January, 2004 Are Entrepreneurs Eternal Optimists or do they ‘Get Real’? Stuart Fraser* and Francis Greene Centre for Small and Medium Sized Enterprises, Warwick Business School, The University of Warwick JEL Classifications: Self-Employment J23; Government Policy, I28; and Discrete Regression and Qualitative Choice Models, C25. Abstract The first contribution of this paper is a model of entrepreneurial learning in which both optimistic bias and uncertainty diminish with experience. The shape of the business failure distribution, by experience, is explained by the relative effects of learning on optimism and uncertainty respectively. The second contribution is an empirical analysis using British data on optimism spanning the period 1984-1999. This analysis supports the propositions that entrepreneurs are optimists but that optimism and uncertainty diminish with experience. Changes in public policy account for related findings: i) entrepreneurs’ optimism is higher in the 1980s relative to the 1990s; and ii) uncertainty rose in the 1980s but remained stable in the 1990s. Acknowledgements: We would like to thank Andrew Burke, Peter Elias, Andrew Oswald, Simon Parker, David Storey and Mirjam van Praag for their edifying comments on earlier drafts of this paper which led to many improvements. Thanks also go to lunchtime seminar participants at the Institute for Employment Research, in Warwick Business School, and to Marie Screene for her assistance. We are, of course, solely responsible for all remaining errors. *Corresponding Author: Stuart Fraser, Centre for Small and Medium Sized Enterprises, Warwick Business School, The University of Warwick, Coventry CV4 7AL, United Kingdom. Tel: (0) 24 765 22899, Fax: (0) 24 765 23747, email: Stuart.Fraser@wbs.ac.uk. 1 Are Entrepreneurs Eternal Optimists or do they ‘Get Real’? Section 1: Introduction It is often argued that entrepreneurs are a self-selected group of optimists. This is perhaps unsurprising given the inherent uncertainties in running a business. In this paper we explore, theoretically and empirically, the notion that both optimism and uncertainty vary with experience. In particular: i) experience reduces optimistic bias in expected outcomes; and ii) experience reduces the uncertainty in these outcomes. To put it succinctly, entrepreneurs ‘get real’ over time. The idea that experience alters entrepreneurs’ subjective beliefs is not new (see Jovanovic, 1982). It is an issue, though, that has been largely ignored in previous empirical analyses of selfemployment but which is addressed in this paper. The implications of optimism are not to be underestimated. It is well known, for example, that optimists may fall victim to the ‘winner’s curse’ (Thaler, 1988). That is, they end up with a negative return on their investment since they overestimate the value of resources. An allocation of resources favouring realists would, accordingly, increase economic welfare. The welfare loss arising from optimism formed the basis for Adam Smith’s otherwise uncharacteristic defence of interest ceilings (see Niehans, 1997). Indeed, Smith warned of the prevalence of optimism: ‘The chance of gain is by every man more or less over-valued, and the chance of loss is by most men undervalued, and by scarce any man, who is in tolerable health and spirits, valued more than it is worth’ [Smith, 1805, p. 123]. On the other hand, a key implication of 2 entrepreneurial learning is that the welfare loss from optimism will vanish, over time, among a given generation of entrepreneurs.1 In more recent times, research in the psychology literature supports Smith’s view that optimism prevails (Taylor, 1989) whilst realism is more or less confined to depressed individuals (Alloy and Abrahamson, 1979). Super-optimism among entrepreneurs follows naturally from other psychology based evidence that optimistic excess is greatest for events that are seemingly under the person’s control (Zackay, 1984; McKenna, 1993). In fact, entrepreneurship is such a tempting prospect for many precisely because they believe that it will afford them a more independent lifestyle (Blanchflower and Oswald, 1998). In the economics literature de Meza and Southey (1996) argue that super-optimism can explain several stylized facts about small business including high start-up failure rates. Here, we argue that entrepreneurial learning is able to account for the shape of the business failure distribution by experience. Indeed, this shape is explained by the relative effects of entrepreneurial learning on optimism and uncertainty respectively. The speed of decline in optimism determines the early phases of the distribution whereas it is the rate of decline in uncertainty (equivalently, the rate of increase in confidence) which determines the tail-shape. Specifically, high start-up failure rates are explained by a relatively rapid initial decline in optimism. The positive skew in the distribution, on the other hand, is determined by the rate at which confidence accumulates – the slower the accumulation the greater the skew. It seems plausible that the tail-shape has more to do with changes in confidence rather than optimism. 1 However, we may expect optimism to be ‘reborn’ with each new generation of entrepreneurs. Further developments of this idea include the possibility that the old generation of entrepreneurs mentor younger generations thereby mitigating the optimistic excesses of the latter group (see also section 3). 3 Optimists, after all, will tend to be forced out of business as soon as their lack of talent is realised. Confidence, on the other hand, takes time to accumulate; not only self-confidence but also the confidence of entrepreneurial backers, such as banks, requires some track-record of success. The limited empirical evidence seems to support a state of super-optimism among entrepreneurs. In particular, Arabsheibani et al (2000) have shown that, in the UK context, the self-employed were more likely to forecast an improvement in their financial situation, compared to employees, but were also more likely to experience worse outcomes. However, regarding the prevalence of optimism, the same study showed that even employees were susceptible to baseless optimism. Our empirical analysis seeks to develop this limited literature by examining changes in optimism, experience and self-employment choices in Britain, over the 1980s and 1990s, using data from the British Social Attitudes Survey (BSAS). These data, uniquely to our knowledge, allow analysis of changes in optimism over two decades. The principal findings from this analysis are that: i) entrepreneurs are more optimistic than wage-workers; and ii) experience reduces optimism and its influence on selfemployment choices. The changing policy backdrop for the analysis explains some important further findings. In particular, three successive Thatcher administrations of the 1980s (19791983, 1983-1987, 1987-1991) offered public support for the creation of new ventures. Arguably, this was an era of renewed entrepreneurial optimism (Bannock and Peacock, 1989). Young people, females and the previously unemployed, with no previous experience, received support and encouragement to start businesses (Meager 4 et al. 1996). This is echoed in our results where we find that optimism was relatively high, and uncertainty rose markedly, in the 1980s. In the 1990s however the focus of policy in the UK switched to enhancing the quality of existing businesses. Arguably, this policy switch may have helped to inject a dose of realism into entrepreneurial forecasts. Indeed, we find the level of optimism is lower in the 1990s and uncertainty is stable which support the predictions of the learning model. The remainder of this paper is divided along the following lines. In Section 2, we outline the ways in which enterprise support policy has changed over the last 20 years. In Section 3, we set out a theoretical framework for the analysis of selfemployment, optimism and uncertainty. In Section 4 five propositions are set out for empirical testing. The principal data sources – the BSAS for 1984-1999 – and selfemployment trends are then presented in section 5. In section 6 we present an empirical analysis of the relationship between optimism and experience. In section 7 the analysis turns to examining the role of optimism and uncertainty in selfemployment choices using structural heteroscedastic probits. The final section of the paper discusses the findings and highlights some policy implications. Section 2: Quantity vs. Quality - Policy Background to the 1980s and 1990s; Until the 1980s, self-employment in the UK was largely seen as a marginal activity (Stanworth and Curran, 1973) and the UK small firm sector - as a whole - was seen as lacking vitality (Bolton, 1971) or vibrancy (Boswell, 1973). Indeed prior to the 1980s, policy initiatives towards the small firm sector were limited. For example, Beesley and Wilson (1984) showed that there were only two programmes from 19461960. In the 1960s, this increased to thirteen (1961-1970) and then, in the 1970s, on 5 to thirty-three (1971-81). Very many of these schemes sought not to improve access to self-employment or improve its attractiveness but, instead, to provide employment subsidies for the unemployed or the young2. In the 1980s, however, the intensity of policy initiative increased markedly: by 1989 there were 103 public policy initiatives directed at the small firm sector (Curran and Blackburn, 2000). Given this number is would be unsurprising if there was not some heterogeneity in terms of objectives. That said, there would appear to be two discernible public policy thrusts throughout the 1980s. First, there was an attempt to increase the number of individuals entering self-employment. To support this, ‘enterprise zones’ were created (1981), the Small Firms Loan Guarantee Scheme (SFLGS) (1981 onwards) and schemes such as the Enterprise Allowance Scheme (EAS) (1982-1991) were set up. The EAS provided the unemployed (unemployed for more than 13 weeks – later reduced to 8 weeks) with a payment of £40 a week for a year. Individuals also had to have access to capital of £1,000, work full-time on the business, were between 18-59, had to be based in Britain and have an idea that was suitable for public support (the last requirement was introduced after a massage parlour was set up in South Wales). The second public policy thrust in the 1980s was to shift the non-pecuniary career preferences of individuals (Lawson, 1984). To achieve this, a number of schemes were set up: the Technical and Vocational Educational Initiative, ‘Compacts’ between schools and business, the Mini Enterprise in Schools Project, and Youth Training initiatives (e.g. ‘Training for Enterprise’). 2 For example: Job Creation Programme (October 1975 - December 1977); the Recruitment Subsidy for School Leavers (October 1975 – September 1976); the Work Experience Programme (September 1976 – April 1978); Youth Employment Subsidy (October 1976 – March 1978); Small Firms 6 In the 1980s, however, enterprise support was not confined solely to public policy. Indeed, what is particularly noteworthy about the period was that it saw the rise of corporate responsibility in the UK. This led to the creation of schemes such as Shell LiveWIRE, the Prince’s Youth Business Trust (now the Prince’s Trust) and Business in the Community: all of which sought to convert individuals into self-employment (IMS, 1989, 1987; Pilkington, 1984). It is also hard to ignore cultural influences (e.g. films such as Wall Street and comic characters such as ‘Loads-a-Money’ and ‘DelBoy’). By the early 1990s, however, it would appear that there was a discernable shift in policy towards self-employment. Partly, this may be because Thatcher left office in 1991. Another reason may have been that the UK’s recession of the early 1990s spelt the end of the euphoric optimism of the late 1980s. Government policy itself towards self-employment also changed in three important ways in the 1990s. First, in the early part of the decade the government moved away from delivering training through a centralised mechanism (the Manpower Services Commission) to the provision of localised support (Business Links and Training and Enterprise Councils) (Deakin and Edwards, 1993). Second, the government also sought to focus upon improving the quality of existing businesses rather than increasing the quantity of businesses through the creation of Business Links (House of Commons Trade and Industry Select Committee, 1996). Third, the government also changed the way it supported ventures. Financial support provided by schemes such as the SFLGS are now in the minority. Attention, instead, has instead shifted to providing support to improve the Employment Subsidy (July 1977 – March 1980); the Special Temporary Employment Programme (April 1978 – March 1981); and the Youth Opportunities Scheme (April 1978 – September 1983). 7 capabilities and skills of individuals (Straw and Blair, 1991) through changes to education and training (see DTI, 1994, 1996, 1998). In summary, there were two observable policy imperatives in the 1980s. First, there was an attempt to increase the quantity of existing businesses in the UK economy. The second imperative was to improve the supply of potential entrants into selfemployment. In terms of the 1990s, it is argued that there was a change in focus towards enterprise support. Hence, whilst support was still concentrated upon improving the appeal of self-employment, many of the actual policies in the 1990s were, instead, concentrated upon improving the quality of existing businesses. Section 3: Theoretical framework for optimism and self-employment choices The principal aim in this section is to develop the dynamics of entrepreneurial optimism and uncertainty laying the foundations for the empirical analysis later in this paper. To emphasize, the focus here is on the dynamics of optimism and not, for example, the relationship between optimism and finance (see de Meza and Southey, 1996; Manove and Padilla, 1999). Our first assumption is that individuals have a straight choice between entrepreneurship (e) and wage-work (w) (in contrast, see Parker, 1996). We assume a framework in which talent is observed with noise and individuals differ according to their subjective beliefs about their entrepreneurial talent (Jovanovic, 1982; Frank, 1988). In such a setting, individuals with higher expectations are more likely to become entrepreneurs. As in Jovanovic (1982), the entrepreneur, through experience, 8 learns to forecast talent with increasing confidence. Unlike Jovanovic, however, we allow for the possibility of optimistic bias in expectations. Entrepreneurial income ( y e ) is stochastic embodying the entrepreneur’s uncertainty about their talent. In particular, we assume this income deviates from a representative level ( y e ) according to the level of noisy talent: y e = (θ + ε ) y e (1) where θ is actual talent and ε is luck. Assuming θ is non-negative, but that the support of the distribution for ε is the real line, implies negative self-employed incomes are possible. This is in accord with empirical evidence on self-employed incomes (Parker, 1997). 3 The entrepreneur makes an expectation of talent on the basis of accumulated business experience in order to form an opinion about prospects. Assuming a sequence of luck with distributions, ε i ~ NIID (0, σ 2 ), i = 1, Κ k , then talent expectations are unbiased. In that case prospects are given by E [y e Ω(k )] = θy e where {θ + ε i }i =1 ≡ Ω(k ) is the k information on talent available to an entrepreneur with k years of experience. Assuming also that individuals maximize their subjective expected utilities, then a risk neutral individual will choose entrepreneurship over wage-work, if and only if, E [u e − u w Ω(k )] = y e − y w + Xβ > 0, (2) where u i , i = e, w are utilities in entrepreneurship and wage work; y w is certain wage income; and X is a vector of personal characteristics (life-style preferences) and other taste shifters. 3 This representative level of income will vary over different levels of capital and labour inputs. We choose not to elaborate here on the entrepreneur’s technology since it adds nothing substantive to the current analysis. 9 This, however, is only the static half of the story. The entrepreneur’s beliefs are updated as new information on noisy talent accrues over the course of running the business – the entrepreneur learns. Specifically, a repeated application of Bayes’s theorem gives the following recursive formula for the posterior talent distribution: [ f θ Ω(k ), σ 2 ]= [ ][ f θ Ω(k − 1), σ 2 f ω (k )θ , σ 2 f [ω (k )] ] (3) where ω (k ) = θ + ε k is incremental sample information and the recursion is initialized ( ) with a prior (pre-start up) distribution f θ µ 0 , σ 02 . The derivation of this recursion [ ] [ ][ ] can also be seen noting that f θ , Ω(k )σ 2 = f θ , Ω(k − 1)σ 2 f ω (k )θ , σ 2 since ω (k ) is independent from Ω(k − 1) (recall, the ε i are independent). The posterior distribution is normal if we assume a normal prior and given the normality assumption on the ε i . From this formulation of the posterior distribution we show, in Appendix 1, that the posterior variance has the following recursive representations: [ [ ] var θ Ω(k ), σ 2 = W (k ) var θ Ω(k − 1), σ 2 =σ 2 0 ] (4) k ∏W (i ), i =0 where, −1 ⎡ 1 1 k ⎤⎥ + W (k ) = ⎢ , k > 0, k −1 2 2 2 ⎢ σ 0 ∏ W (i ) σ ⎥ σ 0 ∏k −1W (i ) i =0 i =0 ⎣ ⎦ W (0) = 1. (5) Since we see that 0 ≤ W (k ) < W (k − 1) < Κ < W (0) = 1 , it follows that the posterior variance diminishes as experience is gained. The interpretation of this result is that confidence in talent forecasts grows with experience. In terms of the occupational choice model (2) this adds a supplementary condition for the variance 10 var[u e − u w Ω(k )] = y e2σ 02 ∏ W (i ) , k (6) i =0 indicating that uncertainty in utility forecasts also diminishes with experience. We now relax the assumption that expectations of talent are unbiased. The rationale for this is the empirical observation that individuals, and especially entrepreneurs, tend to forecast events with an optimistic bias. In terms of self-employment choices, quite straightforwardly, this entails the inclusion of a bias function Β into (2) E [u e − u w Ω(k )] = y e − y w + Xβ + Β > 0. (7) where Β = (µ − θ ) y e and µ are biased talent expectations. According to (7), optimists (Β > 0) are more likely than realists (Β = 0) or pessimists (Β < 0) to be entrepreneurs holding actual earnings and tastes constant. Note that, in the optimistic scenario, the marginal entrepreneur’s (i.e., the individual with a zero ex-ante relative utility) ex-post relative utility is negative which implies there is over-investment in entrepreneurship. The variance of net utility remains as in (6) assuming that optimistic bias affects only the location of the posterior talent distribution.4 The final development is to synthesize optimism with entrepreneurial learning. By this we mean optimistic entrepreneurs learn to form unbiased forecasts of relative utility and their confidence in these forecasts grows over time. This replaces the static prediction that entrepreneurs are optimists with the dynamic prediction that experience increases realism. To begin this analysis we observe that the posterior mean has the following recursive representation (see Appendix 1) 11 µ (k ) = W (k )µ (k − 1) + [1 − W (k )]θˆ(k ) (8) where θˆ(k ) = k −1 ∑i =1 (θ + ε i ) are sample based estimates of talent and µ (0) = µ 0 are k [ ] prior expectations. Since µ (k ) − θˆ(k ) = W (k ) µ (k − 1) − θˆ(k ) < µ (k − 1) − θˆ(k ) , it follows that optimistic bias diminishes with experience - µ (k ) − θ < µ (k − 1) − θ < Κ . Also, since lim W (k ) = 0 , infinitely experienced entrepreneurs are realists (i.e., talent k →∞ forecasts are consistent). This leads to the culmination of the model with the following criteria for selfemployment choices: E [u e − u w Ω(k )] = y e − y w + Xβ + Β(k ) > 0, (9) where Β(k ) = [µ (k ) − θ ]y e Β k ≤ 0 , lim Β(k ) = 0 and the variance of net utility is given k →∞ by (6). Accordingly, from (9), we see that the corollary to the diminution of optimism with experience is that its impact on self-employment choices will also attenuate. One interpretation of this result is that untalented (low actual earnings) optimists drop out of entrepreneurship, over time, leaving behind a pool of talented realists. However, it is quite possible that these talented realists were themselves once optimists but, having sufficient actual talent, managed to survive. Regardless, the fundamental prediction is that, among a given generation of entrepreneurs, optimistic bias eventually goes to zero. The learning process, as set out in this section, is totally individualistic – the only way to learn is through personal experiences. However, it would be straightforward to allow for learning across different generations of entrepreneurs. This development 4 A more general formulation in which optimism produces over-confidence could also be envisaged. We leave this development for future work. 12 would allow inexperienced entrepreneurs to learn from the accumulated wisdom of more experienced entrepreneurs.5 The prediction, in that case, is that mentoring will reduce both optimistic excess and uncertainty among start-ups. We are, unfortunately, unable to test this particular prediction with our current data. The normality of the posterior distribution means that the likelihood of entrepreneurship is given by ⎡ y − y + Xβ + Β(k ) ⎤ w ⎥ Pr ob[s = 1 Ω(k )] = Φ ⎢ e ⎢ y eσ 0 ∏k W (i )1 2 ⎥ i =0 ⎣ ⎦ (10) where Φ is the cumulative standard normal distribution function. Estimation of the model using a structural probit is therefore appropriate (Lee, 1978). However, since uncertainty varies with experience, a heteroscedastic probit should be estimated. Failure to take heteroscedasticity into account will result in biased and inconsistent parameter estimates (Yatchew and Griliches, 1984). 3.1 Implications of learning for the firm failure distribution A well documented stylized fact from the small business literature is that the firm failure distribution, by experience, has an inverted U-shape with a positive skew (see e.g., Ganguly, 1985). It is important that the learning model, presented above, is able to offer a plausible explanation for this shape (see Cressy, 1999, for an alternative, entrepreneurial learning based, explanation for the shape of the firm failure distribution). 5 This feature could be incorporated in the current model via the parameters of the prior (pre-start up) distribution. In particular, mentoring by an experienced entrepreneur may yield a prior distribution which more accurately reflects the start up entrepreneur’s true talent. New entrepreneurs may also benefit from mentoring by other experienced sources such as banks. 13 Firstly, we note that the failure distribution is given by 1 − Pr ob[s = 1 Ω(k )] (i.e., the probability of failure given k periods of experience). Accordingly, concavity of this distribution in experience, which is implied by the inverted U-shape, is equivalent to the convexity of equation (10) in k . Taking the partial derivative of (10) with respect to k we obtain ⎡ M (k ) ⎤ ⎡ M (k )⎤ Bk (k )σ (k ) − σ k (k )M (k ) Φk ⎢ = φ⎢ ⎥ ⎥ σ (k ) ⎣ σ (k ) ⎦ ⎣ σ (k ) ⎦ (11) using M (k ) and σ (k ) as shorthand notation for the numerator and denominator respectively of the index function in (10) and φ (⋅) is the standard normal density function. It can be seen from (11) that the shape of the failure distribution depends on the relative effects of learning on optimism and uncertainty - the parameters Bk and σ k - respectively. The convexity of (11) (i.e., the concavity of the failure distribution) requires the sign of Bk − σ k [M (k ) σ (k )] to be initially negative before turning positive. In this regard, we note that Bk and σ k are strictly non-positive – the effects of experience on optimism and uncertainty are strictly non-increasing – and that M (k ) σ (k ) is strictly positive for an entrepreneur [this follows from the selfemployment criterion (9)]. Therefore, convexity requires optimism to fall fast, relative to the decline in uncertainty, in the early stages of business with a reverse in this situation later on. For example, the initial bite of reality from starting a business may hit optimism hard in the early stages, resulting in a surge in failures. Later on, with optimism less prevalent, the speed at which confidence is accumulated (i.e., the rate of decline in uncertainty) becomes the critical factor in survival. Regarding the positive skew in the distribution, we note firstly that the likelihood of failure approaches zero as k → ∞ . This follows since uncertainty is asymptotically 14 [ ] zero lim σ (k ) = 0 implying lim Pr ob[s = 1 Ω(k )] = 1 . Accordingly, the degree of skew k →∞ k →∞ in the distribution is determined by the rate of increase in confidence (rate of decline in uncertainty); the slower is this increase (decline) the more positively skewed will be the failure distribution. The rate at which confidence accrues will depend not only on the rate at which self-confidence accrues but also on the rate at which the confidence of external backers, such as banks, can be built up. For example, if entrepreneurs can build up a track record with banks quickly then the chances of failure will tail-off faster (again, this is an implication that we are unable to explore with our current data). Section 4: Propositions Aided by the predictions from the theoretical analysis, and with the benefit of the policy background, we are now in a position to state some testable propositions regarding optimism and uncertainty. We start with general propositions and, from them, develop specific propositions relating to the policy periods. The actual testing of the propositions involves a combination of survey questionnaire analysis and econometric estimation. It will therefore make sense, at the testing stage, to occasionally depart from the numerical ordering of the propositions used in this section. We begin with the following basic proposition: PROPOSITION 1: Entrepreneurs are more optimistic than wage-workers. This proposition will be tested in the structural probit for self-employment choices. The central prediction, arising from the entrepreneurial learning model, is framed in the following proposition: 15 PROPOSITION 2: Optimism diminishes with experience. This proposition will be tested directly using survey analysis of optimism rates among entrepreneurs with different levels of experience. In addition, the corollary to this proposition, i.e., that the impact of optimism on self-employment choices diminishes with experience [see (9)], will be tested using estimates from the structural probit. Proposition 2 is further developed in view of the distinct quantity and quality policy periods. In particular, we expect higher rates of optimism in the 1980s, relative to the 1990s, reflecting greater inexperience among the self-employed during the 1980s. In contrast, the emphasis on improving the quality of established entrepreneurs in the 1990s is expected to reduce optimism rates. This view is stated in the following: PROPOSITION 3: Entrepreneurs were more optimistic in the 1980s than in the 1990s. Testing this proposition can be achieved by comparing optimism rates in the 1980s and 1990s respectively. The key prediction of the learning model, regarding entrepreneurial uncertainty, is stated in the following proposition: PROPOSITION 4: Uncertainty diminishes with experience. This proposition is tested using estimates of the variance function from the structural probit. Specifically, the testing entails comparison of the variance estimates for experienced and inexperienced entrepreneurs respectively. The shift from quantity to 16 quality policies is also expected to manifest itself in terms of changes in uncertainty. In particular, we anticipate that the level of uncertainty increases in the 1980s due to rising inflows of inexperienced entrepreneurs. In contrast, we expect a stable or falling variance in the 1990s: PROPOSITION 5: Uncertainty rose in the 1980s and remained stable in the 1990s. This proposition is tested in the structural probit by comparing trends in estimates of the variance functions in the 1980s and 1990s respectively. Section 5: Data and trends in self-employment For the empirical analysis we use repeated cross sectional samples of BSAS data. The BSAS is an annual survey designed to yield a representative sample of adults, aged 18 or over, living in private households in Britain (south of the Caledonian Canal). The survey began in 1983 and, with the exception of 1988 and 1992, it has used the same set of core questions in each year. In total, we use 13 surveys covering the years 1984-1999. The omitted years from this analysis are: 1988 and 1992 (no survey); and 1983 and 1997 (no question relating to optimism – see section 6). In these surveys, the employment status of individuals is ascertained from their response to the question regarding their main economic activity in the previous seven days. To be self-employed, individuals must be working more than ten hours per week, on their own account, and not paying tax through PAYE. 17 Figure 1 shows that the self employment rates for BSAS respondents increased throughout the 1980s in a similar fashion to the Labour Force Survey (LFS) rates.6 In the 1990s, however, when compared to the LFS rates, it is clear that BSAS respondents were more likely to be in self-employment although it is also clear, as with the LFS rates, that the rate of self-employment has generally plateaued since the late 1980s (see section 2 for possible explanations of these trends). INSERT FIGURE 1 HERE Section 6: Analysis of optimism One of the advantages of using BSAS data is that we are able to directly observe attitudinal shifts including trends in business optimism. In particular, self-employed individuals were asked, in each survey year except for 1983 and 1997, whether they felt their business prospects for the following year were better, the same, or worse than the present. We define optimists as respondents who believe their prospects for the coming year are better than present.7 The binary optimism variable used in this section is coded to equal unity if the respondent is optimistic, on the above definition, and zero otherwise. Analysis of the survey responses, among groups with different business experience, will allow us to test directly PROPOSITIONs 2 and 3 pertaining to the relationship between optimism and experience. A test of the more fundamental PROPOSITION 1, viz., entrepreneurs are more optimistic than wage workers, is deferred to the analysis of self-employment choices in section 7. 6 Self-employment status is ascertained in the LFS from the answer to the question ‘were you working as an employee or were you self-employed [reference week]’. 7 Although, unlike Arabsheibani et al (1998), we are unable to compare expected outcomes with actual outcomes and so we are unable to infer the extent of self-deception in the data. 18 In Figure 2 we start by looking at a time-series plot of optimism rates and GDP growth. INSERT FIGURE 2 HERE The first observation from Figure 2 is that optimism rates vary markedly through time. Also we see that economic growth and optimism appear highly positively correlated. Notably, though, optimism lags the economic downturn in 1989. In contrast optimism appears to lead economic growth in the early mid-1990s. This is compatible with a state of relative euphoria in the late 1980s which was slow to adjust to economic reality. By the 1990s, however, levels of optimism are lower and more attuned to the actuality. Before analysing in detail the determinants of optimism we take a summary look at the relationship between optimism and experience. The level of business experience may be ascertained in BSAS data by responses to questioning on the state of the respondent’s business one year ago; a response that the business did not exist one year ago is taken to denote less than a year of experience.8 We note that 7.8% (n=1280) of self-employed had less than one year of experience between 1984 and 1991 whereas the corresponding figure for the period 1993-1999 is 5.9% (n=1442). The hypothesis that levels of experience are the same over the two periods is rejected against the hypothesis that experience is lower in the 1980s (p=0.023). This supports the contention, underlying PROPOSITION 3, that average levels of experience are lower in the quantity, relative to the quality, policy periods. 8 This obviously ignores the possibility that the entrepreneur may have had experience running a different business at an earlier time. 19 In Table 1 we present analysis of optimism rates by sub-groups of different age and levels of business experience: INSERT TABLE 1 HERE Optimism rates are significantly higher among the under 30s and among those with less than one year of business experience. This supports the central PROPOSITION 2 that optimism diminishes with experience. Comparing rates of optimism between the quantity and quality policy periods, we see that they are higher in the quantity era with a statistical significance approaching the 5% level. This offers some support for the view that optimism was higher in the 1980s than in the 1990s (PROPOSITION 3). The next stage in this analysis is to estimate a probit model for optimism with sample selection (recall, views on business prospects are elicited from the sub-sample of selfemployed only). The key determinant of optimism is business experience as indicated by the theoretical analysis. Additional controls for: personal characteristics; education; housing wealth; economic growth; region and industry dummies are also included in the specifications. A summary analysis of the main exogenous variables, used in the analysis of both optimism and self-employment choices, is given in Appendix 2, Table A2.1 (see also section 7.1 for background information on these variables). In the following Table 2, in which marginal effects from the optimism probits with selection are reported, the (reduced-form) self-employment selection equations are not listed to conserve space.9 INSERT TABLE 2 HERE These estimates again support the contention (PROPOSITION 2) that optimism diminishes with experience. In particular, entrepreneurs in the 1980s, with less than 9 These equations include an enterprise support variable in addition to the previously mentioned controls in the optimism equation. 20 one-year’s experience, are around 17 percentage points more likely to be optimistic regarding their business prospects relative to more experienced entrepreneurs. The corresponding effect for the 1990s is more than 30 percentage points. Regarding age, there is no consistent relationship with optimism over the 1980s and 1990s. In the 1993-1991 period there is a significant convex relationship between age and optimism; optimism rates diminish with age, up to around 64 years, and pick-up thereafter. It is also notable that, in Table 2, the apparent association between optimism and economic growth (Figure 2) vanishes with the inclusion of the experience variable and other controls. Finally, we note that the correlations between unobservables in the self-employment selection and optimism equations (ρ ) are insignificant. Aside from showing the determinants of optimism, the probits in Table 2 have a further important use. Specifically, the predicted marginal probabilities from these probits are used to construct an optimism variable for wage workers. This is a binary variable which equals unity if the predicted marginal probability of optimism exceeds one-half and equals zero otherwise. This variable is joined, with the existing binary optimism variable for the self-employed, to form an optimism variable spanning the whole sample. The conjoined optimism variable will play a central role in the following analysis of self-employment choices. Section 7: Analysis of Self-Employment Choices In this section we will show estimates of a structural probit for self-employment choices. Firstly, though, we begin with a discussion of the principal determinants of these choices. These determinants affect choices through expected relative utilities 21 and through uncertainty (see section 3). Within expected relative utilities there is a further sub-division between pecuniary and non-pecuniary (taste) effects on preferences 7.1 Expected relative utilities Pecuniary Effects Optimism – Optimists tend to over-estimate pecuniary gains in self-employment increasing their likelihood of self-employment (PROPOSITION 1). The construction of this variable is discussed at the end of section 6. Self-employment minus wage income differential –The first issue here is that the income data are truncated on occupational choices – a working individual reports either a self-employed or a wage income but not both. Which income is actually reported is the result of an occupational choice made, possibly, on the basis of where the individual’s comparative advantage lies.10 This raises the problem of (self) selection bias in estimating earnings. The second issue is that income variables in BSAS are recorded as interval data. To address these issues, an income differential variable is constructed as follows. Ordered probits for earnings, with occupational selection, are used to predict self-employed and wage income marginal probabilities.11 These probabilities are then used to predict individuals’ self-employed and wage income categories. Finally, an income dummy variable is constructed which equals unity if predicted self-employment income exceeds wage income and equals zero otherwise. (see Appendix 3 for estimates of the income ordered probits). 10 Formally, comparative advantage exists if an individual, from the self-employed (wage-employed) sub-sample, earns more in self-employment (wage-employment) than would an observably identical individual, from the wage-employed (self-employed) sub-sample, were they to be placed in selfemployment (wage-employment). 11 Estimates from ordered probits, without selection, would yield probabilities which are conditional on occupational choices. 22 For identification of the income differential effect, industry dummies are included in the earnings (and the reduced form self-employment selection) equations but not the structural self-employment equations. This is the scheme also used by Rees and Shah (1986) and Taylor (1996) to identify their structural self-employment probits. This identification is based on the assumption that individuals do not switch industry on changing between occupations. Non-pecuniary effects Personal characteristics and education – Unlike Taylor (1996), Blanchflower and Oswald (1998) and Burke et al (2000), the BSAS does not have ‘desirable job characteristic’ variables to directly measure desire for independence.12 In this study, we use variables for individuals’: sex (Male); race (Black and Asian); marital status (Married); age (Age and Age squared); trade union membership (Union); manual occupational status (Manual); and education as controls for non-pecuniary lifestyle preferences. Financial Independence – Black et al (1996) use housing equity and the regional value of housing to examine the role of collateral in business formations. In this study, we construct a housing wealth variable that is given by the individual’s predicted probability of being a home owner multiplied by the real average regional house price to give an estimate of the individual’s expected housing wealth13 (Data Source: Nationwide Building Society)14. Predicted probabilities of home ownership 12 These authors were able to use measures of the importance of being one’s own boss and job security as characteristics of the respondent’s job. 13 These predicted probabilties were obtained from reduced form probits for home ownership in which all the exogenous variables (including the industry dummies) and real interest rates appear as explanatory variables. Real interest rates are excluded from the mean of the structural self-employment probit to identify the impact of housing wealth. 14 www.nationwide.co.uk. These data measure mix adjusted average prices. This adjustment ensures the price series are not biased by changes in, for example, the types of property being sold or property locations. We also calculated the housing wealth variable using data from the leading UK mortgage lender – the Halifax Building Society (www.hbos.plc.com/view/housepriceindex/housepriceindex.asp). Their methodology for constructing price series is similar to that used by the Nationwide. It is 23 are used as instruments since home ownership itself may be endogenous in selfemployment decisions. Note that, given we control for earnings differentials (and earnings themselves are a function of wealth – see Appendix 3), the housing wealth variable has a non-pecuniary interpretation in the structural probit. In other words, the ability to self-finance may raise self-employment utility by increasing independence from external sources of equity and/or provide opportunities to pursue non-profit objectives (see Burke et al, 2000). Enterprise Support – Non-pecuniary effects of enterprise support on self-employment are examined using (log) real value of lending under the SFLGS (Data Source: Department of Employment). This measure is deflated by the population aged 15 to 64 as a proxy for the total working population (Data Source: ONS). It might be expected that greater government involvement in enterprise support would raise general awareness and tastes for self-employed occupations. In addition variables for economic growth, regional unemployment rates and region dummies are included in expected relative utilities. These capture variations in tastes for self-employment over the business cycle and over different geographical locations 7.2 Uncertainty The model suggests a parsimonious specification of uncertainty which centres on experience. The business experience variable, used earlier, cannot be used here since it is defined on the self-employment sub-sample only. Instead, respondent’s age (and age-squared) are used as experience proxies. An additional key variable, real interest rates, is included in the specification of uncertainty. We expect that rising borrowing costs will increase the prospect of insolvency thereby raising uncertainty. unsurprising therefore that the empirical results are unaffected by the version of the housing wealth 24 The functional form for the uncertainty function is the typically used exponential form, σ 2 (w) = [exp{γw}] (see Harvey, 1976), where w , the vector of uncertainty 2 covariates, does not include a constant term. This functional form ensures that a positive variance is estimated. 7.3 Estimates Next, we turn to estimates of the structural probits for the quantity (1984-1991) and quality (1993-1999) policy periods. In Table 3, we show the marginal effects on selfemployment probabilities along with estimates of the uncertainty function. Note that the estimation samples are diminished due to missing earnings data (cf. Table 2). INSERT TABLE 3 HERE Looking firstly at the marginal effects for the 1984-1991 period, the principal result is the strong effect of optimism. Specifically, optimists are 14 percentage points more likely to be self-employed than non-optimists. This offers support for the proposition that entrepreneurs are more optimistic than wage workers (PROPOSITION 1). Also, individuals with higher expected relative earnings in self-employment are about nine percentage points more likely to be self-employed. This finding is compatible with Rees and Shah (1986) and Taylor (1996) who found a positive effect of income differentials on self-employment probabilities. 15 Turning to taste effects in the 1980s, personal characteristics are individually significant (except Asian) pointing to the importance of lifestyle preferences in occupational choices. For example union members have lower preferences, ceteris variable used in the analysis. 15 It is possible, however, that this effect is understated due to unobserved tax advantages in selfemployment (Pissarides and Weber, 1989; Baker, 1993). 25 paribus, for self-employment reflecting better (wage) working environments relative to non-union workers. Also, individuals with 13 years of education have lower tastes for self-employed occupations relative to individuals with only 10 years of education. Notably, however, there is no role for wealth (financial independence) in the quantity periods. Nor, surprisingly, does government support (SFLGS) appear to influence attitudes to self-employed occupations during this time. On the other hand, each percentage point increase in economic growth, in the 1980s, increases selfemployment likelihoods by about 1.5 percentage points. Finally, for the quantity periods, unemployment has no influence on tastes and there are no apparent regional variations in attitudes toward self-employed occupations. Looking at the marginal effects in the quality policy period, we again notice a strong impact of optimism on self-employment (12 percentage points). Income differentials, on the other hand, have no effect on self-employment choices in the 1990s (see Parker, 2003, and Hamilton, 2000, who also found no earnings effect, in the UK and US respectively, using data from the 1990s). While pecuniary incentives appear to have a lesser role in the 1990s there are, however, some interesting non-pecuniary effects. For example, Asians are more likely than individuals from white ethnic backgrounds to be self-employed in the 1990s. This effect may reflect variations in cultural resources, such as family networks, between Asians and non-Asians (see Metcalf et al, 1996 and Clarke and Drinkwater, 1998).16 There is also an interesting sign shift in the effect of marriage 16 However, interestingly, this effect is not significant in the 1980s. This is surprising since evidence from alternative data sources suggests the self-employment boom in the 1980s was particularly important for non-whites (General Household Survey – Clarke and Drinkwater, 1998; Labour Force Survey – Daly, 1991). 26 between the 1980s and 1990s. Whereas marriage promotes self-employment in the 1980s it appears to act as a barrier in the 1990s. Significantly, we notice that self-employment choices are increasing in wealth in the 1990s. Specifically, each 1% increase in housing wealth is associated with a 0.076 percentage point rise in self-employment likelihoods. Interestingly, this suggests that, unlike the 1980s, a desire for financial independence is a motive for choosing selfemployment during the 1990s. In light of this result, it is also notable that enterprise support (SFLGS) has a significantly negative effect in the quality periods. Presumably, the 1990s entrepreneurs find the strings attached to external finance distasteful. Finally, we note that economic growth is negatively associated with selfemployment which contrasts with the effect in the 1980s. On this evidence, falling self-employment rates in the 1990s may be partly explained by faster economic growth leading to enhanced wage employment opportunities. The corollary to PROPOSITION 2 is that the influence of optimism on selfemployment choices diminishes with experience. To test this corollary we examine, in Figure 3, how the marginal effect of optimism varies with age holding the other explanatory variable at their sample means. INSERT FIGURE 3 HERE This figure shows a concave relationship, in both sub-periods, between the marginal effect of optimism and age. The effect rises up to ages in the late 40s (more accurately, age 47 in the 1984-1991 sub-period and age 48 in the 1993-1999 subperiod) and attenuates thereafter. This attenuation supports the diminishing role of optimism in self-employment choices beyond a threshold level of experience. To be more precise regarding this threshold, we note that the average ages of entrepreneurs 27 with more than one year of business experience are 43 and 44 in the 1980s and 1990s samples respectively. The turning points in Figure 3 are, accordingly, compatible with an experience threshold which lies above one year. Next, we turn to estimates of the uncertainty in self-employment choices which are reported at the end of Table 3. The effects of age (and age-squared) are significant in both sub-samples which points to the role of experience in uncertainty. Interestingly, however, the relationship is convex in the 1980s and concave in the 1990s. The turning points occur at around 46 and 29 years of age respectively. Also, real interest rates are positively signed, as expected, but are individually insignificant in both subperiods. To conclude the analysis, the relationship between experience and uncertainty is explored in more detail. In the following Table 4 we report: i) summary statistics for uncertainty, by level of experience and policy period; and ii) estimates of regressions of uncertainty on a trend and trend-squared, in both policy periods. INSERT TABLE 4 HERE Firstly, we notice that uncertainty is higher among less experienced entrepreneurs in both the 1980s and 1990s. This difference is, however, only significant in the quality policy periods. This finding provides an empirical bolster to PROPOSITION 4 – viz., uncertainty diminishes with experience. Secondly, the regression estimates are indicative of a concave trend in uncertainty in the 1980s with no trend in the 1990s. This finding supports PROPOSITION 5 which predicted rising uncertainty in the quantity policy periods and stability in the quality periods. Note that incomes are higher in the 1990s (see Table A3.1) so that the greater absolute level of uncertainty 28 in the 1990s, compared to the 1980s, is unsurprising [see also equation (6) which indicates that the variance is increasing in the level of representative income]. On the evidence presented in this section, the motivation for choosing self-employed occupations has changed markedly over time. The strong pecuniary incentive, which characterises entrepreneurship in the Thatcher era, is replaced in the 1990s with a desire to satisfy non-pecuniary lifestyle preferences. Also, rising uncertainty in the 1980s is contrasted with a more stable environment in the 1990s. The one constant feature in this analysis is the high impact of optimism on self-employment choices in both the 1980s and 1990s. Section 8: Conclusions and policy implications In this paper we have presented a model in which entrepreneurs’ optimistic excesses are mitigated by their capacity to learn from their initial errors in judgement. The model predicts that the relative effects of learning on optimism and uncertainty/confidence respectively will determine the shape of the business failure distribution by experience. High initial failure rates are explained by the forced exit of optimists soon after start-up. The degree of positive skew in the distribution, on the other hand, is determined by the speed at which confidence accumulates; the faster is this accumulation the quicker is the tail-off in failure probabilities. The empirical analysis supports the central propositions that entrepreneurs are optimists but that this optimism diminishes with experience. In addition, we find that rates of optimism are high and uncertainty in self-employment choices is rising in the 1980s. This, we argue, is a result of policies which encouraged young people, and 29 other inexperienced types, into self-employment. In contrast, in the 1990s, optimism rates are lower and uncertainty is more stable which, we believe, reflects the shift in policy emphasis toward increasing the quality of incumbent businesses. The empirical analysis also lends support to the popular view that entrepreneurship in the Thatcher era was driven predominantly by the prospect of financial gain. The profile of the 1990s entrepreneur, on the other hand, is somewhat ‘softer’ with the principal motivation being to satisfy lifestyle preferences. The policy implications from this analysis are particularly apposite given recent developments. For example, the UK government has, through the Davies review (2002) of enterprise education, promised to provide £60m by 2005/06 so that each secondary school student will experience five days of ‘enterprise activity’. Similarly, the government has also recently spent £43.9 million in promoting undergraduate entrepreneurship education through the Science Enterprise Challenge (DTI, 2000). One of the stated intentions of this expenditure is to promote entrepreneurship. However, the opposite intention may be seen as more desirable in the presence of optimism. Specifically, in helping nascent entrepreneurs form better forecasts of their future performances, entrepreneurship education may help persuade some individuals of the wisdom that they choose not to become entrepreneurs. Another policy implication relates specifically to direct attempts to increase the rate of new venture creation which the UK government sees as one of its seven ‘pillars’ to support smaller enterprises (SBS, 2004). 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(1984) ‘The Influence of Perceived Events’ Controllability on its subjective Occurrence’, Psychological Record, 34, 233-240. 33 Figure 1: LFS and BSAS Self-Employment Rates in the UK, 1983-1999 25 15 LFS data BSAS data 10 5 0 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 Percentage 20 Year 34 Figure 2: Annual Rates of Optimism and GDP Growth (%) optimism growth 40.97 5.2 growth optimism 28.93 -1.4 83 84 85 86 87 88 89 90 91 92 year 93 94 95 96 97 98 99 35 Table 1: Survey Questionnaire Analysis of Optimism Rates (%) by Age, Business Experience and Policy Sub-Periods – Sub-Sample of Self-Employed Only (n is the number of observations in the sub-sample) (p – values for tests on the equality of proportions between sub-samples). Age<30 Age≥30 59.1 (n=303) 35.2 (n=1988) < 1year experience ≥ 1year experience 65.7 (n=134) 36.6 (n=2157) p=0.000 p=0.000 1984-1991 (excl. 1988) 1993-1999 (excl. 1997) 40.4 (n=896) 37.0 (n=1395) p=0.051 36 Table 2: Optimism: Probit model with selection (Self-employment selection equations not reported) – Marginal Effects ( ∂Φ ∂x ) (p-values in parenthesis) 1984-1991 (excl. 1988) 1993-1999 (excl. 1997) Business experience 0.174 (0.023) 0.301 (0.000) < 1 year experience Personal characteristics Male Black Asian Married Age Age squared/100 Manual Years of Education (relative to 10 years) 11 12 13 14 or more 0.111 (0.009) 0.443 (0.021) −0.025 (0.806) −0.012 (0.852) 0.002 (0.864) −0.011 (0.305) −0.164 (0.061) 0.083 (0.024) −0.090 (0.448) −0.153 (0.039) 0.025 (0.652) −0.025 (0.020) 0.020 (0.044) −0.104 (0.064) 0.011 (0.839) 0.041 (0.570) 0.132 (0.166) 0.111 (0.076) 0.011 (0.798) 0.011 (0.862) 0.005 (0.931) 0.048 (0.363) (log) Real Housing wealth Real GDP Growth −0.263 (0.218) −0.033 (0.499) −0.141 (0.398) 0.062 (0.068) Regional Unemployment rate Region dummies (p-value) −0.030 (0.167) −0.061 (0.053) 0.497 0.853 Trend Year dummies (p-value) Industry dummies (p-value) 0.051 (0.359) 0.391 0.067 −0.035 (0.233) 0.329 0.000 ρ χ (p-value) 0.159 (0.544) 0.000 0.069 (0.703) 0.000 Log-likelihood n Censored obs. Uncensored obs. −2835.180 9183 8295 888 −4250.701 9349 8016 1333 2 Notes: Survey weights are used in estimation. Discrete changes in probabilities calculated for dummy variables. 37 Table 3: Structural Self-Employment Probits (Marginal Effects ∂Φ ∂x ) with Estimates of the Uncertainty Equation (p-values in parenthesis). 1984-1991 (excl. 1988) 1993-1999 (excl. 1997) Pecuniary 0.140 (0.000) 0.121 (0.000) Optimism 0.091 (0.000) −0.019 (0.556) Income Differential Non-pecuniary Personal characteristics 0.041 (0.000) 0.074 (0.000) Male −0.043 (0.000) −0.025 (0.235) Black 0.022 (0.423) 0.078 (0.029) Asian 0.023 (0.004) −0.020 (0.051) Married 0.007 (0.000) 0.018 (0.000) Age −0.007 (0.001) −0.018 (0.000) Age squared/100 −0.062 (0.000) −0.106 (0.000) Union 0.028 (0.001) 0.044 (0.000) Manual Years of Education (relative to 10 years) −0.002 (0.747) 0.009 (0.313) 11 −0.003 (0.714) −0.031 (0.018) 12 −0.027 (0.000) −0.011 (0.341) 13 −0.004 (0.653) 0.009 (0.455) 14 or more 0.054 (0.598) 0.015 (0.864) Still at college Financial independence 0.027 (0.166) 0.076 (0.000) (log) Real Housing wealth Enterprise Support 0.019 (0.118) −0.215 (0.002) (log) SFLGS 0.013 (0.005) 0.004 (0.344) −0.147 (0.000) 0.002 (0.617) 0.812 0.337 0.010 (0.076) 0.117 −0.040 (0.000) 0.022 0.038 0.034 Age Age squared/100 Real Interest Rates χ 2 (p-value) −0.063 (0.001) 0.068 (0.009) 0.037 (0.165) 0.000 0.030 (0.016) −0.053 (0.001) 0.012 (0.774) 0.000 Log-likelihood n Wage workers Self-Employed −2047.583 8491 7763 728 −3126.194 8679 7536 1143 Real GDP Growth Regional unemployment rate Regional Dummies (pvalue) Trend Year dummies (p-value) χ 2 (p-value) UNCERTAINTY Notes: Survey weights are used in estimation. Discrete changes in probabilities calculated for dummy variables. 38 Table 4: Uncertainty: i) summary analysis by experience and policy sub-period; and ii) regression on time trend and trend-squared. 1984-1991 (excl. 1988) 1993-1999 (excl. 1997) 0.351 1.474 < 1 year experience (σ 1 ) 0.338 1.379 ≥ 1 year experience (σ 2 ) 0.155 0.002 p-value (H 0 : σ 1 = σ 2 vs. H 1 : σ 1 > σ 2 ) Regression 0.021 (0.010) 0.026 (0.541) Trend −0.002 (0.002) −0.001 (0.525) Trend-sq 0.000 0.001 Year dummies (p-value) Robust standard errors used in regression analysis 39 Figure 3: Optimism: Marginal Effects on Self-Employment Probabilities by Age. optimism_mfx8491 optimism_mfx9399 .6 .5 .4 .3 .2 .1 0 20 25 30 35 40 45 50 55 60 age 65 70 75 80 85 90 95 100 40 Appendix 1 Recursive formula for the posterior variance Given the normality of the prior distribution, and assuming σ 2 is known, we may write the posterior variance for k = 1 as var θ Ω(1), σ 2 = W (1)σ 02 [ ] where [ −1 ] ⎡ ⎤ ( prior var iance ) = ⎢ 12 + 12 ⎥ 12 W (1) = ( prior var iance ) + (sample var iance ) ⎣σ 0 σ ⎦ σ 0 (see e.g., Judge et al., 1982, p. 123). The process of Bayesian learning implies that the posterior density, from the current period, forms the prior density in the following period [see equation (3)]. Accordingly, var θ Ω(2 ), σ 2 = W (2 )W (1)σ 02 −1 −1 −1 [ ] −1 [ = W (2 ) var θ Ω(1), σ 2 ] where −1 ⎡ 1 2 ⎤ 1 + 2⎥ W (2 ) = ⎢ . 2 2 ⎣W (1)σ 0 σ ⎦ W (1)σ 0 The recursive formula for var θ Ω(k ), σ 2 , given in equation (4), is arrived at by a [ ] repeated application of the preceding logic. Recursive formula for the posterior Mean The posterior mean for k = 1 is given by E θ Ω(1), σ 2 = W (1)µ 0 + [1 − W (1)]θˆ(1) [ ] (see e.g., Judge et al., 1982, p. 123) which is simply a weighted average of the prior mean and the initial sample estimate of talent. In the next period: this posterior mean will form the prior mean; new sample information will give rise to a new sample estimate; and the weighting matrices are updated (as in the posterior variance). Repeated application of this logic gives rise to the recursive formula for E θ Ω(k ), σ 2 given in equation (8). [ ] 41 Appendix 2 Table A2.1: Summary statistics for principal exogenous variables (standard errors in parenthesis)† Male Black Asian Married Age Union Manual Years of education 11 12 13 14 or more Still at college (log) Real Housing Wealth (log) SFLGS Real GDP Growth (%) Real interest rates (%) n † 1984-1991 excl 1988 (self-employed) 1984-1991 excl. 1988 (wage-workers) 1993-1999 excl. 1997 (self-employed) 1993-1999 excl. 1997 (wage-workers) 0.761 (0.012) 0.010 (0.003) 0.028 (0.005) 0.804 (0.011) 42.581 (12.375) 0.410 (0.014) 0.467 (0.014) 0.532 (0.005) 0.014 (0.001) 0.017 (0.001) 0.714 (0.005) 38.966 (12.734) 0.608 (0.005) 0.429 (0.005) 0.722 (0.012) 0.011 (0.003) 0.036 (0.005) 0.721 (0.012) 43.665 (12.311) 0.203 (0.011) 0.427 (0.013) 0.482 (0.005) 0.021 (0.002) 0.020 (0.002) 0.659 (0.005) 39.260 (11.873) 0.421 (0.005) 0.373 (0.005) 0.254 (0.012) 0.097 (0.008) 0.059 (0.007) 0.168 (0.010) 0.002 (0.001) 0.294 (0.005) 0.096 (0.003) 0.081 (0.003) 0.147 (0.004) 0.001 (0.000) 0.318 (0.012) 0.074 (0.007) 0.089 (0.007) 0.210 (0.011) 0.001 (0.001) 0.325 (0.005) 0.101 (0.003) 0.114 (0.003) 0.202 (0.004) 0.002 (0.000) 10.527 (0.443) 10.424 (0.474) 10.716 (0.307) 10.670 (0.335) −17.689 (0.611) 2.270 (1.950) −16.964 (0.506) 3.015 (0.788) 6.269 (1.669) 3.641 (0.779) 1280 8527 Standard errors for binary variables are calculated as 1442 8338 ⎛ πˆ (1 − πˆ ) ⎞ ⎜ ⎟ where πˆ is the proportion of ⎝ n ⎠ observations on the binary variable equal to unity and n is the number of observations in the (sub-) sample. Note that the estimation sub-samples are smaller than reported in this table due to missing observations on business prospects and income. 42 Appendix 3: Construction of the income differential variable and estimates of heteroscedastic ordered income probits with selection We begin this appendix with a brief look at the income distributions for selfemployed and wage workers. Table A3.1: Income distributions 1984-1991 Income 1984-1991 (excl. 1988) (thousands £) (excl. 1988) self-employed wage workers (%) (%) 51.73 65.15 <10 22.02 20.58 10-15 14.04 8.78 15-20 10.00 4.94 20-30 0.77 0.33 30-35 1.44 0.23 >35 1993-1999 (excl. 1997) self-employed (%) 32.87 20.67 16.68 14.56 2.36 12.86 1993-1999 (excl. 1997) wage workers (%) 35.91 24.62 17.09 15.62 2.06 4.69 The consistent finding in these distributions is the higher proportion of self-employed ‘superstars’ relative to wage-workers (i.e., incomes in the upper sextile). At the other end of the income distributions, it is notable that the proportion of wage workers in the bottom sextile is 44% lower in the 1990s, relative to the 1980s, as compared to a fall of only 36% among the self-employed. This suggests that, among the very lowest earners, the self-employed are the most disadvantaged in terms of income growth. Next, heteroscedastic ordered probits, with selection, are estimated using the above income categories (coding the first category as zero). These earnings equations include as explanatory variables: human capital, wealth, enterprise support (selfemployed earnings only); and industry dummies. Using the estimated marginal probabilities we may estimate wage earnings as: E ( y w ) = prob( y w = 1) + 2 × prob( y w = 2) + ... + 5 × prob( y w = 5) . Similarly, estimated self-employment income is given by: E ( y e ) = prob( y e = 1) + 2 × prob( y e = 2 ) + ... + 5 × prob( y e = 5) . The income differential variable, used in the structural self-employment equation, is then calculated as a dummy variable equal to unity if E ( y e ) > E ( y w ) and zero otherwise. The presence of comparative advantage in career choices will depend on the correlations between occupational choice and earnings. Denoting latent earnings by y i* , i = e, w and prob(s = 1) by Φ (Zγ ) , where Zγ is the index function from the reduced form self-employment equation, then we may write φ (Z γ ) E y w* s = 1 = E y w* − ρ yws Φ(Zγ ) φ (Zγ ) . E y w* s = 0 = E y w* + ρ yw s 1 − Φ (Z γ ) If ρ yws , the correlation between unobservables in wage earnings and occupation ( ( ) ) ( ) ( ) choices, is positive then self-employed individuals earn below average earnings in wage employment whereas wage earners earn above average in wage employment E ( y w* s = 1) < E ( y w* ) < E ( y w* s = 0 ) (comparative advantage). Similarly, 43 φ (Z γ ) 1 − Φ (Z γ ) φ (Zγ ) . E ( y e* s = 1) = E ( y e* ) − ρ ye s Φ (Z γ ) E ( y e* s = 0 ) = E ( y e* ) + ρ ye s If ρ ye s is negative then wage earners earn below average incomes in self-employment whereas self-employed individuals earn above average incomes in their chosen careers - E ( y e* s = 0 ) < E ( y e* ) < E ( y e* s = 1) (comparative advantage). In the following tables marginal effects on income cell probabilities are reported. The reduced form self-employment selection equations are not reported to conserve space: Table A3.2 Heteroscedastic Ordered Probits with Selection (Marginal Effects) and Estimates of the Uncertainty Equation (p-values in parenthesis): SelfEmployed Income; 1984-1991 (excl. 1988) Income category(thousands £) <10 10-15 15-20 20-30 30-35 >35 Personal characteristics -0.561762 0.436046 0.0937575 0.031142 0.0004953 0.0003213 Male (0.001) (0.004) (0) (0.001) (0.024) (0.046) Black Asian Age Age squared/100 Manual Union Married 0.1131402 (0.286) 0.1453861 (0.287) -0.0312871 (0.007) 0.000379 (0.005) 0.3280526 (0.005) 0.0735005 (0.067) -0.1362563 (0.044) -0.0878207 (0.291) -0.1128503 (0.294) 0.0242854 (0.012) -0.0002942 (0.01) -0.2546381 (0.01) -0.0570519 (0.085) 0.1057637 (0.055) -0.018883 (0.286) -0.0242648 (0.284) 0.0052218 (0.005) -0.0000633 (0.004) -0.0547516 (0.002) -0.0122672 (0.041) 0.022741 (0.039) -0.0062721 (0.3) -0.0080597 (0.296) 0.0017344 (0.016) -0.000021 (0.014) -0.018186 (0.008) -0.0040746 (0.046) 0.0075535 (0.058) -0.0000997 (0.331) -0.0001282 (0.325) 0.0000276 (0.063) -0.0000647 (0.346) -0.0000831 (0.339) 0.0000179 (0.092) -0.000000334 (0.061) -0.000000217 (0.09) -0.0002892 (0.046) -0.0000648 (0.081) 0.0001201 (0.112) -0.0001876 (0.072) -0.000042 (0.103) 0.0000779 (0.139) -0.0169861 (0.724) -0.0655302 (0.286) -0.054321 (0.458) -0.1176408 (0.089) 2.49314 (0.002) 0.0131848 (0.725) 0.0508653 (0.29) 0.0421646 (0.458) 0.0913141 (0.103) -1.935204 (0.007) 0.002835 (0.725) 0.0109369 (0.289) 0.0090661 (0.465) 0.0196341 (0.077) -0.4161025 (0) 0.0009416 (0.726) 0.0036327 (0.304) 0.0030114 (0.475) 0.0065216 (0.093) -0.1382103 (0.003) 0.000015 (0.729) 0.0000578 (0.337) 0.0000479 (0.494) 0.0001037 (0.14) -0.002198 (0.03) 0.00000971 (0.73) 0.0000375 (0.352) 0.0000311 (0.503) 0.0000673 (0.164) -0.0014258 (0.054) 0.1438718 (0.391) 0.1265875 (0.027) -0.1116749 (0.394) -0.0982587 (0.039) -0.024012 (0.392) -0.0211273 (0.017) -0.0079757 (0.401) -0.0070175 (0.029) -0.0001268 (0.422) -0.0001116 (0.073) -0.0000823 (0.432) -0.0000724 (0.1) 0.0639766 (0.231) -0.0496594 (0.239) -0.0106776 (0.226) -0.0035466 (0.24) -0.0000564 (0.275) -0.0000366 (0.292) 0.0210705 (0.329) -0.0163551 (0.337) -0.0035166 (0.318) -0.0011681 (0.323) -0.0000186 (0.343) -0.0000121 (0.354) Years of Education (relative to 10 years) 11 12 13 14 or more Still at college (log) Real Housing wealth (log) SFLGS Real GDP Growth Regional Unemployment rate χ 2 (p-value) 0.9864 44 UNCERTAINTY Age Age squared/100 Real Interest Rates ρy s e Log-likelihood n 0.0207446 (0.177) -0.0001873 (0.289) -0.040480 (0.009) -0.2457243 (0.000) -3500.1883 8775 Table A3.3 Heteroscedastic Ordered Probits with Selection (Marginal Effects) and Estimates of the Uncertainty Equation (p-values in parenthesis): Wage Income; 1984-1991 (excl. 1988) Income category(thousands £) <10 10-15 15-20 20-30 30-35 >35 Personal characteristics 0.3914347 0.1087805 0.0254897 0.0003134 0.0000699 Male -0.5260882 (0) (0) (0) (0) (0) (0) Black Asian Age Age squared Manual Union Married 0.122638 (0.029) 0.2012271 (0) -0.0647874 (0) 0.0007216 (0) 0.2507401 (0) 0.0038361 (0.754) -0.0408409 (0.048) -0.0912485 (0.03) -0.1497225 (0) 0.0482049 (0) -0.0005369 (0) -0.1865625 (0) -0.0028542 (0.754) 0.0303875 (0.049) -0.0253581 (0.026) -0.0416082 (0) 0.0133962 (0) -0.0001492 (0) -0.0518461 (0) -0.0007932 (0.754) 0.0084448 (0.045) -0.005942 (0.025) -0.0097497 (0) 0.003139 (0) -0.000035 (0) -0.0121487 (0) -0.0001859 (0.754) 0.0019788 (0.043) -0.0000731 (0.023) -0.0001199 (0) 0.0000386 (0) -0.00000043 (0) -0.0001494 (0) -0.00000229 (0.754) 0.0000243 (0.042) -0.0000163 (0.023) -0.0000267 (0) 0.00000861 (0) -0.0000000959 (0) -0.1105018 (0) -0.1572529 (0) -0.2175503 (0) -0.3511501 (0) -0.1790357 (0.54) 0.0822186 (0) 0.1170036 (0) 0.1618678 (0) 0.2612724 (0) 0.1332111 (0.54) 0.0228487 (0) 0.0325156 (0) 0.0449834 (0) 0.0726081 (0) 0.0370196 (0.54) 0.005354 (0) 0.0076191 (0) 0.0105406 (0) 0.0170137 (0) 0.0086745 (0.54) 0.0000658 (0) 0.0000937 (0) 0.0001296 (0) 0.0002092 (0) 0.0001067 (0.541) 0.0000147 (0) 0.0000209 (0) 0.0000289 (0) 0.0000467 (0) 0.0000238 (0.541) -0.0951087 (0.082) 0.0322298 (0.081) 0.0707654 (0.083) -0.0239805 (0.081) 0.0196659 (0.079) -0.0066642 (0.081) 0.0046082 (0.077) -0.0015616 (0.081) 0.0000567 (0.076) -0.0000192 (0.082) 0.0000126 (0.076) -0.00000428 (0.083) -0.0083833 (0.245) 0.0062376 (0.246) 0.0017334 (0.242) 0.0004062 (0.239) 0.00000499 (0.236) 0.00000111 (0.235) -0.0000333 (0) -0.00000051 (0.754) 0.00000543 (0.041) Years of Education (relative to 10 years) 11 12 13 14 or more Still at college (log) Real Housing wealth Real GDP Growth Labour Market Regional Unemployment rate χ 2 (p-value) 0.0000 UNCERTAINTY 45 Age Age squared Real Interest Rates ρy ws -0.0498216 (0) 0.0005964 (0) -0.0196204 (0.035) 0.3779155 (0.000) -7768.6719 Log-likelihood n 8775 Table A3.4 Heteroscedastic Ordered Probits with Selection (Marginal Effects) and Estimates of the Uncertainty Equation (p-values in parenthesis): SelfEmployed Income; 1993-1999 (excl. 1997) Income category(thousands £) <10 10-15 15-20 20-30 30-35 >35 Personal characteristics -0.39042 0.026072 0.1249157 0.1332219 0.022061 0.0841494 Male (0) (0.742) (0) (0.029) (0.087) (0.176) 0.1226205 (0.161) 0.0308813 (0.748) -0.0329611 (0) 0.0003672 (0) 0.2499082 (0.001) 0.0083296 (0.796) -0.1146483 (0.032) -0.0081885 (0.755) -0.0020622 (0.809) 0.0022011 (0.752) -0.0000245 (0.751) -0.0166887 (0.742) -0.0005562 (0.849) 0.0076562 (0.746) -0.0392327 (0.16) -0.0098805 (0.747) 0.010546 (0) -0.0001175 (0) -0.0799586 (0) -0.0026651 (0.796) 0.036682 (0.03) -0.0418414 (0.199) -0.0105375 (0.751) 0.0112472 (0.011) -0.0001253 (0.011) -0.0852755 (0.037) -0.0028423 (0.796) 0.0391211 (0.089) -0.0069288 (0.237) -0.001745 (0.753) 0.0018625 (0.047) -0.0000208 (0.049) -0.0141213 (0.098) -0.0004707 (0.795) 0.0064783 (0.146) -0.0264291 (0.289) -0.006656 (0.757) 0.0071043 (0.122) -0.0000792 (0.125) -0.0538641 (0.186) -0.0017953 (0.796) 0.0247108 (0.222) -0.112166 (0.017) -0.049262 (0.376) -0.0843596 (0.155) -0.2372522 (0.001) -0.487073 (0.255) 0.0074904 (0.743) 0.0032897 (0.76) 0.0056335 (0.75) 0.0158436 (0.744) 0.0325265 (0.755) 0.0358877 (0.015) 0.0157615 (0.375) 0.026991 (0.152) 0.0759093 (0.001) 0.15584 (0.253) 0.0382741 (0.076) 0.0168095 (0.397) 0.0287858 (0.204) 0.0809569 (0.035) 0.1662025 (0.288) 0.006338 (0.137) 0.0027836 (0.417) 0.0047668 (0.247) 0.0134061 (0.093) 0.0275224 (0.318) 0.0241757 (0.217) 0.0106177 (0.444) 0.0181825 (0.303) 0.0511363 (0.178) 0.1049815 (0.36) 0.1770178 (0.123) 0.0092265 (0.793) -0.0118212 (0.752) -0.0006161 (0.841) -0.0566372 (0.121) -0.002952 (0.793) -0.0604033 (0.168) -0.0031483 (0.793) -0.0100025 (0.211) -0.0005213 (0.794) -0.0381536 (0.27) -0.0019886 (0.795) -0.0039821 (0.862) 0.0002659 (0.88) 0.0012741 (0.862) 0.0013588 (0.862) 0.000225 (0.862) 0.0008583 (0.862) Labour Market Regional Unemployment rate -0.008926 (0.729) 0.0005961 (0.81) 0.0028559 (0.729) 0.0030458 (0.731) 0.0005044 (0.733) 0.0019239 (0.737) χ 2 (p-value) 0.9974 Black Asian Age Age squared/100 Manual Union Married Years of Education (relative to 10 years) 11 12 13 14 or more Still at college (log) Real Housing wealth (log) SFLGS Real GDP Growth UNCERTAINTY 46 Age Age squared/100 Real Interest Rates ρy s e Log-likelihood n -0.0029757 (0.819) 0.000082 (0.546) 0.1382268 (0.001) -0.1041501 (0.006) -4885.9402 8722 Table A3.5 Heteroscedastic Ordered Probits with Selection (Marginal Effects) and Estimates of the Uncertainty Equation (p-values in parenthesis): Wage Income; 1993-1999 (excl. 1997) Income category(thousands £) <10 10-15 15-20 20-30 30-35 >35 Personal characteristics -0.0264633 0.1790892 0.2183856 0.0230115 0.0337957 Male -0.4278187 (0) (0.293) (0) (0) (0) (0) Black Asian Age Age squared/100 Manual Union Married 0.1163536 (0.022) 0.1533183 (0) -0.0591171 (0) 0.0006586 (0) 0.3042053 (0) -0.0832779 (0) -0.0558866 (0.002) 0.0071972 (0.345) 0.0094837 (0.308) -0.0036568 (0.29) 0.0000407 (0.289) 0.0188171 (0.295) -0.0051513 (0.302) -0.0034569 (0.317) -0.0487068 (0.022) -0.0641806 (0) 0.024747 (0) -0.0002757 (0) -0.1273434 (0) 0.034861 (0) 0.0233947 (0.001) -0.0593942 (0.032) -0.0782633 (0.001) 0.0301771 (0) -0.0003362 (0) -0.1552856 (0) 0.0425103 (0) 0.0285281 (0.005) -0.0062584 (0.042) -0.0082467 (0.003) 0.0031798 (0) -0.0000354 (0) -0.0163626 (0) 0.0044793 (0) 0.003006 (0.009) -0.0091914 (0.05) -0.0121114 (0.005) 0.00467 (0) -0.000052 (0) -0.0240308 (0) 0.0065786 (0.001) 0.0044148 (0.013) -0.0987545 (0) -0.1560326 (0) -0.2242277 (0) -0.3345015 (0) -0.0965213 (0.524) -0.0061086 (0.309) -0.0096516 (0.299) -0.0138699 (0.299) -0.0206911 (0.297) -0.0059705 (0.593) 0.0413396 (0) 0.0653168 (0) 0.093864 (0) 0.1400257 (0) 0.0404048 (0.524) 0.0504105 (0) 0.0796489 (0) 0.11446 (0) 0.1707506 (0) 0.0492706 (0.527) 0.0053118 (0.001) 0.0083927 (0) 0.0120607 (0) 0.0179921 (0) 0.0051917 (0.53) 0.0078011 (0.003) 0.0123258 (0.001) 0.0177129 (0.001) 0.026424 (0.001) 0.0076247 (0.532) 0.0702099 (0.072) 0.0108798 (0.164) 0.0043429 (0.36) 0.000673 (0.411) -0.0293906 (0.072) -0.0045544 (0.163) -0.0358396 (0.083) -0.0055537 (0.176) -0.0037764 (0.092) -0.0005852 (0.186) -0.0055463 (0.1) -0.0008595 (0.193) 0.0102432 (0.27) 0.0006336 (0.44) -0.0042879 (0.269) -0.0052288 (0.275) -0.000551 (0.281) -0.0008092 (0.285) Years of Education (relative to 10 years) 11 12 13 14 or more Still at college (log) Real Housing wealth Real GDP Growth Labour Market Regional Unemployment rate χ 2 (p-value) UNCERTAINTY Age Age squared/100 0.1507 -0.0312191 (0) 0.0003901 (0) 47 Real Interest Rates ρy ws Log-likelihood n 0.0250339 (0.175) 0.0529026 (0.366) -13001.605 8722 Notes to Tables A3.2-A3.5: Estimates of region, industry and year dummies as well as a time trend are not reported to conserve space A consistent finding in the above tables is that males earn more than females in both self-employment and wage-employment. Blacks and Asians tend to have lower wage earnings but their self-employed earnings are the same as Whites, ceteris paribus. Both self-employed and wage earnings increase with experience (age) at a diminishing rate. In contrast, formal education has no affect on self-employed earnings but tends to increase wages. Importantly wealth appears to play no part in self-employed incomes in either the 1980s or 1990s. This, contrary to Evans and Jovanovic (1989), suggests the absence of liquidity constraints having controlled for human capital (Cressy, 1996). The pattern of correlation coefficients in the 1980s is compatible with occupational self-selection on the basis of comparative advantage ρ yw s > 0; ρ ye s < 0 . Interestingly ( ) though, in the 1990s, ρ yw s is statistically insignificant which means that the selfemployed could expect to earn the same as wage workers in wage employment. The implication here is that the self-employed, in the 1990s, are not a group of employees who choose self-employment because of low wage earnings ability (Hamilton, 2000, reaches a similar finding with US data for the 1980s). Indeed, the structural analysis of self-employment choices, in Table 3, supports the idea that lifestyle preferences rather than financial necessity is the driver of self-employment in the 1990s. 48