Michael Sumner

JEL Code: E41 -Demand for Money < E4 -Money and Interest Rates < E -Macroeconomics and Monetary Economics

After a brief review of recent literature, new estimates on a long run of annual observations of the Thai demand for all the standard measures of money are presented. The results demonstrate that the demand for real money balances is a stable function of a scale variable and a coherent measure of opportunity cost, with all the properties predicted by economic theory.

Introduction

The resurgence of interest in the demand function for money stimulated by the development of cointegration techniques has generated a substantial literature on emerging as well as advanced economies. Thailand, as the first victim of the 1997 crisis, is a particularly intriguing example; but existing (English-language) studies raise more questions than they resolve.

After a brief review of this literature, new estimates of the Thai demand for all the standard measures of money are presented. All the results demonstrate that the demand for real money balances is a stable function of a scale variable and a coherent measure of opportunity cost, with all the properties predicted by economic theory.

Literature Survey

All previous work adopts the [START_REF] Cagan | The monetary dynamics of hyperinflation[END_REF] specification of the demand function as a maintained hypothesis, utilises quarterly data in estimation, defines real GDP as the scale variable, and agrees that the standard measure of opportunity cost, a domestic interest rate, is not appropriate for Thailand. As quarterly data on GDP are of recent origin, use of interpolation or a proxy is necessitated. Alternative scale variables have not been investigated.

The treatment of opportunity cost raises more substantial difficulties. [START_REF] Chowdhury | The financial structure and the demand for money in Thailand[END_REF] asserts that regulations on interest rates and limited availability of alternative financial assets raise doubts about the appropriateness of standard interest rate measures; but he does not explain why controls on rates should ipso facto limit their appropriateness, or investigate his doubts empirically. He suggests 3 insignificant for M1, perhaps because they include lags up to order 9 on the dynamic terms, most of which are also insignificant. The claimed significance of the error-correction term for M2 is based on an inappropriate standard critical value.

In the aftermath of the 1997 crisis more recent investigations have focused on short-run interactions between monetary and real variables, using very short samples for estimation which preclude consideration of long-run properties. For example, [START_REF] Disyatat | Monetary policy and the transmission mechanism in Thailand[END_REF] employ quarterly data for 1993(1)-2001(4), and [START_REF] Fung | A VAR analysis of the effects of monetary policy in East Asia[END_REF] estimates a twelfth-order VAR using monthly data for 1989(1)-2001(6), subsequently split into pre-and post-crisis sub-samples.

In short, the existing literature sheds very little light on the demand for money in Thailand.

Data and Methodology

The long-run demand function is provisionally assumed to be of the Cagan form, in which the log of the real stock of money demanded is determined by the log of a real scale variable and a measure of opportunity cost (entered as a proportion). The assumption of zero-degree homogeneity in prices is subsequently tested, and alternative measures of the scale variable and of opportunity cost are examined. The long-run function is estimated within an unrestricted error-correction model which incorporates short-run dynamics. The null hypothesis of non-cointegration is tested by deletion of the 'level' variables, using non-standard critical F-values [START_REF] Pesaran | Bounds testing approaches to the analysis of level relationships[END_REF]. Within this framework it is not necessary to test for the order of integration of the variables, but it is nevertheless informative. The ADF tests reported in table 1 show that all measures of the real money Table 1 about here stock, the two scale variables of primary interest, and the three measures of the cost of holding money (measured as proportions) are unambiguously I(1); any residual doubts about the order of demand deposits were resolved by inspection of the plots of the series and the autocorrelation function. Accordingly the upper bound of the non-standard F-distribution is used as the critical value in the variable-deletion tests of non-cointegration.

The serial correlation test included in the standard diagnostics reported for the estimates is for firstorder; in all cases tests for up to third-order were conducted but revealed nothing to cause concern.

All the CUSUM and CUSUMSQ plots for the reported equations were satisfactory. Predictive failure was tested with a break at end-1993; shifting the break to end-1996 to isolate the post-crisis period made no difference to the results.

A Digression on Measurement

The interest semi-elasticity (F) of the Cagan demand function plays a crucial role in the monetary model of exchange-rate determination, which expresses the spot exchange rate as a function of current and expected future fundamentals and the expected exchange rate at the horizon, with a per-F o r P e e r R e v i e w 5 period discount factor of F/(1+F). The student who struggles successfully through the hoops of purchasing power parity, uncovered interest parity, rational expectations and the associated algebraic manipulations to arrive at this result may be forgiven for questioning the purpose of the exercise on being informed by (for instance) [START_REF] Hallwood | International Money and Finance[END_REF] that F I 0.02, on the authority of Bilson (1978a); if so, the coefficient on expected future fundamentals asymptotes to zero so rapidly that they might as well be ignored. On the other hand [START_REF] Engel | Exchange rates and fundamentals[END_REF] attribute an estimate of F I 60 to the same author in a different paper (Bilson, 1978b) in support of their contention that the quarterly discount factor is around 0.98, in which case expected fundamentals in the distant future matter a great deal. Is this an illustration of the rhetoric of economics?

The substantive issue here concerns the measurement of interest rates. Engel and West assert (p497) without discussion that Bilson uses quarterly interest rates that are annualized and multiplied by 100 in his empirical study. So his actual estimate [of F = 0.15] should be multiplied by 400 to construct a quarterly discount rate. Three questions arise. Did Bilson use annual percentage rates of interest? Was his actual estimate F = 0.15? And should interest be expressed at a quarterly proportional rate? Bilson's (1978b, p61) own summary of the key result sheds light on the first two questions:

The interest rate elasticity, which is equal to the product of the regression coefficient [-1.3853] Digressing further, this is not their only careless slip: in the same footnote they cite [START_REF] Macdonald | The monetary approach to the exchange rate[END_REF] as adopting Bilson's (1978a) estimate of F = 0.15, rather than 60; but the number they adopt is actually 0.015. They may take some consolation from the fact that other contributors to this arcane literature have also displayed carelessness: Bilson (1978a, p85), whose calculations reveal that interest rates are here entered as annual percentage rates, offers a baffling comment: US studies of the demand for money have found interest rate elasticities of approximately

0.015 if the nominal rate of interest is 10 per cent. [Italics supplied].
In a context where precise numbers are crucial, experienced professionals might reasonably have been expected to exercise the degree of care customarily required of undergraduate students.

The remaining question is substantive. Expressing interest at quarterly rates in a quarterly model seems intuitively plausible, but the larger issue of measurement units is less easily resolved. In a static model it appears that the investigator is completely free to choose between proportions and percentages, or for that matter basis points, with dramatically different implications for the value of the interest semi-elasticity and for the properties of the monetary model. The unrestricted errorcorrection model provides an answer. With the dependent variable expressed as a proportionate rate of change, the conformable measure of the interest rate is as a proportion. Engel and West got the numbers wrong and in consequence overstated their case that the discount factor is almost one, but they selected the appropriate unit of measurement.

Demand for Cash

Cash in the hands of the public plays a major role in the Thai monetary system, accounting on average over the sample for 70% of M1 and 11% of M2. Attempts to model the determinants of demand for cash produced results similar to those reported by [START_REF] Reilly | Demand for money in Sri Lanka, 1952-2002[END_REF] for Sri Lanka. The only interest rate available for the full sample is the central bank's discount rate, of rather limited direct relevance to the personal sector but a highly visible influence on other rates.

With either this or the inflation rate (DLP, defined on the GDP deflator) to represent the cost of holding cash, the diagnostics were unsatisfactory and the CUSUM test failed; in addition, with the former measure the null of non-cointegration was not rejected. Including both together did not improve matters; but a coherent measure of opportunity cost as the highest available rate of return on alternative assets, defined as OPC RD = MAX (RD, DLP) produced the more promising results detailed in equation 1 of table 2.

Table 2 about here

The fit is appreciably better than with either of the standard cost measures; all the dynamic terms (indicated by prefix D) are well-determined; apart from a marginal problem with the functional form all the diagnostics are satisfactory; and the F-test in the last row is consistent with a stable long-run relationship among the level variables. In contrast to Sri Lanka there were only four years (1955, 1957 and 1973-74) Close substitutes for GDP (domestic absorption, GNP) as scale variable made no material difference to the results, but a later start of the estimation period enables comparison with consumers' expenditure, in equations 2 and 3. Equation 3 (also 5) uses the consumption deflator in the construction of OPC, the real stock of cash and hence the dependent variable, so comparison of fit relies on the standard error of the regressions, not the (strictly) incomparable coefficients of determination. The improvement in fit with the anticipation that these would be at least partially financed by seignorage led to the collapse of the fixed exchange rate regimes when the expectation was formed, rather than when large-scale money creation began.

There is, however, an alternative explanation which focuses on money demand rather than supply as the source of disturbance. A regression of the forecast errors in 1994-2002 from (re-estimated) equation 1 yields an insignificant negative intercept, coefficients which sum to zero on dummies for 1999 and the following year, an R 2 of 0.85 and satisfactory diagnostics. Fortunately millennia are sufficiently rare events as to make further examination unnecessary.

Demand Deposits

Modelling the determinants of demand deposits proved much simpler. The main differences are that inflation makes no contribution to the measurement of opportunity cost, and consumers' expenditure is clearly inferior to GDP as the scale variable. Both findings are consistent with the predominant use of demand deposits for business purposes rather than personal expenditure. No role was found for dynamics. No millennial problem emerged, so estimation is over the full sample period; the error in 1999 is (unsurprisingly) negative, but small. The results are summarised in table 3. does not change the estimates of the long-run income elasticity and opportunity cost semi-elasticity. The former, at around 0.65, is conspicuously lower than the estimate of about 0.95 for cash. This difference, the superior performance of consumption as scale variable for cash, and the absence of dynamics in the deposit demand function all raise doubts about the usefulness in Thailand of combining the two categories of money in conventional M1.

A major advantage of unrestricted error-correction modelling is that the long-and shortrun parameters are estimated simultaneously. The unusual absence of dynamics in this instance provides a rare opportunity to compare this approach with alternatives on level terms. The static equation estimated over the full sample in the first step of the Engel-Granger procedure produced a similar value to equation 6 for the (long-run) income elasticity but a much lower (absolute) value for the interest semi-elasticity, 1.7 against 5.5. Both the standard tests on the residuals, the ADF of -3.51 (-3.92) and the CRDW of 0.80 (0.99), failed to reject the null of non-cointegration at the 5% level (whose critical values are parenthesised). Proceeding nevertheless to the second stage, the errorcorrection model confirmed the absence of dynamics but narrowly rejected noncointegration: the t-ratio for the error-correction term was -3.96 (-3.92). This rose to -0.03 when the implied error-correction term from equation 6 was added to implement [START_REF] Davidson | Several tests for model specification in the presence of alternative hypotheses[END_REF] test of specification; the t-ratio on the latter was -2.44, falling to -4.87 when the Engel-Granger term was deleted.

The Johansen procedure fared little better. With 1 lag in the VAR as indicated by the choice criteria, estimation with unrestricted intercept and restricted trend showed the 2 cointegrating vectors, in the first of which opportunity cost appears with the wrong sign, as does the disequilibrium term in the error-correction model. The second was highly correlated (0.99) with that implied by equation 6, with an identical long-run income elasticity, a slightly lower interest semi-elasticity, but a much higher speed of adjustment (0.79). It attracted a t-ratio of -4.81 (-3.92) in the error-correction model; but with a coefficient of only (-)0.57, close to the ratio of the estimated adjustment parameters and far below the expected value of unity.

The obvious conclusions to draw from this methodological digression are that the Johansen procedure is extremely sensitive and both the alternative procedures entail a serious risk of bias. The comparisons cannot establish that the equivocal results of both these methods are 'wrong' and the unambiguously positive ones from the unrestricted error-correction model are 'right', but they do demonstrate that the latter has substantially greater explanatory power.

Interest-Bearing Deposits

The question of primary interest in relation to time and savings deposits (SAV) is their relative responsiveness to opportunity cost and their own-rate of return. Equation 9 in table 4 shows that the magnitudes of response, in both levels and (log-) differences, are very similar. The hypothesis of coefficients which sum to zero cannot be rejected for levels (p=0.33), differences (p=0.17) or both (p=0.29), and these parameters all appear to As SAV accounts for much the greater part of broad money, these results carry over to the M2 regressions in equations 11 and 12. Indeed the p-values for the interest constraints are considerably higher (at 0.81, 0.98 and 0.97 respectively), so their imposition carries no cost. The only additional feature is some weak evidence of a dynamic role for GDP.

The coefficients on the GDP level are not well-determined, but the higher point-estimate of the long-run income elasticity, around 1.4, than was found for other aggregates is plausible. The alternative scale variable and alternative measures of opportunity cost performed less well. The speed of adjustment is comparatively leisurely in all cases. The forecast error for 1999 is negative and substantial for SAV (almost 50% greater than its standard deviation), negative but tiny for M2. The hypothesis of non-cointegration is decisively rejected in all the equations, and none of the diagnostics causes any concern.

Conclusions

Economic theory is alive and well in Thailand. The demand for money in all its forms is a stable function of a few key variables. There is no evidence of money illusion. Agents adjust their (personal) money holdings in line with inflation when, but only when, real interest rates are negative. The differential between opportunity cost and the own-rate of Models estimated on annual data clearly cannot shed light on currency substitution or other extremely short-term influences, but it is doubtful whether quarterly models (even if appropriately specified) would be much more informative. Until the 1997 crisis, the Thai baht had moved closely with the US dollar except during the latter's appreciation in the early 1980s, even after a currency basket was substituted for the formal dollar peg, and anticipations of the crisis developed at a very late stage. [START_REF] Burnside | Prospective deficits and the Asian currency crisis[END_REF] observe that forward premia did not begin to rise significantly until mid-May, only 6 weeks before the initial devaluation. There was a conspicuous jump of 47% in foreign currency deposits with Thai commercial banks and Thai branches of foreign banks in April, but this increased the stock to only 0.6% of total deposits; and half of this increase was eliminated by end-June. Any currency substitution did not show up in end-year data:

the M2 residual from equation 12 was positive and 30% larger than the standard error of the regression in 1997; the increase in time deposits dwarfed the rise in foreign currency deposits.

What models using long runs of annual data can do is to determine whether a stable lowfrequency relationship exists among the variables of interest, and to estimate its parameters with more confidence than would be possible with more but higher-frequency observations over a shorter period. The dependent variable (DLMO), the corresponding lagged stock and the inflation rate included in OPC (and its difference) are constructed using the GDP deflator in equations 1, 2 & 4, and the CPI in equations 3 & 5. SERs (but not coefficients of determination) are comparable across these groups of equations.

F

Absolute t-ratios in parentheses below coefficients.

Diagnostic tests for serial correlation, functional form, normality, heteroscedasticity, and predictive failure, in F-form where available, reported as p-values.

Prediction period is 1994-1998.

Upper-bound critical values for the variable exclusion test in the last row are 4.13 (90%), 4.86 (95%) and 6.31 (99%).

  The data are annual, from the IMF International Financial Statistics Yearbooks (various issues), supplemented by reference to the Bank of Thailand's website and Nidhiprabh(1993). The advantage ' data for the longest available period (from the early 1950s to 2002 in some cases) is believed to more than offset the larger number of observations in quarterly data for the purpose of examining long-run properties of demand for money.

  is noticeable though hardly dramatic, and the residuals now exhibit heteroscedasticity.The performance of the central bank's discount rate and the commercial banks' deposit rate can be compared over the same period. The presumption that the latter is a more appropriate measure of opportunity cost is fully confirmed by the contrast between equations 2 and 4. The measure of opportunity cost in equation 4, OPC RDEP = Max (RDEP, DLP), for which DLP > RDEP in 1979-80 as well as 1973-74, produces better-determined dynamic effects and a better fit than in equations 2 and 3, but does not rectify the heteroscedasticity problem. That disappears when both modifications are combined, in equation 5, which appears to be completely satisfactory.All specifications strongly reject the null of non-cointegration. Breaking the estimation period in 1993 produces no evidence of predictive failure. The speed of adjustment parameter (on the lagged stock) and the long-run semi-elasticity with respect to the different measures of opportunity cost (OPC coefficient divided by the speed of adjustment) are largely unaffected by the specification changes in equations 2-5; equation 1 implies slower adjustment and a larger semi-elasticity in the full sample, but estimates of the long-run scale elasticity are remarkably robust across all specifications. Despite these positive results there is one apparently embarrassing problem. It will not have escaped the reader's attention that the end-date of estimation precedes the end of the data series by 4 years. The reason is that inclusion of the remaining data points would produce a serious breakdown of all the demand functions reported in table 2: specifically, the prediction error for equation 1 in 1999 is 24%! The enormous increase in real cash year is the crucial piece of evidence adduced by[START_REF] Burnside | Prospective deficits and the Asian currency crisis[END_REF] in support of their argument that the Asian currency crisis of 1997 is explicable in terms of the 'first-generation' model of speculative attack. Despite the manifest fiscal rectitude of the Thai and other affected economies in the period preceding the crisis, large prospective deficits were caused by the implicit bailout guarantees to failing financial systems, and

  key determinant of demand for quasi-money. Precautionary cash balances are increased (dramatically in 1999) in response to uncertainty.

Page 8 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  in which DLP > RD. Entering the two components of OPC RD separately yielded -value for the hypothesis of equal coefficients of 0.67. The same property did not hold, however, for the first-differences of the opportunity cost components; instead these dynamic terms enter as separate continuous variables. Entering OPC in logs or the firstdifference of the level rather than log of the interest rate caused a deterioration in the fit, as in the UK[START_REF] Chadha | Shoe-leather costs reconsidered[END_REF] and Sri Lanka.

		Submitted Manuscript
	-1.43 OPC(RD) -1.30 OPC(DLP)
	[2.69]	[3.79]
	with a p
		F o
		r
		P
		e e r
		R e v i e w
		8

Homogeneity was tested by respecifying equation 1 in nominal terms. The appropriate coefficient restrictions were easily satisfied, with p-values of 0.37 for the level terms, 0.43 for the differences, and 0.51 for all constraints. All subsequently reported regressions were re-estimated with the addition of LP(-1) and DLP as a check for nonhomogeneity, but these extra terms were always insignificant.

The unrestricted error-correction model facilitates tests of weak exogeneity. Respecifying equation 1 with DLY or DOPC as dependent variable and appropriate modification of the dynamics yielded F-values for the variable deletion test of 2.17 and 3.86 respectively, far below the critical values. Hence the interpretation of equation 1 as a demand function for money is confirmed.

Table 3

 3

	about here

produces a marginally better fit than the central bank discount rate, but it also raises Page 12 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Page 13 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	latter to be highly insignificant. With restricted intercept and no trend both tests indicate
	F o
	r
	P
	e e r
	R e v i e w
	13

Page 14 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	be well-determined. Imposing the constraints in equation 10 entails little cost in terms of
	fit.
	Table 4 about here
	F o
	r
	P
	e e r
	R e v i e w
	14

Table 1 : ADF Tests

 1

	o
	r
	P
	e e r
	R e v i e w

Page 21 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o
	r
	P
	e e r
	R e v i e w
	21

Table 3 : Demand Deposits

 3

		Submitted Manuscript
	Equation	6	7	8
	Sample	1953-2002	1967-2002
	Intercept	-0.24	0.08	-0.16
		[1.57]	[0.37]	[0.79]
	LDD(-1)	-0.42	-0.46	-0.61
		[4.01]	[3.44]	[4.26]
	LY(-1)	0.29	0.27	0.39
		[3.99]	[3.22]	[4.18]
	RD(-1)	-2.31	-2.63
		[3.27]	[3.22]
	RDEP(-1)			-3.11
				[3.87]
	R 2	0.33	0.37	0.41
	SER%	11.99	11.41	11.05
	Serial Correlation	0.99	0.16	0.89
	Functional Form	0.99	0.82	0.73
	Normality	0.19	0.36	0.54
	Heteroscedasticity	0.72	0.96	0.94
	Predictive Failure	0.30	0.41	0.06
	F (Levels exclusion)	7.58	6.23	7.35
	Additional notes to table 3:
	Dependent variable is DLDD.
	Prediction period is 1994-2002.

Page 22 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 4 : Interest-Bearing Deposits

 4 LEVEL denoted the stock whose first difference is the dependent variable.The upper-bound critical value of the F test for levels deletion in equations 9 and 11 is 5.62 (99%).

		9	10	11	12
	Equation
	Dependent Variable	DLSAV		DLM2
	Intercept	-0.26
		[0.53]

24 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Mika Haapanen

Professor Hannu Tervo
email: htervo@econ.jyu.fi

Statistical Methods: Special Topics < C -Mathematical and Quantitative Methods, R23 -Regional Migration|Regional Labor Markets|Population < R2

Keywords: self-employment, duration, urban and rural labour markets Self-employment, duration, urban and rural labour markets JEL Classification numbers: J23, C41, R23

published or not. The documents may come

Self-employment duration in urban and rural locations I. Introduction

Individuals in small, dispersed labour markets may be pushed into self-employment if they see no other realistic employment options in the region [START_REF] Ritsilä | Effects of Unemployment on New Firm Formation: Micro-Level Panel Data Evidence from Finland[END_REF][START_REF] Moore | The transition from paid to self-employment in Canada: the importance of push factors[END_REF][START_REF] Carrasco | Transitions to and from Self-Employment in Spain: An Empirical Analysis[END_REF]Ejrnaes, 2003, Tervo, 2006). Typically, rural as compared to urban labour markets are characterized by weaker employment conditions. For example in Finland, rural labour markets hold worse rates of employment and self-sufficiency in jobs than urban labour markets. Weak paid-employment opportunities push workers into selfemployment in Finnish rural labour markets [START_REF] Tervo | Self-Employment Dynamics in Rural and Urban Labour Markets[END_REF]. The non-agricultural selfemployment rate has been nearly twice as high in rural than urban locations. Individuals in Finnish rural locations have also more alternation between self-employment, paidemployment and non-employment in their working careers than individuals in urban locations, where employment opportunities are more varied.

While the decision to enter self-employment has been widely studied, fewer studies have dealt with the duration of self-employment spells (see, however, [START_REF] Taylor | Survival of the Fittest? An Analysis of Self-Employment Duration in Britain[END_REF][START_REF] Carrasco | Transitions to and from Self-Employment in Spain: An Empirical Analysis[END_REF][START_REF] Johansson | Essays on the Determinants of Self-Employment[END_REF][START_REF] Falter | Self-Employment Entry and Duration in Switzerland[END_REF][START_REF] Cueto | An analysis of self-employment subsidies with duration models[END_REF]). An interesting, but yet largely unstudied question concerns self-employment duration in different labour markets. Earlier studies show that rates of exit out of self-employment and lengths of self-employment spells depend upon personal characteristics and cyclical trends in the economy. But what is the role played by region-specific factors?

The purpose of this paper is to analyze the role of region-specific factors on the duration of self-employment spells in Finland. As rural areas are characterized by weaker conditions of employment than urban areas, it is hypothesized that exit rates from selfemployment are lower in rural than urban areas. The data used are based on a Longitudinal possibly right-censored self-employment spell is fourteen years. This is a longer period than in most previous studies.

Our analysis affirms the importance of region-specific factors in the determinants of self-employment duration in Finland. First, the descriptive analysis shows that the exit rates from self-employment and the length of self-employment spells depend upon location (urban vs. rural area) and the cyclical trends in the economy. Second, self-employment duration is modelled using discrete time survival analysis. A flexible, semiparametric specification of the baseline hazard is adopted, as in [START_REF] Meyer | Unemployment Insurance and Unemployment Spells[END_REF]. The analysis is further generalized by allowing the baseline hazard to differ between the two locations. Our main finding is that, after controlling for other factors, the estimated survival functions differ. Self-employment spells typically are longer in rural than urban areas. This is due to the lower hazard rates in rural areas in the first years of self-employment. It seems that a weak labour market situation forces individuals to continue in self-employment, even though its profitability is questionable. The push effect operates.

The rest of the paper is organized as follows. Section II discusses the theoretical framework for the analysis of self-employment duration. The data and methods are described in Section III. Then life-table estimates and other descriptive results are presented (Section

II. Theoretical framework

The theoretical background of this study rests on the human capital theory and utility maximising paradigm [START_REF] Knight | Risk, Uncertainty, and Profit[END_REF][START_REF] Becker | Human Capital[END_REF][START_REF] Evans | Some Empirical Aspects of Self-Employment[END_REF][START_REF] Tervo | The Impact of Unemployment on New Firm Formation in Finland[END_REF][START_REF] Taylor | Survival of the Fittest? An Analysis of Self-Employment Duration in Britain[END_REF][START_REF] Uusitalo | Homo entreprenaurus?[END_REF], and [START_REF] Jovanovic | Selection and the Evolution of Industry[END_REF] dynamic selection model. Entrepreneurs have imperfect information about their innate abilities, which they can learn about only by trying entrepreneurship. Individuals less suited to self-employment give up quite soon. The longer an individual has been self-employed the more likely (s)he is to continue. The dynamic selection model emphasizes the importance of dynamics, with entrepreneurs learning about their abilities to compete and survive in the market post-entry [START_REF] Taylor | Survival of the Fittest? An Analysis of Self-Employment Duration in Britain[END_REF][START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF].

The utility maximizing paradigm predicts that individuals choose the occupation that offers the greatest expected utility. A rational self-employed person compares the utility of entrepreneurship with that of paid employment and other labour market states in each period, and decides accordingly whether or not to continue in her/his current status. The choice of labour market status is continually subject to revision as individuals' situations change. If the present value of the expected net benefits of continuing as self-employed is positive, the individual remains in self-employment, but if it is negative, (s)he quits. Continuation of selfemployment is not necessarily equivalent to the survival of a business since an individual can remain self-employed while starting up and closing down successive businesses [START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF].

The utility maximizing approach should not be understood too literally. In a world of uncertainty and imperfect information, individuals will weigh up the pros and cons of continuing in self-employment only intuitively. As many factors play a part in the The items comprising expected benefits and costs range widely, and include both financial and non-financial items. The main focus of this paper is the role of region-specific factors on surviving in self-employment. In addition to factors relating to the local labour market, however, it is assumed that the duration of self-employment, and thus survival, depends upon many other factors such as assets, personal and household characteristics, earlier activity and experience, and type of industry. In general, many of these factors can be assumed to affect duration in the same way as they affect entry into self-employment. 1 The factors and hypothesis related to these factors are derived below, while the following section includes a more specific description of the data, including the formation and means of the variables used (see Table 1

below).

I Region-specific factors. Two sets of variables measure the situation in the local labour market. Our key variable defines whether the firm is located in a rural or an urban area.

As rural areas are characterized by weaker conditions of employment than urban areas, it is hypothesized that exit rates from self-employment will be lower, especially during the first years of self-employment. Better survival rates in rural areas are assumed to follow more from the push than the pull effect of the market. In addition, rural areas typically have a strong tradition of entrepreneurship, which may also have a positive effect on survival rates.

Thus, the predicted effect on survival is the same as it is for entry into self-employment.

A second set of region-specific variables describes the unemployment situation in the local labour market. On the one hand, it is assumed that high unemployment in the region forces self-employed individuals to continue as they are, since other employment options are scarce. On the other hand, the regional unemployment rate, and especially change in it, is also an indicator of opportunities for self-employment. A decrease in unemployment creates opportunities, and vice versa. Therefore, a rise in unemployment is expected to be positively related to exits from self-employment.

II Personal and household characteristics. Personal and household characteristics include gender, age, mother tongue, education, marital status and children. In general, these characteristics may help to describe individuals' entrepreneurial ability, the probability of receiving alternative job offers, and tastes and preferences.

Earlier studies show that there is a positive relationship between business survival and an entrepreneur's human capital, although formal educational qualifications have shown mixed effects on survival rates [START_REF] Taylor | Survival of the Fittest? An Analysis of Self-Employment Duration in Britain[END_REF][START_REF] Kangasharju | The Role of Education in Self-Employment Success in Finland[END_REF][START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF]. This is because education increases both an individual's human capital and her/his earning capacity in paid employment. Age also affects survival rates, which have been found to be higher for middle-aged than for younger or older self-employed individuals (Holtz-Eakin, [START_REF] Holtz-Eakin | Sticking it Out: Entrepreneurial Survival and Liquidity Constraints[END_REF][START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF].

Many studies have shown a positive association between self-employment status and marital and parental status. Family support may be assumed to help self-employed individuals to survive longer. Gender also predicts entries into self-employment -females are in their minority among the self-employed. It can also be assumed that spells of female selfemployment are shorter than those of male self-employment. Language is another possible predictor of self-employment duration. The overwhelming majority (app. 92%) of the Finns speak Finnish as their mother tongue, but in certain regions, mainly along the southern and western coastlines, Swedish is the first language of a significant part of the population.

Institutional support for the Swedish-speaking minority has traditionally been strong 1 Many studies which analyse both self-employment entry and duration in fact use the same variables 7 [START_REF] Liebkind | The Swedish-Speaking Minority in Finland[END_REF]. The Swedish-speaking community with its shared language, culture and social capital may also improve entrepreneurial success. III Assets. Entrepreneurial activity is restricted by liquidity constraints [START_REF] Evans | An Estimated Model of Entrepreneurial Choice under Liquidity Constraints[END_REF]. Lack of financial resources may not only prevent entry into selfemployment but also successful running of business (see e.g. [START_REF] Holtz-Eakin | Sticking it Out: Entrepreneurial Survival and Liquidity Constraints[END_REF]. Therefore it is expected, other things being equal, that a wealthier selfemployed individual will survive longer than her/his less wealthy counterpart. In the current study three variables describe assets: personal income, income of spouse, and house ownership.

IV Prior activity and experience. The experience variables describe lifetime labour market history and activity prior to the self-employment spell. Previous labour market status may have an effect on the likelihood of remaining in business. It can be assumed that the transition from paid employment to self-employment lays a better foundation for survival than the same transition from non-employment (being unemployed or student). Individuals entering self-employment from paid employment may be expected to have higher human capital and motivation as well as higher quality information about business opportunities. For example, [START_REF] Carrasco | Transitions to and from Self-Employment in Spain: An Empirical Analysis[END_REF] showed that Spanish self-employed males who were unemployed prior to entering self-employment had hazard rates three times greater than those who previously worked in paid employment. In addition, prior experience of migration is likely to increase the exit rates from self-employment. Starting business in a new environment may involve unexpected risks, for example, in finding customers.

Prior self-employment experience indicates the accumulation of business skills. It is an important explanatory variable in accounting for entry into self-employment [START_REF] Evans | Some Empirical Aspects of Self-Employment[END_REF][START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF], and it can also be assumed to be an important factor for in both models (e.g. [START_REF] Falter | Self-Employment Entry and Duration in Switzerland[END_REF]. survival. Individuals who come from entrepreneurial families can also be assumed to have a greater chance of surviving in business because of their experience of running a business gained in their early life as well as their familiarity with the market [START_REF] Niittykangas | Spatial Variations in Intergenerational Transmission of Self-Employment[END_REF].

V Industrial sector. The industry of a self-employed person may further predict survival, as business conditions vary between economic sectors (see e.g. [START_REF] Taylor | Survival of the Fittest? An Analysis of Self-Employment Duration in Britain[END_REF]. It may also capture the changing industrial structure in the economy.

III. Data and methods

The data set

The data are based on various registers kept by Statistics Finland. Since 1970, Statistics Finland has compiled a population census every 5 years, and by 1990, the census had become entirely register-based. By matching the unique personal identifiers across the censuses, Statistics Finland has constructed a Longitudinal Census File with panel data on the entire population of Finland at 5-year intervals from 1970 to 1995. In addition, since 1987, it has maintained the Longitudinal Employment Statistics file, which is updated annually. Since the same personal identifier is adopted in both the census and the longitudinal employment statistics, the two data sets can be merged, providing panel data on each resident of Finland for 1970Finland for , 1975Finland for , 1980Finland for , 1985 and then annually from 1987 to 2002. By using the personal identifier, data from various other registers can be merged with this panel data. In addition, data on spouses and parents can be merged under every individual. we only know an individual's occupational status at the end of each year. Therefore, the beginning of a self-employment spell is defined in this study as follows: An individual's self-employment spell begins in year j, if (s)he is not selfemployed during the last week of year j-1 but is self-employed during the last week of year j, where j = 1988-2001.

The last year of observation is 2002. In consequence, our analysis is based on the inflow samples from fourteen cohorts. The maximum observed duration of a possibly rightcensored self-employment spell is fourteen years. This is a longer period than in most previous studies. Since an observed self-employment spell may also start after 1988, some of the spells are right-censored at shorter duration. Some additional restrictions on the sample of self-employment spells remain to be imposed:

1. Age-restriction. An individual's self-employment spell is included in the sample only if (s)he is aged between 18 and 60 years old at the beginning of that spell.

2. Industry-restriction. As is usual, we excluded from our sample self-employment spells in the primary sector. This is because the concept of self-employment is vaguer in agriculture than in other industries, and farm businesses have very different characteristics from non-farm businesses [START_REF] Blanchflower | Self-Employment in OECD Countries[END_REF][START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF].

Accordingly, the analysis concerns non-agricultural self-employment.

3. Region-restriction. Finally, those who live in the Åland Islands are not included in the sample. Åland is a small isolated region with only 26,000 inhabitants. It has political autonomy and it differs from the other Finnish regions in numerous ways. Due to its special character Åland is left out, as in many other studies.

Definition of self-employment

In this analysis, the concept of self-employment follows from the statistical definitions used by Statistics Finland (see Statistics Finland 2001). The central variable in this regard is "occupational status" which describes the position of the employed in the labour market: wage and salary earners, and entrepreneurs, which unfortunately cannot be divided into employers and self-employed (sole entrepreneurs). The category of entrepreneurs also comprises unpaid family workers. If an individual is not employed, (s)he belongs to a third category, non-employed. The non-employed are either unemployed or outside the labour force (students etc.). The data on occupational status is based on the person's national insurance status and wage, salary and/or entrepreneurial income received. For an entrepreneur, it is required that (s)he had a self-employed person's pension insurance during the last week of the year and that her/his income from entrepreneurship exceeds her/his wage income, if the person is also in an employment relationship (for details, see Statistics Finland,

2001).

Because self-employment is fundamentally a statistical concept used in labour market statistics and national accounting, great diversity can be found among those in this category [START_REF] Johansson | Essays on the Determinants of Self-Employment[END_REF]. As is well-known, there exists a "grey area" between paid employment and self-employment. For example, people may be self-employed by definition but share many of the same features of dependent paid employees. Examples of workers in the 'grey 11 area' include salespersons on commission, freelancers, people working at home, tele-workers and unpaid family workers [START_REF] Parker | The Economics of Self-Employment and Entrepreneurship[END_REF]. In this study, densely populated municipalities and rural-type municipalities are combined.2 Hence, only two types of area are used which we call "urban areas" and "rural areas". Urban areas are those municipalities in which at least 90 percent of the population live in urban settlements or in which the population of the largest urban settlement is at least 15,000. An urban settlement refers to a cluster of buildings which are less than 200 metres apart from each other and which together house at least 200 people. Accordingly, rural areas are municipalities in which less than 90 percent of the population live in urban settlements and in which the population of the largest urban settlement is at most 15,000. In our sample, the total number of recorded spells of self-employment classified as urban is 11,631 (59.8%) and the number of recorded spells of self-employment classified as rural is 7,808 (40.2%).

Urban and rural areas

Statistics

Duration model

The main emphasis of this to study is to analyse the duration of self-employment spells and the factors influencing it. To do so, we need a measure for the probability of leaving self- If we could observe the exact length of self-employment spell i, then the continuous time hazard of the spell at duration time t could be parameterised, for example by using a proportional hazard specification [ ]

) ( exp ) ( ) ( t X t t i i = , (1)
where ) (t is a baseline hazard at time t, ) (t X i is a vector of (time-varying) covariates, and is a vector of unknown parameters to be estimated with Cox regression (see e.g. Wooldridge, 2002, Ch. 20). However, the duration data available to us is interval-censored (grouped) -the status of a self-employment spell is only observed at the end of each year (maximum of 14 observations per spell). Therefore, the hazard rate requires a discrete time representation.

Fortunately, a discrete time model, which is consistent with continuous time model and interval-censored survival data, can be specified (see e.g. [START_REF] Prentice | Regression Analysis of Grouped Survival Data with Application to Breast Cancer Data[END_REF][START_REF] Sueyoshi | A Class of Binary Response Models for Grouped Duration Data[END_REF]. Suppose that i T is the actual (unobserved) length of a self-employment spell. Then the discrete (grouped) interval hazard rate, the probability of a spell being completed by time 1 + t , given that it was still continuing at time t , can be defined as

( ) ( ) [ ] ) ( ) ( exp exp 1 | 1 ) ( t t X t T t T prob t h i i i i + = + < = , K , 2 , 1 = t ( 2
+ + = = = i i d t i i i i d t i i i t h c d h t h c L 1 1 1 ) ( 1 ln ) 1 ( ) ( ln ) ( 1 ln log . ( 3
)
The log-likelihood for the whole sample of N spells is given by sum of all contributions i, which is maximized with respect to and 's to provide maximum likelihood estimates. 5The empirical specification for the set of the covariates X is given below (see Table 1).6

Variables

The five groups of covariates and the hypotheses related to them were depicted in Section 2.

Table 1 compiles the covariates, their definitions and means. First, some covariates such as gender or prior self-employment experience or parental covariates do not change in time.

Another group of covariates such as level of income/wealth or prior activity is measured on 14 year before the self-employment spell in order to analyse if the initial situation has had an impact on the length of the spell. This assures that a covariate of this type is treated as a cause rather than a consequence of the self-employment spell. Third, a covariate describing the regional location of the company is measured at the outset of the self-employment spell. The reminder of the covariates, such as age, level of education, marital status, family size and regional unemployment, are treated as time-varying covariates. In addition to these covariates, duration dependence in the exit rates from self-employment is explained with duration time dummies (d t ), one for each year (see notes in Table 1). Year dummies (y j ) are used to capture seasonal changes in the self-employment hazards.

IV. Life-table estimates

Before discussing the estimation results of the discrete time duration model, it will be useful to take a look at some descriptive statistics from our data on self-employment spells in Finland. Table 2 shows the number of self-employment spells started, proportions of selfemployed surviving to the end of the next year and 2002 for each cohort in both types of area (urban and rural).

Firstly, the annual changes in the number of self-employment spells started between 1988 and 2001 are noteworthy. The downward trend in the flows into self-employment in 1989-1992 can be explained by the deep recession of the Finnish economy. The downward trend was more dramatic (and began earlier) in urban than rural areas. Flows into selfemployment increased considerably in 1993. The 1993 tax reform, the so-called dual income tax system, is one of the key factors responsible for this sudden increase. The reform made self-employment more attractive. The new tax system requires that the income of a selfemployed person and the income of the owner of a firm are split into a labour income component and a capital income component [START_REF] Riihelä | Inequality in Finland during 1990s', in Down from the Heavens, up[END_REF]. A progressive tax rate on capital income was also replaced by a flat rate of 25 percent (currently 28%), but labour Table 3 presents the life-table estimates of self-employment survival and hazard rates for urban and rural areas. The hazard rate is defined as the probability that a self-employed individual who has survived to the beginning of an interval will experience a terminal event in an interval of one year. We can see that the hazard rate is around 24 percent in the first year of self-employment spell in both areas. Over the next two years, the hazard rate drops more in rural than urban areas. Hazard rates continue to decrease as spells get longer, falling to only 3-5 percent during the last interval (so called negative duration dependence). Interestingly, it seems that hazard rates are considerably lower in rural areas compared with urban areas at the Comparison of the survival functions also indicates a statistical difference between the two areas. The observed level of significance for the Log-rank test that the survival distributions are the same for both areas is less than 0.001, leading us to reject the null hypothesis that the distributions do not differ.7 A comparison of the mean survival times also shows considerable differences. The estimated mean survival time is 8.49 years for urban areas and 8.66 years for rural areas. 8 As we can see from Table 3, an estimate of the median survival time is four years in both areas.9

V. The determinants of self-employment duration

Table 4 displays the results obtained from the discrete time hazards models. 10 A variable with a positive coefficient is associated with an increased hazard rate and decreased survival time, while a variable with a negative coefficient is associated with a decreased hazard rate and increased survival time.

Three model specifications are given that differ in the specification of the baseline hazard in terms of the rural variable. The first and simplest specification allows us to test whether hazard rates are universally at different levels in rural and urban areas regardless of the duration of self-employment. The second specification is general in the sense that the baseline hazard is allowed to be completely different in rural and urban areas, thus enabling us to study regional differences in duration dependence. That is, do hazard rates in rural and urban areas differ at each duration time point? Finally, a more parsimonious model specification (3) is presented, which is used to test the hypotheses that (i) hazard rates are lower in rural than urban areas at the beginning of a selfemployment, and

(ii) hazard rates are lower in urban areas than in rural areas in the latter part of the spell.

Before presenting our conclusions regarding these hypotheses, we briefly discuss other results, which turned out to be robust to the specification of duration dependence.

Of the personal characteristics, gender and age behaved as expected. Men have a higher probability of remaining in business than women. Young and old self-employed individuals show a higher propensity to leave self-employment than their middle-aged counterparts. The estimates suggest that exit rates are lowest when a self-employed individual is in her/his forties. The results on the effect of education support the hypothesis that higher education increases duration of self-employment. The language variable did not quite reach statistical significance in all specifications. Hence, contrary to our expectations, we did not find that the Swedish-speaking minority has a significantly higher probability of remaining in business than the Finnish-speaking majority. Marriage increases the duration of selfemployment substantially, while having children does not seem to have an impact. These results at least partly strengthen the importance of family support.

Initial wealth seems to have an impact on self-employment duration: both house ownership and the family's income level prior to the self-employment spell lower the exit rates and thus increase length of self-employment. Differences in exit rates by prior activity and experience also merge. The estimated effect of previous labour market status shows that 10 As our data include multiple self-employment spells experienced by single individuals, the standard errors are adjusted to allow for the same individuals being repeatedly at risk. In addition, the hazard rates are allowed to differ according to the experience of previous self-employment spells. [START_REF] Carrasco | Transitions to and from Self-Employment in Spain: An Empirical Analysis[END_REF]. Experience of migration before entering self-employment increases hazard rates, as was expected. Industry also plays an important role in self-employment duration.

Individuals self-employed in transport, storage or communications and private services have slower exit rates than individuals in manufacturing. On the contrary, in the hotel and restaurant industry the exit rates from self-employment are greater than in manufacturing.

What is surprising is the result that prior self-employment experience has a significant negative effect on self-employment duration. For example, [START_REF] Taylor | Survival of the Fittest? An Analysis of Self-Employment Duration in Britain[END_REF] found previous business experience to be an important determinant of survival in Britain. On the other hand, many individuals alternate between self-employment and other labour markets states in Finland [START_REF] Tervo | Self-Employment Dynamics in Rural and Urban Labour Markets[END_REF], and for these individuals previous self-employment spells do not inevitably predict a high probability of remaining self-employed. However, an individual's self-employment duration increases if her/his father has been self-employed. Although the estimated effect of mother's self-employment does not reach significance, these results

suggest the importance of early life experience.11

Turning now to our main question, the effect of environment on self-employment duration, the results of the first specification show that the location (urban vs. rural) does not seem to have a universal effect on exit rates. As regards local unemployment, we do not find evidence that high unemployment in the region forces self-employed individuals to continue in self-employment. Instead, we find that a rise in the local unemployment rate increases exits from self-employment. The preceding descriptive analysis based on follow-up life-tables showed that hazard rates are on average lower in rural areas compared with urban areas at the beginning of a spell, but might be even slightly higher at later intervals. The second specification allows us to study whether these findings still hold after other factors have been controlled for. The estimation results are in line with the descriptive analysis. Figure 1 shows the predicted hazard rates for a typical self-employed individual (median observation). 12 We can see that the longer this individual remains self-employed the smaller are the hazard rates in both areas.

However, the hazard rates for the second and the third year of the spell are considerably lower in rural areas than in urban areas. 13 Finally, the third specification lends further support to our findings. The estimated coefficient on the covariate rural

VI. Conclusion

This paper showed that self-employment duration depends on many factors. Environmental factors and circumstances in the local labour market also have resonance, but this effect is not straightforward. The survival functions between rural and urban areas differ. On average, survival times are longer in rural than urban locations. Rural areas as compared to urban areas 12 Hazard rates have been predicted using Model 2 estimates in Table 4 and sample median values for covariates. That is, the self-employed individual is a 40-year-old married male with children, whose native language is not Swedish. He is a house-owner and has secondary education. Before the current self-employment spell in wholesale or retail trade he was in paid employment with an annual income of 13,300 €. He did not move or was not previously self-employed and his spouse's annual income was 5,200 €. His parents have not been self-employed. The regional unemployment rate is 15.1%, it has fallen by 4.8% and year is 1997. 13 The negative estimated coefficients of the covariates rural× d j (j = 1, 2, 3, 4) suggest that exit rates are lower in rural areas compared with urban areas during the first four years of self-employment. The reverse seems to hold for most of the remainder of the spell (t S 5). in Finland are characterized by weaker employment conditions. Self-employment is also on a higher level in rural areas.

Our estimation results showed that, after controlling for other factors, the location does not have a universal effect on exit rates from self-employment, but after separating the lengths of the spells significant effects were found. Rural areas have lower hazard rates in the first years of spells, while urban areas may even have slightly lower rates in spells lasting at least five years. Long-lasting self-employment spells are, however, much rarer than short spells.

These results would suggest that the push effect is strong in rural locations: aside from the fact that labour markets with weak paid-employment opportunities push workers into selfemployment they force individuals to continue in self-employment, even if the firm did not turn out to be very profitable in the first place. If the firms survive the difficult first years, hazard rates will be considerably smaller thereafter.

F

  the Longitudinal Employment Statistics File constructed by Statistics Finland. Since 1987, these files have been annually updated. These two register-based data sets, together with some other registers, provide panel data on each resident of Finland, from which a 7 percent random sample has been taken for this study. The longitudinal data allow us to observe transitions into self-employment and how long self-employed individuals remain in business in 1987-2002. The individual level panel data were pooled into a sample of self-employment spells that began during the period 1988-2001. The sample consists of 19,439 spells from 16,867 different individuals. The maximum observed duration of a

  Self-employment duration is modelled using discrete time survival analysis and results are discussed in Section V. Finally, concluding remarks bring the paper to an end.

  returns, these returns will be subject to a constant process of adjustment. Individuals' perceptions of their returns may also suddenly alter in response to change in certain important factors.

  We have in use a 7 percent random sample of those individuals who resided permanently in Finland in 2001. The data set includes thousands of variables from the Longitudinal Census File, Longitudinal Employment Statistics and other registers from the period 1970-2002. The individual level panel data were transformed and pooled into a sample employment spells that began during the period 1988-2001. Due to interval censoring,

  way the sample consists of 19,439 self-employment spells. If spells in primary production had also been included, the number would have been 26,668. Note that we place no restrictions on the number of self-employment spells per person. Our sample consists of all the spells of 16,867 different individuals, 2,264 (13.4%) of whom have two or more transitions into self-employment during the period1988-2001.

  Finland uses a classification which divides Finland's municipalities (448 in 2000) into three categories: urban-type municipalities (68 in 2000), densely populated municipalities (75 in 2000) and rural-type municipalities (305 in 2000); see Statistics Finland 2001. This classification is based both on the degree of urbanisation of the municipality and on the population of the largest urban settlement.

  next period, given that an individual has survived in business up to the current period.

  taxed on progressive schedule[START_REF] Saarimaa | Taxation and Debt Financing of Home Acquisition: Evidence from the Finnish 1993 Tax Reform[END_REF]. Another explanation for this rise in the flows to self-employment relates to mass unemployment. Since 1984, the Finnish government has provided financial assistance to unemployed job-seekers who set up a new business. In response to the mass unemployment caused by the recession, the number of the start-up grants awarded more than doubled in 1993. Since 1993, there has been a marginally declining trend in the number of started self-employment spells in both types of location.Secondly, the proportions of self-employed individuals surviving to the end of the next year are presented. On average, around 76 percent of those who entered self-employment in 1988-2001 were still self-employed at the end of the following year. The average survival rate is very similar in both rural and urban areas. The survival rates vary more substantially from year to year. The rates dropped during the deep recession, but have increased markedly in recent years. For example, the survival rate was around 71 percent for spells starting in 1992, whereas it was over 85 percent for spells starting in 2001. Finally, survival rates to the end of 2002 are given for spells originating in 1988-2001. We can see that of the selfemployment spells starting in urban (rural) areas in 1988 only 18.2 (17.3) percent survived to the end of 2002. Since 1996, these survival rates have been higher in rural than in urban areas.

  spell (i.e. during the first 4 years), but do not differ much during the later intervals (or are even slightly higher in rural areas).

  in paid employment prior to the self-employment spell were more successful in remaining self-employed than those who were unemployed or students (cf.

×

  is significantly negative. This implies that exit rates are significantly lower in rural areas than in urban areas when a self-employment spell has lasted less than five years. The estimated coefficient on the covariate rural

  hazard to vary freely with duration time t (see e.g.[START_REF] Meyer | Unemployment Insurance and Unemployment Spells[END_REF]). 3 That is, the full set of 's are estimated by adding an indicator variable per duration time t to the model.4 The model can be further generalized by allowing the baseline hazard to differ

	allowing the baseline between populations. In this study we are particularly interested in whether it varies between
	rural and urban regions. Therefore, we allow the 's to be different for self-employed persons
	living in rural and urban areas.
		If i d is the observed duration of the ith self-employment spell (completed or censored)
	and i c is an indicator variable equal to 1 if the spell is completed and 0 if it is censored, then F r o the contribution of the ith spell to the log-likelihood is given by
										[	P ] [	]	[	]
											e
											e r
												R
												e
												v i e
												w
												)
	where	( t	)	=	ln	t t	+1	( u	)	du	summarises the pattern of duration dependence in the interval
	hazards ( i h ), and the hazard rate is specified by a complementary log-log distribution (Type I
	extreme value). Below the discrete time duration model is estimated semi-parametrically by
												13

Table 3 .

 3 Life-table estimates of self-employment: survival and hazard rates, % Notes: Estimated mean survival time was 8.49 years for urban areas and 8.66 years for rural areas. Estimated median survival time is 4 years for urban and rural areas. Log-rank test for the equality of the survivor functions: 2 = 17.03 with d.f. = 1 (p < 0.001).

	Interval		Urban areas			Rural areas
	start time (years)	Number of observations	Survival rate, %	Hazard rate, %	Number of observations	Survival rate, %	Hazard rate, %
	1	11,631	75.7	24.3	7,808	75.8	24.2
	2	8,203	61.8	18.3	5,534	63.6	16.2
	3	6,167	52.6	15.0	4,310	55.1	13.3
	4	4,779	46.7	11.3	3,442	48.9	11.2
	5	3,817	42.0	10.0	2,800	44.0	10.0
	6	3,058	38.3	8.8	2,288	39.7	9.7
	7	2,475	35.4	7.5	1,864	36.4	8.4
	8	1,956	32.6	7.9	1,508	33.4	8.2
	9	1,517	30.7	5.8	1,161	31.4	6.0
	10	1,136	29.0	5.7	857	29.6	5.6
	11	884	27.1	6.5	657	27.7	6.5
	12	628	25.7	5.1	483	26.4	4.8
	13	392	24.2	5.9	282	24.9	5.7
	14	165	23.5	3.0	116	23.6	5.2

Table 4 .

 4 Parameter estimates of the discrete time duration models

	Covariate			Model 1 Coeff. (Std.err.)	Model 2 Coeff. (Std.err.)	Model 3 Coeff. (Std.err.)
	I Region-specific factors
	Rural					-0.032	(0.021)
	Rural	×	4 1	d	t			-0.056*	(0.023)
	Rural	×	14 5	d	t		0.068	(0.044)
	Unemplev			0.002	(0.003)	0.002	(0.003)	0.002	(0.003)
	Unempcha			0.119** (0.039)	0.113** (0.039)	0.115** (0.039)
	II Personal and household characteristics
	Female				0.126** (0.022)	0.127** (0.022)	0.127** (0.022)
	Swedish				-0.093*	(0.047)	-0.092	(0.047)	-0.092	(0.047)
	Age					-0.102** (0.007)	-0.102** (0.007)	-0.102** (0.007)
	Age2					0.123** (0.009)	0.123** (0.009)	0.123** (0.009)
	Marri					-0.260** (0.031)	-0.260** (0.031)	-0.261** (0.031)
	Childr				0.038	(0.027)	0.038	(0.027)	0.039	(0.027)
	Interedu				-0.069** (0.023)	-0.070** (0.023)	-0.070** (0.023)
	Highedu				-0.109** (0.028)	-0.108** (0.028)	-0.108** (0.028)
	III Assets
	Income				-0.049** (0.010)	-0.049** (0.010)	-0.049** (0.010)
	Spincome			-0.024** (0.009)	-0.024** (0.009)	-0.023** (0.009)
	House				-0.206** (0.022)	-0.206** (0.022)	-0.205** (0.022)
	IV Prior activity and experience
	Unempl				0.287** (0.027)	0.287** (0.027)	0.287** (0.027)
	Studen				0.230** (0.026)	0.231** (0.026)	0.231** (0.026)
	Migrat				0.174** (0.042)	0.175** (0.042)	0.174** (0.042)
	Entrexpe				0.132** (0.022)	0.132** (0.022)	0.132** (0.022)
	Entrfath				-0.140** (0.030)	-0.141** (0.030)	-0.141** (0.030)
	Entrmoth			-0.054	(0.029)	-0.054	(0.029)	-0.054	(0.029)
	V Industrial sector (reference category manufacturing)
	Trade				0.064	(0.038)	0.064	(0.038)	0.064	(0.038)
	Hotel					0.232** (0.049)	0.232** (0.049)	0.232** (0.049)
	Building				-0.030	(0.043)	-0.030	(0.043)	-0.030	(0.043)
	Transpor				-0.765** (0.060)	-0.766** (0.060)	-0.767** (0.060)
	Businser				0.020	(0.050)	0.020	(0.050)	0.020	(0.050)
	Otherser				-0.290** (0.049)	-0.290** (0.049)	-0.290** (0.049)
	Otherind				0.682** (0.037)	0.682** (0.037)	0.682** (0.037)

Table 4 .

 4 (Continued) Notes: Standard errors are adjusted for clustering at the individual level. Number of observations: 79,918. Variable definitions are given in Table1. * (**) = Statistically significant at the 0.05 (0.01) level. Predicted hazard rates in urban and rural areas (Model 2 in Table4)

	Covariate	Model 1 Coeff. (Std.err.)	Model 2 Coeff. (Std.err.)	Model 3 Coeff. (Std.err.)
	VI Duration dummies
	0.609** (0.151) 0.345* (0.154) 0.205 (0.156) 0.040 (0.157) -0.018 (0.159) -0.047 (0.161) -0.153 (0.164) -0.056 (0.166) -0.286 (0.175) -0.292 (0.181) -0.111 (0.185) -0.344 (0.204) -0.115 (0.226) -0.331 (0.338) VII Year dummies (reference category 1989) 0.606** (0.152) d 1 0.393* (0.155) d 2 0.253 (0.157) d 3 0.037 (0.159) d 4 -0.029 (0.162) d 5 -0.106 (0.165) d 6 -0.214 (0.170) d 7 -0.089 (0.174) d 8 -0.319 (0.187) d 9 -0.305 (0.197) d 10 -0.136 (0.204) d 11 -0.335 (0.233) d 12 -0.104 (0.261) d 13 -0.588 (0.472) d 14 -0.003 (0.031) Rural× d 1 -0.135** (0.044) Rural× d 2 -0.131* (0.054) Rural× d 3 -0.002 (0.067) Rural× d 4 0.016 (0.079) Rural× d 5 0.125 (0.091) Rural× d 6 0.126 (0.109) Rural× d 7 0.064 (0.121) Rural× d 8 0.065 (0.161) Rural× d 9 0.021 (0.190) Rural× d 10 0.048 (0.203) Rural× d 11 -0.034 (0.274) Rural× d 12 -0.037 (0.325) Rural× d 13 0.524 (0.604) Rural× d 14	0.629** (0.152) 0.365* (0.155) 0.226 (0.156) 0.061 (0.158) -0.049 (0.159) -0.079 (0.161) -0.185 (0.164) -0.088 (0.166) -0.318 (0.175) -0.324 (0.181) -0.143 (0.185) -0.376 (0.205) -0.147 (0.227) -0.363 (0.338)
	y 1990 y 1991 y 1992 y 1993 y 1994 y 1995 y 1996 y 1997 y 1998 y 1999 y 2000 y 2001 y 2002	0.114 0.149 0.164* 0.195* -0.001 0.117 0.084 -0.149* -0.193** (0.070) (0.068) (0.091) (0.079) (0.080) (0.075) (0.074) (0.073) (0.071) -0.248** (0.069) -0.242** (0.067) -0.271** (0.068) -0.863** (0.074)	0.119 0.159 0.168* 0.197* -0.001 0.119 0.086 -0.149* -0.193** (0.070) (0.068) (0.091) (0.079) (0.080) (0.075) (0.074) (0.073) (0.071) -0.248** (0.069) -0.242** (0.067) -0.270** (0.068) -0.862** (0.074)	0.115 0.155 0.165* 0.195* -0.002 0.116 0.083 -0.150* -0.195** (0.070) (0.068) (0.091) (0.079) (0.080) (0.075) (0.074) (0.073) (0.071) -0.250** (0.069) -0.243** (0.067) -0.272** (0.068) -0.864** (0.074)
	Log-likelihood	-30,276.0	-30,267.0	-30,272.6

30 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

We combined densely populated municipalities with rural rather than with urban municipalities, since the first two areas have greater similarity in their population densities. The population densities of the densely populated and rural municipalities were 25 and 10 inhabitants per km 2 in 2000, whereas the corresponding figure for the urban municipalities was

inhabitants per km 2 .

That is, our discrete time duration model corresponds to the continuous time Cox proportional hazards model, but the estimates of the baseline hazard are derived directly as part of the estimation procedure.

If a constant term is included in X, one of the interval-specific dummy variables needs to be removed from the model specification.

Guidelines for practical implementation are given, for example, in[START_REF] Jenkins | Easy Estimation Methods for Discrete-Time Duration Models[END_REF].

Note that since the analysis is conditioned on a set of covariates X, then duration is implicitly a function of the entire time path of the variable X(t), t = 1, 2,…, which may have changed during the interval[START_REF] Greene | Econometric Analysis[END_REF].

The same result is obtained with the Kaplan-Meier survival analysis designed for continuous time duration analysis. Wilcoxon and Breslow tests also suggested that we should reject the null hypothesis that the survival functions are the same for the two areas.

In order to account for censoring, survival functions were exponentially extended to zero when computing the estimated mean survival times.

Average hazard rates can also be computed for the two areas. The average hazard rate is 0.151 for urban areas and 0.143 for rural areas.

We also tried out more general specification, which included parents' education as additional variables. Since their estimated coefficients were very small and insignificant, they were dropped from the final specification.

Acknowledgements

The authors would like to thank session discussants at the 52 nd North American Meetings of the Regional Science Association International, Las Vegas (10-12 November 2005), 45 th Congress of the European Regional Science Association, Amsterdam ( 23-27 August 2005), and ONS Analysis of Enterprise Microdata Conference, Cardiff (7-9 September 2005) for their useful comments. The paper forms part of a Research programme on Business Knowhow (LIIKE 2, project no. 112116) financed by the Academy of Finland.

Using information from 1970, 1975, 1980 and 1985.