Modelling and forecasting regional service employment in Great Britain1

Economic Modelling 16 Ž1999. 429]453

Modelling and forecasting regional service employment in Great Britain q Nicholas Sarantis a,U , Caspar Swales b a

Department of Economics, London Guildhall Uni¨ ersity, 84 Moorgate, London EC2M 6SQ, UK b Northern Ireland Ci¨ il Ser¨ ice, DFP Economics Di¨ ision, Belfast, N. Ireland, UK

Abstract This paper attempts to forecast employment growth in the service sector, on a regional basis across Great Britain. Four forecasting models are used: Time-varying parameters, regression, state space, and ARIMA. The empirical results suggest that the regional growth rates in service employment displayed a steady convergence during the 1980s, but deconvergence in the 1990s, and that the composite leading indicator exerted a strong influence on regional service employment. In terms of out-of-sample forecast accuracy, none of the models dominates the others, though the state space model has a slight edge on average, particularly in the case of multiperiod predictions. In addition, the relative forecasting performance of a professional structural model of the GB regions is compared to the estimated models. Q 1999 Elsevier Science B.V. All rights reserved. JEL classifications: J23; J44; R23; C53 Keywords: Service employment; Regional; Forecasting

1. Introduction This paper is an attempt to forecast employment growth in the service sector, on a regional basis across Great Britain,1 using seasonally unadjusted employment q

Previous versions of this paper have been presented to the Joint Seminar Series, Economics Department and NIERC, Queens’ University of Belfast, Northern Ireland, 8 December 1995, and the 27th Annual Conference of the Regional Science Association International, British and Irish Section, 23]25 September 1996, Edinburgh. We are grateful to the participants at those meetings and to an anonymous referee for their helpful remarks and suggestions. U Corresponding author. Tel.: q44-171-320-1411; fax: q44-171-320-1498; e-mail: [email protected] 0264-9993r99r$ - see front matter Q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 2 6 4 - 9 9 9 3 Ž 9 9 . 0 0 0 0 9 - 7

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data over the period 1978Q2]1993Q4.2 Fig. 1 shows a strong upward trend in the share of service employment to total employment in Great Britain ŽGB.. This share jumped from 57% at the late 1970s to 73% by 1993. Fig. 2 suggests a high degree of cross-region variation in the growth rates of service employment. The gap between the highest and lowest growth rates has been widening since the early 1980s, with the widest gap observed during the recession of the early 1990s. The disparity in service sector employment performance across regions can also be seen from Fig. 3. The standard deviation of cross-region service employment growth rates exhibits sharp fluctuations, particularly since the late 1980s, and a small upward trend. Given that service employment now represents just over three-quarters of total employment in the UK Ž1993 Census of Employment., predictions of employment in the service sector are important for assessing fluctuations in aggregate economic activity and for employment and regional policies. The regional variations in the behaviour of service employment imply that it would be more appropriate to model and forecast service employment at a regional rather than aggregate level. The worsening forecasting performance of the various UK macroeconomic forecasting institutions who failed to predict either the beginning or length of the late1980srearly 1990s recession may partly be due to the failure of these models to 1 The following 10 regions are covered by this study: South East ŽSEAST.; East Anglia ŽEANG.; South West ŽSWEST.; West Midlands ŽWMIDS.; East Midlands ŽEMIDS.; Yorkshire and Humberside ŽYORK.; North West ŽNWEST.; North ŽNORTH.; Wales ŽWALES.; Scotland ŽSCOT.. Northern Ireland was not included in the analysis due to difficulties in identifying comparable data for the region. The regions’ share of public services employment is ‘distorted’ by the large subvention directed at the economy of Northern Ireland, centred around security related activities. The variable that we model is the growth rate Žmeasured by the percentage change. of service sector employment in each region of Great Britain. 2 The service sector employment data used in this paper was that derived from the Department of Employment’s surveys of employers, Ž Historical Supplement No., 4. October 1994, Vol. 102, No. 10.. The data is constructed from a postal survey of a cross section of manufacturing and service sector employers, the Quarterly Service Sector Survey, and a number of centralised returns from the public services such as the NHS, Education Department, Civil Service and mining. This is the same data set used by Button and Pentecost Ž1993., but covers a longer period and is more up to date. An advantage in using the employer based data rather than the Labour Force Sur¨ ey ŽLFS. household data is the availability of a very long time-series and industry level analysis as it is coded by employers more accurately than individual employees. Employers tend to have a better idea of who works in what industry compared to individuals when answering their questionnaires in the LFS. The lag in publishing data is of the order of three months so that in March of each year data up till last year’s December is published. Some element of data splicing was required as the time-series suffered a discontinuity in 1991:3 due to improvements in the classification of some local authority employees in the 1991 Census of Employment in Great Britain which led to a small reduction in the reported numbers in service sector employment. Standard Industrial Classification 1980 ŽSIC80. was used in preference to SIC92 based data in order to satisfy the requirements for data continuity over a long sample of regional data. SIC92 data is now available at both industrial and regional levels as far back as 1981, but the method used by the Office for National Statistics, formerly the CSO, is not totally valid between 1981 and 1991. The cross-classification matrix used between the two bases was fixed across all regions using UK data as its origin. Also, using SIC80 data suits our purposes as we can measure the comparative accuracy of old NIERC-MRM forecasts based on SIC80, against our own from extrapolative means.

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431

Fig. 1. Share of service sector employment to total employment Ž%., 1978]1993.

account for cross-regional variations. Murfin and Wright Ž1994. argue quite reasonably that an examination of regional differences is necessary so as to understand the nature of economic cycles and the effects on the economy that different shocks might occasion through their regional impacts. Our paper can be placed amongst other regional forecasting work, of which there is much less of a prevalence in the UK than in Northern America Že.g. Stekler and Schepsman, 1973; Weller, 1979, 1989; Hoehn et al., 1984; Kinal and Ratner, 1986; Talwar and Chambers, 1993.. The prevalence in those parts can be attributed to the careful orchestration by powerful private interests who have much to gain from inward investment mediation ŽCox and Wood, 1994. and the fact that in the USA there are available to individual states both monetary and fiscal powers that are not in evidence in the UK at present ŽBell, 1994.. Our starting point is the work of Button and Pentecost Ž1993., who examined variously the recent evidence for convergence in service sector employment amongst the regions within Great Britain. They undertook original work in this field by applying the time-varying parameter ŽTVP. technique, first used by Haldane and Hall Ž1991., and Hall et al. Ž1992. to exchange rate convergence. Their motivation for doing so was to assess the degree of concurrence between alternative convergence measures. However, they did not undertake forecasts and instead left the

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Fig. 2. Minimum and maximum growth rates in service sector employment across GB regions Ž%., 1979]1993.

possibility of so doing to a minor footnote. The present paper takes Button and Pentecost’s Ž1993. work one step further by examining the out-of-sample forecasting performance of the TVP model. In addition to the TVP model, we use three forecasting models which have been utilised widely in this area Žsee Hoehn et al., 1984; Nelson, 1984; Weller, 1989, 1990; Talwar and Chambers, 1993; West and Fullerton, 1996.: Seasonal ARIMA, regression and state space models. As Weller Ž1989, 1990. points out, data limitations at the small regional level makes the construction of traditional structural econometric models very difficult. Hence time series models Žunivariate and multivariate., with their more limited informational requirements, offer a cost effective and flexible alternative for obtaining forecasts of regional variables. To assess the performance of these models, we also compare their out-of-sample forecasting performance with those produced by a professional, large multi-regional structural model for the UK regions. The contents are organised as follows: Section 2 outlines the theoretical models chosen for estimation and forecast evaluation. Section 3 analyses the model estimations. Section 4 presents and compares the out-of-sample forecasts. Section 5 presents and compares our ex ante forecasts with those of the NIERC-MRM.3 Section 6 draws up the main conclusions.

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433

Fig. 3. Standard deviations of percentage growth rates in service sector employment ŽGB s mean., 1979]1993.

2. Specification of models 2.1. Time-¨ arying parameter model (TVP) This model is taken from Button and Pentecost Ž1993., who used the technique of TVP and the Kalman Filter to measure and depict the degree of convergence in service sector employment in the regions of GB. The TVP model is specified as follows: Ž EGB ,t y Eit . s a Ž t . q b Ž t .w EGB ,t y EBASE ,t x q « t

Ž1.

where EGB ,t s the growth rate of service employment across Great Britain ŽGB.; Eit s the growth rate of service employment in the ith region; 3

The NIERC-MRM or Northern Ireland Economic Research Centre’s Multi-Regional Model is a simultaneous model that forecasts employment and GDP for 28 SIC92 industries across the 11 Standard Planning Regions of the UK and Northern Ireland Žplus Greater London and the Rest of the South East.. The model uses regional accounts, employment, unemployment, population and migration data whilst aggregate national inputs and constraints are presently supplied by Oxford Economic Forecasting’s World and UK Industry Forecasts.

434

EBASE,t

«t

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

s the growth rate of service employment in the base region Žthis is taken as the South East for all non-South East regions and Scotland when analysing the South East’s employment pattern over time.; and s error term.

As the data was used in percentage change format a Ž t . was expected and proven to be always equal to zero when included in the specification and was therefore omitted from further analysis 4 . This fact is important for two reasons. First, it confirms the results already established by Button and Pentecost Ž1993.. Second, and more importantly, if the value of alpha was significantly different to zero it would be symptomatic of the variable proxying some unknown relationship. This could only happen if the variablerregion in question was drifting away from the GB average, implying non-convergence, and if neither variable was affected by the lead region. Given that this is not the case across all regions, we are analysing regions that either follow GB or lead region growth in service employment. Tracking the bŽ t . co-efficient 5 over time would show either a movement towards some constant that indicated convergence, or the co-efficient would appear to be stochastic indicating no clear evidence to suggest convergence in rates of change amongst the regions. We can interpret the bŽ t . co-efficients accordingly: b Ž t . G 0 then

EGB G Ei

Ž 1.1.

b Ž t . G 1 then

Ei G EBASE

Ž 1.2.

Basically, if bŽ t . G 0, service employment in the ith region grows at near to the national growth rate in service sector employment. If bŽ t . G 1, then service employment in the ith region grows at near the same growth rate as the lead region. 2.2. Regression model (MVM) One widespread constraint in regional economic forecasting is the difficulty in finding regional data to build models from the bottom up, hence the many models 4 It is worth noticing that Button and Pentecost Ž1993. estimated their model both with and without a constant just to prove that the constant would not be significantly different from zero, which proved to be the case. 5 The TVP a Ž t . and bŽ t . were estimated using a Kalman Filter utilising a random walk with drift process. The alternative available was an ARŽ1. process which assumed an eventual return to some mean over time. Intuitively, this would have imposed some sort of ‘convergence’ most probably in the latter stages of our sample. By using a random walk with drift process if the series were non-convergent we might expect to find very volatile behaviour in the parameters over the sample period. The same methodology applied to different data need not produce steady time paths in the time varying parameters. See Drake Ž1996., whose time varying parameters across UK regional house prices are appreciably volatile, especially in the first stage of his sample.

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435

that utilise some form of trickle down Žfrom national to regional level. such as that produced by the Northern Ireland Economic Research Centre ŽNIERC. who use the Oxford Economic Forecasting ŽOEF. model for both UK growth rate drivers and total UK constraints ŽBell, 1994.. There have been a number of studies occasioned in Northern America which utilise national data sets, especially composite leading indicators to explain regional variables Že.g. Stekler and Schepsman, 1973; Weller, 1979, 1989.. Weller found that the composite leading indicator performed best compared to US aggregate employment and industrial production. We have therefore used a composite leading indicator ŽLONG.,6 as our explanatory variable. The composite index is designed to give prior warning of turning points in the economic cycle and for this reason any derived effect should be positively signed, i.e. a positive upturn in the national economy should filter through to a positive upturn in service sector employment. Quarterly seasonal dummies Ž Q s ., a time trend ŽT ., and lagged employment Etyj Žintended to capture partial adjustment. were also included. Hence the estimated model for the growth rate of service employment is: Et s a0 q a1 Q s q a2 T q a3 LONGtyj q a4 Etyj q u t

Ž2.

2.3. State space regression model (SSR) The SSR methodology models the residuals of the regression model with a nonseasonal state space model Žsee Goodrich, 1989.. Statistically, this is similar to modelling the regression residuals via a full Box]Jenkins autoregressive-moving average ŽARMA. model instead of the more restrictive AR model. Let us denote the residuals of the regression model by ¨ t . Then the ARMA process for ¨ t can be represented by the following state space model Žin its Kalman filter form., ¨ t s hz t q « t Ž observation equation .

Ž3.

z tq1 s F z t q k « t Ž updating equation .

Ž4.

0 0 F s .. 0 fn

1 0 .. 0

f ny1

0 1 .. 0

f ny2

h s w1 0 0 . . . . . . 0x k s w k1 k 2 k 3 . . . . . . k n x9 6

... ... ... ... ...

0 0 .. 0 f1

Ž 5a .

Ž 5b . Ž 5c .

Given that we are modelling the growth rate of service sector employment, the composite longer leading indicator ŽLONG. was measured as follows: We took 100 Žin the published longer leading index. as indicating ‘no change’ in economic conditions and then converted the data to LONG s Index y 100, so that an index figure of, say, 106.2 would become q6.2, etc.

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where z t is an Ž n = 1. vector of state variables, f i are the autoregressive coefficients, k i are complex functions of the autoregressive and moving average coefficients Žsee Goodrich, 1989., n indicates the number of parameters in matrix F and vector k, and « t denotes the disturbance term. Having specified the regression model in Section 2.2, the algorithm estimates simultaneously the parameters of the regression model and the parameters of the state space model Žsee Stellwagen and Goodrich, 1991.. In modelling the residual autocorrelations the state space regression ought to produce lower and hence improved BICs ŽBayesian Information Criterion. for each region along with higher adjusted R 2 . 2.4. Seasonal autoregressi¨ e-mo¨ ing a¨ erage (ARIMA) model The multiplicative seasonal ARIMA Ž p,d,q . = Ž P, D,Q .s methodology was applied in the form: f Ž b . F Ž B . DdDDs Et s u Ž b . Q Ž B . « t

Ž6.

where b and B denote the non-seasonal and seasonal backward operators, fŽ b . and F Ž B . are the non-seasonal and seasonal autoregressive ŽAR. polynomials Žof order p and P ., uŽ b . and QŽ B . are the non-seasonal and seasonal moving average ŽMA. polynomials Žof order q and Q ., d and D denote the simple and seasonal difference operators, and « is the error term. The seasonal and non-seasonal parts of the model are fitted to the data simultaneously using the Bayesian Information Criterion ŽBIC., while the Ljung]Box statistic and the autocorrelation function ŽACF. of the estimated residuals are used to test for white noise errors.

3. Estimation results We first investigate the stationarity of the time series Žover the full sample period, 1978Q2]1993Q4. by using the Dickey]Fuller ŽDF. and augmented Dickey]Fuller ŽADF. tests for integration Žsee Dickey and Fuller, 1981..7 The results are shown in Table 1. In all cases the DF and ADF statistics are smaller than their corresponding 5% critical values and we therefore accept the hypothesis that all regional growth rates in service sector employment are stationary irrespective of the inclusion of a time trend. The ADF test statistic without a trend indicates that the leading indicator is also stationary. Turning to estimation and forecasting, we have used the observations over the period 1978Q3]1991Q4 for estimation, while the data for 1992Q1]1993Q4 were retained for out-of-sample forecast evaluation. 7

Notice that the variable under investigation is the growth rate of service employment.

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437

Table 1 Dickey]Fuller tests for the growth rate of regional service employment Augmented Dickey]Fuller

Dickey]Fuller

South East East Anglia South West West Midlands East Midlands York and Humber North West Northern Wales Scotland LONG Critical values

ŽA.

ŽB.

ŽA.

ŽB.

y8.3954 y9.0916 y8.7792 y8.8606 y11.6555 y13.3109 y9.9708 y8.3936 y9.5768 y9.1746 y2.0907 y2.9092

y8.5907 y9.0126 y8.7268 y8.8089 y11.5741 y13.3821 y10.2038 y8.6221 y9.7067 y9.3066 y2.0758 y3.4836

y3.3881 y8.2732 y9.2700 y4.7431 y5.0601 y3.4568 y4.5416 y4.7254 y5.4640 y6.8753 y3.1816 y2.9101

y3.3177 y8.1999 y9.2310 y4.7773 y5.0654 y3.5290 y4.9774 y5.0247 y5.6198 y7.0829 y3.146 y3.4849

Notes. The statistics in the ŽA. columns include no time trend, but those in column ŽB. do. Critical values are based upon a 5% level of significance. Only one lag was required in undertaking the ADF tests with white noise in the residuals. The estimation period used was from 1978Q2 to 1993Q4.

3.1. Time ¨ arying parameter mo¨ ements To compare our results with those obtained by Button and Pentecost Ž1993., we report the smoothed b coefficients for the entire sample period 1978Q3]1993Q4. These coefficients, shown in Fig. 4, give a pictorial representation of steady convergence, thus confirming the earlier results by Button and Pentecost Ž1993., who covered the shorter period of 1978Q3]1992Q1. Most regions prior to 1990 exhibit negativity which is indicative of a lagging behind the national average growth rate. Only the regions of the South East ŽSEAST., Yorkshire and Humberside ŽYORK., the West Midlands ŽWMIDS., the North ŽNORTH. and the North West ŽNWEST. show positivity between zero and unity until 1990, indicative of service sector employment growth in line with the national average. Around 1990 the range of b coefficients lies between near zero for the SEAST to just over minus unity for Scotland ŽSCOT.. The spread of values from then on tends to increase again which can be interpreted as a tendency towards ‘deconvergence’ in the rates of change of service sector employment. The SEAST as expected shows the most constancy in value over the sample period due to its lead region status and its value is always above zero indicating a slightly higher than national growth rate. East Anglia ŽEANG. shows a marked capacity towards unity in the latter stages of our sample, indicating an increasingly close relationship between that region and its neighbour and lead region, the SEAST. The South West ŽSWEST. begins with the largest negative value, and shows remarkable aptitude in ‘catching up’ with the other regions by the late 1980s.

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Fig. 4. TVP beta values, 1978:2]1993:4.

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439

The WMIDS achieved the largest positive value up to the late 1980s indicative of the requirement to have in place a service sector large enough to meet the needs of the predominantly manufacturing sector in that particular region. With the decline in the manufacturing base over the 1980s its value has declined to below zero. Once the effective ‘renaissance’ in manufacturing circa early 1990s began with the UK’s export led recovery, its fortunes have improved and its b value has returned to a positive by end 1993. The regions of the NWEST, YORK and the NORTH have shown the same capacity due to their similarity in terms of manufacturing dependent economies. For most regions our a priori expectations, especially given southern bias towards services and northern bias towards manufacturing, reflect well in our interpretation of b values over the sample. 3.2. Regression and state space models The estimates of the regression and state space models are shown in Tables 2 and 3, respectively. The former were estimated by the OLS method, or the Cochrane]Orcutt method whenever autocorrelation was present. We started with lags of up to 4th order for LONGt and Et and tested down to produce a parsimonious representation. The R 2 values suggest good explanatory power for both models and all regions. The Ljung]Box statistics indicate absence of autocorrelated residuals in all regions. The test for heteroscedasticity checks for systematic variation of error variance with fitted values of the dependent variable. The reported statistics do not suggest any significant problems across the regions. The Chow test divides the data set into two equal halves to check for parameter constancy and is a test for a structural break. The Chow statistics reject the presence of a structural break in all regions except EANG. The latter two tests are reported for the OLS results and not their SSR counterparts. This is because the modelling methodology requires only that a well specified OLS model is derived first of all that produces residuals that are white noise prior to state space modelling being run with the same specified set of variables. It is interesting to note that only two of the fŽ i . coefficients ŽSWEST and SCOT. and four of the k Ž i . Žsee Table 3. coefficients were significant, so in terms of in-sample performance the state space formulation does not provide an improvement on the regression models in most regions. The coefficients on the leading indicator are positive for all regions. This concurs with theoretical expectations, i.e. that a positive increase in the longer leading indicator will feed the growth in employment throughout the economy. In the EMIDS, use is made of a negative and positive signed coefficient on the leading indicator variable. This was proven to be a ‘better’ specification in terms of diagnostics compared to that when the negatively signed variable is dropped. On balance, the coefficient on the two period lagged independent variable outweighs the negative coefficient ensuring a positive response in the long run. The fact that the lags on the longer leading indicator were significant for all regions from one to four periods, but not five or more periods confirm the Central Statistical Office’s

440

South East Constant Q2 Q3 Q4 LONG LONG Žy1. LONG Žy2. LONG Žy3. LONG Žy4. E Žy1. E Žy4. AR Ž1. AR Ž4. Adjusted R2 Durbin]Watson Ljung]Box Ž18. BIC SER Heteroscedasticity c Structural stability d

East Anglia UU

y0.501 Žy3.508. 1.264 Ž8.345.UU 0.481 Ž2.852.UU 1.498 Ž10.018.UU 0.0447 Ž2.003.U

y 0.0896 Žy0.324. 1.973 Ž3.537.UU 0.309 Ž0.797. 0.154 Ž0.406.

South West 0.0673 Ž0.423. 0.288 Ž0.592. y0.069 Žy0.321. y0.100 Žy0.479. 0.0807 Ž4.142.UU

0.0841 Ž2.970.UU

0.388 Ž2.831.UU 0.726 1.842 21.35 0.559 0.461 0.93 1.78U

0.638 2.457 27.50 1.127 0.950 1.15 4.18UU

East Midlands UU

y1.216 Žy5.683. 2.210 Ž6.987.UU 1.303 Ž5.873.UU 2.192 Ž9.319.UU

0.0475 Ž2.700.UU

0.0551 Ž2.518.U 0.330 Ž2.393.U

West Midlands

0.839 Ž7.250.UU y0.568 Žy3.969.UU 0.805 2.379 20.44 0.954 0.774 0.01 0.76

y0.527 Žy2.665.UU 2.119 Ž7.597.UU 0.621 Ž2.210.UU 1.358 Ž4.865.UU y0.116 Žy2.474.U 0.183 Ž3.935.UU

0.435 Ž3.568.UU

0.676 2.011 14.02 0.638 0.540 0.00 0.92

0.621 2.150 22.47 0.839 0.710 2.33 0.30

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Table 2 Regression estimates Žestimation period: 1978Q3]1991Q4.

Table 2 Ž Continued. North West

Northern

y92.274 Žy2.512.U 2.009 Ž10.27.UU 0.518 Ž2.643.UU 2.012 Ž10.25.UU 0.0461 Ž2.492.U

y109.51Ž2.825.UU 1.099 Ž4.148.UU 0.629 Ž2.812.UU 1.100 Ž4.001.UU 0.0549 Ž2.813.UU

y0.554 Žy2.510.U 0.929 Ž2.979.UU 0.906 Ž2.904.UU 1.475 Ž4.718.UU

Scotland y176.48 Žy2.73.UU 1.938 Ž5.838.UU 0.528 Ž1.648.U 0.518 Ž1.621. 0.0887 Ž2.725.UU

Wales

0.114 Ž1.320.

0.0702 Ž4.105.UU 0.0782 Ž5.338.UU

UU

0.0676 Ž2.869.UU

0.0366 Ž2.187.U

0.0468 Ž3.379. 0.201

0.792 1.465 25.05 0.589 0.499 0.02 1.21

0.685 1.928 20.64 0.558 0.457 1.32 0.95

0.336 2.085 25.36 0.914 0.795 1.30 2.39U

0.334 Ž2.348.U 0.704 2.321 18.53 0.648 0.531 0.04 0.73

0.717 Ž8.083.UU y0.367 Žy2.638.UU 0.594 1.983 18.36 0.859 0.765 0.19 0.64

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Constant Q2 Q3 Q4 Time trend LONG LONG Žy1. LONG Žy2. LONG Žy3. LONG Žy4. E Žy1. E Žy4. AR Ž1. AR Ž4. Adjusted R2 Durbin]Watson Ljung]box Ž18. BIC SER Heteroscedasticity Structural stability

Yorkshire and Humberside

Notes. Dependent variable: growth rate Ž E . in total service sector employment by standard planning region. Figures marked U and UU represent significance at the 0.10 and 0.05 levels, respectively. Abbre¨ iations. Q2, Q3 and Q4, quarterly dummies; LONG, composite longer leading index Žsource: Central Statistical Office.; SER, standard error of the regression; AR, autoregressive process of n lags, ARŽ n.. 441

442

South East Constant Q2 Q3 Q4 LONG LONG Žy1. LONG Žy2. LONG Žy3. LONG Žy4. E Žy1. E Žy4. F1 F2 k1 k2 Adjusted R2 Durbin]Watson Ljung]box Ž18. BIC SER

East Anglia UU

y0.490 Žy3.578. 1.263 Ž8.206.UU 0.484 Ž2.565.UU 1.495 Ž9.817.UU 0.0452 Ž2.160.U

y0.147 Žy0.529. 1.854 Ž3.299.UU 0.393 Ž0.991. 0.220 Ž0.496.

South West y0.026 Žy0.026. 0.852 Ž1.530. 0.022 Ž0.076. y0.140 Žy0.575. 0.0719 Ž3.670.UU

0.0816 Ž5.298.UU

0.0441 Ž0.132. 0.426 Ž2.880.UU

y0.429 Žy2.649.UU

0.731 1.909 21.10 0.563 0.454

0.687 2.021 17.15 1.108 0.884

East Midlands UU

y1.231 Žy3.802. 2.233 Ž4.387.UU 1.310 Ž7.581.UU 2.203 Ž7.581.UU

0.0472 Ž2.063.U

0.0571 Ž2.828.UU 0.377 Ž3.250.UU 0.111 Ž0.350.

West Midlands

0.690 Ž5.230.UU y1.349 Žy4.866.UU y0.777 Žy2.439.U y0.159 Žy1.04. y0.122 Žy1.052. 0.815 1.906 18.10 0.993 0.751

y0.527 Žy2.609.UU 2.120 Ž7.408.UU 0.622 Ž2.167.U 1.359 Ž4.746.UU y0.116 Žy2.420.U 0.183 Ž3.849.UU

0.447 Ž1.860. 0.753 Ž0.193.

y0.249 Žy0.012.

y0.0139 Žy0.056.

y0.0065 Žy0.043.

0.662 2.012 17.35 0.688 0.552

0.605 2.136 22.76 0.905 0.726

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Table 3 State space estimates Žestimation period: 1978Q3]1991Q4.

Table 3 Ž Continued. Yorkshire and Humberside y9.955 Žy2.001.U 2.002 Ž11.556.UU 0.513 Ž2.444.U 2.007 Ž11.497.UU 0.046 Ž1.986.U

y109.33 Žy2.61.UU 1.099 Ž4.035.UU 0.630 Ž2.740.UU 1.100 Ž3.872.UU 0.0548 Ž2.598.UU

Northern y0.531 Žy2.245.U 0.918 Ž3.015.UU 0.889 Ž2.865.UU 1.454 Ž4.737.UU

Scotland y110.77 Žy2.101.U 2.101 Ž7.355.UU 0.437 Ž1.279. 0.398 Ž1.623.

Wales

0.122 Ž0.836.

0.0695 Ž2.696.UU 0.0805 Ž4.448.UU

y0.139 Žy0.341. 0.312 Ž2.054.U

0.800 2.037 17.58 0.610 0.489

0.0468 Ž3.226.UU

0.0689 Ž2.472.U

0.201 Ž1.532. 0.296 Ž0.010.

0.521 Ž0.454.

0.00544 Ž0.032.

0.105 Ž0.654.

0.669 1.939 20.85 0.603 0.468

0.298 2.303 27.90 0.993 0.818

0.0526 Ž2.004.UU

0.410 Ž1.332. y0.514 Žy1.659.U 0.208 Ž0.646. 0.0591 Ž0.376. y0.141 Žy0.875. 0.447 Ž2.910.UU 0.720 2.136 19.56 0.734 0.534

0.695 Ž6.820.UU 0.847 Ž0.030.

y0.00098 Žy0.007.

0.523 2.724 35.25UU 0.948 0.821

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

Constant Q2 Q3 Q4 Time trend LONG LONG Žy1. LONG Žy2. LONG Žy3. LONG Žy4. E Žy1. E Žy4. F1 F2 F3 k1 k2 k3 Adjusted R2 Durbin]Watson Ljung]box Ž18. BIC SER

North West

Notes. Dependent variable: growth rate Ž E . in total service sector employment by standard planning region. Figures marked U and UU represent significance at the 0.10 and 0.05 levels, respectively. Abbre¨ iations. Q2, Q3 and Q4, quarterly dummies; LONG, composite longer leading index Žsource: Central Statistical Office.; SER, standard error of the regression. 443

444

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

view that it should predict turning points approximately 1 year ahead, Ž CSO, Cyclical Indicators: Standard Notes on Compilation, 1995.. Quarterly seasonal dummy variables were significant for most regions except for Wales. All specifications included the use of some form of deterministic trend component, i.e. autocorrelation coefficients were used in the SEAST, SWEST, SCOT and WALES, a lagged dependent variable was included in EANG, SWEST, WMIDS, NWEST and WALES, and a time trend was used in YORK, NWEST and SCOT. These are to be expected due to the definite secular upward trend in service sector growth, and this is confirmed by the positive effects of these variables. 3.3. Seasonal ARIMA model The specification and diagnostic statistics for the regional models are summarised in Table 4. All regional models use a seasonal difference save for the North region which proved to be no more complicated than a random walk with drift. A few of the Ljung]Box statistics were on the high side but all reject serial correlation at the 5% significance level across all regions. All coefficients were significant and their absolute values were less than unity thus satisfying the requirement for invertibility.

4. Model forecasts The reported parameter estimates for the period 1978Q3]1991Q4 were used to produce one-step-ahead forecasts over the period 1992Q1]1993Q4.8 These were generated by employing the sequential re-estimation procedure Žsee Sarantis and Srewart, 1995.. That is, the initial estimates were used to generate one-step-ahead forecasts for 1992Q1. Next, data for 1992Q1 were added to the sample and the

Table 4 Seasonal ARIMA specifications Region

Model

Ljung]Box

BIC

South East East Anglia South West West Midlands East Midlands Yorks and Humberside North West Northern Wales Scotland

Ž0,1,0. Ž0,1,1. Ž0,0,0. Ž1,1,1. Ž0,0,0. Ž1,1,0. Ž0,1,1. Ž0,1,1. Ž0,0,0. Ž2,1,0. Ž1,0,0. Ž0,1,1. Ž0,0,0. Ž0,1,0. Ž0,0,0. Ž1,0,0. Ž0,0,0. Ž1,1,1. Ž0,0,0. Ž3,1,0.

7.39 14.09 22.15 9.04 7.39 21.73 18.03 24.98 21.40 25.93

0.58 1.09 0.91 0.73 1.04 0.65 0.61 0.94 0.94 0.64

Note. d.f. for Ljung]Box s 18; critical value Žat the 5% significance level. s 28.9.

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

445

parameters of each model Žand for each region. were re-estimated. The new parameter estimates were then used to generate one-step-ahead forecasts. This procedure continued up to the last estimation point, 1993Q3, thus producing a series of eight observations for one-step-ahead forecasts. Schinasi and Swamy Ž1989. have criticised the sequential estimation and production of fixed step-ahead predictions on the grounds that professional forecasters do not update their models every period due to prohibitive development costs. Consequently, we have also followed Schinasi and Swamy Ž1989. in using the initial parameter estimates to produce multistep predictions for eight periods. The predicted variable in all forecast experiments is the growth rate of service employment. Forecast evaluation is carried out from the stance of the mean absolute error ŽMAE., the root mean squared error ŽRMSE. and percentage turning point accuracy ŽTPA. statistics. The advantage of the MAE measure is that it is dimensionless and is best used when the cost of forecast error is proportionate to the size of the error. The use of the RMSE is in line with recent discussion on the choice of error measures in that the use of an error measure with a well specified loss function is not sufficient, and the RMSE is preferred on the grounds that it is dimensionless when the same variables are compared ŽArmstrong and Fildes, 1995.. Thus, we are able with the RMSE to compare across models and across regions in terms of relative forecasting accuracy. Unlike the MAE and RMSE criteria, the TPA measure indicates the ability of the model to predict turning points in the data and it ignores actual forecasted error size altogether. The forecasting results are reported in Table 5. In terms of one-step-ahead forecast accuracy, as measured by the RMSE statistic, none of the models dominates the others completely. The TVP model produces the more accurate forecasts in three regions ŽEANG, WMIDS and WALES., the SSR model performs best in three regions ŽSEAST, SWEST and YORK., and the ARIMA outpredicts the other models in three regions ŽEMIDS, NWEST and NORTH.. However, if we consider the forecast performance of the models across regions, as measured by the

8

The TVP forecasts were produced with the model Ft s EGB ,ty4 y Ž b ty1Ž EGB ,ty4 y EBase ,ty4 ..

where Ft s EGB ,ty4 s b ty 1 s EBa se,ty4s

predicted growth in service sector employment for the ith region; growth in GB service sector employment at time t y 4; the TVP parameter estimate for the region of interest at time t y 1; and growth in service employment in the base region at time t y 4.

In the true spirit of the Kalman filter the last b ty 1 was determined from using the Button and Pentecost derived methodology of convergence on the lead region wsee Eq. Ž1.x, and was then used as part of the above forecasting equation. Other variants of the TVP model Žusing EGB and EBase at time t y 1. were tested over the forecast period but proved less accurate, especially with respect to one-step ahead forecasts. The final choice of a fourth lag operator was unsurprising given the seasonal nature of our dataset.

446

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

weighted average RMSE,9 the SSR model is the ‘best’, with the TVP coming second and the ARIMA last. With regards to the models’ ability to capture turning points, the TVP model clearly dominates. This model succeeds in capturing most turning points in the growth rate of service employment in the majority of regions. Again the ARIMA model performs worst. Turning to the multistep predictions, the TVP technique’s robustness breaks down, as it is appreciably worse in terms of both accuracy and turning points compared to all other methods employed. On the basis of the RMSE criterion, the ARIMA model produces the more accurate predictions in four regions ŽEMIDS, YORK, NWEST and NORTH., followed by the SSR model which is best in three regions ŽSWEST, WMIDS, SCOT.. Looking across all regions, the weighted average RMSE suggests that the SSR method is the best, with the regression model a close second. This pattern is also observed when we consider the prediction of turning points. The SSR and regression models tend to be more successful, on average, in capturing turning points over an eight-quarters forecast period.

5. Ex ante forecasts: the NIERC-MRM vs. time series models A comparison of the relative forecasting accuracy of a professional multi-regional structural model which constrains to a UK industrial forecast provides yet another benchmark with which to measure the success or otherwise of the specifications detailed in the previous section. Ashley Ž1983. came to the conclusion that full structural models might not be a worthwhile exercise due to the introduction of additional forecasting bias from using macro-economic forecast constraints and drivers.10 Additionally, the associated running costs have been claimed to be excessive when compared to perhaps cheaper and more accurate time series models, ŽWeller, 1989, 1990; Lesage, 1990; Shoesmith, 1990.. There has been to date a paucity of rigorous statistical testing of such claims. West and Fullerton Ž1996. examined both means of regional forecasting and found there to be no clear winners in terms of methodology. They were unable to establish any clear link between methodological success in terms of accuracy as applied to a particular region and its economic characteristics. Full structural models did not appear to sacrifice accuracy unduly and offered the usual advantages for policyrscenario analysis. Perhaps one reason for the paucity of such relative accuracy testing is due to the 9

The weights used in calculating these forecast criteria were the share of service employment in each region to total service employment in GB as at 1993Q4. A similar pattern emerged when using unweighted average forecast criteria. 10 Notice that the OEF macroeconomic model provides sets of growth forecasts across employment sectors which are then used by the NIERC-MRM to derive individual regional employment forecasts. These in turn require scaling to the OEF total UK employment forecasts by sector for consistency across models. More importantly, national constraints allow the NIERC-MRM regional forecasts to be scaled to OEF national forecasts. This ensures that any upward bias in the NIERC-MRM projections are reigned in by OEF constaints, and vice versa.

Table 5 Forecasting results Region

RMSE

TPA

Multistep forecasts MAE

RMSE

TPA

EANG

SWEST

WMIDS

EMIDS

YORK

NWEST

NORTH

WALES

SCOT

Weighted average

TVP MVM SSR ARIMA TVP MVM SSR ARIMA TVP MVM SSR ARIMA

0.74 0.79 0.70 1.06 1.06 1.16 1.03 1.27 7.00 6.00 6.00 6.00

0.65 1.17 1.07 1.00 0.83 1.51 1.35 1.43 7.00 5.00 5.00 6.00

1.09 0.88 0.80 0.97 1.34 1.05 0.97 1.17 6.00 5.00 5.00 3.00

1.04 1.20 1.20 1.48 1.23 1.45 1.46 1.85 6.00 5.00 5.00 4.00

1.18 0.88 0.93 1.13 1.35 1.27 1.29 1.26 4.00 6.00 5.00 4.00

0.93 0.76 0.78 0.93 1.05 0.97 0.96 1.04 5.00 5.00 5.00 5.00

0.90 0.81 0.81 0.61 1.03 0.91 0.91 0.73 5.00 4.00 4.00 5.00

0.80 0.67 0.69 0.63 1.08 0.84 0.84 0.81 5.00 6.00 6.00 3.00

0.64 0.90 0.92 1.03 0.93 1.28 1.27 1.26 8.00 7.00 7.00 6.00

0.93 0.70 0.79 0.72 1.01 0.79 0.85 0.80 4.00 5.00 4.00 3.00

0.86 0.84 0.81 0.98 1.09 1.11 1.05 1.17 5.96 5.46 5.31 4.87

TVP MVM SSR ARIMA TVP MVM SSR ARIMA TVP MVM SSR ARIMA

1.31 0.59 0.59 1.23 1.43 1.07 1.09 1.29 5.00 7.00 7.00 3.00

1.14 1.47 1.47 1.44 1.38 1.71 1.69 1.74 4.00 5.00 5.00 5.00

1.33 0.71 0.69 0.76 1.55 0.90 0.85 0.94 3.00 6.00 6.00 5.00

1.57 1.04 1.04 1.13 1.72 1.33 1.33 1.43 3.00 5.00 5.00 7.00

1.41 0.92 0.92 0.90 1.76 1.23 1.26 1.15 3.00 6.00 6.00 4.00

1.31 0.76 0.76 0.74 1.43 0.99 0.99 0.90 3.00 6.00 6.00 6.00

1.06 0.69 0.69 0.61 1.32 0.84 0.84 0.73 4.00 6.00 6.00 6.00

1.29 0.67 0.65 0.53 1.39 0.85 0.83 0.77 2.00 6.00 6.00 5.00

1.09 0.70 0.70 1.00 1.47 1.10 1.10 1.24 3.00 6.00 6.00 5.00

0.77 0.76 0.61 0.65 0.98 0.89 0.72 0.78 4.00 5.00 5.00 5.00

1.25 0.74 0.72 0.97 1.43 1.05 1.04 1.12 3.93 6.16 6.16 4.54

447

Note. Weighted average of errors calculated with respect to regional shares of total GB service sector employment as at 1993:4.

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

One-step-ahead forecasts MAE

SEAST

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N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

difficulty in conducting such an exercise. Most regional datasets are subject to fairly heavy revision and lead times can be as much as 2r3 years. Trying to marry the same vintage of data that was at least available to structural modellers to the same series as used in this paper is problematic and for our purposes we took the forecasts from the NIERC-MRM dated February 1992. Such a point in time allowed the use of a full 2 years of forecasts Ž1992 and 1993. from the NIERC-MRM to match against our own eight-step-ahead forecast across the GB regions, Žsee Tables 6]8.. As the NIERC-MRM uses the Census of Employment to rebase their most recent historical data, we were forced into using the third-quarter actuals from our preceding analysis, so as to compare as closely as possible data from the same part of the year. While the NIERC-MRM forecast was taken from 1992, the time lag involved in the then CSO published regional employment series was of the order of 3 months. Hence, no prior knowledge of employment in 1992 was likely to have entered the forecast, save for that derived from any conjunctural analysis that may, or may not, have taken place at the time of forecast. Over the full 2 years and by taking a suitably weighted average of absolute errors Žsee Table 8., the NIERC-MRM proves to be the ‘best’ and is closely followed by our SSR forecast. The 1991]1992 ‘winner’ was the seasonal ARIMA model Žsee Table 6., and that for 1992]1993 was the SSR model Žsee Table 7.. As in the previous section there is no outright methodological winner, but a mix of ‘best’ performing methodologies across the regions, although in the case of the NIERCMRM over the 1991]1993 period the model stands alone in notching up ‘best’ performance across the majority of regions. On what perhaps is a fairly obvious point, the ability to forecast accurately the SEAST endows the particular methodology with very low overall errors when using our weighted averaging technique. The SEAST accounts for approximately a third of all service sector employment within GB. Despite this fact, the SSR model over 1992]1993 Žsee Table 7. manages to do slightly better than the NIERC-MRM, simply because the size of its other errors are low where there are other high regional weights involved.

6. Conclusions On the basis of in-sample criteria, all models perform satisfactorily. The estimates of the TVP model indicate that the growth rates of service employment across the 10 British regions displayed a steady convergence during the 1980s. However, there are more recent signs that this tendency might have been reversed for some regions during the 1990s. Our results also confirm the strong influence of the composite leading indicator on the growth of regional service employment. In terms of out-of-sample forecasting performance, the results vary across regions and forecast horizons. In the case of one-step-ahead forecasts, the TVP model performs better than all other models in terms of turning points captured. However, in terms of forecast accuracy, none of the models dominates the others, though the state space methodology has a slight edge on average. A clearer pattern

1991]1992 Actual growth SEAST y4.65 EANG y0.37 SWEST y0.72 WMIDS y0.63 EMIDS y0.96 YORK 1.14 NORTH 1.81 NWEST y0.98 WALES y0.92 SCOT 1.21 Weighted average

TVP

MVM

SSR

ARIMA

MRM

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

y4.27 0.37 y2.49 y2.61 y2.02 y1.71 y0.83 y3.00 y16.82 y0.28

0.38 0.74 1.77 1.97 1.06 2.85 2.64 2.02 15.90 1.49 1.96

y1.62 3.69 0.08 y0.08 2.02 2.28 2.36 0.73 0.46 3.91

3.03 4.06 0.80 0.55 2.98 1.14 0.56 1.71 1.38 2.70 2.15

y1.43 2.77 y0.32 y0.08 2.02 2.28 2.78 0.73 0.46 3.13

3.22 3.14 0.40 0.55 2.98 1.14 0.97 1.71 1.38 1.92 2.10

y4.82 4.61 0.56 y1.42 1.49 1.06 2.09 y0.67 1.68 3.34

0.17 4.98 1.28 0.79 2.45 0.08 0.28 0.31 2.60 2.13 0.93

0.26 1.87 1.47 0.56 1.30 1.07 1.41 1.05 0.94 0.39

4.91 2.24 2.19 1.19 2.26 0.07 0.40 2.03 1.86 0.82 2.67

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

Table 6 Ex ante performance of time series econometrics vs. simultaneous model Ž1991]1992.

449

450

1992]93 Actual growth SEAST 0.38 EANG 1.67 SWEST 3.15 WMIDS 2.31 EMIDS 3.12 YORK 1.77 NORTH 1.64 NWEST 2.10 WALES 3.09 SCOT 1.19 Weighted average

TVP

MVM

SSR

ARIMA

MRM

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

y4.36 y1.65 y2.88 y3.81 y3.37 y3.48 y4.07 y3.72 15.26 y1.85

4.75 3.32 6.03 6.12 6.49 5.26 5.71 5.82 12.17 3.05 5.40

0.55 3.02 0.24 0.47 0.94 2.15 0.27 1.88 0.91 3.70

0.17 1.36 2.91 1.83 2.18 0.38 1.37 0.22 2.17 2.50 1.09

0.58 2.51 0.72 0.47 0.94 2.15 0.41 1.82 1.07 2.76

0.20 0.85 2.43 1.83 2.18 0.38 1.23 0.28 2.02 1.56 0.95

y4.96 4.59 0.00 y1.36 1.15 1.85 1.50 y0.68 1.95 2.55

5.34 2.92 3.15 3.67 1.96 0.08 0.14 2.78 1.13 1.35 3.20

0.32 1.22 0.90 0.42 1.19 0.64 0.88 0.55 1.20 0.39

0.06 0.45 2.25 1.89 1.93 1.14 0.75 1.55 1.89 0.81 0.96

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

Table 7 Ex ante performance of time series econometrics vs. simultaneous model Ž1992]1993.

1991]1993 Actual growth SEAST y4.28 EANG 1.29 SWEST 2.41 WMIDS 1.66 EMIDS 2.13 YORK 2.93 NORTH 3.48 NWEST 1.10 WALES 2.14 SCOT 2.42 Weighted average

TVP

MVM

SSR

ARIMA

MRM

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute error

Forecast growth

Absolute Error

y8.44 y1.29 y5.30 y6.32 y5.32 y5.13 y4.87 y6.61 y4.13 y2.13

4.16 2.58 7.70 7.98 7.45 8.07 8.34 7.71 6.27 4.55 5.96

y1.08 6.83 0.32 0.39 2.98 4.48 2.64 2.63 1.38 7.75

3.20 5.54 2.09 1.26 0.85 1.55 0.83 1.53 0.76 5.33 2.55

y0.85 5.35 0.40 0.39 2.98 4.48 3.20 2.57 1.53 5.97

3.43 4.06 2.01 1.26 0.85 1.55 0.28 1.47 0.61 3.56 2.36

y9.54 9.41 0.56 y2.78 2.66 2.93 3.62 y1.35 3.67 5.97

5.26 8.12 1.85 4.42 0.53 0.00 0.14 2.45 1.53 3.56 3.40

0.58 3.11 2.38 0.98 2.50 1.72 2.31 1.61 2.15 0.77

4.87 1.82 0.02 0.68 0.37 1.22 1.17 0.51 0.01 1.64 2.26

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

Table 8 Ex ante performance of time series econometrics vs. simultaneous model Ž1991]1993.

451

452

N. Sarantis, C. Swales r Economic Modelling 16 (1999) 429]453

emerges in the case of multistep predictions. The TVP model is outperformed by all models irrespective of the forecast criteria employed, while the SSR model produces on average the best forecasting performance. On comparing the four extrapolative based methods to a professional structural model, initial results imply neither is superior in ex ante forecast performance. Our forecasting results have four important implications. First, the method chosen for predicting regional service employment is likely to differ depending on the forecast horizon. Relative accuracy clearly reflects the time horizon effects identified by Nelson Ž1984.. Second, no one methodology outperforms all others across all regions, thus confirming West and Fullerton’s Ž1996. conclusions that a judicious combination of methodologies across regions is likely to improve forecast performance. Third, as regards the superiority of time series econometric to simultaneous equation forecasts, or vice versa, our results add further support to those of West and Fullerton’s Ž1996. who concluded that the choice between methods must be based on the requirement for policyrscenario analysis where simulation properties are required. The fact that regional structural models rely heavily on some form of national constraint, supplied in the case of the NIERCMRM by OEF, does not appear to seriously affect their accuracy when compared to extrapolative forecasts, as suggested by Ashley Ž1983.. Finally, the poor forecasts of aggregate employment reported by macroeconomic forecasters over the last decade may be due to regional variations in the behaviour of employment. This supports Murfin and Wright’s Ž1994. argument that an examination of regional differences is necessary so as to understand the nature of economic cycles and the effects on the economy that different shocks might occasion through their regional impacts.

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