Unemployment and business formation rates: reconciling time-series and cross-section evidence

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1 Environment and Planning A, 1989, volume 21, pages Unemployment and business formation rates: reconciling time-series and cross-section evidence R T Hamilton Department of Business Administration, University of Canterbury, Christchurch 1, New Zealand Received 22 October 1987; in revised form 18 April 1988 Abstract. Time-series analyses generally show rates of business formation increasing with unemployment. In cross-section studies the areas with the highest rates of formation are generally those with the lowest levels of unemployment. In a study using both types of data, the negative cross-section relationship is confirmed but it is suggested that the time-series may be nonlinear, becoming negative at a critical unemployment level around 20%. The paper concludes with a reconciliation of these findings. Introduction This paper stems from my unease with the 'push-pull' model of new business formation, in the face of the very high levels of unemployment which have been experienced in particular areas of the United Kingdom. In the next section, I describe the 'push-pull' framework which has been the basis of a number of empirical studies in recent years. This is followed by a discussion and estimation of alternative specifications of the time-series relationship between new business formation rates and the level of unemployment. It is the results of this analysis which prompt a revision to the time-series relationship based on the evidence on company formation rates and the level of unemployment in Scotland between 1950 and I then consider the cross-section evidence and use new data to estimate this relationship. The paper concludes with a reconciliation of the revised timeseries model and the behaviour apparent over the cross-section. The 'push-pull' model of business formation The 'push-pun" model of new business formation has been discussed at length in previous issues of this journal (Hamilton, 1986; Harrison and Hart, 1983) and elsewhere (Creedy and Johnson, 1983; Johnson and Darnell, 1976; Nunn, 1980). A distinctive feature of this approach to new business formation and one which can be traced back to Oxenfeldt (1943) is that it is based on the behaviour of people in the labour market, in contrast to the 'barriers to entry' approach of the theory of the firm. In the 'push-pull' model the transition to self-employment is seen as the outcome of a subjective calculation done by members of the labour force (both employed and unemployed). When individuals reckon that the discounted stream of monetary and nonmonetary net benefits of being self-employed exceed those of remaining in their present positions, they will move into self-employment. Unemployment has emerged as a particularly important 'push' variable in this model: the higher the level of unemployment (and with it the threat of further unemployment), the greater the perceived net benefits of self-employment and the higher the rate of new business formation. Alternative versions of the 'push-pulp model The particular unease I want to explore in this paper is that, at some 'critical' level of unemployment, the model will break down. This would happen under either of the two situations described in this section.

2 250 R T Hamilton First, as local economies become more and more depressed as unemployment rises, the necessary 'push' towards self-employment on those made unemployed will no longer be accompanied by sufficient 'pull' of new business opportuntities. To explain this in more graphic terms, we can imagine a long line of those who are to become unemployed in the ensuing time period, with those at the head of the queue being the first to lose their jobs. When the job losses do begin, those who are first will still have a fairly buoyant economy within which to become selfemployed. They will also experience less direct competition for new business opportunities because most of their competitors will still be employees. So, in these early stages there will be 'push' and 'pull' working to bring about some marked increases in the rate of new business formation as unemployment begins to rise. But, consider those who happen to be at the end of the long line of candidates for unemployment. When their turn finally comes, the local economy to which most of them are tied will be more depressed; there will be very few opportunities left for new business development the good ones will have been taken and the poor ones will have been revealed by the bitter experience of others; and, indeed, the majority of role models for those who are unemployed last will be models of failure (because the vast majority of all new businesses fail in their early stages). Thus, on this basis alone, beyond some presumably high level of unemployment we would expect a negative relationship to emerge between unemployment and the rate of new business formation. An alternative approach is to assert that there is a fixed supply of potential business founders in the labour force and regard increasing unemployment as the trigger, forcing these people into exercising their latent potential. It is generally accepted that new business founders tend to set up in the industry of which they have experience and in the locality where they reside, irrespective of better opportunities elsewhere. So, if we take from this that potential founders are not deterred by the state of the local economy in which they are located, then we would expect to see formation rates rise with unemployment but reach a constant 'plateau' level determined by the fixed supply of potential founders. Estimation of the time-series models The discussion in the previous section leads to the following alternative specifications of the time-series model: >Y t = a+bu^ + cu^+et, (1) Y t = d+e-^-+e t, (2) where Y t is the annual rate of business formation, U t - X is the unemployment rate (lagged one year), and E t represents the random error term. Equation (1) is a parabola, allowing the possibility of a turning point in the relationship. Equation (2), a hyperbola, would permit a 'plateau' level of business formation to be reached. From the discussion in the previous section, we expect the estimated coefficients to be: in equation (1), b > 0, c < 0 ; in equation (2), d > 0, e < 0. Both equations were estimated by ordinary least squares. Y t is measured by the number of new companies registered in Scotland for each of the calendar years , expressed per thousand of the home population in each year. The company registration numbers were obtained in the main from Companies, published annually

3 Unemployment and business formation rates 251 by the Department of Trade. However, for some of the earlier years the data were provided by the Registrar of Companies in Edinburgh. The Scottish unemployment rate data came mainly from the Annual Abstract of Statistics supplemented for the earliest years by British Labour Statistics: Historical Abstract (Department of Employment, 1971). The estimated equations are as follows, Y t = c7,_ c7, 2 _ 1, (8.158) (-3.588) R 2 = n = 35, ' Y t = , (19.428) ( )^-1 R 2 = 0.828, n = 35, where the figures in parentheses are ^-values. In both equations the key coefficients have the expected signs and they are all highly significant. From the estimated equation (1) there is the indication of a turning point in the relationship with the 'critical' unemployment level being 20%. The constant term in equation (2) is the 'plateau' rate of company formation (expressed per thousand of population). This translates to around 4600 new company registrations in Scotland per year. However, it is equation (1) which explains most of the variation in the dependent variable and it is this specification which is discussed further here. Since equation (1) as estimated is nonlinear in the independent variables but not in the parameters, it can be estimated by means of ordinary least squares (Kmenta, 1971, pages ). Even so, the model does suffer serious problems of two types. First, there is inevitably a high degree of multicollinearity between the explanatory variables (the correlation matrix is given in the appendix). This alone will not bias the estimated coefficients but it does result in lowered ^-values. It may also lead to questions about the contribution of the squared variable to the explanatory power of the model. The second problem is that the calculated Durbin-Watson (D-W) statistic of (with 32 degrees of freedom) indicates the presence of temporal autocorrelation in the error terms. This means that the parameter estimates are inefficient and that the Mests are biased. Although there is a multicollinearity problem, the ^-values are nevertheless highly significant. The question remains, however, as to whether the two-variable nonlinear model is in fact superior to the simple regression of Y t on U t _ v To treat this formally we can test the null hypothesis {H 0 ) that parameter c equals 0, against the alternative that this null hypothesis is untrue. The essence of the test (see Kmenta, 1971, pages ) is that, if the squared term is irrelevant as an explanator of Y n then the regression sum of squares from the simple regression would be equal to that of the two-variable model (any observed difference in this regression sum of squares would be a result of sampling error). In this case (that is, H 0 being true) the test statistic would follow the F-distribution (with 1.32 degrees of freedom) with the critical value of F (at the 1% level) being The actual value of the test statistic is 12.85, and so we can reject the null hypothesis. Thus the evidence suggests that, despite the high multicollinearity involved, the inclusion of the squared unemployment rate variable does contribute to the explanation of the variations in Y t. There remains the more serious problem of autocorrelation. This has to be removed before we can have any confidence in the values of the estimated parameters and their significance. One way to handle this is to incorporate a partial adjustment process into the model. This seems reasonable because our independent variable

4 252 R T Hamilton measures the number of companies actually registered in each calendar year and there are likely to be some applications carried over from one year to the next. Including the lagged dependent variable in equation (1) gives the following, Y t = U t. x ^ Y t _ x, (-3.205) (5.296) (-2.947) (6.853) R 2 = 0.978, n = 35. The D-W statistic for this regression, at 1.806, is large enough for us to assume the absence of autocorrelation. The parameters on each of the unemployment rate variables are still statistically significant and retain the expected signs. [The coefficient reported on U^u , has been rounded up from Thus the 'critical' unemployment level from this equation is 18%; compare 20% from equation (1). I intend to use the expression "around 20%" to define the 'critical' level.] So we confirm that the time-series relationship between the rates of business formation and unemployment does appear to be nonlinear, such that, beyond the 'critical' unemployment level, the rate of business formation and so the prospects for indigenous economic recovery will fall with further rises in unemployment. Cross-section analysis of unemployment and new business formation There has in recent times been a large amount of work done on the regional variation in business formation rates. Much of this work was brought together by Storey (1982) and the general conclusions of this study are not in dispute here: "... policies which rely exclusively upon small firms to generate jobs, risk having their greatest impact upon employment in prosperous areas and their least impact in areas of high unemployment. In this sense they risk being regionally divisive" (page 208). In a more recent paper on this issue (Storey and Johnson, 1987), Storey's 1982 conclusion is confirmed in the context of new firm formation rates: those are shown to be higher in the more prosperous areas of the United Kingdom and lower in the least prosperous areas. To take this one step further, it means that general policy incentives to start a business will cause the formation rates in prosperous regions to rise even further relative to those of the poorer areas of the country. We can take local unemployment rates as the gauge of the prosperity of an area, and, if Storey is correct, we should observe a negative cross-section relationship between unemployment and business formation rates. There are, of course, many other factors determining the regional variation of business formation rates. Most of these are included in the Index of Regional Entrepreneurship constructed by Storey (1982, pages ) and refined somewhat by Whittington (1984). Of particular significance here is the negative association between regional formation rates and the percentage of manual workers in the local labour force. Also, Gudgin and Fothergill (1984) argue that regional formation rates are significantly different in urban and in rural areas (with lower rates in the urban areas). These authors show that the manual percentage in the local labour forces does not fully account for the urban - rural effect, but such a measure will act as a proxy for this. Manual workers are most likely to be found in manufacturing industries and so I include the percentage of a local area employment which is engaged in manufacturing (M r ) as an explanatory variable in the cross-section analysis. The clear expectation is that M r will be negatively associated with the rate of business formation. In addition to its convenience as a measure of the occupational structure of the local labour force, there are two other reasons why M r in particular should be included and why its affect on formation

5 Unemployment and business formation rates 253 rates should be negative. First, in terms of sector life cycles, there has been a steady decline in the overall significance of manufacturing. Second, the costs (and risks) of entry into manufacturing are likely, in most cases, to be greater than those associated with entry into a nonmanufacturing activity. We would expect both these factors to show up in lowered formation rates in areas dominated by manufacturing industry. The linear model which should capture the essence of the cross-section variation can be written as follows, Y r = d+eu r +fm r + E r, where Y r is a measure of the business formation rate in region r, U r is the local rate of unemployment, M r is the percentage of a local area employment which is engaged in manufacturing, and E r is the random error term. From the foregoing discussion the hypothesis is that e and / are both negative. The estimated version of the cross-section equation is as follows, Y r = U r -0AlM r, (-4.36) (-3.19) R 2 = 0.33 n = 64, where Y r is the total number of VAT registrations for each county for the period (from Ganguly, 1985, table 25, pages 91-99), expressed per thousand of the 1981 labour force of each county. The unemployment percentage rate for each county is for 1979, the year just prior to the flow of new registrations. County data for labour force and the percentage employed in manufacturing are for 1981 and, along with the unemployment data, were obtained from editions of Regional Trends (HMSO, London). The correlation matrix of these explanatory variables is given in the appendix: the extremely weak correlation between U r and M r should be noted. The estimated coefficients are again highly significant and both have the expected negative sign. So, on this measure of business formation, the rates are lowest in areas of highest unemployment where there is still a predominance of manufacturing areas such as Tyne and Wear, Merseyside, and Cleveland. It is indeed the more prosperous areas which have the highest formation rates. Reconciling time-series and cross-section evidence There is at first glance something of a paradox in the evidence: at least up to some critical though high level of unemployment, business formation rates rise with unemployment, yet the lowest formation rates are in areas with the highest rates of unemployment. My purpose in this section is to reconcile these findings. The general features of the reconciliation I have in mind are set out in figure 1 (see over). Contained in figure 1 is a family of cross-section relationships, each pertaining to a different time period (7^, T l9..., T n ). Each of these graphs is more negatively sloped than its predecessor to reflect Storey's point that, as time passes, prosperity breeds more prosperity because the impact of policy incentives to start businesses have a disproportionate effect on the formation rates in already prosperous areas. However, I have presumed another effect of such policies is to cause the whole cross-section relationship to shift gradually upwards through time. This I would defend on the grounds that the plethora of policies in support of business start-up in the United Kingdom will indeed have served both to popularise and to legitimise self-employment throughout all areas of the country. The final point to note is that, as the cross-section functions move out over time, the gap between

6 R T Hamilton them is progressively reduced to reflect diminishing impacts of successive policy measures. This stops at time T n when it is assumed that no more can be done to stimulate new business formation. We begin from a position of 'low' average unemployment (U 0 ) with the business formation rate Y Q being determined by the cross-section relationship at that point in time (labelled T 0 ). Now, unemployment rises over time to a level U 1, and for the reasons outlined above, the cross-section relationship rotates clockwise and shifts upwards. As a result, the business formation rate which would otherwise have fallen along the cross-section at T 0 is observed to rise from Y 0 to Y 1. This process repeats itself as unemployment levels continue to rise. However, a stage is reached at T n when further increases in unemployment can only give rise to a movement down that negatively sloped cross-section. So, in terms of time-series observations, what we should observe as the concomitant of the steady rise in unemployment is the parabolic trajectory through points A, B, C, D, and E. I have shown above that this type of trajectory is in fact consistent with the evidence for Scotland from 1950 to There is one important point that needs to be stressed and for this I am grateful to Professor Michael Beesley of the London Business School. It is not changes in average unemployment per se which cause the rotation and shift of the cross-section relationship. Average unemployment could rise over time without any change in the estimated cross-section relationship. All that would happen is that the distribution of regions over the cross-section would change with time. It is the movement of the cross-section relationship which generates the observed timeseries behaviour and this movement is caused by the general policy response to increasing unemployment and, in accordance with Storey and Johnson (1987), the clear bias of such policies in favour of the already prosperous areas. i 5-^. ^0 T. ^ ^~~~~~~- ^^ _.1 B T A ^ ^E l ^ \ ^ \ ^ U 0 17, Unemployment rate Figure 1. Time-series and cross-section findings on the relationship between unemployment and business formation rates. Conclusions I have tried to show here that the time-series relationship between unemployment and business formation rates may be nonlinear such that, beyond the 'critical' unemployment level (estimated to be around 20%), further rises in unemployment will be associated with falling formation rates. I then showed this time-series pattern to be consistent with what we know about the cross-section relationship given the probable impact on this of a stream of policies designed to stimulate new business formation rates. The conclusions are tentative at this stage and more empirical work is needed, particularly to estimate the actual cross-section relationships at different points in time with the same data source.

7 Unemployment and business formation rates 255 References Creedy J, Johnson P S, 1983, "Firm formation in manufacturing industry" Applied Economics Department of Employment, 1971 British Labour Statistics: Historical Abstract (HMSO, London) Ganguly P, 1985 UK Small Business Statistics and International Comparisons Ed. G Bannock (Harper and Row, London) Gudgin G, Fothergill S, 1984, "Geographic variation in the rate of formation of new manufacturing firms" Regional Studies Hamilton R T, 1986, "The influence of unemployment on the level and rate of company formation in Scotland, " Environment and Planning A Harrison R T, Hart M, 1983, "Factors influencing new-business formation: a case study of Northern Ireland" Environment and Planning A Johnson P S, Darnell A, 1976, "New firm formation in Great Britain", WP-5, Department of Economics, University of Durham, Durham DH1 3HP Kmenta J, 1971 Elements of Econometrics (Macmillan, New York) Nunn S, 1980, "The opening and closure of manufacturing establishments in the UK, ", WP36, Regional Series No.l, Department of Trade and Industry, 1-19 Victoria Street, London SW1 Oxenfeldt A R, 1943 New Firms and Free Enterprise (American Council on Public Affairs, Washington, DC) Storey D J, 1982 Entrepreneurship and the New Firm (Croom Helm, Beckenham, Kent) Storey D J, Johnson S, 1987, "Regional variations in entrepreneurship in the UK" Scottish Journal of Political Economy Whittington R C, 1984, "Regional bias in new firm formation in the UK" Regional Studies APPENDIX Correlation matrices of explanatory variables Time-series model t/,-i UU Y, tf,-l /, 2 -i Y, Cross-section model U r M r Y r u r M r Yr