producing superior product designs. In this situation small firms have the advantage and enter in large numbers. The larger firms among these entrants have an advantage over the smaller and are more likely to survive over the short run. In the later, or mature stages of the industry, design matters less and there is less entry. Furthermore, knowledge, that in the early stages, is discovered by the small entrant has now been codified and embodied in products, reducing the advantage of the small firm. Furthermore, the surviving small firm will have grown by now and will itself embody some of this knowledge.

Audretsch and Argarwal (2001) (AA) find that the position of the failure curve for new entrants is indeed influenced by the industry's development stage (formative vs. mature) and by the technological regime (low vs. high tech). Size of entrant has a short run impact on survival, but this is a function of the stage of the industry and in the longer run, size doesn't matter: the curves converge. AA speculate that this may be due to the influence of growth.53 Studies relating not to time trading but to calendar time also demonstrate that the form of exit matters. Cressy and Storey (1994), for example, find that the overall exit rate is relatively constant through time, but that, as might be expected, bankruptcies and insolvencies vary counter-cyclically, being much higher in recessions than in booms.54

Finally, as mentioned earlier, little empirical work has examined the determinants of different business outcome types. However, a recent paper by Van Praag (Van Praag, 2003), examines the firm-level determinants survival of two outcomes: survival duration and success. Her data is a large sample of American small (p. 178) businesses and she applies a hazard rate methodology55 to estimate the determinants of each outcome. Hence she is able to effectively distinguish the determinants of voluntary and involuntary exits. Her research also produces empirical hazard rate curves that mimic the failure distributions derived by Cressy (1997, 2005) its characteristic positive skew over time trading.

Van Praag defines business survival duration as the expected period in business ending in either voluntary or compulsory dissolution.56 By contrast, success is defined as the expected period in business conditional on involuntary exit.57 This enables her to estimate a model with ‘competing’ risks, namely the risk of voluntary closure versus that of involuntary closure, and to examine the factors that determine the two. She finds, as predicted by Schary (1991), that empirically the competing risk model explains the data better than a single (homogeneous) risk model, which ignores the type of exit. The main differences however are not in kind but in quantity: for example, consistently with Bates (1990), Cressy and Storey (1994) and others, start-ups run by older entrepreneurs survive longer in both the voluntary and involuntary senses.58 However, young starters are more likely to find better outside opportunities than their more mature counterparts and therefore to voluntarily exit entrepreneurship; these youngsters are also more likely to fail due to a lack of leadership or ‘knowledge of the world’.59

7.5 Survival, growth and credit constraints

A credit constraint exists if an entrepreneur with insufficient wealth cannot obtain debt to fund a viable project, that is, one with a positive net present value (p. 179) (NPV).60 In such a situation the capital market is inefficient and the wealth of the economy will be lower than it would be with an efficient market. It is commonly believed that credit constraints exist in most economies at most times and that small firms are the most likely to experience them.61 Credit constraints in turn are expected to have an impact on such firms' survival and growth rates, lowering both. The academic literature in this area is massive. In this section, therefore, we examine a particular subset of this literature that has been subject to intensive empirical testing, namely, the literature on the switching decision—the choice to move into, or out of, self-employment. We first outline the theory to show how it generates a theory of credit constraints and how these in turn affect survival and growth of the afflicted firms. We then examine a number of empirical tests of the theory and finally raise some issues of interpretation of the results.

Evans and Jovanovic (1989) (henceforth EJ) in a now celebrated paper,62 developed a theory of credit constraints based on the idea that banks lend in proportion to a firm's assets rather than on the basis of its expected cash-flow profits. The result may be that there is insufficient lending and excessive failure of cash-starved businesses. Since collateral tends to fall with business size, a given loan demand is less likely to be supplied the smaller the business. Since under-capitalization will reduce profits, it is expected that small firms will be more likely to fail as a result of credit constraints. Finally, since such constraints cause entrepreneurs to invest a larger proportion of their assets in the business and to reinvest earnings back into the business, smaller firms will have higher rates of return on assets and will be expected to grow faster than large ones.

EJ argued that empirically we should find credit constraints to self-employment (henceforth SE) if, and only if, there was an empirical correlation of assets and switching into SE (or equivalently between assets and SE survival). This is based on the idea of a bank lending rule in which lending is proportional to a fims's assets. A relaxation of the lending rule (or equivalently an unanticipated increase in fixed assets) will, if businesses are constrained, increase switching into SE and increase business survival rates. EJ estimated their model on a sample of 1,94963 American white males aged between 14 and 24 years in 1966 who were wage workers in 1976 and who were either wage workers of self-employed in 1978.64 These individuals (p. 180) were between the ages of 24 and 34 in 1976, the typical age of entrepreneurial entry. The average SE man in 1978 earned US$15,746 compared with US$16,760 for a wage worker. Net assets of the total sample were about US$20,000. The average work experience and education of the sample individuals was 12 and 14 years respectively. About 4 percent of those who were wage earners in 1976 switched into SE by 1978.

EJ estimated the probability of SE as a function of assets (and its square), wage experience, education, starting wage, income and controls. The coefficient on assets was positive and significant (at the 2 percent level). On the (questionable) assumption of zero correlation of assets and entrepreneurial ability, they concluded that liquidity constraints exist. EJ also estimated SE earnings as a function of the same variables in the switching equation and found that wealthier individuals earned more in SE because they ‘will have started businesses with more efficient capital levels’ (p. 820). Finally, they found that people with smaller assets are forced to devote a larger proportion of their wealth to their businesses.

7.5.1 Questioning the EJ result

While a growing number of studies have apparently provided support to the EJ finding of credit rationing (see especially Holtz-Eakin et al., 1994a, b; Blanchflower and Oswald, 1998), there are questions about a number of features of their study that have in turn led to extensions of the model and more sophisticated tests of its hypotheses:

  1. (a) How appropriate is the model EJ used? In particular are assets endogenous to the system as they assume, or e.g. are they a function of the human capital of the entrepreneur, thus making the latter the primary constraint? (Cressy, 1996; Astebro and Bernhardt, 2003; Parker and Van Praag, 2003).

  2. (b) How should one interpret the EJ finding of a positive correlation of assets and survival? For example, it has been questioned whether the repeated findings of various studies can ‘really’ be explained by the existence of uncontrolled-for effects such as control- or risk-aversion of the would-be/actual entrepreneur (Cressy, 1995, 1998) or the existence of sunk costs that differentially affect small and large firms (Cabral, 1995)?

  3. (c) How representative are the datasets used in the EJ-replication studies? For example, the US work by Holtz-Eakin et al. (1994b) examined only the top end of the wealth distribution and found evidence supporting EJ. More recent evidence suggests, however, that the pattern may be radically different for most of the wealth spectrum where the relation between wealth and switching vanishes (Hurst and Lusardi, 2004).

(p. 181) 7.5.2 Structure of the EJ model

Cressy (1996b) using a large representative dataset of UK start-ups and a rich vector of entrepreneurial, firm and financial characteristics argued that the true constraint on business survival was not financial, but rather human, capital of the entrepreneur. His evidence showed the correlation between assets and survival was spurious, arising from the correlation of both with the human capital of the entrepreneur. Human capital here was measured by entrepreneurial age (‘general experience of life’ and greater realism),65 industry-specific work experience, managerial human capital (measured by team size) and whether the start-up was a business purchase (measuring the existence of economic networks). These same human capital factors were found to explain the provision of bank finance to the firm. Cressy concluded that so far from subsidizing start-ups, governments should focus more on the provision of training to would be entrepreneurs.

Astebro and Bernhardt (2003) (henceforth AB) provide a sophisticated examination of the ‘endogeneity of capital constraints’ issue raised in Cressy's paper. Working with US self-employment data they they include measures of both transferable human capital (education, etc.) and of entrepreneurial ability (business experience, etc.)66 They employ a two-stage estimation procedure At the first stage, the relationship between an owner's human capital, entrepreneurial ability and financial wealth are examined; at the second stage the relationship between the firm's start-up capital, entrepreneurial ability, human capital and financial wealth are analyzed, with financial wealth the predicted value determined from the first stage.67

At the first stage, wealth is found to increase with both human capital and entrepreneurial ability, suggesting that collateral constraints are indeed endogenous, contrary to EJ. At the second stage, while controlling for financial wealth, start-up capital requirements are found to increase with entrepreneurial ability and human capital, implying that better quality entrepreneurs are perhaps more credit-constrained, consistent with the EJ model.68 The marginal effect of wealth on capital demand diminishes significantly once human capital is added to the equation, whereas adding entrepreneurial ability increases the marginal effect of wealth. This suggests that the human capital does indeed mitigate wealth constraints which bite harder on better entrepreneurs. Capital constraints are thus (p. 182) endogenous (as Cressy (1996b) found), but controlling for human capital and entrepreneurial ability does not completely eliminate them.69

Parker and Van Praag (2003) (henceforth PVP) also address the important endogeneity issue in EJ using Dutch self-employment data. They employ a different definition of capital constraints loan (down-scaling rather than loan denial) and examine established businesses rather than start-ups, but demonstrate empirically the existence of an ‘endogenous triangle’ of relationships between human capital, capital constraints and performance among the Dutch self-employed. They too find that credit constraints, measured by the extent of loan downscaling70 are endogenous, being reduced by human capital of the individual: more educated individuals are less constrained in starting a business because they are better capitalized (possess more initial assets). Capital constraints are found in turn to impede performance (measured by profits from the business) since they constrain it to a sub-optimal initial scale. Finally, human capital enhances business performance directly (via the effect of entrepreneurial ability on productivity) and indirectly (via the relaxation of capital constraints).71, 72

7.5.3 Sample issues

Other criticisms of EJ-replicative studies revolve around the dataset EJ and others (Holtz-Eakin et al., 1994b) used. EJ's original sample was, as we have seen, of American young white males with an (p. 183) average wealth of US$20,000, a very modest figure indeed. The sample used by a confirmatory study by Holtz-Eakin et al. (1994) (henceforth HE), however, was by contrast, of rather rich US individuals with an average wealth of US$72,000 in 1981.73 While the original HE paper suggested capital constrained entrepreneurs throughout the wealth spectrum, a very recent paper by Hurst and Lusardi (2004) examining a wider sample of US citizens suggests that throughout most of the wealth range there is in fact no correlation of the chances of starting a business with individual wealth levels. They find that it is only at the very top of the distribution that the correlation becomes positive. These high net worth individuals are potentially of high entrepreneurial ability relative to their assets and allegedly credit constrained.74 Thus studies such as that of HE, that use high net worth individuals to argue more generally for the existence of credit constraints are shown to be much more restrictive in scope than had been imagined.75

7.5.4 Contrarian evidence

Other studies of capital constraints from different methodological perspectives have tended to conclude that credit constraints are in general of little importance, for example, Aston (1990) in a survey of potentially fast growth businesses and their financial search procedures found that at most 6 percent of growth potential businesses were constrained. This is a rather small proportion of businesses if capital constraints are as widespread as the empirical work suggests. Likewise, (p. 184) Cambridge (1996) also adopting a survey approach found little evidence of constraints in the UK.

7.5.5 Alternative explanations for the findings

The fact that a theory is consistent with the data does not of course prove that it explains it. We need to check that there are no competing explanations available. Thus, in the following sections, we examine alternative explanations, theoretical and empirical, for the correlation of assets and switching/survival. Risk aversion of the entrepreneur

Another potential explanation exists for the EJ finding that assets and switching into SE are positively correlated but which does not imply credit constraints. This explanation depends merely on some plausible assumptions and limited evidence about human tolerance of risk. It is commonly believed (and there is evidence to show) that people in general dislike risk. Studies of the stock market show that people need to be offered higher returns to invest in more risky securities. This is consistent with risk aversion. Likewise, most people take out some kind of insurance policy against fire, theft and so forth, which involves the payment of a premium. This also suggests dislike of risk since by the mechanism of insurance the risk is transferred to another party.76

Imagine then, that when I increase your assets you become less risk averse, that is to say you become more willing to take risks. For example, if I offer you simultaneously an increase in your wealth W by £1 and a bet which yields +£1 with probability 1/2 and −£1 with probability 1/2, with your additional assets you are now more likely to take the bet than before. In the language of economics, this means your utility of income function displays Decreasing Absolute Risk Aversion (or DARA). Since available empirical evidence suggests that entrepreneurship tends to be more income-risky than wage employment, this means that the marginal entrepreneur (one for whom the expected costs just outweigh the expected benefits) would switch into self-employment should he/she receive a windfall gain. There is, furthermore, some empirical evidence to support the assumption that entrepreneurs have decreasing absolute risk aversion (see Guiso and Paiella, 1999).

(p. 185)

Thus we have the result that higher wealth is associated with greater propensity to enter SE which gives us the EJ result but without capital constraints. No direct test of this proposition is yet available even though it is straightforward to set up. Control aversion of the entrepreneur

Entrepreneurs of smaller firms are well known to be control averse.77 Control aversion is defined here as the dislike of perceived interference by outsiders in a business. Control aversion among small firms may in general affect their decision to take on external equity providers or their decision to take on external debt. Empirically there is growing evidence that such aversion does exist and does influence both the capital structure and performance of small firms. (Cressy and Olofsson, 1997; Mueller, 2004). So how can it explain the empirical results on credit constraints?

Determinants of Small firm survival and growthClick to view larger

Figure 7.3 Effects of control aversion on the amount of borrowing

Entrepreneurs do not like any kind of interference in their operations, in particular by Big Brother in the form of the local bank manager. (Cressy, 1995). For this reason (and for other reasons) they tend to borrow little.78 In the language of economics, this means that the psychological costs of borrowing outweigh the benefits (at the margin) for the entrepreneur of the smaller firm. As firms get larger, things get less personal, management tends to be rewarded by salaries rather than simply profits, and the aversion to perceived bank interference starts to wane. But at the level of the micro business (one with less than ten employees) control-aversion is likely to restrict borrowing not from the supply—but from the demand-side. The equilibrium trade-off is illustrated in Figure 7.3 (taken from Cressy, 1995) where the red line indicates profits of the firm as a function of borrowing. This represents the utility function of the financial manager of a larger firm. By contrast, the green line represents an indifference curve for the entrepreneur of a small firm. While profits are a ‘good’ yielding (positive marginal utility), borrowing is ‘bad’ (yielding negative marginal utility). Thus the indifference curve is upward-sloping—its slope being the ratio of the marginal utility of borrowing to that of profits.79 Utility is therefore increasing as we move to the north-west of the diagram with higher profits and lower borrowing. The highest indifference curve attainable with the red profit constraint is the green one. The optimum for the larger firm is where profits are maximized, at L*. The optimum of the control-averse (p. 186) entrepreneur, equates the marginal disutility of borrowing with the marginal utility of profits, yielding the smaller borrowing amount L**. Sunk costs

Cabral (1995) provides a model of sunk costs which constitutes on the one hand a possible explanation for why small firms grow faster than large ones, and on the other a potentially competing explanation for the alleged role of capital constraints. Cabral argues that the presence of sunk costs together with the well-tested assumption that smaller firms have a lower survival rate implies that small firms will grow faster than large ones. If this claim were true Gibrat's law would be false on theoretical grounds.

Cabral's argument rests on the notion from Jovanovic (1982) discussed on p. 169 above, that entrepreneurs only learn about their efficiency as entrepreneurs after entering the industry. Cabral presents an infinite horizon model, but one in which the significant changes occur only in periods 1 and 2. The remaining periods repeat what happens in period 2. In period 1, firms get a signal about their productivity. In period 2, they learn exactly what their type (productivity) is going to be for that (p. 187) period and for all subsequent periods. Productivity types are one of a triplet: Low, Medium or High. The Low types never make a profit and have no chance of improving productivity; hence they do not invest in capacity and exit once their type is revealed to them. The High types are also ‘locked in’ to their state and have no chance of declining in quality, so that once their type is revealed they know they will remain with that productivity forever. Therefore, High types install their long run capacity immediately and choose an output constant through time—implying zero growth rate. Only the Medium types may change state, either remaining as they are or rising or falling in efficiency with positive probability between periods 1 and 2. The crucial point is that if the Medium types fail (falling to Low in period 2) viewed ex ante of the decision to invest, the owner incurs a loss on the capital invested since he has to quit the industry. Medium types have a survival probability (probability of productivity remaining constant or rising) less than one and hence smaller than that of the High types. This means that Medium types in period 1, in view of their higher expected losses from closure, will install capacity below the long run level. In period 2, when their type is revealed, Mediums will increase capacity and output. Hence their growth rate will be positive and higher than that of the High types. In a word, surviving small firms (Mediums) grow faster than large ones (Highs).80

7.6 Control aversion, outside equity and growth

If debt cannot easily be raised by a small firm due to absence of collateral then one might imagine that equity would be the alternative, and indeed more suitable, form of finance. Outside equity funding involves the purchase by an outside organization, or individual, of shares in the firm. However, despite its seeming attractiveness there are insurmountable problems with this as a solution to the provision of small business finance.

First, outside equity is by definition irrelevant to the majority of small businesses who are unincorporated and hence cannot (legally) issue equity. Secondly, even if we confine our interest to small incorporated businesses, control aversion operates even more strongly in the case of equity (by comparison with debt) to discourage (p. 188) most small firms from gaining finance this way.81 The decision not to take advantage of outside equity may well result in more gearing and slower growth for the firms involved, but their owners seem to prefer the disutility of this to the disutility of control-loss (Mueller, 2004).82 Thirdly, venture capitalists, or Business Angels, the likely source of such finance are not interested in buying equity in the vast majority of small Limited Companies (typical firms) as they offer no prospects of capital gain of the order they are used to and require. Traditionally, VCs have required rates of return (IRRs) of 30 percent plus per annum on their investments. These rates of return are only possible however if the firm grows very fast and in a short time (three–five years) ends up with a stock market flotation or a trade sale. The vast majority of firms, even the majority of sophisticated firms, do not fall into this category.83

7.7 Conclusions

Over the last half century, our knowledge of the determinants of small firm survival and growth has evolved substantially in tandem with the data available and the theories used to explain it. Initial theories of growth were purely statistical in nature and offered no intuitive explanation other than constant returns to scale in production for the alleged validity of Gibrat's Law of Proportional Effect. More detailed studies based on data that covered a wider range of firm sizes showed that systematic factors could be identified in growth, namely the role of firm size and age. However, from these studies for statistical and data-based reasons it was initially unclear if size in fact conferred advantage. Subsequent studies dealing with the problems of selection bias arising from the fact that small firms have higher failure rates than large ones, eventually established that, controlling for the difference in survival rates, small is indeed ‘beautiful’.

Focus in the literature now shifted from simply identifying survival and growth patterns to explaining them by the construction of optimizing models of firm behaviour. The decision to enter entrepreneurship was modelled as a learning experiment in which the entrepreneur received feedback on his performance only by taking the plunge and setting up. These theories, moreover, could claim to (p. 189) explain a number of key stylized facts in the literature, for example, that young firms had more variable growth rates and were more failure prone. In the late eighties, researchers also began to develop theories of, and to empirically identify, the potential role of capital and other constraints on firm growth. Early seminal papers now spawned a huge industry seemingly identifying capital constraints at every turn and in every country where there was data. However, these findings were based on very simple criteria and research now began to question the validity of these assumptions. So, although by and large the findings of the empirical capital constraints literature suggests the widespread existence of capital constraints based on a very simple correlation of assets and survival or state switching, theories were suggesting that capital might even be provided to small firms in surplus. Later empirical contributions with more sophisticated methodologies indeed confirmed that these findings needed to be modified in the light of the role of human capital in the survival and asset accumulation processes. Later theoretical contributions also questioned the interpretation of the findings. A final paradox has now arisen from the most recent American empirical work: capital constraints on the so-called ‘switching’ criterion seem to exist only in the upper end of the wealth spectrum, implying that it is now the rich that need to be subsidized to entice them into entrepreneurial risk-taking!

Alongside this theme there developed a literature that examined how failure evolved along the firm, and industry, life cycle. This curve demonstrated that the first two and a half years of a firm's life were the most risky but that if you, as entrepreneur, survived this initial ‘valley of death’ your long run chances of failure were rather low. Factors influencing the position of this curve have now begun to emerge but a fascinating finding is that initial size matters only in the short run: in the long run other factors take over and the failure curves of big and small entrants converge on low asymptotic rates—as predicted by theory. Future research promises to both elaborate these findings on new datasets and to refine the underlying economic theory.


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                                                                                                                                                        Weiss, C. R. (1998). ‘Farm Growth and Survival: Econometric Evidence for Individual Farms in Upper Austria’. American Journal of Agricultural Economics, 81: 103–16.Find this resource:


                                                                                                                                                          (1) Berger and Udell, in an important survey of small business finances (Berger and Udell, 1998), define a small firm as one with less than 20 employees and less than $2m in annual sales (in constant dollars). A large firm is thus one either with more than 20 employees or more than US$1 m in sales revenues in any one year.

                                                                                                                                                          (2) Profits convert readily into wealth by the use of discounting.

                                                                                                                                                          (5) While a firm operating in several industries can exit one industry and still continue to trade in others, small firms tend to be little diversified along the product dimension and we shall, by and large, assume that exit from the industry means cessation of trading generally.

                                                                                                                                                          (6) In the US, bankruptcy refers to firms, whereas in the UK to individuals, who fail to meet their debt obligations. In the UK, firms that fail to meet debt obligations are termed insolvent.

                                                                                                                                                          (7) For example, consider an expected equity maximizer facing two equally likely permanent states of the world—High, when with profits net of debt servicing payments are £10,000, and Low when they are −£5,000. With the relevant discount rate at 10%, and the probability of either state at 50%, equity value at £50,000 is positive. Future profits should ensure a continuing loan from the bank. However, if future events alter the probabilities, say to 10% and 90% respectively, and these events are unforeseen (Knightian uncertainty—see Knight, 1965), the firm may find that the bank will no longer finance its operations at that future date when it defaults on its loan.

                                                                                                                                                          (8) See Schary (1991) for a detailed discussion of these conditions.

                                                                                                                                                          (9) It also assumes that there is no other asset in the owner-managers' portfolios.

                                                                                                                                                          (10) A variant on this definition occurs when the entrepreneur, now allowed to be risk averse rather than risk neutral, maximizes the PDV of expected utility over some horizon. Once again there will exist an exit threshold below which the entrepreneur will exit the industry. See Cressy (1997, 2005) for an example.

                                                                                                                                                          (11) On the other hand a rational entrepreneur would recognize that bankruptcy was a possible outcome of the business and one outside her control while perhaps praying for manna from heaven to enable her to continue in business.

                                                                                                                                                          (12) The recent literature on the role of optimism in entrepreneurial failure shows that overestimates of one's ability as an entrepreneur for example may lead one to enter business when a more objective assessment would lead one to stay out. Behaviour is still, in a sense, rational, but is skewed by a wrong set of beliefs. See de Meza and Southey (1996).

                                                                                                                                                          (13) Cressy (1996a) found empirical support in UK start-ups for the target income motive for start-up growth.

                                                                                                                                                          (14) As we have noted, this might sometimes happen for reasons quite outside the owners' control. In this case we might say that the business failed but the entrepreneur did not.

                                                                                                                                                          (15) Some exceptions include Schary (1991), Cressy (1996b), Everett and Watson (1998), Van Praag (2002).

                                                                                                                                                          (16) If a variate X is Lognormally distributed then log(X) is Normally distributed.

                                                                                                                                                          (17) Needless to say, chance is a mere label for our ignorance. Every event necessarily has a cause, and any assertion to the effect that chance underlies growth patterns should be interpreted as meaning that the causes are so complex as to make it impossible to predict their outcome. White noise is the result.

                                                                                                                                                          (18) Firm size thus follows a Random Walk (see Feller, 1957).

                                                                                                                                                          (19) For a numerical example of this process see Prais (1971).

Determinants of Small firm survival and growth

Determinants of Small firm survival and growth and 
Determinants of Small firm survival and growth.

                                                                                                                                                          (22) Other studies by Utton (1974) and by Samuels (1965) found similar values for beta in the post-war periods 1951–65 and 1951–60. The interpretation of Prais' results has been the subject of some controversy. He and Hart (1962) tended to follow the line of Evely and Little (1960) that mergers were relatively unimportant as an explanation of firm growth, whereas Hannah and Kay (1977, 1981) argued that the dominant force in increasing concentration during the post-war period was due to merger activity. A beta greater than one implies that the variance of the underlying lognormal distribution increases over time and this in turn is associated with higher concentration levels measured by e.g. the five-firm concentration ratio.

                                                                                                                                                          (23) Some 87,000 independent companies.

                                                                                                                                                          (24) A Google Scholar search as of today (18 January 2005) reveals this article, published in the highly technical journal Econometrica, to have been cited no less than 652 times. This implies an annual citation rate of about 22, extraordinary by most standards for such a journal and for an industrial economics paper.

                                                                                                                                                          (25) Earlier models by Lucas (1978) and Kihlstrom and Laffont (1979) preceded Jovanovic in providing optimising models of firm behaviour underlying the growth process, but were non-stochastic in nature and did not produce the range of empirically valid predictions associated with the Jovanovic model.

                                                                                                                                                          (26) Under the assumption that technology is Cobb-Douglas with decreasing returns to scale growth is independent of size for mature firms; while under the additional assumption that the distribution of ability in the population is Lognormal, growth is independent of size for firms entering the industry at the same time.

                                                                                                                                                          (27) A shakeout is essentially a situation when the number of firms in an industry declines significantly after initial growth in numbers, alongside slowing and eventually declining industry output. See Klepper (2001) for references.

                                                                                                                                                          (28) These include: mergers and acquisitions (a large literature finds these important), initial size (by assumption in Jovanovic variations are ruled out), capital constraints (another larger literature supports this factor's role), financial risk (firms have no debt in Jovanovic), learning by doing (firms learn only about their static ability), and so on.

                                                                                                                                                          (31) The entrepreneur in choosing q assumes that he will behave optimally with respect to all future decisions, which obviously depend on the current decision.

                                                                                                                                                          (32) A variation on this assumption has been explored by Frank (1986).

                                                                                                                                                          (33) Notice the parallel here with Gibrat's law of equation 1. There the expectation of log(output) in t+1 conditional on log(output) in t is simply the latter.

                                                                                                                                                          (36) Since the larger this period's output the smaller the possible growth defined by the upper bound to next period's output.

                                                                                                                                                          (37) These models assume that entrepreneurs are risk neutral wealth-maximizers. Their focus is in explaining the stylized facts of firm growth and failure. The optimal growth-risk model resulting from this process determines the systematic part of the firm's growth. However, it allows that part of a firm's growth is determined outside the entrepreneur's control by random proportional shocks to the firm's equity value.

                                                                                                                                                          (38) Ideally, studies of small firms should be based on a panel of data which allows for the control of unobserved heterogeneity at the firm and time level in the population, and hence avoids biases that may arise from simpler cross-sectional or time series regressions. Most of the datasets studied prior to Hall (1987) (and many since then) unfortunately do not possess this property and studies based on them were therefore subject to potential biases. However, even with a panel of data, biases can still arise and should be controlled for.

                                                                                                                                                          (39) Only Hall seems to have noticed both these potential biases, and she like other authors attempts to test for the influence only of potential failure bias.

                                                                                                                                                          (42) To see this note that ∂Eg t/∂ln(a t) = ∂γ/∂ln(a t) = ∂ln(S t/S t−1)/∂ln(a t) and similarly for x.

                                                                                                                                                          (43) Thus an x-derivative of −0.5 shows that a 1% increase in size, holding age constant, lowers growth by .5% per annum.

                                                                                                                                                          (44) It is worth noting that the average size of the startups in these samples, unlike the earlier study of Hall, is very small, being always less than five employees. The figures for failure rates of small firms contrast dramatically with those for large firms. For example, Evans (1987b) found that US manufacturing firms with 250–499 employees had a failure (closure) rate of 11.3% per annum rising to 31.9% for plants of six years or less, while DRS found that for manufacturing plants with more than 250 employees exit rates were 19% per annum for all ages of plant rising to 22% per annum for plants of aged five years or younger.

                                                                                                                                                          (45) A size transition matrix shows the proportion of firms starting in a given size class in one year that move to another size class in another year. In this case it is four years.

                                                                                                                                                          (46) Defined as the tendency of a firm to switch size classes over time.

                                                                                                                                                          (50) In this context, by dying we mean closing voluntarily.

                                                                                                                                                          (51) Cressy (2005) derives from theoretical considerations an Inverse Gaussian distribution of failure rates. Bruderl et al. (1992) however, fit a log-logistic curve to the German data. The same general pattern of skewness is however apparent in both models.

                                                                                                                                                          (52) The term industry life cycle refers to the passage of the industry through infancy, growth, consolidation and decline and the effects of this are distinguished from those due to the passage of calendar time or history.

                                                                                                                                                          (53) In view of the Cressy (2005) model, the relationship may also be influenced by the effects of initial capital constraints and risk which have not so far been controlled for in empirical studies.

                                                                                                                                                          (54) Bankruptcy rates among are in fact three times as high in the UK recession of the early nineties as in the boom which preceded it in the late eighties.

                                                                                                                                                          (55) The hazard rate of failure is defined as the probability that a business which has survived to time t should fail in the next instant. Van Praag estimates a log-logistic hazard rate function which is non-monotonic in calendar time and takes the form:

Determinants of Small firm survival and growth

                                                                                                                                                          where x is a vector of explanatory variables, t is time and k(x) = exp (x′β) with beta a vector of parameters.

                                                                                                                                                          (56) This is consistent with our definitions of failure above.

                                                                                                                                                          (57) In effect this defines success as the ability to stave off bankruptcy for as long as possible.

                                                                                                                                                          (58) This means that there are more or longer lasting opportunities available to firms ending in solvent closure, and that managers of older firms can stave off bankruptcy for longer.

                                                                                                                                                          (59) This echoes the finding of Cressy (1996b) whose strongest human capital measure predicting survival was the average age of the entrepreneurial team.

                                                                                                                                                          (60) This definition assumes that debt is the appropriate financial instrument to fund the project. See Cressy (2002) and the papers contained in the associated symposium for a more detailed discussion of the issues.

                                                                                                                                                          (61) Many billions of dollars are spent annually by governments around the world in attempts to alleviate such constraints.

                                                                                                                                                          (62) 334 citations were found for this paper as of November 2004.

                                                                                                                                                          (63) The actual estimation sample is 1,443 since negative net worth or SE income individuals were deleted from the sample. This is of course a potential source of bias.

                                                                                                                                                          (64) And who were not unemployed, out of the labour force, in the military or in school full-time in either 1976 or 1978.

                                                                                                                                                          (65) The degree of optimism of an entrepreneur decreases with age. See De Meza and Southey (1996).

                                                                                                                                                          (66) EJ assumed that human capital in wage and self-employment were independent.

                                                                                                                                                          (67) Identification of this instrument is accomplished by using county-level indicators of household income for the owners.

                                                                                                                                                          (68) Their model predicts that individuals with greater entrepreneurial ability for given wealth will be more credit constrained. AB show that the demand for capital will be higher for better entrepreneurs at any given wealth.

                                                                                                                                                          (69) Astebro and Bernhardt are also able to control for the fact that some industries have a larger efficient minimum scale (MES) and for differences in risk across industries, both of which may militate against the decision to enter. Industries with larger MES are entered by wealthier entrepreneurs and firms with greater risk of failure start with less capital, suggesting that credit constraints bite more strongly in these categories. However, using interaction terms between each of these items and wealth they find no marginal impact on capital requirements and hence on credit constraints.

                                                                                                                                                          (70) The term downscaling is mine. PVP argue that downscaling of a loan is evidence for the existence of a credit constraint on a firm. This is plausible if one were able to control adequately for other factors that might explain the downscaling. These include the degree of optimism of the borrower. Since younger borrowers are more likely to have their applications downscaled (as optimists they will ask for too much), their entrepreneurial age variable in effect controls for a potential fly in the ointment. However, PVP do in fact implicitly control in their study for this effect with the inclusion of the entrepreneurial age variable. See De Meza and Southey (1996) for some of the theory underlying the optimism hypothesis in entrepreneurship.

                                                                                                                                                          (73) Holtz-Eakin et al. following Blanchflower and Oswald (1998) examined the impact of both the wealth of the individual defined as her liquid assets and her house equity and any inheritance on the decision to enter business and the capitalization of the business once started. In fact, only the inheritance variable had any impact and that impact was quite substantial. For example, a $100,000 inheritance increased the probability of transition into SE by about 15%, proportionately. Importantly, HE also show that the inheritance effect is not due to the inheritance of businesses. If the latter were true then the observed correlation of inheritance and start-up propensity would simply have been the decision by inheritors to continue running their parents' businesses.

                                                                                                                                                          (74) This finding is inherently implausible too. The argument for credit constraints is, if anything, about whether relatively poor or cash-strapped individuals can efficiently start their own firms. The fact that it now appears that only the richest individuals in society are ‘cash-strapped’, surely constitutes a rather exquisite paradox for the theory of credit constraints. It might, of course, be the case that such individuals are indeed the ones to target with loan guarantee schemes and government subsidies, but this seems socially reprehensible to say the least.

                                                                                                                                                          (75) To be fair, Holtz-Eakin et al. are aware that their results may not generalize to the broader population, but argue that it is plausible to assume that they do.

                                                                                                                                                          (76) There are, of course, counter-examples. The most glaring is the fact that huge numbers (millions) of people, often the poorest, engage regularly in an unfair bet, namely the national lottery. This is inconsistent with risk aversion.

                                                                                                                                                          (77) Evidence for this goes back at least 30 years to the UK's Bolton Committee, a landmark in the study of smaller firms (Bolton, 1971). However, of more recent vintage, and referring specifically to aversion to bank control is Cressy (1995).

                                                                                                                                                          (78) In Cressy (1993), I showed that only one-third of firms borrowed even on overdraft at start-up. This grew to one-half within three years, but was still a minority of (surviving) firms. Indeed, the attrition rate in the sample was considerable (many businesses closed within three years) but the propensity to borrow among survivors, and the average amount borrowed, increased over time.

                                                                                                                                                          (79) The standard formula for the slope of an indifference curve is −MUx/MUy where x and y are the two commodities yielding utility to the consumer.

                                                                                                                                                          (80) Cabral also uses this model to provide an interesting alternative (possibly complementary) explanation for why allegedly capital constrained businesses grow faster than unconstrained ones. But on that issue, see later.

                                                                                                                                                          (81) Cressy and Olofsson (1997) found that some small Swedish firms would rather sell the business altogether than give up a share to an outsider. The aversion to outside equity declined with younger firms in the service industries.

                                                                                                                                                          (82) Greater under-diversification of the entrepreneur is also a consequence of not taking on outside equity.

                                                                                                                                                          (83) Bhide (1999) found that the vast majority of his fast growth firms grew from retained profits.