Review of Industrial Organization 17: 229–248, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. 229 Theories of Firms’ Growth and the Generation of Jobs P. E. HART⋆ Department of Economics, Faculty of Letters & Social Sciences, PO Box 218, Whiteknights, Reading, RG6 6AA, U.K. Abstract. This paper relates recent empirical research on the growth of U.K. companies to the main economic theories of firms’ growth and to empirical results for the U.S.A. Smaller and younger firms have been growing more quickly than larger and older firms, thus generating proportionately more new jobs. These results do not support the various theories of static and dynamic economies of scale. Serial correlation of growth is very low, so success does not persist. The systematic tendency for small and younger firms to grow more quickly is the main reason why firm growth is not entirely stochastic. Key words: Age, firms’ growth, jobs, size. I. Introduction There is an enormous literature on the theories of the growth of firms. In addition to summaries in standard textbooks (e.g., Scherer and Ross, 1990), there are surveys such as that by Trau (1996) which has some 160 references and many more could have been cited. There are also a large number of empirical studies of firms’ growth and an extensive literature on the relationship between the size of a firm and its generation of jobs, or employment growth. It is true that employment is merely one measure of size, but all size measures are so highly correlated across firms that this limitation is not important. The present paper is concerned with companies, a subset of firms, and relates the empirical findings of Hart and Oulton1 (1995, 1996a, b, 1997, 1998a, b, 1999) for the U.K. to those of other researchers and to the theories of firms’ growth. It uses the Galtonian regression model summarised in Section II. The empirical results are related to the main theories of firms’ growth in Section III following Trau (1996), and to other empirical studies for the U.K. and U.S.A. in Section IV. The conclusions are given in Section V. ⋆ I am indebted to an anonymous referee for most helpful comments on an earlier version of this paper. 1 Denoted by HO. 230 P. E. HART II. The Galtonian Regression Model This model uses the regression and correlation coefficients of the bivariate distributions of companies by logarithms of employment at two dates. These are directly relevant to the theories of the relationship between the size and growth of firms. To study the relationship between job generation and size of company, we have to use the first moment distribution rather than the original size distribution. That is, we consider the distribution of employment between employment size classes rather than the distribution of companies between those classes. Assume that the univariate size distribution of companies is lognormal with two parameters µ and σ 2 denoting the mean and variance of the logarithms of corporate employment. Hence the first moment distribution is also lognormal with parameters µ + σ 2 and σ 2 . This implies that the median size of company is exp[µ] whereas the median of the first moment distribution is exp[µ + σ 2 ]. The latter is sometimes called the Florence median and gives the size of company below which there is 50% of total employment. This is quite different from exp[µ] which is the size of company below which there is 50% of the companies. Note that the original and the first moment distributions have the same variance of the logarithms of size, σ 2. P Denote the employment of the ith company by Xi , then the arithmetic P mean is Xi /N where N is the number of companies. Assuming lognormality, X/N = exp[µ + 1 σ 2 ]. The arithmetic mean of the first moment distribution is given by P 2 P2 X / X = exp[µ + 3σ 2 /2]. Both averages may be increased by increasing µ and/or σ 2 , if increases in employment are desired. Writing log Xit = Yit and yit = Yit −µt we have the Galton regression equation yi (t) = βyi (t − 1) + εi (t) (1) where β is an elasticity indicating “regression towards the mean” when β < 1. This is based on the hypothesis that the proportionate growth of a company may be decomposed into a systematic component, d log G/dt, where log G = µt , and a stochastic component εit . Thus d log Xit /dt = (d log G/dt) + εit (2) or dyit /dt = εit where yit = log(Xit /G) = Yit − µt . Converting (2) to discrete time and dropping i subscripts, we have the Gibrat model y(t) = y(t − 1) + ε(t). (3) This is a special case of the Galton model with β = 1. In (3) V [y(t)] increases over time, but in (1) with (β < 1), V [y(t)] need not increase: V [y(t)] = β 2 V [y(t − 1)] + V [εi (t)] = ρ 2 V [y(t)] + (1 − ρ 2 )V [y(t)] (4) THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 231 with ρ 2 = 1 − {V [εi (t)]/V [y(t)]}. Hence β 2 V [y(t − 1)] = ρ 2 V [y(t)] or β 2 /ρ 2 = V [y(t)]/V [y(t −1)], so that companies’ sizes converge, with V [(t)] < V [y(t −1)], if β 2 < ρ 2 . Note that companies diverge if β > 1, but can diverge or converge if β < 1, depending on ρ. Since the variance of the logarithms of the original distribution and of the first moment distribution are the same, it follows that Equations (1) and (4) also hold for the bivariate first moment distribution. For example, weighting (1) by employment implies regressing log[X(t)2 ] on log[X(t − 1)2 ], or 2y(t) on 2y(t − 1), to give the same regression coefficient. Thus all the results for β and ρ based on the original bivariate distribution in the relationship between size and growth of firm carry over to the bivariate distribution when weighted regression is used with employment as weights. There is no need to introduce employment weights when switching from models of the size and growth of firms to models of the job generation propensities of firms of different sizes. Keeping to the original size distributions is extremely convenient. It means that the theories of the growth of the firm can be used to model the growth of employment among those firms. There is no need for a new statistical model. It takes time for companies to regress towards the mean, so the time interval in (1) to (4) is longer than one year. As shown by the summaries of previous estimates of β by Prais (1976 p. 205), covering periods from 1885 to 1969, and by Dunne and Hughes (1994, p. 128), covering periods 1948–1990, the interval between the initial and terminal years of the cross-section regression has reached 17 years in earlier work. In practice, the interval chosen has been largely determined by the availability of data. In the periods between 1885 and the early 1950s (except for 1907–24), estimates of β (denoted by b) were less than unity, indicating Galtonian regression towards the mean. From the late 1950s to about 1969, the usual result was b > 1, indicating that larger firms were growing more rapidly than smaller firms. The highest estimate was b = 1. 12 for 1951–58, but standardised on ten years, in Prais (1976). From the 1970s, b < 1 was the usual result. This regression towards the mean is confirmed by the more recent standardised estimates summarised in Table I, covering periods up to 1995. Why do smaller firms usually grow more quickly than larger firms? Possible answers to this question lead us to consider various economic theories of firms’ growth in Section III. A more detailed discussion of the estimates in Table I and a comparison with estimates of Hall (1987) and Geroski et al. (1997), which use different techniques, is postponed until Section IV. 232 P. E. HART Table I. Recent estimates of Galtonian regression elasticities, b′ , standardised on 10 year intervals Study Sample period Sample frame Evans (1987a) 1976–82 U.S. Small Business Data Base, firms in manufacturing Aged < 7 years 7–20 years 21–45 years >45 years U.S., SBDB, firms in manufacturing Aged < 7 years 7 yrs and more U.K. EXSTAT companies, financial and non-financial U.K. OneSource Data Base, independent companies, all industries U.K. OneSource U.K. OneSource U.K. OneSource Evans (1987b) 1976–80 Dunne and Hughes (1994) 1975–80 1980–85 HO (1996) 1989–93 HO (1998) 1986–89 1989–92 1992–95 Sample size Size measure b′ Employment 4343 6124 5412 1520 0. 63 0. 49 0. 77 0. 81 Employment 9221 24244 1172 1696 Net assets 0. 68 0. 85 0. 86 0. 86 29, 230 34, 774 55, 098 Employment Sales Net assets 0. 64 0. 64 0. 63 8103 8103 8103 Employment Employment Employment 0. 52 0. 70 0. 80 III. Theories of Firms’ Growth2 1. N EO -C LASSICAL T HEORY OF THE F IRM This postulates single product firms in an industry with a U -shaped average cost curve. Firms grow until they reach the size corresponding to miminum average cost. There is no incentive to grow beyond this size. Thus the dispersion of firms sizes will be very small, attributable to disequilibrium or mistakes, and this dispersion will reduce over time as firms converge towards the equilibrium size. Companies in the OneSource database used in HO(1995–98) are not usually single-product firms, their dispersion and skewness of sizes are very large and many of them grow by merger and acquisition. At first sight it might appear that the neo-classical theory does not provide any useful insights into the growth pro2 Though this section follows Trau (1996), it excludes many of the theories in Trau’s excellent survey which are not relevant to the HO evidence, and adds others which are. THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 233 cess of such companies. However, the faster growth of small companies below 16 employees reported in HO (1995, 1996a) could be explained by their successful attempts to reach minimum efficient scale as soon as possible and this is consistent with neo-classical theory. This explanation was used by Mansfield (1962). Other explanations are possible. For example, it is argued in HO (1988a) that the OneSource data oversample the faster growing small companies. Again, in Hart and Prais (1956), the faster growth of smaller companies 1939–50 was linked to non-linearity in the regression, probably resulting from war-time controls which favoured smaller companies. In more recent years, the faster growth of smaller companies may also be the result of various Government policies which foster the growth of small businesses. Thus the neo-classical explanation of the faster growth of smaller firms is not convincing: institutional influences on firms’ growth are probably more important. In any case, the neo-classical forces must have been outweighed by other factors, including imperfect competition, in the 1950s and 1960s when larger companies were growing more quickly than small companies. Furthermore, there is no clear evidence that the dispersion is decreasing, which would occur if companies tended to converge towards some optimum size. For the whole sample of independent companies, Table A2 in HO (1995) shows that the dispersion decreased in terms of employment and sales but increased in terms of assets over the period 1990–94. Over the longer period 1986–95, HO (1998b, Table 3) show that the dispersion of company employment increased. 2. I MPERFECT C OMPETITION The U -shaped average cost curve of a firm is purely a theoretical concept: obviously a firm would avoid growing large enough to encounter increasing average costs and so we cannot expect to observe such cases unless the firms make mistakes. Empirical cost curves are likely to be L-shaped, with firms of widely different sizes beyond minimum efficient scale, MES, producing at much the same average costs. In this world of constant returns, the limit on the growth of a firm is determined by the demand for its particular product rather than by cost conditions. This was the implication of the various theories of imperfect competition which superseded neo-classical theory. The typical firm faces a downward sloping demand curve for its product. In practice, this constraint does not limit the growth of a firm because it can always introduce another product line. Firms may be classified into SIC industries, according their predominant product, but these do not correspond to the concept of industry in economic theory. In each SIC industry, companies seek to compete by price, credit conditions, product differentiation, quality of product and service, advertising etc. Small companies can hold their own by providing “niche” products. Hence, we observe a wide dispersion of companies within any SIC industry. 234 P. E. HART The relaxation of the assumptions of the neo-classical theory of the firm permits many other explanations of firms’ growths. The following are considered here: economies of scale, goals other than profit maximisation, evolutionary and stochastic growth. 3. T ECHNICAL E CONOMIES OF S CALE If each of a firm’s inputs increases by p per cent and its output also increases by p per cent there is said to be constant returns to scale, and hence constant average costs. This case is consistent with the L-shaped empirical average cost curves when firms are above MES. If output increases by more than p per cent, there are increasing returns to scale and, in the limit, there would be only one firm in the industry as the largest firm would be able to undercut all the other firms. If output increases by less the p per cent, there are decreasing returns to scale. This case is unlikely to be observed in practice because firms would not increase all inputs unless they achieved a corresponding increase in output. But increasing returns to scale have been observed in practice and are often given great emphasis (Chandler, 1990). The problem is to assess whether such cases are offset by technological progress which favours smaller firms, so that on the average large firms have no technical advantages over smaller firms in all industries. In the above theoretical models of the firm, factor proportions are constant, whereas in practice there might be a fixed factor of production, such as management or entrepreneurship, which cannot be increased by p per cent. The resulting change in factor proportions leads to diminishing returns which constrain expansion. In such companies job generation is limited by fixed managerial input: a small owner-managed company might not take on more employees because the extra administrative and supervisory work might be unacceptable to the owner. Managerial constraints on a firm’s growth have loomed large in the theoretical literature: rapid growth is particularly difficult to manage and the resulting loss of control reduces organisational efficiency (Robinson, 1934; Richardson, 1964; Williamson, 1967; Penrose, 1980). Firms know this and hence avoid rapid growth. Indeed, smaller owner-managed companies in the Onesource database may well opt for a quiet life and refuse to expand output even though they would increase profit by so doing. (Sargant Florence, 1934). Differences between managerial hierarchies and abilities are substantial and are sufficient to generate positively skew size distributions of firms (Tuck, 1954; Lucas, 1978). Casson (1998) also emphasises the importance of entrepreneurial ability as a determinant of a firm’s growth, particularly the ability to synthesise information on the many shocks which affect the firm and its market. Another example of a fixed factor might be capital equipment indivisibilities. Small companies cannot purchase the large and expensive machinery which would enable them to grow and hire more employees. Only large companies can afford such equipment and are able to exploit the cost economies of larger plants, whereas THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 235 any advantages enjoyed by small plants can be obtained by large multi-plant firms. This asymmetry leads to positively skew size distributions of firms. Sylos Labini (1969) combined the discrete jumps in a firm’s growth, which result from technological discontinuities of capital inputs, with downward sloping demand curves which constrain growth. The two together generate positively skew size distributions of firms because only a few firms have potential demands which are large enough to exploit the lower costs provided by larger plants. Over time the advantages of large scale plant and equipment have been reduced by the widespread availability of electric power, road transport and, in recent years, by the rapid developments in information technology. For example, computer technology has revolutionized the printing industry and has enabled new and smaller companies to enter the newspaper industry. Many service industries, which are thought likely to generate many jobs in the future, have also been changed by developments in computing and it may well be that the indivisibilities of large and expensive capital equipment are now less important constraints on job generation. According to the theories of the economies of scale, the advantages of large firms should result in their faster growth and we should expect to see b > 1. This has not happened in recent years. Nevertheless, the size distribution of firms continues to be positively skew, as the result of a multiplicative stochastic process, with b < 1 HO (1995, 1996b). 4. P ECUNIARY E CONOMIES OF S CALE These advantages of larger firms reduce money costs but do not involve a reduction in the use of resources in real terms. For example, larger firms may be able to obtain better financial terms from lenders. It is possible that the growth of smaller companies is constrained by their poorer access to capital markets. Large companies are also likely to be more effective at political lobbying which might give them money cost advantages. They may also reduce their money costs by obtaining lower prices from their suppliers as a result of their stronger bargaining positions. This is often the case in retail distribution where a few giant supermarket retailers obtain lower prices from their suppliers, in return for larger quantities purchased, and are driving out the smaller retailers. This process has important implications for job generation: the employment expansion of the giant retailers often takes the form of increasing the number of part-time jobs for adult females, whereas the smaller retailers have traditionally provided full-time jobs for youngsters entering the labour market. 5. E XTERNAL E CONOMIES OF S CALE These are external to the firm. For example, a successful industry might establish a tradition of skilled labour, which can flow between firms. Appropriate training centres and technical schools are created which overcome the constraints on 236 P. E. HART growth imposed by shortages of skilled labour. A successful country might foster the growth of inter-industry networking to smooth the exchange of inputs of raw materials and intermediate inputs by improving quality and eliminating attempts at “hold-up”. A more harmonious industrial culture can increase the efficiency of all firms. There may be important economies of scale which are external to a country and which can be obtained by economic integration. For example, the Single European Market is thought to improve efficiency and generate more employment by eliminating non-tariff barriers to trade and by stimulating competition. Caballero and Lyons (1990) claim that for some European countries (Belgium, France, Germany and the U.K.) such external economies are important whereas they find little evidence of internal economies of scale. Not surprisingly, their results are controversial, but they are supported by evidence for the U.K. compiled by Oulton (1996a). 6. DYNAMIC E CONOMIES OF S CALE It is possible that much of the internal economies which stimulate the growth of a firm are specific to that firm and are independent of its size. (Penrose, 1980). These firm-specific advantages are “essentially transient” and after they are exploited by the firm might not recur, e.g., a successful patent might generate more output and hence more jobs until the patent is exhausted. These firm-specific advantages generate unbalanced growth in the form of quantum leaps between periods of zero growth. Learning-by-doing is another dynamic economy of scale. This concept dates from Wright’s (1936) paper on the costs of building aircraft. His learning curve was partly the result of technical and pecuniary economies of scale and partly the result of firms increasing their productive efficiency by learning how to solve the multitude of problems arising in the construction of a new airplane. The learning curve was generalised into an experience curve by the Boston Consulting Group (1972). The basic idea is that average costs of production decrease logarithmically with the accumulation of the past output of a firm rather than depending on its output size at any one time. This principle of learning-by-doing is widely accepted by businessmen and by economists, though particular estimates of learning or experience curves are more controversial. In economic theory, the cost of past output may be regarded as an exogenous sunk cost which a firm had to incur in order to produce at lowest average cost now (Dasgupta and Stiglitz, 1988). In terms of job generation and size of firm, the theory implies that small firms are at a disadvantage because their accumulated past outputs are lower than those of the large firms. In theory, larger firms are further along the learning curve and hence are in a better position to generate more jobs. If this were true, we should expect to see b > 1 whereas the usual result is b < 1. Further evidence, based on the ages of companies, is discussed in Section IV. THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 7. G OALS OF THE 237 F IRM Most of the theories discussed so far assume that firms aim to maximise profits. Other assumptions have different implications for firms’ growths. For example, Sargant Florence (1934) suggested that many owner-managed companies adopt satisficing rather than maximising policies; they do not maximise profits or sales, opt for a quiet life and hence tend to employ fewer people than they could. Satisficing theories were subsequently developed by Simon (1959), Cyert and March (1963). Baumol (1959) postulated that firms maximise sales, subject to the constraint that profits satisfy the shareholders and the company’s plough-back policy. Marginal revenue is zero when sales are maximised whereas it is positive (since it equals positive marginal costs) when profits are maximised. Thus output and sales are higher than when the goal is profit maximisation, even if the satisficing profit constraint is imposed. The net result is that more jobs might be generated in order to produce the higher output. However, the shareholders of large quoted companies might not be satisfied if their companies do not attempt to maximise profits. It may well be the case that managers like to maximise sales, especially if their remuneration, perquisites, and power are linked to corporate size measured by sales. If shareholders disapprove they can sell the shares, driving down share prices and facilitating hostile takeover bids. This potential conflict of interest arises from the separation of ownership from control (Berle and Means, 1932). The threat of takeover constrains managerial behaviour: there is a trade-off between the maximum percentage of profit retained to boost corporate growth and the minimum required for distribution to shareholders to maintain share prices (Marris, 1964). Managers may be regarded as the agents of the shareholders (principals) who own the companies. These agents may have expense preferences, such as their emoluments or number of staff in their empires, which are non-optimal in the eyes of their principals (Williamson, 1964, 1970). In the short run, managerial empire building might generate more jobs. In the longer run, the resulting inefficiency and lack of competitiveness might destroy them. Employees are more interested in firms’ growths which generate secure jobs in the future than in temporary jobs created by empire building. They are also interested in the economic rents enjoyed by management and might attempt to “hold-up” the company in order to obtain some of these rents themselves. The firm becomes a field of bargaining between the employees and their ultimate principals, the shareholders, with the managers acting as mediators in the game of allocating rents. With the increase in unemployment in the U.K. since 1979, and subsequent trade union legislation, the bargaining position of the employees has been weakened so much that the game now may be between the shareholders and the management. Both sets of players have incentives to reduce labour costs, if necessary by reducing company employment, providing sales are maintained. This can be done in many ways: for example, by sub-contracting work formerly done by a company’s employees, by reducing quality of service, by substituting 238 P. E. HART part-time workers for full-time workers at peak periods, by reducing training and other non-productive work such as research and development. Managers achieving such “downsizing” produce “lean and mean” companies with enhanced profits in the short-run and higher share prices to please the principals and the agents. Downsizing is thought to be a major factor in increasing labour productivity in manufacturing, though whether this is true is another matter. The American evidence suggests that it is false (Baily et al., 1996). Perhaps a firm’s goals change through its life cycle so that the conflict between its principals and their agents will not be permanent (Mueller, 1972). Young, dynamic companies have rapid growth and high profitability so managers and shareholders are happy. But as a company matures and its investment opportunities decline, a conflict arises: managers attempt to maximise growth at the expense of profitability. Cyert and March (1992) suggest that a company has several goals or targets and will seek policies which satisfy them rather than try to “find the best imaginable solution”. In the short run it will use rules of thumb or routines in a sequential search for local goals. In the longer run, as its true capabilities become clearer, it will settle down to satisficing behaviour. It is possible that we observe b < 1 because the directors of the larger companies do not have the same growth goals as the owner managers of the smaller companies. However, their goals and policies will change over time and differ between firms as each firm continuously adapts to changes in the economic, political and physical environment. 8. E VOLUTIONARY AND S TOCHASTIC G ROWTH Nelson and Winter (1982) propose an evolutionary model of the growth of firms. Instead of optimising, agents tend to react automatically to changes in the market environment using routines which are often specific to the firm. They stem from the skills and experience of the managers and workers in the firm and this “knowhow” is passed on to new members of the firm. Thus successful routines which have produced growth in the past, are likely to continue to do so in the future. It is true that circumstances change, but successful firms have successful routines for changing previous methods to meet new market environments. One measure of such a “success” is labour productivity. Oulton (1996b, 1998) has shown that companies with high productivity tend to maintain it over two or four years. Even so, over the period 1989–93, the correlation of value added per capita across companies was given by r = 0. 476, leaving most of the variation unexplained. This suggests that there was still considerable mobility of companies up and down the league table of productivity over the period. Of course, some firms may become unsuccessful inspite of having favourable routines. In their study of sharp-bending firms which are turned round after a decline, Grinyer et al. (1988) review the extensive management literature on the THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 239 subject and list 180 first order hypotheses which might explain sharp-bending. There is no shortage of plausible explanations of firms’ growths. The evolutionary approach to firms’ growths implies that there is some serial correlation in growth: “success breeds success and failure breeds failure”. This contrasts with purely stochastic models of growth, such as Gibrat’s (1931) law of proportionate effect, which postulate that the proportionate growth of surviving firms is random and hence independent of previous success. The Galton model in (1) allows for growth to vary inversely with size so that the dispersion of company sizes does not increase indefinitely (4), as it would in the Gibrat case (3). Further modifications of the Gibrat model include the introduction of corporate births, (Simon and Bonini, 1958), and of serial correlation in the growth process, (HO 1998b). An alternative to the Gibrat model of firm growth was provided by Steindl (1965). This leads to a Pareto rather than to a lognormal distribution but once again the stochastic growth of firms is emphasised. This Pareto process excludes small firms and is not very useful in the analysis of the relationship between employment growth and size of company. Furthermore, it does not seem to fit the OneSource data for the largest companies, HO (1997). Perhaps this limitation is more important because it might be argued that the growth process of small companies is quite different from that of large companies and so they merit separate treatment, (Penrose, 1980). Stochastic growth also underpins the model of the evolution of industry proposed by Jovanovic (1982). In his model each firm’s cost curve is subjected to randomly distributed, firm-specific shocks. Over time a firm learns about the effects of these shocks on its efficiency. Firms experiencing favourable shocks grow and survive. Others do not grow and may decline and even leave the industry. His model also results in small firms having higher, but more variable, growth rates and higher failure rates than large firms. If his theoretical model is a true reflection of the evolution of firms, then empirical studies which omit firms deaths are likely to overestimate the growth rates of small firms relative to large firms. There are three company populations: (a) those which survive over a period, (b) those which die during the period, and (c) those which are born during the period. HO (1995, 1996a, 1998b, 1999) use very large samples of companies drawn from population (a) and while the results are unbiased estimates of the parameters in population (a), they might not be unbiased estimates of the parameters in populations (a) + (b) and (a) + (b) + (c). Similarly, estimates derived from a sample drawn from (a) + (b), used by other authors, might be biased estimates of the parameters of the combined population (a) + (b) + (c). HO (1998a) took large samples from populations (b) and (c) and then uprated the sample results to the population, using lognormal theory in an attempt to overcome the problem of the undersampling of small firms which seems to be common to most databases of firms. Some form of uprating is essential before reaching any reliable conclusion on the effects of company births and deaths on the relationship between company size and growth. 240 P. E. HART Adequate correction for the undersampling of small corporate births and deaths is difficult and it may be safest to confine any analysis to samples from population (a), the survivors. Sutton (1997) develops a new model of stochastic firm growth, and surveys the literature since Gibrat (1931). His discussion relates to the industry level in manufacturing, rather than to the aggregate level of all firms, and is in the context of economic theories of market behaviour, including the game-theoretic literature. But many of the most important cases of strategic behaviour occur in industries with very few firms – too few to justify the use of the lognormal or any other theoretical distribution. Indeed, in the important cases of near monopoly, or tight oligopoly, size distributions are unnecessary and concentration ratios are not published because of the disclosure rules, Walshe (1974). Hence, Sutton (1997, p. 52) is surely correct in arguing that the search for a typical size distribution of firms at the industry level may not be wise. Nevertheless, his new model of the stochastic growth of firms can be related to the aggregate of all firms. After all, many firms are multi-product and overlap many industries. His new model uses two conditions: first, the probability that the next market opportunity is filled by any currently active firm is a non-decreasing function of the size of that firm, and second, the probability that this opportunity is taken up by a new entrant is constant over time. His inclusion of firm births thus makes his model more general than that of Gibrat. His survey of firm “turbulence” relates to the entrance and exit of firms from the firm population and must be distinguished from the size mobility of firms, which relates to movements of surviving firms up and down the size distribution. The emphasis on stochastic growth by Jovanovic (1982) and Sutton (1997) is consistent with HO (1996) and the generation of skew size distributions of firms as the result of multiplicative stochastic shocks. But the faster growth of smaller firms suggests that small size is linked to systematic factors influencing growth, including Government small business policies and the information technology revolution which have reduced the comparative advantages of large firms. These systematic forces had their effects after the 1950s and 1960s, which could explain the switch in regime from b > 1 to b < 1. The evolutionary theories suggest that the growth of successful firms should persist over time: there should be positive serial correlation of growth between consecutive periods and that older companies should have faster average growth than younger companies. The evidence on this is discussed in Section IV, first for the U.K. and then for the U.S.A. THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 241 IV. Recent Evidence for the U.K. and U.S.A. 1. T HE HO E VIDENCE FOR THE U.K. The various theories of economies of scale and scope have a long history and are well established in the literature. Yet the OneSource database does not reveal any supporting evidence. For the whole size distribution HO (1995, 1996), for individual industries, and even for individual size classes, HO (1998), smaller companies have been growing proportionately more quickly than larger companies, whether size is measured by employment, sales or assets. This result probably arises because Government policies and technological progress have offset the advantages which large companies used to enjoy. Again, while dynamic economies of scale arising from learning by doing are plausible enough in some firms, it is not clear that these cases can be generalised to all companies. If this process were typical, we should expect older companies to have a lower death rate than younger companies. The Companies House CD-ROM in HO (1998a, Appendix C) shows that this is true for those aged up to sixteen years but there is no strong tendency for older companies above this age to have lower death rates. We should also expect that older companies, with their larger accumulations of past output, to be further along the learning and experience curves and hence to be able to grow more quickly as a result of these dynamic economies of scale. This does not happen. HO (1998b) show that there is negative relationship between age and growth among surviving companies. It also reveals that 242 companies founded over 100 years ago, though few in number, account for nearly 9% of the total employment of independent companies in the database. Such long term survivors support the theory of dynamic economies of scale, but the 9% weight to be attached to them is very small. The relative importance of systematic and stochastic factors in the growth of companies may be indicated by the degree of serial correlation of growth. We should expect systematic factors to produce persistent company growth and hence a high degree of serial correlation. HO (1998b) found that between the two periods 1986–1989 and 1989–92, the serial correlation of growth was 0. 024, compared with 0. 046 between 1989–92 and 1992–95. There appears to be some serial correlation but it is very small. The implication is that stochastic factors are more important than systematic factors in determining company growth. While large companies have grown less quickly than smaller companies in the boom 1987–89, in the recession 1990–92 and in the recovery 1993–95, the average employment of surviving companies, (whether measured by arithmetic or geometric means, or by the median) clearly increased over the whole period 1987– 95. This is difficult to reconcile with the common belief in a general tendency for large companies to “downsize” in order to become “lean and mean”, though it does appear to be true for the very largest companies above 65, 536 employees, HO (1998b). 242 2. T HE D UNNE P. E. HART AND H UGHES (1996) E VIDENCE FOR THE U.K. Dunne and Hughes (1996) summarised the results of previous studies covering periods between 1948 and 1990. For the 1950s, and 1965–69 OLS estimates of β were significantly greater than unity. Their own study shows that for 1975–80 and for 1980–85 b = 0. 93 and was significantly below unity. When compared with the earlier studies back to 1885 summarised by Prais (1976), and with the later HO (1998) results up to 1995, it is clear that the typical result is b < 1. This implies that while Gibrat’s law of proportionate effect is a good first approximation to the pattern of U.K. company growth, there is typically some Galtonian regression towards the mean with smaller companies on the average having faster growth than larger companies. This does not imply that in the long run there is a tendency for company sizes to converge. First, the results relate to surviving companies within each period and exclude births and deaths. Second, even among surviving companies, V (t) increases if ρ 2 < β 2 < 1 and divergence occurs. In fact, there is no long term downward trend in V (t) since 1885 and hence there is no evidence of convergence among surviving companies. Nor do the authors find any evidence of persistent company growth between 1975–80 and 1980–85. This is consistent with the results in HO (1998b) and does not support the various theories of company growth based on systematic firmspecific factors. However, there is one firm-specific factor, namely company age, which does have a small negative effect on proportionate growth even though it adds little explanatory power to their fundamental regression equation, increasing R 2 from 0. 81 to 0. 82 for the period 1980–85. Nevertheless, the negative effect of age on growth is inconsistent with the “learning by doing” model. Finally, the authors show that their key results are not affected by any sample selection bias resulting from excluding company deaths. 3. T HE G EROSKI (1998) S URVEY The second of Geroski’s (1998) six stylised facts is that corporate growth rates really are very nearly random. This assertion is based on a sample of 280 large quoted companies in the U.K. 1972–82. This sample is unrepresentative of the company population, yet the results still show the same slight Galtonian regression to the mean when the logarithm of sales is used to measure size, with b = 0. 8560 for the 280 companies and b = 0. 8294 for the unbalanced panel of 649 companies. Clearly, 0 < b < 1 and the very largest companies grow less quickly than the smaller (but still large) companies in this sample. These results are consistent with previous findings in Sections IV. 1 and IV. 2. If proportionate growth were completely random, as Gibrat (1931) suggested, b would be unity. The fact that it is slightly less than unity, but of course still positive, justifies Geroski’s second stylised fact. THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 243 Geroski (1998) cites panel data estimates in Geroski et al. (1997), based on 77 companies 1955–85, to support his belief that there is very little persistence of company growth and that there is no tendency for convergence. He prefers panel data estimation to cross-section estimation. The reasons for using a series of cross-section estimates rather than panel data estimates in this context are discussed in Appendix B of HO (1998b). The main problem with including timeseries regressions is the occurrence of structural breaks: the implicit assumption that b is constant over the time-period used in the regression, does not hold. This difference in methodology, however, must not be allowed to obscure the fact that the same results emerge from both estimation techniques: company growth shows very little persistence and there is no long run tendency for the sizes of companies to converge. 4. T HE E VANS (1987 A , B ) E VIDENCE FOR THE U.S.A. Evans (1997a) drew a sample of some 20,000 U.S. manufacturing firms from the dataset created by the Small Business Administration from Dun and Bradstreet information. Size is measured by employment and the period covered is 1976–82. Small firms grew more quickly than large firms, which is consistent with the U.K. results. However, this negative relationship between size and growth was highly non-linear. This is inconsistent with the bivariate lognormal model. Gibrat’s law of proportionate effect is not supported. Evans studied the effect of the age of firm on its growth and stratified his sample into those firms younger than 7 years in 1976 and those which were older. For the young firms, smaller firms had faster growth and there was a significantly positive effect on growth of the interaction between the logarithms of age and size. By itself, the logarithm of age had no significant effect but its square had a significantly negative effect on growth, which supports the view that in this stratum younger firms grew more quickly than older firms. This might be inconsistent with the “learning by doing” model but even the oldest of the firms below 7 years is unlikely to have progressed very far along the learning curve. There was no continuous age data for older firms but it was possible to group the data into age classes 7–20, 21–45, and 46+. For each group, smaller firms grew more quickly than larger firms, but the relationship between size and growth in each group was highly non-linear, approximating a third or fourth degree polynomial even after logarithmic transformation. While HO (1995, 1996) reported marked non-linearity in the bottom tail of the bivariate size distribution of companies, there was no evidence of non-linearity for most of the distribution. This particular finding of Evans is inconsistent with HO (1995, 1996) and may be linked to his use of a much larger sample of very small firms outside the corporate sector. Evans (1987b) took another sample from the same database for the period 1976– 80. At the first stage a random sample of 100 4-digit manufacturing industries was drawn from the 450 available and included 105,186 firms in 1976. At the second 244 P. E. HART stage he took a 25% sample of firms below 20 employees and 100% sample of those above, except for two industries with very large numbers of firms for which he took a 25% sample of all firms. The resulting size of sample was 42, 339 firms. This is much larger than the U.K. samples of companies, particularly for small firms and once again probably explains some of the differences between the results for the U.K and the U.S.A. For example, he found that Gibrat’s law fails, but that the severity of failure decreases with increases in firm size. The U.K. samples are less representative of small firms than are those drawn by Evans which probably explains why the departures from Gibrat’s law are less severe for the U.K. data. Nevertheless, there are still departures: small U.K. companies grew more quickly than large companies and this basic result is consistent with Evans (1987b). The greater coverage of Evans’ samples may also explain the differences of emphasis on the effects of a firm’s age on its growth. Evans (1987b) confirms Evans (1987a), even though different samples and different time periods were used, and in both studies age was found to have a negative effect on growth, which is inconsistent with “learning by doing”. In comparison, HO (1998b) found that age had a small but significantly negative effect on company growth 1986–89, 1989–92 and 1992–95, and that the size of this effect diminished over time. These results were based on a constant sample 8103 companies, a much smaller sample than that of Evans, and because it was confined to companies it did not represent the many thousands of unincorporated firms. When the maximum possible sample of OneSource companies was used, the size increased from 9389 for 1986–87 to 29, 855 for 1994–95. The coefficient on log age still decreased over time, which suggests that the decreasing effect of age on growth observed for the constant sample cannot be explained by their common movement on the learning curve while they all aged at the same rate. The decreasing importance of age might be explained by technical progress in the learning process. Every year new information technology makes it easier for new firms to learn the necessary techniques and reduces the gap between them and incumbent firms which also have to learn the new techniques. The result is that over time differences in age of company become less important determinants of differences in growth. 5. T HE H ALL (1987) E VIDENCE FOR THE U.S.A. Hall (1987) used Compustat files and sampled 1349 and 1098 quoted companies in manufacturing over the periods 1972–79 and 1976–83. In terms of employment, small companies grew more quickly than large companies, which is consistent with previous results. Company age was not included in her analysis, but she did include the logarithms of capital expenditure and of R&D, which were found to have significant positive effects on corporate growth. These are important systematic determinants of growth. Both Evans and Hall found that sample attrition did not have much effect on their results, that the chance of survival increases with size, and that variance of THEORIES OF FIRMS’ GROWTH AND THE GENERATION OF JOBS 245 growth decreased with size of firm. Both used a variety of interesting econometric techniques. Hall (1987) used an errors-in-variables model and showed that the OLS and lagged value instrumental variable estimates revealed similar results: small companies grew more quickly than large companies. Hence the typical result that b < 1 cannot be attributed to the downwards bias of the OLS estimator which can arise when the size measures used are subject to errors or “transitory components”. V. Summary and Conclusions The main aim was to relate the size of company to the generation of jobs. This is not quite the same as the generation of employment, because this may be increased by extending overtime rather than by hiring more employees. There are many reasons why firms may prefer to grow without increasing the number of jobs, such as avoiding various non-wage labour costs (pension contributions, national insurance contributions, sick pay, holiday pay, etc.). These do not feature in the theory of the growth of firms but they are nevertheless important for employment policy. Firms may also grow while substituting capital for labour or sub-contracting work to outside labour, including former employees. While some firms have adopted such policies, their aggregate effect has not been large enough to make the Galtonian regression dependent on the size measure used. HO (1995) used employment, sales and net assets and obtained similar results on the relationship between size and growth of company. Thus we are able to concentrate on employment as a measure of size. Though the distribution of employment across companies relates to the first moment distribution, rather than to the original size distribution, the lognormal model enables us to use theories of size and growth based on the original distribution in the context of job generation. In recent years, smaller companies have been generating proportionately more jobs than larger companies. The standardised regressions in Table I show that a one per cent increase in initial size is associated with an increase in terminal size of between 0. 5 and 0. 8 of one per cent. To explain this, we turn to the very many theories of the growth of the firm. Neoclassical theory suggests that in the long run the dispersion of firm sizes should be reduced. There is no evidence of such a reduction in the century since 1885. Any tendencies towards convergence must have been offset by other forces, including imperfect competition. This theory also suggests that the very smallest firms should grow more rapidly in order to reach Minimum Efficient Scale. There is evidence to support this theory, which may be linked to the young ages of the smallest firms with young firms growing more quickly than older firms. However, there are more plausible explanations. In particular, institutional forces such as Government taxation and industry policies which have been more favourable to small businesses in recent years, probably explain the change in the relative growth of smaller firms since the 1970s. In contrast, neo-classical theory cannot explain this change from 246 P. E. HART the 1950s and 1960s when smaller firms were growing less quickly than larger firms, in spite of the alleged rapid growth towards MES. Technical economies of scale have been emphasised so much in the literature that we should expect to observe larger companies growing more quickly than smaller companies, unless these economies have been counterbalanced by other forces such as managerial diseconomies. In fact, most studies relating to periods since 1885 show that smaller firms grow more quickly than larger firms. This does not imply that dispersion decreases, as shown by equation (2). External economies of scale are a different matter and may exist (Cabellero and Lyons, 1990; Oulton, 1996a). Dynamic economies of scale in the form of “learning by doing” imply that small firms have a cost disadvantage because of their low accumulation of past output and experience. Yet age tends to have a negative effect on a firm’s growth, though this tendency appears to becoming less important over time. It is possible that technological progress is becoming so rapid that past experience, or lack of it, is becoming less important. Irrespective of age, companies have to adopt new technology: much of the larger accumulation of output and experience of older companies is obsolete. The empirical results are not directly related to the different goals of the firm. The faster growth of younger firms is consistent with the belief that such goals change through the life cycle of the firm. The importance of stochastic shocks in the models suggests that most firms have to modify their goals over time. Many theories highlight stochastic growth and there is ample evidence in their support. 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