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Sectoral imbalance and unemployment in the United Kingdom: 1963-84.

The high levels of unemployment in the UK, and much of Europe, in the early and mid-1980s have attracted considerable interest. The central question which we consider in this paper is whether the increase in the UK unemployment rate in the late 1970s and the 1980s was in part attributable to an increase in sectoral imbalance in the labour markets.

The possible importance of labour market imbalance in affecting the level of unemployment has been known since the early discussions of Lipsey (1960) and Archibald (1969) concerning the aggregate Phillips curve. Recent empirical discussions of labour market sectoral imbalance in the UK, using annual data, are provided by Jackman, Layard and Pissarides (1989), Jackman and Roper (1987), and Jackman, Layard and Savouri (1991).

As has long been recognized, increases in sectoral imbalance can lead to an adverse shift in the trade-off between unemployment and vacancy rates. Evidence of a shift in the UV (unemployment-vacancy rate) curve in the UK, for the period here studied, can be seen in Fig. 1. This paper re-examines the UV curve and goes beyond previous empirical research in the following respects:(1) (i) quarterly measures of regional and industrial imbalances are constructed; (ii) an attempt is made to correct for cyclical influences on imbalance measures; and (iii) the data are used to estimate the degree to which changes in sectoral imbalance affect the position of the UV curve and, in particular, to assess the extent to which the observed increases in industrial imbalance explain the rise in UK unemployment which began in 1980.(2)

1.Methodology

1. 1. Theoretical background

In conventional macroeconomics models which combine aggregate demand and supply equations, sectoral imbalance affects the system via the aggregate supply side. For example, in a stochastic disaggregated model with temporary sectoral wage floors and a gradual movement of labour between sectors, Evans (1985, 1989) showed that the position of the aggregate supply curve, in both the short-run and the long-run, depends upon the extent of imbalance between sectors. The degree of imbalance, which is increased by random sectoral shocks and diminished by equilibrating changes in sectoral wages and labour supplies, is appropriately measured, in the stochastic steady state, by the standard deviation of sectoral excess demands for labour, computed at the (temporary) nominal wage floors.

In the formulation just described, an increase in aggregate demand leads, in the short run, to a decrease in unemployment in excess supply sectors and an increase in wages and prices in excess demand sectors. There is no role for vacancies because of the assumed upward flexibility of wages.

Both labour market unemployment and vacancies arise if instead wages are assumed to be predetermined, i.e. temporarily inflexible in both directions. A dynamic disaggregated general equilibrium model along these lines appears to be intractable. However a partial equilibrium analysis of the aggregate supply side using this framework, as in Hansen (1970), shows that the position of the aggregate unemployment rate - vacancy rate curve (UV curve) - depends on the degree of sectoral imbalance. Thus neutral variations in aggregate demand now lead to movements along the UV curve, while a change in sectoral imbalance, which can again be measured by the standard deviation of sectoral excess demands for labour, affects the position of the UV curve.(3) This is the basic framework used for the empirical analysis in Section 3. In the econometric results reported in that section, a time trend is also included to allow for shifts in the UV curve due to other factors.

1.2. The basic measure of imbalance

Based on the above discussion, we choose our basic sectoral imbalance measure as S = AD(ln([D.sub.i]/[L.sub.i])).100 where [D.sub.i] = [N.sub.i] + [VA.sub.i] = labour demand in sector i and [L.sub.i] = [N.sub.i] + [UN.sub.i] = labour supply in sector i.(4) Here [N.sub.i] = number of persons employed in sector i, [VA.sub.i] = number of vacancies in sector i, [UN.sub.i] = number of unemployed in sector i, and AD represents the average deviation(5) with labour force weights, i.e.

[Mathematical Expression Omitted] where

[Mathematical Expression Omitted] This measure of sectoral imbalance thus calculates the average deviation across sectors of the percentage difference between labour demand and labour supply. Using the approximation ln(1 + x) = x for small x it can be seen that S is approximately equal to the average deviation of the net unemployment rate ([UN.sub.i] - [VA.sub.i])/[L.sub.i].

The measure S calculates imbalance as a proportion of the labour force in each sector and therefore has the property that a neutral change in the aggregate demand for labour, i.e. one in which the demand for labour in each sector changes by the same percentage, leaves S unchanged. Alternative measures of `structural imbalance' are given in Jackman and Roper (1987).(6) Measures based on different transformations of sectoral unemployment and vacancy data have the disadvantage, from the viewpoint of the previous section, that they are not invariant to even neutral changes in aggregate labour demand. Other measures, such as the dispersion of employment growth introduced by Lilien (1982), estimate thE magnitude of sectoral shocks, but do not measure the overall state of labour market imbalance nor (without additional assumptions) the contribution of the shocks to the state of imbalance.

1.3. Data

We consider separate measures of sectoral imbalance, computed quarterly, based on regional and on industrial data. Regional imbalance is calculated using data from nine geographical regions and covers the period 1965:2-1984:4. Industrial imbalance is based on a 24 sector industrial classification and is available for 1963:1 to 1982:4 (publication of unemployment data by industry group ended after 1982). A listing of regions and of industrial sectors is provided in Evans (1988). Data sources and further details are given in Appendix 1.

There are several problems with the data of which two should be noted. First, a substantial fraction of vacancies are not reported. The data on vacancies have been adjusted for non-notification by factors which depend on both the sector and the period to obtain an estimate of true vacancies. Second, a significant segment of the unemployed are not classified by industry. These unclassified unemployed have been assumed to be distributed across industries in the same proportion as the labour force.(7) See Appendix 1 for further discussion.

1.4. Correction for cyclical sensitivity

Although the index S is by design invariant to neutral changes in the aggregate demand for labour, the measure can exhibit a cyclical pattern if (i) changes in aggregate output are systematically non-neutral in their sectoral impact and (ii) there is a correlation across sectors between the elasticities of labour demand with respect to aggregate output and the net unemployment rates. In particular, a positive correlation would lead to S behaving countercyclically, so that demand driven fluctuations in the unemployment rate might be mistakenly attributed to changes in sectoral imbalance. A similar argument was made by Abraham and Katz (1986) concerning the Lilien (1982) measure of sectoral shifts.

An attempt was made to deal with this point by directly estimating the sectoral elasticities of labour demand with respect to aggregate output and using these to remove the effects on S of variations in aggregate output. The procedure is described in Appendix 2.

2. The sectoral imbalance measures

2.1. Estimates of sertoral imbalance

Figures 2 and 3 plot the quarterly estimates of [SI.sup.*] and [SR.sup.*], the cyclically corrected imbalance measures for the industry and regional breakdowns, respectively, together with data on the UK aggregate unemployment rate U. Two main points emerge from the figures. First, both [SI.sup.*] and [SR.sup.*] show substantial variation over the period and are at their highest levels at the end of the period. Second, while [SR.sup.*] does not show a clear systematic relationship with U, the timing of the large increase in [SI.sup.*] does closely match the increase in U which began in 1980.

2.2. Discussion of the cyclical corrections

The sizes of the cyclical corrections themselves are in most cases not large. The biggest correction occurs for the industry imbalance measure in 1982:3 which yields a value of [SI.sup.*] 17% lower than the unadjusted measure SI. However, in many cases, particularly over the pre-1980 period, the adjustment is small or negligible. The principal effect of the adjustment is to reduce the size of the increase of SI in the 1980s.

There are several possible reasons for the typically small sizes of the cyclical corrections. First, for both regions and industries there is a low (weighted) correlation of estimated elasticities with the average net unemployment rates across the sample: 0.066 for regions and 0.053 for industries. As a result, the effects of the level of aggregate output Q on S should be essentially second order.(8) A second possible reason is that labour market adjustments may largely eliminate those sectoral imbalances which arise from movements in Q. This will particularly be expected if changes in Q are not too fast and regarded as permanent rather than transitory. Third, over the sample period pure aggregate demand shocks may have been much less important than sectoral shocks in determining S.

Finally, it may be that our procedure for cyclical correction is inadequate.(9) We therefore check the robustness of our findings to this possibility in two ways. Appendix 2 shows that the substantial increase in [SI.sup*] in the early 1980s cannot plausibly be due to cyclical factors, even if the estimation errors of the elasticities are large. Section 3.2 shows that our estimates of the effect of [SI.sup.*] on the U V curve are not due to omitted aggregate demand channels.

2.3. Source of increase in [SI.sup.*]

What are the sources of the dramatic increase in [SI.sup.*] beginning in 1980:1? Although we will not attempt to give an explanation in terms of fundamental factors, it is possible to give an accounting of the sectors responsible for the increase in industrial imbalance. The increase in [SI.sup.*] essentially occurred between 1979:4 and 1981:1, over which period [SI.sup.*] more than doubled from 1.54 to 3.83. Most of this increase was accounted for by four industrial sectors: construction (36.6% of the increase); professional and scientific (31%); metal manufacturing (7.8%); and insurance and banking (7.4%).

Table 1 gives some details of the accounting. In particular, note that between these periods the difference between the (corrected) excess supply of labour in construction and the average for all sectors increased from 5.2% in 1979:4 to 17.9% in 1981:1, while for professional and scientific (which has over twice as great a weight in terms of labour force) the (corrected) excess demand for labour moved from 1.8% to 6.2% above the average for all sectors. As already indicated, only a modest amount of the relative shift in net labour demand is ascribed to a normal cyclical response to the recession itself.(10)

[TABULAR DATA OMITTED]

3. Effect of imbalance on the UV curve

3.1. Main econometric results

We now consider whether variations in the imbalance measures can explain the behaviour of the UV curve in the UK over the 1963-1984 period, and in particular the increase in the aggregate unemployment rate beginning in 1980. We use the framework described in Section 1.1. Thus changes in aggregate demand lead to movements along the UV curve, with increases in demand leading to lower unemployment and higher vacancy rates. Changes in sectoral imbalance shift the position of the UV curve, with higher measures of imbalance leading to a higher unemployment rate at each vacancy rate. Variations in frictional and other factors (e.g. benefit ratios, employment taxes, social stigma of unemployment) may also lead to shifts in the position of the UV curve, and we include a time trend to capture any secular change in these influences (Jackman et al., 1989, argue that the positive time trend which they find should be interpreted as a diminishing intensity in search for work).

Preliminary investigation of alternative specifications established the following points: (i) the effect of industrial imbalance SI* on the level of the unemployment rate U (conditional on the vacancy rate) is, as expected, positive and statistically significantly different from 0; (ii) the size of the effect of SI* on U is, however, quite sensitive to the functional form; and (iii) there is no support for a separate adverse affect on U of regional imbalance SR*, since the estimated coefficients on SR* are negative, small and insignificantly different from zero when SR* is included together with SI*. (For further discussion of the role of SR* see Appendix 3.)

In view of these results, SR* was dropped from further analysis and the econometric investigation focussed on estimating the size of the effect of SI* on the position of the UV curve, allowing for a range of functional forms. Adopting the Box-Cox family of functional forms, the model

[Mathematical Expressions Omitted]

was estimated by maximum likelihood. Here [U.sub.t] is the aggregate unemployment rate for the UK in percent, [V.sub.t] is the aggregate vacancy rate for the UK, in percent and adjusted for under-reporting, SI* is the measure of industrial imbalance corrected for cyclicality, and trend is the time trend in quarters. The notation

[Mathematical Expressions Omitted]

denotes the Box-Cox transformation. Note that [lambda] = 1, [lambda] = 0 and [lambda] = - 1 correspond to linear, logarithmic, and inverse functional forms, respectively.(11) For a discussion of Box-Cox estimation see, for example, Judge et al. (1985).

Comparison of the log likelihoods indicates that four lags are appropriate and the results are reported in Table 2. Several points emerge concerning the functional form. First, when we consider the transformation for U and V, both the linear form (column 2) and the logarithmic form (column 3) are strongly rejected against an intermediate form. Secondly, the transformation for SI* is insignificantly different from 1n(SI*). Thirdly, the estimated functional form for the time trend is insignificantly different from the linear form. In view of these results a restricted model was estimated which imposes L2 = 0 and L3 = 1:

[Mathematical Expressions Omitted]

These results are given in column 4 of Table 2. Also reported are several misspecifications tests of equation (3).

[TABULAR DATA OMITTED]

The presence of a structural break is tested using the Chow covariance statistic (with L1 = 0.706 imposed), the heteroscedasticity statistic is the ratio of sum of squared errors in the two equal sized sub-periods, and autocorrelation is tested using the LM statistics. None of these misspecification tests is significant at the 5% level. (See also Section 3.3 below.) It is clear that (3) is an acceptable restriction of (2).

We now turn to the issue of the magnitude of the shift of the U V curve attributable to the increase in SI*. Solving (3) for its stationary state at U = V we obtain

[Mathematical Expressions Omitted]

for fixed values SI* and T of the imbalance measure and time trend, respectively, and where [Mathematical Expression Omitted]. An analogous formula holds for the general functional form (2).

Over the sample period SI* increased from round 1.5 to about 4.0 at the end of the period. Using (4) we can estimate the magnitudes of the shift in the UV curve (measured at U = V), due to the increase in SI* and due to the time trend, respectively. The results are

[Mathematical Expressions Omitted]

Here the contribution of each variable is calculated by evaluating (4) at the mean of the other variable. Reported in brackets are asymptotic standard errors based on the linearizations of (4) around the estimated parameters.(12)

These results support the hypothesis that the increase in industrial imbalance in the 1980-2 period had a substantial effect on the level of unemployment.(13) The combination of this effect with the adverse time trend yields a shift out of the UV curve, measured at U = V, from an estimated U = 2.4% in 1963 to an estimated U = 6.7% at the end of 1982. The difference between the latter figure and the actual unemployment rate of U = 11.0% in 1982:4 is largely due to the low level of the vacancy rate, V.(14)

3.2. Further results

In this section we report the results of additional econometric estimates as a check on the robustness of the findings of the preceding section. First, we ask if the statistical effect of SI* on the UV curve depends completely on the relatively short period 1980-1982 during which SI* dramatically increased. Re-estimating (3) over the 1964:1-1979:1 period we obtain

[Mathematical Expressions Omitted]

(In the estimates reported in this section L1 = 0.706 is imposed. The reported standard errors are thus conditional on this restriction.) Clearly the effect of SI* remains substantial and statistically well defined. The corresponding Chow prediction statistic is F(15, 42) = 0.64, which is insignificant at the 5% level. (The Chow prediction statistic based just on the final four quarters 1982:1-1982:4 is F(4, 53) = 0.57, which is again insignificant at the 5% level.)

The role of SI* in accounting for shifts in the U V curve is thus statistically established even over the 1964:1-1979:1 period, when the variation in SI* was much smaller (and not of economic importance), and is consistent with its estimated substantial impact over the 1979:2-1982:4 period.

The second issue we consider is whether the results are contaminated by not fully controlling for aggregate demand. That is, is it possible that aggregate demand affects unemployment in part through channels not reflected in vacancy rates (and the estimated dynamics)? If this were the case, and if variations in aggregate demand were also associated with variations in SI* due to an inadequate cyclical correction procedure, then the effect of SI* could be overestimated.

To assess this issue, (3) was re-estimated including current and four lags of real GDP, i.e. [Mathematical Expressions Omitted]. The results

are

[Mathematical Expressions Omitted]

The estimate of [d.sub.i] is small and statistically insignificant and the other coefficients are not substantially altered. The F statistic for exclusion of the GDP variables is F(5, 52) = 0.96, which is also insignificant at the 5% level. Omitted aggregate demand effects thus do not appear to be a problem.

Finally we consider the issue of simultaneity between U and V. Estimation of (3) with [U.sub.t] as the dependent variable implicitly assumes a recursive system in which V is determined by aggregate demand and in which random shocks to the employment sector are reflected in U. This accords with the conventional assumption that V is a more sensitive measure of aggregate demand than U. However, it may well be that U and V are jointly determined. One way of assessing the importance of this point for the problem at hand is to re-estimate (3) with [V.sub.t] as the dependent variable. The results are:

[Mathematical Expressions Omitted]

Rearranging this estimated equation into the format (3) we obtain

[Mathematical Expressions Omitted]

The corresponding estimated shifts in the UV curve (measured at U = V) due to the increase in SI* and the time trend are

[Mathematical Expressions Omitted]

Comparing the results with those of Section 3.1 it can be seen that the basic findings are not substantially influenced by the treatment of simultaneity.

3.3. Behaviour of measures over 1979:4 - 1982:4

Was the increase in unemployment beginning in 1980 initiated by an increase in industrial imbalance or by a fall in aggregate demand which was compounded by increased mismatch? Table 3 provides some information on this point.
                  Table 3
        Behaviour of aggregate measures

Period   U      V      SI*

1976:4   4.80   1.77   1.96
1977:4   5.23   1.98   1.69
1978:4   4.73   2.61   1.64
1979:4   4.56   2.57   1.54
1980:1   5.07   1.97   1.93
1980:2   5.14   1.90   2.17
1980:3   6.01   1.39   2.36
1980:4   7.16   1.06   3.09
1981:1   8.40   0.97   3.83
1981:4   9.81   1.27   3.96
1982:4  10.98   1.35   4.05
1984:4  11.28   1.68   NA

Note: U = Unemployment rate, V = Adjusted
vacancy rate, SI* = Corrected measure of industrial
imbalance.


The period 1979:4 - 1981:1 is marked by an increase in U and SI* but a decrease in V. Because an increase in imbalance should generate increases in both U and V if aggregate demand remains unchanged, this period is most satisfactorily explained through a combination of a demand driven recession with an increase in sectoral imbalance. The increase in SI* over this period can be interpreted either as an autonomous increase in mismatch or as an integral part of an unbalanced recession which is highly atypical of recent cyclical patterns. The period after 1981:1 is marked by increases in both U and V. This is primarily explained by lagged effects of the increase in SI*.(15)

4. Conclusions

A substantial increase in industrial labour market imbalance appears to have occurred beginning in 1980 and is estimated to have accounted for about 2.7 percentage points of a 4.3 percentage point outward shift of the UV curve between 1963 and 1982.

Estimated aggregate output elasticities of sectoral labour demand have been used to compute cyclically corrected imbalance measures and it appears that most of the increase in industrial imbalance cannot be interpreted as a normal response to low levels of aggregate output.

There are several qualifications which must be made concerning our results. First, there are significant deficiencies in the data used to construct the measures of imbalance. Secondly, we are unsure of the appropriate explanation for the lack of a significant positive association of unemployment with regional imbalance. Thirdly, we do not know what has recently happened to SI* since the relevant data are not available subsequent to 1982.

Subject to these qualifications, the results of this paper strongly suggest that increased industrial imbalance was a significant factor in the 1980-2 increase in the unemployment rate. The extent to which subsequent decreases in the unemployment rate are sustainable may depend upon the industrial composition of increased demand and upon any changes in the degree of mobility of workers across industries.

University of Edinburgh

ACKNOWLEDGEMENTS

This research was supported by the Center for Economic Policy Research, Stanford University, and by the Centre for Labour Economics, London School of Economics. Susan Wolcott provided first-rate research assistance throughout most of the project. Tom Wilson also provided substantial assistance at an early stage. I am indebted to S. Roper and the Centre for Labour Economics for the provision of data. Helpful comments were received from Andrew Oswaid and the referees of this journal.

REFERENCES

Abraham, K. G. and Katz, L. F. (1986). `Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances', Journal of Political Economy, 94, 507-22. Archibald, G. C. (1969). `The Phillips Curve and the Distribution of Unemployment', American Economic Review Papers and Proceedings, 59, 124-34. Evans, G. W. (1985). `Bottlenecks and the Phillips Curve: A Disaggregated Keynesian Model of Inflation, Output and Unemployment', Economic Journal, 95, 345-57. Evans, G. W. (1988). `Sectoral Imbalance and Unemployment in the United Kingdom', Centre for Labour Economics Discussion Paper No. 300, London School of Economics. Evans, G. W. (1989). `The Conduct of Monetary Policy and the Natural Rate of Unemployment', Journal of Money, Credit, and Banking, 21, 498-507. Hansen, B. (1970). `Excess Demand, Unemployment, Vacancies and Wages', Quarterly Journal of Economics, 84, 1-23. Jackman, R., Layard, R., and Pissarides, C. (1989). 'On Vacancies', Oxford Bulletin of Economics and Statistics, 51, 377-94. Jackman, R., Layard, R., and Savouri, S. (1991). 'Mismatch: A Framework for Thought', F. P. Schioppa (ed.), Mismatch and Law Mobility, Cambridge University Press, Cambridge, England. Jackman, R. and Roper, S. (1987). `Structural Unemployment', Oxford Bulletin of Economics and Statistics, 49, 9-36. Judge, G. G., Griffiths, W. E., Carter, R. C.. Lutkepohl, H., and Lee, T. (1985). The Theory and Practice of Econometrics, John Wiley and Sons, New York; Second Edition. Layard, P. R. G. and Nickell, S. J. (1986). `Unemployment in Britain', Economica, 53, S121-70. Lilien, D. M. (1982). `Sectoral Shifts and Cyclical Unemployment', Journal of Political Economy, 90, 777-93. Lipsey, R. G. (1960). `The Relation Between Unemployment and the Rate of Change of Money Wages in the United Kingdom, 1862-1957: A Further Analysis', Economica 27, 1-31. Loungani, P. (1991). `Structural Unemployment and Public Policy in Interwar Britain', Journal, of Monetary Economics, 28, 149 59. Loungani, P., Oyer, H. E., and Rush, M. (1992). `Sectoral Shifts and Unemployment in Postwar Britain', mimeo, Federal Research Bank of Chicago.

APPENDIX 1

Data sources

The quarterly regional imbalance figures are calculated from data on unemployment, vacancies and employment by region for March, June, September and December, collected from various issues of the Department of Employment Gazette. `Unemployment' is the total number of registered unemployed, `vacancies' are the numbers notified to job centres or employment offices and remaining unfilled, and employment is 'employees in employment'. All data are seasonally unadjusted. Data are not available for Northern Ireland, and several missing data problems were encountered. described in Evans (1988). In these cases interpolation was used to fill in missing values.

Quarterly data on unemployment, vacancies and employment for the 24 industrial sectors were provided to the author by the Centre for Labour Economics, London School of Economics, and were originally collected from the Department of Employment Gazette. All data are seasonally unadjusted. Some unemployed persons are not classified by industry and thus not included in any of the 24 sectors.

Both regional and industrial vacancy series are adjusted for under-reporting by combining sector-specfic estimates of under-reporting with an annual series which estimates under-reporting of aggregate vacancies. These adjustment factors were obtained from the Centre for Labour Economics, and the adjustment factors and adjustment procedure are described in Jackman and Roper (1987) and in the CLE Discussion Paper version of their study. The annual adjustment series was interpolated to obtain a quarterly series.

The aggregate output series used in the cyclical corrections is GDP at 1980 market prices and was taken from Economic Trends. The aggregate UK unemployment and vacancy rates used in the Section 3 regressions were computed from the 'employed labour force', unemployed excluding school-leavers' and `vacancies at job centres' series (all seasonally unadjusted) reported in the CSO Economic Trends, 1987 Annual Supplement. The number of vacancies was multiplied by the quarterly adjustment factor, as described above' to correct for under-reporting.

The data used in this study are available from the author.

APPENDIX 2

Correction of imbalance measures for cyclicality

For each point in time, and a given sectoral breakdown, we define the 'imbalance curve' by

S'(Q') = AD(ln([D'.sub.i]/[L.sub.i])) . 100 (A1)

where [D'.sub.i] is the estimate of what labour demand in sector i would be at each specified level of real aggregate output Q':

ln [D'.sub.i] = ln [D.sub.i] + [epsilon.sub.i](ln Q' - ln Q) (A2)

Here [epsilon.sub.i] = elasticity of [D.sub.i] with respect to real aggregate output and Q is the observed level of aggregate output.(16) The imbalance curve S'(Q') thus describes what the estimated level of S would have been at varying levels of aggregate output.

Given the imbalance curve at a point in time, the desired summary measure of the degree of sectoral imbalance is given by the minimum of the curve, i.e.

S* = min S'(Q')/Q' (A3)

This measure is a cyclical correction to S in the sense that it extracts from S the degree of imbalance which cannot be attributed to variations in the level of aggregate demand.

A possible alternative to S* would be to use (A1) and (A2) to compute the level of S that corresponds to a measure of trend or potential output. However, in addition to well-known econometric difficulties in obtaining a suitable estimate of the trend, this procedure would not provide the appropriate measure for our purposes since sectoral patterns will to some extent adapt to the current state of economic activity.(17) These objections are avoided by our direct approach (A3) of finding and using the level of aggregate output which corresponds to the minimum degree of imbalance.

To implement the procedure empirically, an autoregressive-distributed lag regression of [delta] ln [D.sub.it] on [delta] ln [Q.sub.t] was estimated for each sector i. C, was then obtained as the estimated long-run effect of [delta] ln [Q.sub.t] on [delta] ln [D.sub.it]. (ln [Q.sub.t] and the ln [D.sub.it] appear to have unit roots but not to be cointegrated.) Evans (1988) reports the estimated [epsilon.sub.i] for industries and for regions. The imbalance curves S'(Q') and the cyclically corrected imbalances S* were then computed numerically, with industrial and regional measures calculated separately as SI* and SR*, respectively.(18)

To check the robustness of the large increase in SI* near the end of the period, seen in Fig. 2, the values for SI* in 1979:4 and 1981:1 were recalculated with the elasticity of the construction sector at 2.013, two standard errors above its point estimate, and the elasticity of the professional and scientific sector set at 0.303, two standard errors below its point estimate. The effect is to reduce SI* from 1.542 to 1.399 in 1979:4 and from 3.829 to 3.371 in 1981:1, but the proportional increase in SI* between the periods is virtually unchanged.

APPENDIX 3

Discussion of the role of regional imbalance

As an illustration of the results obtained when SR* is included in estimated equations, Table A.1 reports the results for the linear specification

[TABULAR DATA OMITTED]

for k = 4. (Further details are available in Evans (1988).)

In both regressions in which industrial imbalance SI* is included the variable shows a strong, well defined, statistically significant positive effect on [U.sub.t]. The estimated effects of the regional imbalance measure SR*, on the other hand, does not provide much support for the importance of SR* on the position of the UV curve. Although when SI* is not included, the sum of the coefficients on SR* has the expected positive sign, the sign of the SR* effect becomes negative when SI* is included. However, when both SI* and SR* are included, the sum of coefficients on SR* is small and not significant at the 5% level. Indeed the magnitude of [c.sub.i], the sum of coefficients on SI*, is 7.8 times as large as the magnitude of [d.sub.i], the sum of coefficients on SR* (the extent of variation over the period in SI* and SR* is comparable). Finally, the F test of the null hypothesis that the SR* variables can be excluded is not significant at the 5% level. It would appear that SR* has only minor explanatory power once SI* is included in the regression.

Experimentation with alternative functional forms failed to yield a satisfactory role for SR* when SI* was included. One possible explanation, which might apply if occupational and regional mismatch moved in opposite directions over the earlier part of the period, is bias in the coefficients on SR* due to omission of the occupational imbalance measure. Unfortunately, occupational imbalance cannot be calculated because occupational employment data are unavailable.

Another possible explanation, suggested by a referee, is that it may be easier for workers to migrate between regions than to change the skills required for them to be employable in those industries with high demand. Then when both variables are included, the regional imbalance effect is dominated by the industrial balance effect. (1) There is also some difference in theoretical orientation. For example, Jackman et al (1989) and Jackman et al, (1991) focus on frictional factors in equilibrium labour markets, whereas the framework for this paper emphasizes the aggregate impact of sectoral imbalance on labour markets in short-run disequilibrium. (2) Layard and Nickell (1986) also estimate the effect of sectoral mismatch on unemployment, but use a proxy for mismatch. (3) Sectoral imbalance is determined by the structure of relative wages, by the sector composition of labour supplies and by productivity and taste parameters determining sectoral labour demands. No attempt is made in this paper to explain changes in sectoral imbalance in terms of these more fundamental factors, only to measure sectoral imbalance and estimate its aggregate impact on the labour market. (4) The empirical sectors used to compute (1) are, of course, regarded as aggregates of markets. (5) The average rather than the standard deviation was chosen to reduce sensitivity to extreme observations, but computations of S based on the standard deviation appear quite similar. Another variation of (1) would be to use labour demand rather than labour supply weights. (6) Jackman and Roper (1987) report annual estimates of S as the measure [I.sub.4]. (7) This somewhat drastic assumption is in practice the most straightforward of the possible alternative treatments. (8) Let VS stand for the variance analog of S and let Q represent the normal level of output (i.e. the level of output corresponding to the average aggregate net unemployment rate). Then VS(Q) = VS(Q) + 2(ln Q - ln Q).Cov + (ln Q - ln [Q).sup.2] V(E) where V(E) measures the weighted variance of elasticities across sectors and Cov measures the weighted covariance across sectors of [E.sub.i] with ln [D.sub.i]-ln [L.sub.i]. Since Cov approximately equals zero, VS(Q) depends on the square of the proportional deviation of Q from normal levels. (9) In addition to the usual sampling and specification errors in the elasticity estimates, the implicit assumption that the dynamics of the adjustment process can be ignored (by using long-run elasticities) may be unsatisfactory. (10) The estimated elasticities (standard errors) for these four sectors are: construction, 1.014 (0.499); professional and scientific, 0.955 (0.326); metal manufacturing, 2.077 (1.836); and insurance (11) The argument sometimes made in favour of the logarithmic versus the linear functional form is that it avoids the potential difficulty of encountering fitted or predicted negative unemployment rates. However, this argument is not persuasive since the problem need not arise in practice and since the central issue for us is which functional form best fits the data within the sample itself. (12) When the linear specification is imposed (column 2) the estimated magnitudes for the shifts are [delta][U.sub.SI] = 3.72 and [delta][U.sub.T] = 1.50, while when the log-linear specification is imposed (row 3) we obtain [delta][U.sub.SI] = 0.58 and [delta][U.sub.T] = 1.79. Although the linear specification has a higher likelihood than the log-linear, both are decisively rejected by the data. For the unconstrained estimates (row 1) we have [delta][U.sub.SI] = 2.654 (0.215) and [delta][U.sub.T] = 1.566 (0.095). Our results thus indicate that the log-linear form greatly underestimates, and the linear form somewhat overestimates, the extent to which the increase in U, beginning in 1980, was due to a shift in the UV curve. (13) The effect attributed to SI* is presumably capturing shifts in the UV curve due to correlated increases in industrial imbalance occurring at finer levels of aggregation as well as those explicitly measured by our 24-sector breakdown. The effect may also in part be due to correlated increases in occupational imbalance during this period. Although the relevant measure of occupational imbalance cannot be computed, the related index [I.sub.2] reported in Jackman and Roper (1987) suggests that occupational imbalance may have increased over 1980-1982. (14) Using (3) we find that the equilibrium level of U which would be associated with values of SI*, V and T fixed at their 1982:4 levels is 12.3%. Lagged adjustment accounts for virtually all of the remaining difference from the observed value of U (the residual error for 1982:4 is less than 0.1 percentage points). (15) Recent work by Loungani, Oyer and Rush (1992), which came to my attention after this paper was completed, also supports the importance of industry mismatch. Their complementary approach measures the intensity of sectoral shocks using a measure of stock market dispersion. See also Loungani (1991). (16) The elasticities [epsilon.sub.i] are reduced form parameters which are composites of underlying taste parameters from the demand side and production parameters from the supply side. (17) Indeed, experimentation with various measures of trend output to compute S' based on (A1) and (A2) showed that such `corrections' often increased the estimated sectoral imbalance. (18) The Q* measure associated with SI* exhibits the expected cyclical pattern although the magnitude of Q*/Q is less than one might have expected (e.g. Q*/Q = 1.034 in 1982:3). For SR* the cyclical pattern of Q*/Q is weaker.
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Author:Evans, George W.
Publication:Oxford Economic Papers
Date:Jul 1, 1993
Words:6204
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