Small Firm Entrepreneur Survival

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SURVIVAL OF THE SMALL FIRMAND THE ENTREPRENEUR

UNDER DEMAND AND EFFICIENCY UNCERTAINTY

Manuel G. Flores-Romero

No 700

WARWICK ECONOMIC RESEARCH PAPERS

DEPARTMENT OF ECONOMICS


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1 I ntroduction

Why do some small rm owners wish to start a new rm after having closed one that was

not successful? In this paper we try to answer this question. Why is this question relevant?Firstly, becausestraightforward intuition provides two conictinghypothesesasanswers. Ononehand, wecan arguethat thesmall rmowner has learned fromhis mistakes and believesthat in thefollowingventurehecan dobetter. This suggests theentrepreneur believeshehasthe potential talent to run successful rms, he was just unlucky in his previous venture. Ontheother hand, wecan arguethat thelack of success in his previous ventureis a reection of thefact that he does not have theskills to run a successful rm. If hedoes not havewhat ittakes, why would hewant to start a new rm? Secondly, because weshow that the desire of opening a new rm after having closed an unsuccessful one is a rather common occurrenceamongst entrepreneurs. Utilisinga survey of entrepreneurs in theUnited Kingdomwhohaverecently experienced abusinessclosure, weshowthat 45%of theseentrepreneurs wish to starta new rm, despitethe lack of success in their previousventure. Do theseentrepreneurs havethetalent to run successful rms?, or are they being irrational by hopingthey will do betterthe next time given that it has been proved they do not have the necessary entrepreneurialskills? Both questions cannot be answered a rmatively. In any case, we believean answerin oneway or another will constitute ndings which should be considered by policy makersinterested in the promotion and encouragement of start-ups and entrepreneurial activity.

Hence, the importance of tackling our initial question.

Our question is also relevant in the context of research on small rms. In the Economicsliterature, theinterest in research on small rmshasbeen increasingin recent years. Thiscanberegarded asa consequenceof the recognition duringthe80s and onwards that small rmsaccount for a considerable share of economic activity (Acs and Audretsch, 1990; Brauner-hjelm, 2000). In spite of the growing importanceof small rms in the economy, it has beenfound that small rms consistently have lower likelihood of survival than larger rms do,a nding which is now regarded as an stylised result in small rm research (Geroski, 1995;

Storey and Wynarczyk, 1996). In the light of these results, eorts have been directed tounravel the determinants of small rm survival (Bates, 1990; Audretsch, 1991; Kallebergand Leicht, 1991; Mata and Portugal, 1994; Storey and Wynarczyk, 1996). Despite the factthat in some of these research the role the entrepreneur plays as owner and manager hasbeen acknowledged to some degree, none of them look at the survival of the entrepreneur,in other words, at the outcome of the decision between keeping in entrepreneurialism bystarting another rm after having closed the previous one, or going to wage work. Glad-

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stone and Lee (1995, p. 27) on discussing the impact of the insolvency system in the UK on entrepreneurialism assert that ...there is still little or no concomitant recognition of, oraccompanying policy, to rehabilitate entrepreneurs forced out of entrepreneurialism (rmowners whose rms did not survive, my brackets), even though they are a vital part of thecompetitive cycle. Theimpact of failureon the individual entrepreneur has been of minimalinterest to most theorists... Therefore, by trying to answer why some small rm ownerswish to start a new rm after having closed an unsuccessful one, we also contribute to theeorts aimed to understand the processes which determine the survival of small rms, andwe also attempt to reduce thegap in thestudy of the forces which inuence thesurvival of the entrepreneur 1.

The paper has the following structure. In the next section, after specifying the deni-tion of entrepreneur to be used throughout our analysis, we present empirical evidence onentrepreneurial survival which shows the relevance of our initial question. Such empiricalevidence also reveals the whole spectrumof entrepreneurs attitudes, which derivefromthecombination of having or not the desire to own another rm in the future, after having theexperience of running successful rms or unsuccessful ones. In Section 3 the model andthe assumptions we use to try to answer our initial question are introduced. In contrastto current literature, in our model we specify that the prots of the small rms depend ontwo rm-specic determinants: the e ciency parameter, which represents the skills of the

entrepreneur to manage and cope e ciently with the everyday tasks of the small rm, andthe demand parameter, which denotes the success of the rms product to attract demandor capture a market niche. We assume such parameters are independent of each other. InSection 4 we introducean alternative model in which we assume the entrepreneurs abilityare not restricted to skills to manage, but that they represent some type of overall skills. The purpose of this is to provide a benchmark case for the predictions obtained by our gen-eral model. In this section we also present the predictions oered by our general model andby thealternative one, and we discuss theanswers both models oer to our initial question.It is found that our general model establishes that those entrepreneurs who start or havethe desire to start a new rm after having closed an unsuccessful one, haveskills to manageas large as those who are running successful rms. Contrary to this, the alternative modelgives the explanation that such entrepreneurs should not exist, because the fact that the

1 Interestinlgy, in Labour Economics, research on thesurvival of individuals as self-employed has attracteda lot of attention (for a survey articlesee Le, 1999). However, such studies concentrate only on theoutcomeof staying in or exitingself-employment by theindividual, without considering thefact that theseindividualsmay or may not have owned several rms in the process. That is, that they may have decided to close arm and havestarted a new one, which is our main concern.

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small rm did not survive is simply theresult that they do not have the necessary skills torun a successful rm. We believe our general model provides a more sensible answer to ourinitial question. However, to determine which model oers more credible results, we statethat such model should providean explanation not only to our initial question, but also tothe whole empirical evidence contained in Section 2.

In Section 5 we discuss which model is able to explain theempirical evidence. Wefoundthat our general model is successful in this task, whilst the alternative model fails. Bymeansof revealingthe existenceof a mechanismof entrepreneurial self-selection, our generalmodel is able to account for the empirical evidence on entrepreneurial survival. Under themechanismof entrepreneurial self-selection, skilful entrepreneurs are the only ones who wishto own another rm in the futureafter having closed one, regardless of the degree of successin their previous venture, whereas unskilful entrepreneurs prefer to go to wage work. Inthis section, given that thealternativemodel, which uses theassumption that entrepreneurshavesome typeof overall skills, is unable to explain theempirical evidence, we also reachthefollowingconclusion: when undertakingresearch on entrepreneurship if weconsider datacomprising small rm owners without any other discriminatory criterion, it is reasonable tosuppose that the skills of such business owners are limited to skills to manage, and thatthey do not comprise skills to innovate or to spot protable opportunities. In Section 6 weaddress the robustness of some of our assumptions and the implications of alternativeones.

Finally, Section 7 summarises our ndings and mentions paths for future research.

In summary, our paper answers our initial question by saying that the reason why somesmall rm owners wish to start a new rm after having closed an unsuccessful one is be-cause they havethe skills to run potentially successful rms. In fact, our ndings state thatsuch behaviour is part of a mechanism of entrepreneurial self-selection. Under such mech-anism, skilful entrepreneurs are the only ones who wish to own another rm in the future,regardless of the degree of success in their previousventure, whereasunskilful entrepreneursprefer to go to wage work. Although this mechanism accounts for theempirical evidence on

entrepreneurial survival in Section 2, we recognise that further research is needed to rejector fail to reject theprediction that those entrepreneurs who havethe desire to start anotherrm, have indeed higher skills than those who prefer to go to wage work. In any case, webelievethe ndings of this paper are a rst step in a research agenda aimed at the study of the survival of the entrepreneur.

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2 P reliminaries

2.1 T he Denition of Entrepreneur

Despitebeingafertileandgrowingareaof research, thereis noagreement amongst academicson the denition of entrepreneur. Across the literature, one article may use entrepreneurto refer to those who simply own and manage a rm, whereas others may include morecharacteristics, for instance, capacity of innovation or risk taking. Moreover, in some casesthese denitions have been used interchangeably. Holtz-Eakin (2000) on addressing thequestion Are small businesses entrepreneurial or just small? points to the problem. Heargues that Theresearch literature to date, however, has not provided a clear resolution tothis question. In part, this question has been avoided; the entrepreneurial virtues of newbusiness are often assumed rather than examined (p. 284).

Contrary to this, we restrict the denition of entrepreneur to be used in this article. To accomplish this we resort to one of the few articles which distinguishes and groups thedierent denitionsof entrepreneurship. Tyson et al (1994) oers four categories to classifythe dierent denitions. Therst oneis Entrepreneurship as innovation. They include inthis category thosedenitions built upon the schumpeterian view of entrepreneurs asagentsof innovation, in termsof developingnewproductsor methodsof productions, identifyingnewmarkets or sources of supply, or developing new organisational forms. Thesecondcategory isEntrepreneurship as risk-taking. They group in this category thosedenitionswhich viewentrepreneurs as having relatively low aversion risk, which enables them to undertake aninnovation that others are not willing to attempt. The third category is Entrepreneurshipas stabilising force. The denitions included here are those which regard entrepreneurs astakingadvantageof thestateof disequilibriumof theeconomy, wheretheine cient allocationof resources generates the opportunity for protable activities. The nal category theysuggest is Entrepreneurship as founding or owning and managing a small business. Theyassert that ...this view surfaces quite often as the empiricists denition - understandably,

given the practical di culties of identifying the population of Schumpeterian innovatorsor risk takers in an economy (Tyson et al , 1994, p. 167).

This paper adheres to the denition used more by the empiricists and regards en-trepreneurs simply as those who start or own and manage a small rm. Several reasonsaccount for this decision. Firstly, me make use of empirical data to show why our initialquestion why do some small rm owners wish to start a new rm after having closed onethat was not successful? is relevant, in thesensethat startinga business after havingclosed

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an unsuccessful one is a rather common occurrence amongst small rm owners. Clearly, thedatabase we use focuses on individuals who own and manage their rms. Accordingly, weare bound to adopt thedenition of entrepreneurship as founding or owning and managinga business. Our decision gains strength when we acknowledge the growing interest in themeasurement of entrepreneurship amongst researchers and institutions, which in general im-plicitly or explicitly denean entrepreneur as an individual who manages his own business 2.Secondly, in order to try to answer our initial question, this paper proposes that the en-trepreneurial skills of thesmall rm owners are in general of a restricted nature. Specicallywe will argue that small rms owners havean endowment of skills to manage the business,that is, to deal e ciently with the day to day activities of the business 3. This endowmentvaries fromindividual to individual. Wearguethat thesemanagerial skills are in general not

related with theability to generate revenue for therm, in other words, with theability toselect a product or servicefor which there is enough demand or there is a market niche. Insummary, this paper will suggest that the entrepreneurial skills of small rm owners are ingeneral restricted to managerial skills. Note that by no meanswe state that it is impossiblefor some small rm owners to have more than one type of skills. As will be shown, ourargument states that when we dene entrepreneur as a small rm owner, then it is moresensible to assume that their skills are limited to managerial tasks in the sense dened lateron in this paper, and that in general this managerial skills arenot correlated with theabilityto select and oer an attractive product. Finally, it must be added that as a consequenceof our denition of entrepreneur, we use the terms rm owner, business owner, andowner-manager as synonyms of entrepreneur.

2.2 Empirical E vidence on Entrepreneurial Survival:Entrepreneurs who R e-enter and Obstinate Entrepreneurs

The study by Stokes and Blackburn (2001) Opening up Business Closures: a Study of Businesses that Close and Owners Exit Routes is one in a kind. It is, perhaps, the only

research which has addressed the question of what happens to the entrepreneur once hisrm has not survived. The study was carried out in the United Kingdom. It comprised,as a rst stage, the elaboration of the questionnaire to be used to interview the small rm

2 For instance, in the project Global Entrepreneurship Monitor where oneof the principal objectives isto measure the level of entrepreneurial activity across several countries, entrepreneurship is dened as Anyattempt at new business or new venture creation, such as self-employment, a new business organization, orthe expansion of an existing business, by an individual, a team of individuals, or an established business(Reynolds et al , 1999, p. 3).

3 A moreextended exposition of what these skills might embody is contained in the next section.

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owners. This questionnaire was built from interviews with 20 organisations of dierenttype, including private organizations (e.g. banks, accountants), non-prot organisations,and government consultants, which had experience in advising small business. In a secondstage, thequestionnairewassent to asampleof 2719owner-managerswhohad recently closedtheir businesses, fromwhich 388 usableobservationswereobtained. Thestudy collects a richset of variables, which includes information on the rm (e.g. size, age), the owner-manager(e.g. reasons to start rm), nancial situation of the business at the time of closure, pathfollowed by the business owner, attitudes to the experience of closing a business, learningexperience, amongst others. Theresultsof thestudy areimpressiveinasmuch asthey providethe existing pictureof the entrepreneurs decision between sticking with entrepreneurialismor other alternatives, once the experience of business closure has occurred. As Stokes and

Blackburn state, SB henceforth, The research has considerable implications for businesseducationalists, policy makers and nanciers. Those who have closed a business are strongcandidates to become involved in a new venture, and should therefore be a prime targetfor those seeking to advise or nance new business (p. ii). In this sense, the ndings bySB are subject to providesupport on the relevance of our initial question. We will proceedas follows. As introduction, we rst provide evidence that some entrepreneurs start newrms after having closed one, that is, evidence on entrepreneurial re-entry. However, ourquestionconcentratesonthoseentrepreneurs who wish to start newrms, after havingclosedunsuccessful ones, that is, on the obstinate entrepreneurs. The SB study is also helpful inthis respect, as it provides evidence that these entrepreneurs do exist, and that they mightrepresent a considerable share of the population of small rm owners. Thus, in a secondstage, we reproduce this evidence.

In this paper we make use of two gures from SB. The rst one, Figure 1, reproducesthe gure Business owner exits - what they did next (SB, p. 17 ), except for the notes(i) and (ii) which were added for explanatory purposes. Figure 1 displays the answers bytheowner-managers, and thepercentagewhich answered in this way, to the question What

did you do after leaving the business? Therefore, F igure 1 eectively provides evidence onentrepreneurial re-entry. The relevance of the ndings from Figure 1 is that, to the bestof my knowledge, a serious research on entrepreneurial re-entry had not been undertaken,until the SB study. Figure 1 speaks for itself, although some features are worth pointingout. Firstly, the gure shows that 62% of the entrepreneurs in the sample remained inentrepreneurialismafter having experienced a businessclosure, asopposed to 29%who optedfor paid employment. Thus, we can eectively say that 29% of entrepreneurs in the sample

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In Existing Business Started a BusinessContinued

paid jobUnemployed

/illEmployed

Continuedother

existingbusiness

Continuedbusiness in

differentform i

Startedsimilarbusiness ii

Started/bought

differentbusiness

Sought Employment Retired Continued asBusiness Owner

29% 9% 62%

29% 33%

20% 9% 18% 15%

20% 3% 7%

Fate of the business owner

i It refers to a different organisational-legal formii It refers to start a similar business in a different location

Figure 1: Business owner exits - what they did next from Stokes and Blackburn (2001, p.17)

did not survive. Thepercentage of surviving entrepreneurs is further classied into thosewhostarted a new business, 33%, and thosewhocontinued in an existingbusiness, 29%. Onepoint is worth noting. Looking at the nal sub-category Continued business in dierentlegal form, it does not seem to t in the denition of closing a business as understood foreconomic purposes. That is, this sub-category refers to those entrepreneurs who did a legalchangeto their businesses, but froman economic point of viewit is still thesamermoeringthesameproduct. Asaconsequence, theobservationsin thissub-category should beignored. This isnot thecasewith thesub-category Started a similar business in a dierent location,

because location itself is a source of product dierentiation. Hence, it can be argued thatthese entrepreneurs indeed started a new rm. Finally, the sub-category Continued otherexisting business reveals that at least 20% of the sample were entrepreneurs that wererunning more than one rm at the same time. This is consistent with the term Portfolioowners suggested by Storey (1994), on referring to the ndings of Storey et al (1987) thatit is not uncommon for some entrepreneurs to have ownership interests in more than onerm. Overall, removing the observations in the nal sub-category Continued business in

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Ailing Thriving

Financial conditions of the closed business

Determined entrepreneur

Despite problem in previous

venture, they return to business

ownership determined to do better.

45%

Serial entrepreneur

Having succeeded in previous

venture, they return with resources to

invest in new business.

37%

Failed entrepreneur

The problems of previous ventures

discourage them from re-entering

into business ownership.

13%

Discouraged entrepreneur

Although their previous business

venture succeeded, they do not wish

to repeat the experience.

5%

Encouraged

Discouraged

A

t t i t u d e of

e x- o

wn

e r t o b u s i n e s s

o wn

e r s h i p

Figure 2: A matrix of owners responses to business closure from Stokes and Blackburn(2001, p.29)

dierent legal form, Figure 1 reveals that 58% percent of the owner-managers in the SBstudy were entrepreneurs who re-entered with a new rm or continued as business owners,despite having closed a previous business.

These gures on entrepreneurial re-entry do not oer any information on whether theclosed business was successful or not. Furthermore, they only show those entrepreneurswhich in fact started a new rm, and not those who wished to do so but did not re-enter. To amend this situation Figure 2 reproduces the gure A matrix of owners responses tobusinessclosure fromSB (p. 29). It classiestheentrepreneursin four quadrants, dependingon the owners view whether the business was nancially ailing or thriving at the time of closure, and on whether the owner felt encouraged or discouraged to own a business in thefuture given the experience of closure. Each quadrant also shows the percentage of ownerswhich t into the category. It is important to add that when answering these questions theowners had the option of choosing from 1 to 5, where 5 meant thriving (encouraged) and1 ailing (discouraged). Thus, F igure 2 should be seen as having in the axis the scale 1 to5. Given the nature of the questions, we can state that the top row of Figure 2 includes

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those entrepreneurs who wish to start a new rm, as opposed to those in the bottom rowwho want to leave entrepreneurialism. On the other hand, the left column comprises thoseentrepreneurs who saw their rms as nancially ailingat the timeof closure. Common sensewould suggest that rms success is related to its nancial performance. We can argue thenthat theleft column showsthoseentrepreneurswhowererunningunsuccessful rms, contraryto those in theleft column who regarded their rms as successful. In this sense, the top-leftquadrant represents the obstinate entrepreneurs, i.e., those entrepreneurs who wish to starta new rm, even though their previous ventures were unsuccessful . According to SB, theseare the determined entrepreneurs, who represent 45% of the sample, and in fact they arethe single largest group of the four. Figure 2 also shows the other three possibilities: thosewho had successful rms and wish to start a new rm, the serial entrepreneurs; thosewho

despitehavingsuccessful rmsdonot want to remain in entrepreneurialism, thediscouragedentrepreneurs; and those who were running unsuccessful rms and do not want to own abusiness in the future, the failed entrepreneurs. Interestingly, the group of discouragedentrepreneurs represents the antagonistic case to the onewe try to explain. Why do theseindividuals want to leave entrepreneurialismif they had theexperienceof runninga successfulbusiness? Is not this proof enough that they are skilful entrepreneurs? As will beshown, inour attempt to explain the reasons which drive the determined entrepreneurs to start anew rm despite not being successful in the previous one, we also try to explain the otherthree possibilities included in Figure 2.

RegardingFigure2, an issuemust beaddressed. Theright column of Figure2may revealan apparent inconsistency: why would some entrepreneurs close their rms despite beingnancially thriving? Although not theonly ones, two possibilities can explain this situation.Firstly, it is hard to imagine a small rm which was nancially thriving throughout its lifespan. Thus, it could be possible that by answering thriving or ailing the owners tended todescribe the recent average performance of their rms. Consequently, it is not unlikely tosupposethat someentrepreneurs in theright column of Figure2had rms whoweremeetingtheir expectations once, i.e., that were successful , but its performance started to decline.Secondly, for those rms in the right column of Figure 2 which were indeed nanciallythriving, it can be the case that such performance might have attracted the attention of other entrepreneurs. In this sense, it is not unlikely that if a price large enough was oeredto the owners of thesesuccessful rms, someof themmight haveaccepted to sell their rms.Under these views, the apparent inconsistency between success and closure reduces.

Themost important point fromFigure2 isthat it reveals that 45%of entrepreneursin the

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sample have the desire of keeping in entrepreneurialism, even though they did not succeedin their previous venture. Wehave no grounds to assert that thesample in theSB study isnot fully representativeof thepopulationsof entrepreneurs who haveexperienced a businessclosure in the UK 4. Nevertheless, we believe that this rather high percentage indicates therelevance of the question we try to tackle. We now introduce the model which might helpus to explain this evidence.

3 T he M odel

Themodel assumes theobjectiveof the individual is to maximisehis lifetimeutility. Hewilldo so by choosing between working in a paid job or setting up and running a rm. Here

we are invoking the so called income choice model which can be traced back to Knight(1921). Theindividual obtains utility U = W when heis an employee and U = + whenhe is running his own rm, where W is the wage from the paid job and are the protsfromrunning the rm. Following Blanchower and Oswald (1998), 0 denotes the extrasatisfaction to theindividual for beinghisown boss, which weassumeasnon-constant acrossindividuals. Wealsodene as theentrepreneurial spirit of theindividual. Theindividualdiscounts the future with rate 0 < 1 over his life span T . Thus, the problem for theindividual is max

P T t=1

t 1U t by deciding between a paid job or running his own rm.

The individual knows his own , which is constant over time, and has perfect foresighton future values of W . For the sake of simplicity we assume W remains constant. If the individual decides to run a rm, hewill enter an industry characterised by monopolisticcompetition wherethetechnological conditionsof such industry and thephaseof theproductlifecycle suggest incumbent rms are not aected by economies of scale, and as a result theydo not need to grow to survive. Thepurposeof theseassumptions is to simplify theanalysisby allowing the rm to ignore its competitors 5 and by eliminating the requirement to growto survive found as empirical regularity for small rms in the manufacturing sector 6. We

4 According to SB, the 388 usable responses were obtained from HSBC bank customers who closed abusiness account (36%), fromDun and Bradstreet lists of existing business (5%), and fromclosures identiedduring research on other projects by the Small Business Research Centre, Kingston University (59%).

5 Weuse the denition of monopolistic competition proposed by Hart (1985). He points out, in the spiritof Chamberlin (1933), that monopolistic competition might be dened as one where there are many rmsproducing dierentiated commodities, each rm is negligible so it can ignore its impact and reactions fromother rms, and each rms faces a downward sloping demand curve.

6 There is an abundant literature which provides empirical support to the fact that small rms presenceand survival in the manufacturing sector depend on the technological conditions of the industry, suggestingthat economies of scale play a role. See, for instance, White (1982), Acs and Audretsch (1989), Audretsch

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now discuss thenatureof theentrepreneurial skills to beused in this paper.

On thesmall rmand entrepreneurship literaturethere is now a tradition to assumethat

theprots of thesmall rmdepend on thetalent or skills of its owner. Lucas (1978) was therst who put forward the notion that rms prots depend on the talent of the managers.In his model heshows how variations in talent across managers lead to a sizedistribution of rms. J ovanovic (1982) proposed that e ciency wasthe rm-specic determinant of prots.In his model, rms start small and those which discover they are e cient grow and survive.Later on, Frank (1988) merged the two ideas by assuming that the skills or talent of theentrepreneur determines the e ciency of the small rm, and thereby its prots and survival.Further theoretical and empirical studies show that it became rather common to assumethat small rm prots depend on the skills of the entrepreneur 7. The points to highlight inthese papers are that they assume the skills of the entrepreneur are the only rm-specicdeterminant of prots, and that they do not discuss what these skills entail. Contrary tothe models such as the ones in J ovanovic (1982) and Frank (1988), we assume the protsof the small rm depend on two rm-specic determinants, which we call the e ciency andthe demand parameters, and we restrict the nature of the entrepreneurial skills of the smallrm owner. More specically, weassumea prot function for thesmall rm of the followingform

ij

= pQ

p;

ij

1 j cQ

p;

ij

. (1)

Thesearethe prots for entrepreneur j 2 J running rm i 2 I , where I \ J = ? , and where p is the price of the good/ service oered or to be oered by the rm, and Q () representsthedemand function. The demand parameter is represented by . It denotes how successfultherms product is in attractingcustomers or in capturing a market niche. A high valueinij would mean that entrepreneur j is running the small rm i which is oering a productor service that is very appealing to customers, which in turn is generating relatively largevolumes of revenue to the small rm. The e ciency parameter is represented by . It

denotes the skills of the entrepreneur to run a business, which are directly translated asthee ciency of therm. A skilful entrepreneur would berepresented by a high value in j ,

(1991), Mata and Portugal (1994), Geroski (1995). Interestingly, the very few studies that have looked atthe servicesector (e.g. Audretsch et al , 1999), or at industries in thematurephase of theproduct life cycle(Agarwal and Audretsch, 1999 and 2001; Agarwal and Gort, 1996) have found that small rms in thesecircumstances do not need to grow survive. This can be explained by accounting for the small size of theminimum e cient scale in these industries.

7 See, for instance, Evans and J ovanovic (1989), Bates (1990), Holtz-Eakin et al (1994), Cressy (1996),Storey and Wynarczyk (1996).

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which in turns meansheis ableto run his own rmmoree ciently 8. Wefurther assumethattheseparameters are a sourceof uncertainty for the entrepreneur because they are unknownto him. He only knows that his true skills and true demand for his rms productare random draws from some distributions. The only way the entrepreneur can learn theparameters ij and j is by running a rm. Specically, weassume that

A .1 is an i.i.d. stochastic variablewith cumulativedistribution function (CDF)A (), with support [0; 1 ). A () is continuous and twice dierentiable. A () isknown by theindividual.

A .2 is an i.i.d. stochastic variable. It has a CDF G () with support (0; 1 ).G () is continuous and twice dierentiable. The individual knows the form of

G ().

One consequence of these assumptions is that the parameters and are uncorrelatedwith each other. Furthermore, note that by assuming the prots of the small rm de-pend on these two uncorrelated rm-specic determinants, and by assuming that the rmsdemand function is only aected by the parameter ij , we restrict the nature of the en-trepreneurial skills of the small rm owner. In other words, our framework supposes thatthe entrepreneurial skills j are limited to skills to manage therm, and do not include theability to select and oer an attractive product, as represented by ij , which might guaran-

tee large revenue to the rm. Without attempting an exhaustive lists, our denition of theparameter j , include theentrepreneursability to organise and assume theresponsibility of the activities of the small rm, to select the cheapest inputs given a desire level of quality,to deal with suppliers and, perhaps, employees, to ensure that the production of goods orservices in the rm is done in the best possible way using the resources available, amongstothers. In general, they represent the skills to undertake e ciently the everyday activitiesof the rm and to tackle the problems that might arise. As can be seen, our denitionof entrepreneurial skills do not includes the notion of Schumpeterian innovators, but iscloser to the denition of the entrepreneurs general ability put forward by Marshall 9.

8 Two other important dimensions of entrepreneurship which might aect the prots of the small rm arethe entrepreneurs degree of risk aversion and the entrepreneurs degree of disutility of eort. To keep ourmodel simple, we omit them in the present analysis. In a later section we discuss the likely impact of theirinclusion.

9 He denes theentrepreneurs general ability as theonewhich allows him to be able to bear in mindmany things at a time, to have everything ready when wanted, to act promptly and show resource whenanything goes wrong, to accommodate oneself quickly to changes, to be steady and trustworthy, to havealways a reserve of force... Marshall (1930, pp. 206 - 207).

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Similarly, this paper follows those which haveexplicitly acknowledge thepossibility that theentrepreneur may haveskills which are restricted to specic activities 10 .

The following additional assumption are made about the prot function and about theindustry the small rm would operate in:

A .3 Q ( p; ij ) = D (ij ) bp is the demand function the small rm faces, whereb > 0 and p is the price of the good/ service. Since the industry is subject tomonopolistic competition, elasticities of substitution between any rms goodand the rest are assumed to be zero, and only the price of the rms own goodaects the rms demand. Thedemand function has the following properties:

@Dij

@ >0, @ 2D

ij

@2 < 0 . (2)

A .4 All operating rms have the same cost structure which they acquire afterpaying the exogenous sunk cost k > 0, which is the same for every rm.

A .5 Thecost function 1j cQ ( p; ij ) presentsconstant marginal costs, where c > 0.

We also assume that there exist a Qmax such that for any Q > Q max , c = 1 .

These assumptions serve dierent purposes. Conditions A.4 and A.5 together imply allrms can potentially producethesameamount of output. Note that, due to theassumptionof monopolistic competition, all rms are by denition small, which means that should thesize of rms be measured by production levels, Qmax is small enough for all rms to tin the small size category. Condition A.5 also tells us that marginal cost is constant overthe feasible production range. Intuitively, this captures the assumption that rms are notaected by economies of scale, since the average cost is constant over the production range. Thus, growing to reach the minimume cient scale is not a requisite for the rms to remaincompetitive.

Prior to owning a rm, the individual ignores his entrepreneurial skills and whether ornot the product/ servicehe is planning to oer will attract enough demand, i.e., he ignoreshis endowment of ij and j . Once the individual runs a rm for the rst time, nature

10 Our model is similar to the ones in Holmes and Schmitz (1990) and Giord (1993) where it is assumedthere are two types of entrepreneurial abilities: talent to manage and talent to develop new products. How-ever, our model diers fromtheirs in weare interested in thestudy of small rm and entrepreneurial survival,whilst Holmes and Schmitz (1990) concentrate on the sale and buy of business, and Giord (1993) focuseson the distribution of rm sizes and the choice of specialisation as innovative entrepreneur or managerialentrepreneur.

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determines these values fromthe CDFs A () and G (), respectively. Additionally, when theindividual is runninga rm, hedoes not observethesevalues directly, but indirectly throughrealisations in every period. This process is represented by

' ijt = ij + ! t , jt =

j + ! t ,(3)

where ! is an i.i.d. normal random variable with mean zero and variance 2 . Once the rmis in operation, the entrepreneur learns about its own e ciency and demand by observingthe realisations ' ijt and

jt in every period. Weassume that thelearning process, or in other

words, the method the entrepreneur uses to estimate and update his beliefs about ij and j in every period is a bayesian method.

P rot M aximisation

The objective of the individual when he is running a rm is prot maximisation. Sinceprots depend on the parameters and , themaximised valueof prots will depend on thespecic parameters theindividual is endowed with. Themaximisation problemis representedas

max pt

T 1X

t=

e

t e ij + j

t subject to

ijB and

jB ,

where pt represents thepricethemonopolistic rm chooses to apply, and ijB and jB denotes

the bayesian estimator of ij and j , respectively. We also assume the individual starts arm in period e. Since the expected value of future values of a bayesian estimator is equalto the current bayesian estimator, i.e., E [B ]t+ z = [ B ]t for any z > 0, where E [] denotesthe expectation operator 11 , theproblem reduces to calculate themaximisation problem justfor the period t = e. Therst order conditions give

p @Q

@p+ Q

p; ijB

c

jB

@Q

@p= 0 , (4)

which rearranged provides the standard mark-up rule

p 1jB

c

p=

1"

ijB

, (5)

11 See Winkler (1972, p. 204).

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Equation (5) spells out theeect thedemand and e ciency parameters have on thepricingstrategy of the rm and, ultimately, on the prots of the rm. The more skilful the en-trepreneur is, i.e., thehigher j , thehigher themark-up is. Likewise, thehigher thedemandparameter, themore inelastic the priceelasticity " ijB is, and thehigher themark-up is.

Let theoptimumprice and quantity beexpressed as

p pijB ;

jB

Q QijB ;

jB

,

and thesolution to themaximisation problem as

max pt

P T 1t=

e t e

ij + j

ts.t. ijB and

jB

ij

B; j

B

+ j

1 T e

1 . (6)

This is the discounted value of the maximum expected utility from running a rm. It canbe shown that the second order conditions for a maximum are satised. As can be seen,the maximum expected prots

ijB ;

jB

, from now on simply prots, are a function of

the parameters ij and j which are updated in a bayesian fashion every period. Thenext lemmas are presented for mathematical rigorousity and establish the properties of theprots with respect to the demand and e ciency parameters. To saveon notation we dropthe superscripts i, and j , and the subscripts t and B .

Lemma 1. The prots are an increasing function of e ciency: @ (;)@ > 0.

P roof. The rst order conditions (4) are expressed as bp + D () bp + cb = 0 , thus p (; ) = D ()2b +

c2. The demand function is Q ( p; ) = D () + bp. Hence, Q (; ) =

D ()2

bc2, and

(; ) = (bc D ())2

4b2 . From here it follows that@ (;)

@ =c

23 (D () bc),which rearranged yields @

(;)@ =

c2

D ()

2 bc2

. Now, the terms insidethebrackets in the

right-hand-sideareequivalent to Q (; ). In this way wecan write @ (;)@ =

c2 Q (; ) and

thus @ (;)

@> 0.

Lemma 2. The prots are a function of the demand parameter in the followingway: when-

ever p (; ) > MC wehave @ (;)@ > 0,.andfor p (; ) > MC +

12b

@D()

@

2 @

2 D ()@2

1we

have @ 2 (;)

@2 < 0, where MC =c is the marginal cost .

P roof. From the proof of Lemma 1 we obtain @ (;)@ =

@D()@

D ()

2b c

2

. From the

value of p (; ) we have D ()2b = p (; ) c

2, which inserted in theterm in brackets renders

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@ (;)@ =

@D()@

p (; ) c

. Thesign of this expression is positive whenever p (; ) > c.

Regardingthesecondpart, wecalculate @ 2 (;)

@2 =12b

@D()

@

2+ @

2 D ()@2

p (; ) c

. Were-

quire @ 2

(;)@2 < 0 , soweevaluateunder which conditions 12b

@D()@

2+ @

2

D ()@2 p (; ) c

c +

12b

@D()

@

2 @

2 D ()@2

1where thesecond term on the right-hand-side is positive.

3.1 T he Decision to Start a F irm

The individual will choose to work in a paid job or to set up and run a rm depending onwhether or not the expected utility in one state is larger than it is in the other. When theindividual has not started a rm before, the only information he has available to calculatethe expected prots from running a rm is the distribution of the parameters and . Atthis stage the only two alternativestates are to start a rmor to work in a paid job. Underthis situation, the maximisation problem for the individual can beexpressed as choosing

argmax

W j ; E

max p

ij + j

, (7)

where ij is specied by (1), and E [] denotes the expectation operator. At this stage, theindividual is constrained to rely on theexpected value of themaximumprots as hehas no

other way to infer better estimators for his trueparameters. This expression is rewritten as

argmax

W j ; E ;

[ (; )]+ j

(8)

where wedene (; ) as the valueof maximised prots, and therefore

E ;

[ (; )] Z 1

0

Z 1

0 (; ) dA () dG () (9)

as its expected value. Rearranging expression (8) we obtain

argmax

W j j ; E ;

[ (; )]

. (10)

We are now in position to state that whenever the following expression is true, theindividual has an incentive to turn down paid job and start a rm

E ;

[ (; )] W j j . (11)

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Note that the above inequality does not state that individual j will enter the industry incase it is fullled. To enter theindustry theindividual requires funds to set up therm andcover thesunk costs. Theprocess whereby individuals gather thesefunds and thedi cultiesthey may face are issues not included in thescopeof this paper 12 13 .

Notethat theassumptions of our model areconsistent with thedenition of entrepreneurwe use in this paper as those who started or own and manage his rm. Firstly, by assumingthat the individual seeks to maximise utility by choosing between running his own rmor being an employee, we eliminate any possibility that entrepreneurs would start a rmbecausethey havegenerated any kind of innovation or becausethey havespotted a protableopportunity. This is reinforced with the fact that we assume the demand parameter to be a random draw and that the entrepreneur is not able to provide a better forecast

apart from the mean of the parameters distribution. Additionally, as has been alreadydiscussed, by assuming that and are independent random variables no correlated witheach other, we restrict the skills of the entrepreneurs to manage. Secondly, by making nospecic assumptions about those individuals who start and run a rm, our model implies allentrepreneurs have the same degree of risk aversion. We now turn to the predictions thismodel oers to answer our initial question.

4 R esults

Once the individual has decided to set up and run a rm at the end of a given period, itis assumed that the rm is formally in operation in the next one. As dened before, theproblem for theindividual is to maximise his lifetime utility. Therefore, when he is runninga rm he has to determine which state provides the largest utility. What are these states?It is straightforward to see that onepossibility is to keep his current rm running. A secondpossibility is the wage worker state. This would imply to close the current rm and go topaid job. Furthermore, a third possibility is theoption of running a dierent rm. In otherwords, the possibility of closing the current rm and starting a new one. Why is this last

12 For research on thetopic see, for instance, Evansand J ovanovic (1989), Blanchower and Oswald (1998), Taylor (2001).

13 Regarding therisk nature of the individual, consider theexpression E ;

[ (; )]+ R j > W j j . From

here, wecan denewhen theindividual is risk averse( R j > 0), risk neutral ( R j = 0 ), or a risk lover ( R j < 0). Thus, in this paper we are assuming that the individual is risk neutral. A more extended discussion on thereasons why it is more sensible to include the entrepreneurs degree of risk aversion on the decision betweenemployment and self-employment, and not asa parameter aecting the prots of the small rm, is containedin a subsequent section.

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possibility relevant? In line with monopolistic competition markets, the situation we arelooking at is, for example, onewhere theentrepreneur was runninga Chinese take away andis decidingto moveto Mexican food, or to open a sport clothes retail outlet. In this sense, bynew rmwerefer to onewherethegood or serviceto beoered by such rmis dierent fromthe oneoered by the previous rm. Therefore, once the entrepreneur is running a rm, tomaximise his utility he must decide whether keeping his current rm is the best choice, orif closing and starting a new rm provides the largest utility, or whether he is better o byclosing and going to a paid job.

Let e represent theperiod in theindividuals lifespan when hestarted a rm. At theendof every period e; e +1 ;:::;T theindividual evaluates which stateprovides thelargest utility.Let s 2 f 1; 2;:::;T eg represent the number of periods the individual has been running arm. Thus, the utility from keeping the current rm running is calculated by

max pt

T 1X

t= s

t s ijt s.t. ijB and

jB .

ijB ; jB

1 T s

1 . (12)

This is the same expression as in (6), in which the entrepreneur uses the bayesian methodto calculate his expectations about the parameters ij and j .

Given thenatureof theparameters ij and j , theprocedure to calculate theprots the

entrepreneur would obtain for starting a new rm is dierent from the one shown by theprevious expression. Recall that j represents the skills of the entrepreneur to manage therm e ciently. These skills are time invariant, that is, talented entrepreneurs are alwaystalented, whereas unskillful entrepreneur are not able to enhance such skills 14 . Therefore,once the entrepreneur has started a rm for therst time and has learned his true valueof e ciency, he is constrained to this valuein thefuture. This meansevery time he starts anew rm, his e ciency parameter remains the same. However, this is not true for the caseof the demand parameter, for we allow dierent products to face dierent levels of demand.In other words, every time the entrepreneurs runs a new rm, he receives a dierent valueof . In the context of the above example, it is easy to think that the new Mexican foodoutlet or thenew sport clothes retail outlet theentrepreneur is planning to set up might not

14 This assumption may seem very restrictive at rst glance, since it eliminates any possibility for theimprovement of skills to manage as a result of learning. However, in our model this is not the case becausewe assume the parameter j embodies the endowment of potential skills, which can be regarded as timeinvariant. In this sense, entrepreneurs with low e ciency may improve the way they manage their rmsover time, but they have a very limited space to improve these skills because by denition they have lowpotential.

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attract enough demand, regardless of the fact that the Chinese take away was a successornot. In terms of our model, this implies theexpected prots of a new rm are calculated asfollows :

E

"max

pt

T 1X

t= s

t s jt s.t. jB

#

Z 1

0

; jB

dA ()

1 T s

1 . (13)

Note the dierence between expression (9) and (13). Expression (9) represents the expectedprots for a de novo entrepreneur, that is, for an entrepreneur which does not have anyexperiencein runninga rm. This meansthat a denovo entrepreneur ignoreshisendowmentof both parameters and , and as a consequence he would calculate expected protsby applying expectation over both parameters. In contrast, in our model an incumbent

entrepreneur, i.e. one which has experience in running a rm, has already discovered hise ciency parameter. Therefore, if he is to start a new rm the unique uncertainty is thedemand parameter. Hence, the fact that the expected prots of a new rm as shown by(13) are calculated by applying expectation only over the demand parameter. To save onnotation we dene

E

; jB

Z 1

0

; jB

dA () .

Finally, the third alternative for the entrepreneur is to close his current rm and go toemployment. Given that expression (11) was the decision rule to enter the market, we set

jR = W j j (14)

to indicatethereservationlevel of prots. Additionally, weassumethat oncetheentrepreneuris runninghisrm, thevalueof thealternativeof returningto wagework startsto depreciate. This can be regarded as the increase in satisfaction the individual receives for being his ownboss. This is indicated by s jR , where 0 < 1 is the rate of depreciation and s is thenumber of periods the individual has been running a rm as dened before. Thepurpose of this is to adhere to thestylised result that theprobability of dropping fromself-employmentdecreases the more time the individual spends as self-employed (Evans and Leighton, 1989;Blanchower and Meyer, 1994). The utility from the employment state are thus expressedas

T 1X

t= s

t t s jR = s jR

1 ( )T s

1 .

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In this sense theproblem for theentrepreneur is written as

argmaxn

ijB ;

jB

; E

; jB

; jR d ( ; ;T; s )

o, (15)

where d ( ; ;T; s ) = s (1 )(1 ( )T s )(1 )(1 T s ) , and the rst argument stands for the prots of the

current rm, thesecondargument for theprots of anewrm, and thethird onefor thevalueof going to wage work. Before proceeding with the predictions oered by expression (15)we will look rst at the predictions obtained from an alternative model, which will providea benchmark for our general model, and will provide a case in support of the denition wehavegiven to the parameter j .

4.1 T he A lternative M odelIn Subsection 2.1 we mention that there is a lack of consistency in the denition of en-trepreneur used by academics across the research literature. To surmount this problem wealso state that the denition of entrepreneur to be used throughout this paper refers tothose individuals who started or own and manage his own business. In agreement with thisdenition wespecify that thee ciency parameter j denotes theability of theentrepreneur,which we restrict to skills to manage and deal e ciently with theeveryday activities of therm. In this context, theobjectiveof this subsection is to build an alternativemodel where

this assumption is relaxed, and to try to providean answer to our initial question using suchalternative model. In turn, the predictions of both the alternative model and the generalonewill beconfronted. Thejustication to do this is simple: if in thespecilised literatureonbusiness and economics there is no agreement on the denition of entrepreneur, in the non-specilised literaturelikenewspapers and magazines and in thepopular knowledgethefeelingis that an entrepreneur is or should rather be an individual which possesses many quali-ties: good management skills, vision, discipline, innovative ideas, willingness to take risks,amongst others. Hence, the attractiveness of modifying the denition of our parameter j

to encompass one or moreof these characteristics.

To this end consider the prot function

j j

. (16)

Let j represents some sort of overall entrepreneur skills for individual j . Accordingly,we assume that the prots are a strictly increasing function of , i.e., @ / @ > 0. Thisfunction generalises the prot function that can be found in J ovanovic (1982) and Frank

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(1988), and in fact, in terms of the assumptions of our general model, it would imply thatthe parameters ij and j are perfectly correlated. To appreciate this consider a protfunction of the form revenuefunction minus cost function

= R () C () ,

where the technology of production is included in the latter and the demand function inthe former. Recall that this is the form of the prot function we consider in our modelas shown by expression (1), where the demand parameter ij aects the revenue functiondirectly, and the e ciency parameter j inuences the cost function. J ovanovic (1982)assumes the small rm produces in an industry with homogeneous product and perfectcompetition. Hence, he eliminates the need for the existence of a parameter like ij andconcentrates on the cost function. In his model the e ciency parameter aects the costfunction and is the only rm-specic determinant. Frank (1988) assumes that the talent of the entrepreneur is the only rm-specic determinant and that it aects the technology of production as well. He does not makeany assumption on the typeof competition thesmallrm faces. His model is equivalent to J ovanovics in the sense that it discards the existenceof a parameter like ij by implicitly assuming homogeneous product and concentrates inthe technology of production. We believe our general model oers a more realistic case byassuming monopolistic competition and hence the existence of dierentiated products, than

by simply assuming small rms compete in markets with homogeneous products. Under ourgeneral model, if weassumetheprots of thesmall rm depend on a single parameter whichembodies the overall entrepreneurial skills of theowner, then it must be the case that suchskills aect both therevenuefunction and thecost function. Hence, our argument that undersuch scenario, it is as though the parameters ij and j were perfectly correlated.

Note that the parameter j therefore represents more than one characteristic of en-trepreneurial skills, because under theform of a prot function like(16), the implications isthat theentrepreneur has talent to generate revenuefor thesmall rm, ashedoes to manage

the rm e ciently. In other words, it implies that if the entrepreneur is a skilful manager,then he also has the ability to identify or develop products which are very appealing tocustomers, in other words, he also has skills to innovate or to spot protable opportuni-ties. Under this assumptions, a skilful entrepreneur running a small restaurant would be assuccessful as he would in running a small video shop, because having a high value on theparameter j implies that he is a skilful managers and skilful in distinguishing protableopportunities.

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Following a similar procedure as in Subsection 3.1, assume is an i.i.d. stochasticvariable which follows a specic cumulative distribution function, and let

E [ ( )] jR (17)

represent the entry decision, where jR = W j j . If inequality (17) is satised, the en-

trepreneur has an incentive to turn down paid job and start a rm. Oncetheentrepreneur isrunning a rm, the entrepreneur evaluates which state provides the largest utility. Thus, hehas the option of keeping his current rm, or closing down and going to wage work, whichis represented by the following expression

argmax

(

max pt

T 1X

t= s

t s j ( ) t s.t. jB ;

T 1X

t= s

t t s jR

)

.

This expression is equivalent to

argmax

jB

; jR d ( ; ;T; s )

, (18)

where jB

are the maximum prots given the bayesian estimation of j . The rst

argument represents the value for the entrepreneur of keeping his current rm, and thesecond denotes the value of the alternative of returning to wage work for an entrepreneurwho has been running a rm for s periods.

Note that thedierencebetween expression (18) and (15) is that theprots of a possiblenew rm are not included in (18), because these prots would be the same as the protsof the current rm. In other words, given that the small rm prots depend only on theoverall skills of the entrepreneur as denoted by j , and since these skills do not changefrom running one rm to another, the entrepreneur would expect the performance in thenew rm to be the same as the oneheexperiences in the current rm: the same success inthe small restaurant as in the video shop 15 . This means it would not make sense for theentrepreneur to shut thecurrent rm and try to start a new onebecause hewill not do anybetter in the new venture.

From expression (18) whenever the rst argument is at least as largeas the rst one theindividual decides to keep running his rm, i.e., the rm survives. Therefore, for the rm

15 As in the case of j in our genereal model, we assume j entails the endowment of potential skills, soentrepreneurs with low values of will always perform poorly.

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to survive, the problem for the entrepreneur reduces to obtain prots satisfying the weakinequality

jB

jR d ( ; ;T; s ) . (19)

From here we obtain thenext proposition.

P roposition 1 Let j ( j ) where j 2 J and @ ( )/ @ > 0. The maximisation prob-lem is the one shown by (18). Dene F as the minimum level of expected entrepreneurialskills which would induce the entrepreneur to start a rm, and min as the minimum level of entrepreneurial skills required to keep the rm running. Let H J be the subgroup for whichexpression (19) is not satised. Therefore, 8 j 2 H , jB < min < F . As a consequence,

the wage work state will always provide the largest rewards to subgroup H .

P roof. Let F solve jR = ( F ). Since @ ( )/ @ > 0, any j > F would satisfy

(17) Let min solve expression (19), ( min ) = jR d ( ; ;T; s ). Thus, we rewrite thisexpression as ( min ) = ( F ) d ( ; ;T; s ). Sincethetermin squarebrackets is smallerthan one for < 1, this implies min < F . If for the subgroup H expression (19) is notsatised and since @ ( )/ @ > 0, then it must bethecase that 8 j 2 H , jB < min < F .Given that the value j does not vary overtime, the second argument of expression (18),which represent the reward in the wage work state, will always be the largest for subgroupH .

Proposition 1 states that when the only rm-specic determinant of the prots of thesmall rm are the overall entrepreneurial skills of the owner-manager, those entrepreneurswhose rms do not survive have skills lower than they expected and lower than the onesrequired to run a rm, therefore, it is optimal for them not to try to start another rm inthe future. In other words, this framework unambiguously implies that for every failed rmthere is a failed entrepreneur. As a consequence, not only the rm will not survive, but alsothe entrepreneur will not attempt to start another rm again.

Figure3 presents graphically the arguments contained in Proposition 1. Recall that jRrepresents thevalueof thewageworker state, and werefer to jR d ( ; ;T; s ) as theupdatedreservation level, that is, once theindividual has started a rm 16 . An individual would starta rm provided hebelieves hewill receiveprots larger than the reservation level. In Figure

16 In Figure 3 we are further assuming B (0) = 0 and @ 2

@2 < 0. None of these assumptions are central totheresults in Proposition 1.

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?

( ) ( )min*,,, = sT d R ( ) F R = *

min F

( ) j B *

0

j H

j

B

Figure3: When theprots of thesmall rmdepend only on theoverall entrepreneurial skillsof the owner-manager.

3 this is depicted as anticipating prots over or above the horizontal dotted line, whichinvolves that the entrepreneur expects to have skills no smaller than F . Once the rm is

running, the entrepreneur will keep the rm and refuse to become a wage worker whenevertheexpected prots are larger than theupdated reservation level, i.e., whenever theexpectedprots are above the horizontal solid line. This suggest the entrepreneur must have skillslarger than or equal to min , where we interpret this last parameter as the minimumskillsto run a rm. The rst fact to note is that min < F . In other words, the entrepreneurcan aord to have skills smaller than theones which would draw him into themarket, andstill opt for runninga rm. This result is a direct consequence of including thedepreciationrate . Focusing on Figure 3, it is easy to see that a rm that did not survive means theowner-manager estimated the expected prots to be lower than the rewards in the wageworker state. In turn, this unequivocally means the entrepreneur has skills to run a rmbelow min . Given that theentrepreneur is conned to this level of skills, hewill ndoptimalnot to start another rm in the future.

More specically, when the prots of the small rm depend only on the overall en-trepreneurial skills of theowner, Proposition 1 indicates two points. Firstly, if thesmall rmdoes not survive, it meanstheentrepreneur has skills lower than herequired. In other words,

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heis not good in runningrms. Secondly, under this scenario, this failed entrepreneur wouldnd it optimal not to own another rm in the future, because having low entrepreneurialskills means he will receive higher rewards from the wage worker state. As it stands, thisalternativemodel does not seem to providean intuitive answer to our initial question as towhy some small rm owners wish to start a new rm after having closed one that was notsuccessful. According to Proposition 1 such entrepreneurs should not exist, because the factthat the small rm did not survive is simply the result that theentrepreneur does not havethe necessary skills to run a successful rm, and therefore it is not rational for him to ownanother rm in the future sincethe wage work state provides higher rewards. However, theempirical evidenceprovided in Section 2 shows that a rather high shareof entrepreneurswhoclosearmwish to own another onein thefuture, despitethelack of success in their previous

venture. Weconcludethat a model wherein the prots of the small rm depend only on theoverall entrepreneurial skills of thesmall rmowner, which implicitly assumes the owner hasthe same level of skills to select an attractive product which generates high revenuefor thesmall rm as he does to manage the rm e ciently, does not help us to answer our initialquestion and to explain the empirical evidence. In the following subsection we present andevaluate the predictions of our general model, which provide a better explanation. Finally,notethat another implication of thealternativemodel is that thetermssurvival of thermand survival of theentrepreneur areequivalent, event though they havedierent meanings.Wecan roughly denesurvival of therm as the term which refers to thesituation whenthesmall rmcontinues trading, and survival of theentrepreneur as theonewhich denoteswhen the entrepreneur keeps running rms instead of going to wage work. According to thealternativemodel, failureby the entrepreneur to keep a small rm trading-the non survivalof the small rm- indicates that he does not have the necessary entrepreneurial skills andtherefore he is better o in a paid job -thenon survival of theentrepreneur-.

4.2 T he General M odel

When the prots of the small rm depend on the demand parameter ij and the e ciencyparameters j as shown by (1), where the former denotes how successful the rms productis in attracting customers and the latter represents the skills of the owner to manage therm e ciently, and under assumptions A .1 trough A .5, the problemfor the entrepreneur is

argmaxn

ijB ;

jB

; E

; jB

; jR d ( ; ;T; s )

o, (20)

which is a repetition of expression (15), where therst argument standsfor theprots of thecurrent rm, thesecond onefor theexpected prots of a new rm, and thethird onefor the

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value of going to wage work. The important feature to keep in mind is that the e ciencyparameter is the same in the rst and second arguments, whilst the parameter for demandchanges. Depending on the valueof theparameters ij and j , the entrepreneur will decidewhether keeping the current rm, opening a new one, or going to wage work, provides thehighest rewards.

The entrepreneurs current rm will survive whenever the rst argument is the largest. Therefore, su cient conditions for the current rmto survive are

ijB ;

jB

> E

; jB

(21)

and

E

; jB > jR d ( ; ;T; s ) . (22)

Our interest is to provide an explanation as to why some entrepreneurs wish to start a newrm after having closed a previous one that was not successful. In terms of our model, itis as though the second term in (20) had the largest value. In other words, the situationis similar to one where inequality (21) is not satised, i.e., when the current rm does notsurvive, whilst inequality (22) is satised, or in other words, whilst the entrepreneur wishesto start another rm. This paves the way to our next proposition.

P roposition 2 Let the prot function be the one shown by (1). The maximisation problemis the one in (20). Dene min as the minimumlevel of entrepreneurial skills which satisesthe su cient conditions for the current rm to survive (21) and (22). Let D J be thesubgroup for which the second term in (20) is the largest. Therefore, 8 j 2 D , jB > min .As consequence, the wage worker state will always provide the smallest rewards to subgroupD .

P roof. Let solve expression (21) as an equality. Lemma 3 in Appendix A establishthe conditions under which exist. Utilising Lemma 2 and assuming p > MC , expression(21) is satised whenever ijB > , where i 2 I , j 2 J , and I \ J = ? . Fromexpression (11)let F solve jR = E [

(; F )], and from expression (22) let min solve E

[ (; min )] =

jR d ( ; ;T; s ). Lemma4in Appendix A establish under which conditions F and min exist. Thus, E

[ (; min )] = E

[ (; F )] d ( ; ;T; s ). Making use of Lemma 1, any jB > min

satises (22). If for subgroup D expression (21) is not satised, but expression (22) is, wemust therefore have ijB < and

jB > min , 8 j 2 D , i 2 I . Under this circumstances the

second argument in (20) is the largest. Oncetheentrepreneurs runs thenew rmhereceives

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a new draw for the demand parameter. Denethe new draw as ljB , where i 6= l 2 I , j 2 D .It can bethe case that ljB R . Under any of these situations, either the rst argument orthe second one in (20) are the largest. This implies the third argument in expression (20),which represents the wage working state, has always the smallest value for subgroup D .

Proposition 2 says that when the prots of the small rm depend on the e ciency anddemand parameters, those entrepreneurs whose rms do not survive, but wish to start anew one, have skills to manage the rm at least as large as the ones required to run apotentially successful rm. This implies that every time their rms fail to survive, theoptimal action for them is to start another one, rather than becoming a wage worker. Notethat this is the opposite result to the oneobtained from Proposition 1, namely, that underthealternativemodel failureby theentrepreneur to keep his rm aoat implies hedoes nothave the necessary skills, whereas under our general model, the fact that the entrepreneurwishes to own another rm is a reection that he is skilful, the only thing his rm lackedwas a more appealing product. Additionally, Proposition 2 establishes that such a skilfulentrepreneur will always nd that the prospects of starting another rm render a highervalueto him than thealternativeof going to wage work does.

Regarding our initial question as to why some entrepreneurs wish to own another rmafter having closed an unsuccessful one, the answer by Proposition 2 is: because these

entrepreneurs have enough skills to run potentially successful rms, assuming such skillsare restricted to managerial skills; the other condition to run a successful rm is to nd aproduct or service which is appealing to customers or for which there is a market niche. Two important questions to ask are: how plausible these assumptions are and hence, howreliabletheprediction oered by our general model by meansof Proposition 2 is. Weprovidethe following arguments to tackle such questions. Firstly, such assumptions are consistentwith the view suggested by Audretsch (1995), who asserts that entrepreneurs are alwaysin the process of discovering whether they possess the the right stu in terms of theproduct they oer for which su cient demand exists and whether they can produce it more

e ciently than their rivals. More specically he states that when a new rm is launched,its prospects are shrouded in uncertainty. If the new rm is built around a new idea, it isuncertain whether there is su cient demand or if some competitor will have the same oreven superior idea. Even if the new rm is a clone, there is the question whether there isenough demand (p. 67) He further asserts that an additional layer of uncertainty is howcompetent the new rm really is (p. 67), which in terms of our model this last statementcan be easily translated as referring to how skilful the owner-manager is. Storey (1990)

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acknowledges a possibility which is also in linewith our assumptions. He declares that thecreation and subsequent closureof a rm may merely bepart of the small entrepreneurs wayof searching out protable opportunities... (p. 47). Secondly, we believe the predictionsof our model will gain strength if they account for all the possibilities as provided by theempirical evidence in Figure 2. That is, whilst Proposition 2 oers an explanation as towhy thedetermined entrepreneurs in Figure2 have thedesire to own another rm in thefuture, such explanation does not involve the other three cases. The following propositionpresent the complete results of our general model, which we believesuggests an explanationfor all theempirical evidence contained in Figure2.

P roposition 3 Let the prot function be the one shown by (1). The maximisation problem

is the one in (20). Dene min as the minimumlevel of entrepreneurial skills which satisesthe su cient conditions for the current rm to survive (21) and (22), and dene the groupR as the one which contain the dierent combinations of ij and j such that ( r ; r ) = 0 (; F ) [f ( ; ;T; s )], 8 (r ; r ) 2 .R

(i) Let M J be the subgroup for which the rst term in (20) is the largest. ThereforeijB > 8 j 2 M ,

jB > min 8 j 2 M 1 , min >

jB >

r 8 j 2 M 2 , i 2 I , r 2 R , whereM 1 [ M 2 = M and M 1 \ M 2 = ? .

(ii) Let D J be the subgroup for which the second term in (20) is the largest. Therefore

ijB < ,

jB > min , 8 j 2 D , i 2 I .

(iii) Let Z J be the subgroup for which the third term in (20) is the largest. ThereforeijB < and

jB < min 8 j 2 Z 1 ,

ijB > and

jB <

r < min 8 j 2 Z 2 , i 2 I , r 2 R whereZ 1 [ Z 2 = Z , and Z 1 \ Z 2 = ? .

(iv) For subgroups M 1 and M 2 the sale of their rms or any shock which makes ijB < , j 2 M , i 2 I , assuming ijB is exposed to unforeseen shocks, has the eect of making thesecond argument in (20) the largest for subgroup M 1, and the third argument in (20) thelargest for subgroup M 2 .

P roof. See Appendix A.

Proposition 3 is represented graphically in Figure 4. It shows under which conditions,in terms of combinations of the parameters and , it is optimal for the entrepreneur tokeep his current rm, start a new rm, or go to wage work. More specically, Figure 4 is anisoprot map in the space (; ), where every point in its surfaceentails specic coordinateswhich formpart of an isoprot curve. In turn, every isoprot curveis associated with a single

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F min

Go to wageworker

D

Z2

Stay with thecurrent firm withthe option to start

another firm inthe future

Stay with the current firm with no optionto start another firm in the future

Close the currentfirm and start a

new one

a a

( )[ ] ( ) sT d E F ,,,,* =

0

Z1M2

M1

ij B

j B

Figure 4: Optimal decision for the entrepreneur when the prots of the small rm dependon the e ciency and demand parameters

value of prots for dierent combinations of and . Lemma 5 in Appendix A establishesthat such isoprots curveshavenegativeslopeand areconvex with respect to theorigin. Thefarther to the north-east the isoprot is placed, the higher theassociated value of prots.

Figure4is divided in veareas. Areas M 1 and M 2 contain thecombinationsofparametersijB and

jB such that thebest optionfor theentrepreneur is to keep hiscurrent rm, becauseit

isprovidingprots larger thantheupdatedreservationlevel E

[ (; F )]d ( ; ;T; s ), whichis represented by the isoprot curve that divides areas M 2 and Z 2 and once it crosses thecoordinates (; min ) continuesupward asa dotted line. Recall that such updated reservationlevel represents the rewards in the wage working state. Therefore, any point to the right of its associated isoprot curve represents prots that exceed such rewards. This explains whyentrepreneurs placed in areas M 1 and M 2 are better o keepinghis current rm, whilst thosein areas Z 1 and Z 2 nd optimal to close their current rm and go to wage work. The bestoption for entrepreneurs in area D is also to close their current rm, but instead of becomingwage workers, they are better o by starting a new rm. Note that area D comprises

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some combinations of ijB and jB which are placed to the right of the isoprot curve of

the updated reservation level, and some combinations located to the left of it. However,according to Proposition 3 the best course of action for entrepreneurs in area D is not tokeep the current rm or close down and go to wage work, but to shut their current rm andstart a new one. Thereason is because by starting a new rm these entrepreneurs havetheoption of oering a dierent product in thehopeof drawing a higher : closing theChinesetake away and opening a sport clothes retail outlet. Takefor example an entrepreneur whonds himself in a situation where his coordinates of parameters are represented by point ain Figure 4. His current rms prots are smaller than the reservation level. However, bystartinga new rmhisexpectationsareto reach a point like a which is placed in an isoprotto the right of the reservation level. As a result, this entrepreneur does not nd optimal to

go to wage work, but to keep in entrepreneurialismby starting a new rm. Thekey point isthat Proposition 3 states that all entrepreneurs in area D have skills above thecuto pointmin , contrary to those in area Z 1 who do not. In this sense, what entrepreneurs in areas Dand M 1 have in common is that all of them have skills above the cuto point min . Noticefrom Figure4 that wecan say that entrepreneurs in area M 1 are theones who are runningsuccessful rms because their rms demand is aboveaverage. Therefore, it is fair to say theonly thing an entrepreneur in area D lacked was to oer a more appealing product, but hisskills to manage the rm e ciently are as good as the ones of those entrepreneurs who runsuccessful rm. This is the case previously pointed out by Proposition 2.

Proposition 3 also establishes that the dierence between entrepreneurs in areas M 1 andM 2 is that, in case their current rms do not survive or in case they sell them, the formerhavethe option of keeping in entrepreneurialism by starting a new rm, whereas the latterdo not and have to go to wage work. The intuition is as follows. Suppose an entrepreneurin area M 1 sells his rm. He has the option of starting a new rm or going to wage work.If he plans to start a new rm, his expectation about his new rms demand is . Giventhat hehas skills above min , his expectation with a new rmin termof Figure4 is to reacha point over the vertical line which starts from the coordinates (; min ) and goes upward.As can be seen, any point in this line above the point (; min ) renders prots higher thanthe updated reservation level. Therefore, it is optimal for an entrepreneur in M 1 to start anew rm. This is not the case for an entrepreneur in area M 2 , since this entrepreneur hasskills lower than min . In other words, by starting a new rm he expects to be placed inarea Z , which means he would receive prots lower than the reservation level. Therefore,entrepreneurs in area M 2 nd optimal to go to wagework after having sold their rms. Thisintuition is equivalent to the one where there is a shock in demand and the rm does not

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survive. For instance, the shock can represent a downturn in demand because another rmentered themarket and is oering a product similar enough to impingein thedemand of theoriginal rm. If theshock is big enough, the small rms demand may fall below . Thus, itis as if entrepreneursin area M 1 were moved to area D , whereaccording to Proposition 3,these entrepreneurs are better o by closing their current rms and starting a new one. Onthe other hand, entrepreneurs in area M 2 would beplaced in area Z after the shock, wherethey are better o by going to wage work.

Notice that Proposition 3 predicts that only entrepreneurs with skills above min havethe option of starting new rms, that is, only those in areas M 1 and D . This is regardlessof whether they were previously running rms with high demand or low demand. In thissense, Proposition 3 suggests the existence of a mechanism of entrepreneurial self-selectionwhereby skilful entrepreneurs self-select themselves by startingnew rms after havingclosedone, regardless of the degreeof success on the previousrm, whereas unskilful entrepreneursgo to paid employment. We are now in position to discuss whether or not this mechanismof entrepreneurial self-selection explains the empirical evidence in Section 2 and thereby,whether or not there is support for our general model. Before proceeding, note that unlikethe alternativemodel our general model does dierentiate between survival of the small rmandsurvival of theentrepreneur. Accordingto Figure4, survival of thesmall rmtakesplaceunder the conditions described by areas M 1 and M 2 , whereas survival of the entrepreneur

occurs under the conditions described by areas D and M 1.

5 Explaining the Evidence

Why do some entrepreneurs wish to start new rms after having closed one that was notsuccessful? This is the question which the present paper tries to tackle. We showed therelevance of such question by means of the empirical evidence in Figure 2 in page 9. Bydoing so, we not only revealed there is potentially a large share of entrepreneurs who have

closed a rm that was not successful and still want to own another rm in the future, butthat there also exist, amongst other cases, someentrepreneurs that despitehaving successfulrms donot havethedesire to run their own rms again. In order to oer an explanation toour initial question and to the empirical evidence in general, we proposed and developed amodel whose principal assumption is that the prots of the small rm depend on two rm-specic parameters: the rst one captures the success of the rms product in attractingdemand, and thesecond theskills of theowner to managetherme ciently, that is, to deal

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e ciently with theday-to-day activities. Weassumesuch parameters arenot correlated, i.e.,we assume the entrepreneurs skills to manage are not correlated with the ability to selectand oer an appealing product. On the contrary, we suppose the demand parameter variesevery time the entrepreneur starts a new rm. From our model we obtained Propositions2 and 3. To compare such results with the ones from an alternative model wherein theentrepreneur has some type of overall skills which includes skills to manage and skills toinnovate or spot protable opportunities, we also obtained Proposition 1.

As regards our initial question, Proposition 2 and 3 establish that those entrepreneurswho start or have the desire to start a new rm after having closed an unsuccessful onehave skills to manage as great as those who are running successful rms. Our model goesfurther by suggesting the existence of a mechanismof entrepreneurial self-selection. Undersuch mechanism, entrepreneurs who are skilful are the only ones who start or have thedesire to start another rm in the future after having closed a previous one. Such desireis independent of whether or not the previous experience of running a rm is regardedas a success or failure. This is not true of unskilful entrepreneurs, who prefer to go toemployment. Does this mechanism oer an explanation to the empirical evidence providedin Figure 2? We believe it does. By means of Figure 4 our theory argues that the reasonwhy the determined entrepreneurs and the serial entrepreneurs in Figure 2 have theintention to own another rm in the future is because they are skilful entrepreneurs. They

would be placed in areas D and M 1 in Figure 2, respectively. Our theory interprets skilfulentrepreneurs as those who have managerial skills at least as large as those needed to runpotentially successful small rms, i.e., rms which would provide larger economic and non-economic rewards than the wage worker state would. In fact our model states that thedetermined entrepreneurs areasskilful as the serial entrepreneurs. Thelatter were justluckier with their rms in the sense that they were running a rm with a very appealingproduct or service. Similarly, the mechanism of entrepreneurial self-selection also accountsfor the cases of failed entrepreneurs and discouraged entrepreneurs shown by F igure 4. Theformer would beplaced in area Z in Figure4 and thelatter in area M 2 . Accordingto ourgeneral model, thefact that a discouraged entrepreneur wishes to leaveentrepreneurialismdespite having owned a rm that was successful, can be explained by saying that he waslucky in running a rm with a very attractive product or service, whose success indeedcompensated for his low skill to manage the rm. However, this unskilful entrepreneur doesnot expect to hit the jackpot again, so heprefers to go to a paid job after having closedhis current rm 17 .

17 Webelievethe closest interpretation to the demand parameter ij in our model is luck. This is because

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To oer such explanations our model relies on theassumption that theskills of thesmallrm owners are restricted to skills to manage the rm e ciently, and that such skills arenot related with theability to oer an attractiveand appealing product. Let usassume theentrepreneur has both abilities. Thus, an entrepreneur who deals e ciently with theday-to-day activitiesof thesmall rmis alsogood at innovatingor spotting protable opportunities. This is the case of the model discussed in Subsection 4.1, from which Proposition 1 wasobtained. Such proposition establishes that those entrepreneurs whose rms do not survivehave skills lower than required, and that it is optimal for them to not attempt to ownanother rm in the future. This means that for those entrepreneurs who run successfulrms, they are better o starting new rms. In other words, under such model only theserial entrepreneurs and the failed entrepreneurs in Figure2 exist. As can be seen, the

alternative model fails to explain the whole spectrum of empirical evidence, whereas ourgeneral model does not. Therefore, we can state that in general, the empirical evidencesupports our assumption that the skills of the small rm owners are restricted to skills tomanage the rm e ciently. The present discussion should be placed in its correct context.Firstly, wedonot suggest that it is impossiblefor someentrepreneursto haveboth high skillsto manageandhighskills to innovateor spot protableopportunities. Secondly, regardlessof the denition of entrepreneurship, our conclusion supports the view that when undertakingresearch on entrepreneurship if we consider data comprising small rm owners without anyother discriminatory criterion, it is reasonable to suppose that the ability to manage andtheability to innovate or spot protable opportunities are in general not correlated amongstsmall rm owners.

Therefore, given that the assumptions of our general model seem plausible, the mecha-nismof entrepreneurial self-selection gains strength. After all, the central argument of suchmechanism is analogous to the idea of survival of the ttest: only the skilful entrepreneurssurvive, whilst the unskilful do not. However, by skills and entrepreneurial survival suchmechanismrefers, in thecaseof theformer, to skills to managedened in this paper as skillsto undertakee ciently the responsibilities of the everyday activities of the small rm, andin thecase of the latter, to theentrepreneurs desire to own another rm, which should notbe mistaken for the survival of the small rm.

we specify it as a random variable which the entrepreneur is unable to predict every time he starts a newrm, even if hehas experience in running previous businesses.

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6 Extensions and Discussion

6.1 R obustness and A lternative A ssumptions

In this subsection we discuss the robustness of some of the assumptions in our model, andwe address some alternatives hypotheses which might also explain the empirical evidenceshown in Section 2.

Transferability of Skills

In our model we dene the parameter j as the one which embodies the entrepreneursskills to managehis own rme ciently. As wedeveloped our model and dened themaximi-sation problemthe

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Small Firm Entrepreneur Survival