Forecasting regional unemployment in Great Britain

Regional Science and Urban Economics 5 (1975) 357-374. fi> North-Holland

FORECASTING

REGIONAL UNEMPLOYMENT GREAT BRITAIN@

IN

A. P. THIRLWALL Unitvrsity of Krnt at Catlterbwy, Cunterbury,~Cl.K.

1. Xntrodnction r many years there has been widespread interest in &e;at Brit:lin in interregi Jnal unemployment rate Sisc;epancies. This interest, and indeed concern, still pe:rsists as a result of the appttrcn! ineffectiveness of regional policies to narrow the discrepancies. The purpose of this paper is two-fold: first, to develop a simple model of regional unemployment rate differcnccs which can be used for forecasting purposes: and secondly, to use the model to examine the regional pattern of demand, as measured by vacancy rates, which hypothetically might equal& the percentage rate of unemployment between regions. One plausible hypothesis to account for the apparent ineffectiveness of policy to narrow regional unemployment rate discrepancies is that regional economies are such, that when policy generates demand and activity in depressed regions as much activity (if not more) is generated in the prosperous regions because depressed regions buy their inputs from prosperous regions in large quantities. Using Leofiiief inverse matrices for two regions, it is easy to construct examples (which arc not unrealistic) showing a given expansion of final demand in a depressed region generating as much total activity outside the region as within [see Thirlwall (1974)]. Without knowledge of interregional input-output relations, however, there is no way of knowing what the extent of interregional linkages arc, and what the ‘optimal’ allocation of i\ew citemand would be to generate a more equal pattern of demand for goods and labour between the regions of the country. An indirect approa,ch is to concentrate on the labour market and to relate regional unemployment to rsgional indices of labour demand in a general equilibrium framework. A simultaneous equation system which links regions (i.e., which relates unemployment in one region to demand *This study was supported in its initial stages by the Industl dl Relations Section, Princeton Urliversity, and in its later stages by the Social Science Research Council. The author gratefully acknowledges the financial assistance of these two institutions, and the rosearch ar:ri computer _ assistance of Miss Joan Bennett, Mrs. E. Mitcheihill and Mr. H. White. The assistance of the Electricity Council is also gratefully acknowledged in supplying elec:tricity data by users and by Area Board over the long period I951 to 1972. i-he paper has also benefitted from discussion with my colleague, Mr. Ian Gordon.

A.B. ??xirlwll, Regional unemploymentifzG. B.

3%

in all other regions), is indispensable for this purpose. A single-equation, region by region, approach is inadequate because it would ignore the linkages and intcrdependencies that exist between regions. The best ordinal indicator of regional demand for labour is the region’s vacancy rat: as an expression of the extent of unsatisfied demand for labour relative to the size of the labour force. If there is no demand for labour there are no vacancies registered and the vacancy rate is zero. As demand expands, we expect the vacancy rate to rise. When we come to using the fc recasting model to examine the pattern of demand which would seem to be required to equalise regional unemployment rates we shall express the demand pattern in terms of vacancy rates. The regions taken for analysis are the standard regions of Great Britain over the period 1951 to 1972. Because of boundary changes, however, some regions, notably in the south and midlands, have had to be amalgamated to form consistent re,gions with unchanged boundaries over the period. The regions we work with are as follows (with their average unemployment rate ower the period given in brackets) : South East’ (I .3 %); South West (2.0%); Midlands2 (I .6x); North West (2.3 74); North (3.3 “/o);Scotland (3.5 %); and Wales (3.3 %). 2.

A

fomasting

model

The model we have in mind for forecasting purposes, and for analysing

the differential regional demand pressure to equalise uner joyment, is exceedingly simple. Its novelty is the simuitaneous det&minatL,n of unemployment in each region which makes allowance for interregional linkages. Srcifically, it is hypothesised that each region’s unemployment rate (U’) is a Cnction of (i) the pressure of demand for labour within the retion [measured bv Cc region’s own vacancy rate (V’)], and (ii) the state of demand for laboui outside the region, which can be measured by the national aggregate rate of unemployment (P”). 3 It is useful on two counts to use aggregatte unemployment as a separate argument in the regional unemployment function. First, a measure of aggregate demand is needed to capture the possibility that the supply of iabour 10 and from a region, and therefore a region’s unemployment, may respond to demand conditions outside the region. The region’s own vacancy rate may not be a good proxy for the: state of demand outside the region [(i.e., I/’ and UGB may vary independently). Secondly, it is convenient to use aggregate unemployment as an *The%utR East region is an amalgamation of the Londcjn and South East wd East and %uth Standard regions before 1966, and >f the South East and East Anglia Stawlawd regims aftsr IYti. T’m Midlands region is an amalgamation of the Midlands, North Kidlands, and Ea,t and Wcsat Ridings regions kfore 1966, and of the West Midllands, East Midland:, and York.-

rkrre tin$ Wunnkside regions after 1966. ‘In earlier papers [Thirlwil 4 19661. Harris and Yhiriwall I 1968)], regional unemployment was relakd to national unemployment in an aftcmpt to measure the cyclical sensitivity of ions COuntx~~~toymcnt. These studies . nd the present ~tx arc nrx directly cornparablsz

;ww of the dilTewnt estintatic~n methods (Ised.

A. P. Thirlwall, Regional unemploymentin G.B.

3$9

to link up regions by using the ident.ity that the aggregate y;U (i.e., I/o”) is a weighted sum of the regional rates of unemployment. I-‘.:nce for each region we specify explanatory

variable

u;

in each

= f(v;,

region

in order

up”).

(0

is further hypothesised that the adjustment of unemployment to changes in the demand for labour within and outside a region does not take place instantaneously but is a distributed lag function of past demand, so that we may write (1) in linear estimating form as It

where E, is a disturbance term. To facilitate estimation we assume the Koyck specification that the coef& cients on each explanatory variable declines geometrically, and also that the distributions on both variables have the same parameter, A, so that: bk = blzk, and c, = CA: (K = 0, 1, . . .) and 0 c A, = A, < 1, Substitution of b, and c, into (2) and some manipulation gives the Koyck transformation which has only three parameters to be estimated,’

u: = a~+bV:+cU~B+AU~_l

+E*,

= E,-IIE,_~. where ai = aO(i-A)andP The model is simultaneous in the sense that UpB is a weighted sum of the U;‘s (r = I,..., 7). The model thus consists of 7 behavioural equations and one identity, giving eight equations in eight unknowns. The system may be written out fully as follows :

USE r

uw t uM'D

t

UNW t c,

rNOR

3UPB+Gt, = a2+y21V~wty22U~_wl+~23UPB+Z2,, Q1+y,r

=

%+Ydt

=

Q44+Y41Vt NW+Y42U~-wl

=

%+Ydt

NoRty&?~+y~~U~B+z~r,

a,+Y61Vt

SCCr+‘)62U~~~T+yo3UPB+z61,

C'SCQ'= t

vsE+Y12e

=

+

1 +y1

M’D+yJ&!!I:+y3JyB+z3,, +y43UPB+z.m

w(ju~coT+ w,U~AL,

(11)

41f the ii parameter is different for each explanatory variable, the Koyck transformatio,n would contain rnorc lagged variables and more parameters to be estimated [SW Christ (1966, p. 208)J.

A.P. Thirlwail,Regional unemploymentin G.B.

360

where the W’s in eq. (11) are the weights measuring the proportional importance of a region in the nation in terms of the workforce. In matrix form, cqs. (4) to (11) may be written

where Y is an m x T matrix of endogenous variablk:s, X is a k x T matrix of predetermined variables (i.e., exogenous and lagged endogenous), I’ is an m x m matrix of coefficients on the endogenous variables, /? is an m x k matrix of coefficients on the predetermined variables, 2 is an mx T matrix of error terms, T is the number of observations, ,Wis the number of endogenous variables, and k is the number of predetermined variables. Assuming no serial correlation of the error terms, the solved reduced form for sach of the endogenous variables is Y=

-t-‘/M.

WI

If 2 is assumed to follow a first-order autoreg;es4ve scheme, then

Z = R&3-E.

(14)

z r-1 = rr,_,+gx,_,,

(13

Since

we have from ( 12)

rY-t+X+R(I’Y;_, +/IX,_,)+ E = 0,

(16)

and the solved reduced form is

where R is an m x m diagonal matrix of serial is an m x T matrix of error terms, which we will properties to allow consistent estimation. The obtained by simply regressing each endogenous variables on the system may be written Y=nX,

correlation coefficients and E assume has the usual desirable direct or fitted redus.ed form variable on all pred/:termined

(18)

where II is a IPZx k matrix of least squares coefficients which can be estimated taking account of serial correlation in the residuals [using the CochraneOrcutt ( 1949) iterative technique ].

A.P. Thirlwdl, Regional unemployment in C. B.

361

Ifi this paper both eqs. (17) and (18) are estimated for forecasting purpose:;, and comparisons made. In general, we expect (18) to have the least residual variance but (17) to be more efficient, in the sense rhat if the restrictions in tile overidentified structural model are correct the estimator that minimises the residual variation subject to the restrictions has a smalller expected squared error than the estimator that violates the restrictions while freely minimking the residual variation, e.g., that obtained from the direct reduced form. [See Christ (1966, p. 467) for a discussion of this point.] Since it is impossible to say a priori whether the model’s restrictions are correct or not, it is not possible to say in advance which reduced form will produ.ce the best forecasting results. Big differences between the direct reduced form and the solved reduced form are not unusual. Differences in the solved reduced form from different estimation procedures of the structural parameters are not unusual either. TO these procedures we now turn. To derive the reduced form estimztes in ( 17) there are a number of diflerent ways that I’, /3 and R may be estimated. Given the nature of the system under consideration two main methods were chosen for comparison. One is ordinary least squares using the Cochrane-Orcutt iterative technique to take account of first-order serial correlation ; the other is two-stage least squares also with adjustment for serial correlation. Ordinary least squares is biased and inconsistent, because the system is simultaneous. Two-stage least squares using the Cochrane:Orcutt technique to account for serial correlation is consistent, however, provided there is no contemporaneous correlation between the lagged dependent variables and the error term in the autoregressive scheme (the E matrix). [See Fair (1970 and 19711.1 Which set of estimates is chosen for policy purposes must depen& on which set of estimates seems most reasonable from an economic point oi’ view given a priori knowledge of the system. In this case we know, especially, that the weighted sum of coefficients on the UGBvariable should sum to unity and that the sign on the Vs should be negative. What set of estimates is chosen for forecasting, however,, must ultimately depend on the forecasting performance of the model. HopeCuIly, there is no clash between the two sets of estimates but often this is not the case. Moreover, there can be no geveral presumption that if one set of structural estimators has smai!er expected squared errors than another set, the reduced form estimator &ained from the first structure wiill necessari,Iy have smaller expected squared errors than the other reduced form estimator. After describing the data used for c4mating the model, the paper will proceed as follows: First, equation syst.er:n(12) will be estimated using the two techniques mentioned above. Secondly. eq. (17) will be used to solve for the reduced form using the two different se:r; of estimates of r, [i and R. The tqio sets of &mates will be compared on h basis of their economic sense arId forecasting performance. The forecastin:, 1 ,?erformance of the two sets Of SOkfd

362

A.P. Thirlwalll, Regional unemployment in G.B.

reduced form estimates built up from the structural coefficients of the system will then be compared with the forecasting performance of the direct reduced form equations in (18). ‘I’hetest of forecasting performance at this stage will be the accuracy of cond?tional forecasts as measured by the mean absolute error? i.e., the mean absolute: errs r of forecasts of the endogenous variables conditional on the actual obsemed values of the predetermined variables outside the sample period. These are outside sample forecasts with no errors in the predetermined variables. On this basis one of the three reduced forms can be chosen for making ex-ante forecasts using forecast values of the predetermined variables. If we have faith in the parameter estimates of the overidentified structural model, we might expect the solved reduced form, incorporating the restrictions of the model, ;ic,produce better conditional forecasts. If the fitted reduced form by ordinary least squares performs better, this may ‘besome indication that the model’s restrictions are incorrect. Finally, one set of reduced form equations will be used for determining the pattern of re:gional demand, as measured by vacancy rates, which would seem to be requireId to equalise regional unemployment rates at some arbitrary level, e.g., at 2 percent unemployment. 3. Data The data used in estimating the model are unseasonalised quarterly data of vacancy and unemployment rates for seven regions, and the unseasonalised quarterly rate of unemployment for Great Britain. Quarterly unemployment data for regions and in ltheaggregate for the period 1951 to 1968 weFe obtained from the Historical Abstract ofkbour Statistics, and for the period since 1968 from issues of the Department of Employment (Gazette. Quarterly vacancy data was obtained from successive monthly issues of the Department of Employment Gazette (formerly the Ministry qf Labour Gazette and the Department of Employwivnt mrdProductivity Gazette).

4. EstinWon of the stmcturaI equation 19514972 The results of estimating the model [eq. (12)] by ordinary least squares-‘using the Cochrane-Orcutt iterative technique to take account of first-order serial correlation of the residuals are shown in table 1. The results are very encouraging. First-order serial correlation i.s confirmed, the standard errors OFthe equations are very low and the coefficients of determination are very high. Equally important, the results, by and large, make economic sense. In only one region, the Midlands, is the sign on the vacancy rate: positive; and the weighted sum of the coefficients an UG*is approximately unity without any restrictions imposed. In five regions the negative coefficients on the vacancy rates are statistically significant at the 0.95 confidence levlelindicating that a region’s unemployment is highly responsive to demand conditions within its own region. All the co-

A.P. Thiriwail, Regional unemploymentin G.b’

363

efficients on the UGB variable are statistically significant at the 0.99 confidence level indicating that unemployment in all regions fluctuates Gth the general pressure of demand - with some regions more cyclically sensitive than others. The fact that the national rate of unemployment is an endogenous variablle, however, gives biased and inconsistent estimates using ordinary least squares. The model was therefore re-estimated using two-stage least squares. As shown by Fair (1970), a necessary condition for consistency is that the predetermined Table 1 OLS estimates(with adjustment for serial correlation

using Cochrane-Orcutt

iterative

technique), 195 l-l 972. w-m _ __._ -__._-._. .._-_._.-----__ -..-- _,.. - .._.__ ___x_ -...-_-. (1)

=

WE

(2) UIsW = (3) Uy’R

=

(4) VW

=

(5) UtN

=

(6) U:‘OT = (7) iJtWA* = -...--.- -.-

__..__.__. -_.___._

.--- -.-_-- -

._____. _.__._ __..____._ _

R2 .

.-- ._ -._.-__ ._..___.__.___ ._-._.-.__ ^_^.._ __.__

0.702-0.286 V,SE+0.004 U,_ 1SE+0.531 UcGB (0.049) (0.040) (0.044) 1.622-0.822 V,sw+O.OIO UI_Isw+0.673 UfGs (0.125) (0.061) (0.108) -0.568+0.115 VzMiD+0.279 U~-IM’D+0.777 UtGB (0.073) (0.048) (0.061) 0.388-0.260 VLNW+0.311U,_INW+0.743 UtciB (0.096) (0.059) (0.038) 0.675-0.099 VfN+0.016 Ut_IN+ 1.434 QGB (0.123) (0.085) (0.042) 0.986-0.530 V~CoT+0.064 U,_lSCoT+ 1.416 U,Ge (0.157) (0.035) (0.077) 0.533-0.227 VtWAL--0.005 Ut_,WAL+1.360 UtGB (0.109) (0.036) (0.077)

c __-___.. ._ __ _ _______.___ ._._-. ._. .-_

__.

-,-_-~-

Final: D. W. rho

.___ .^..__._..^ _ ..______

0.895 2.078 0.734. 0.843 2.257 0.759) 0.876 2.133 p.792: 0.932 2.265 0.661 0.852 I.698 0.952 0.916 2.253 0.884 0.900 1.664 0.973

- -.-_---.- --.----- ,__ ______.____~_---

_.._.__ --.____

--

Table 2 Two-stage least squares estimates (with adjustment for serial correlation using CochraneIOrcutt iterative technique), 1951-1972. ---______ _.______.__ ___ .--__ .I_____-___L__I Final D.W rho R2 .._^_____._______._ -.___I__-___-.___ .. __._._____-_._ ._,___._.__~__.__ ~._______________.^__ -..---.-_-.._ -______.._ = 1.004-0.360 VFE+0;092 U,_1SE+0.372 USC;” (0.065) (0.069) (0.078) (2) utsw = 2.593-1.206 Vtw+0.267 U~_1sw+0.268 UtGB (0.139) (0.083) (0.161) (3) IpD = -0.475-tO.026 V,“‘D+0.451 Ut_1M1D+0.659 UrG” (0.129) (0.090) (0.089) 14) UtNW = 0.824-0.512 VfNW+0.462 Ur_INW+0.482 U? (0.129) (0.059) (0.117) = %449-0.544 VtNi-0.573 U,_lN+0.739 utcu (5) UtN (0.141) (0.067) (0.207) (6) &SCOT-2 1.910-1.265 C’,sco’+0.228 U~-IScoT-t~;;;~JU~GB (0.063) (0.224) (7) v,wA” = 2.076-0.940 VlwAL+0.167 il,_IwAL+0.;51 UtGB (0,177) (0.098) (0.240) ..-

(1) WE

0.852 2.131 0.364 0.780 2.211 0.717 0.945 2.100 0.2s9 0.944 2.332 0.315 0.932 2.070 0.1721 0.897 2.272 0.38;’ 0.793 2.323 0.515

?64

A.P. Thirlwall, Regional unemployment in G.B.

variables of the equation to be estimated should be included as instruments, toget.her with the lagged values of all the variables appearing in the equation on the assumption of first-order serial correlation in the autoregressive scheme. The two-stage least squares results are shown in table 2. Estimation of the rnodei by two-stage least squares with ad.justment for serial correlation seems to give less satisfactory results from an economic point of view than estimation by ordinary least squares, and as one would expect, the residual variance is sometimes higher. In the Midi.ands region the coefficient on the vacancy rate is positive again, and equally worrying is the fact that the weighted sum of coefficients on the UF” variable is considerabiy less than unity. The overall fit of the equations is still good, however, but the forecasting performance of the estimates in the reduced form remains uncertain of course.

5. The solved reduced form using q. (I?)

When the matrices in (17) are multiplied and the coeficients on common variables’ are added, we have a system of equations in which each region’s unemployment rate is related to 29 independent variables. For the South East region, for example, we have

and so on for each region. The multiplicity of variables arises as a result of estimating the model on the assumption of first-order seria1 correlation. Lagged values of the endogenous and predetermined variables enter the system through the rnatrix of serial correlation coefficient5 (the R matrix}. Giw;nnthe formidable task of recording these equations for both sets of szuctural estimates, or.;Iy their forecasting perform3nce is reported here.” The redut:ei_iform predic:ions are similar to one period forecasts of tFie endogenous variables since the actual values of the lagged endogenous variables are assume; to be known for each prediction. %omCcc&Cents arc combinations of - r’appears in both the Xmatrix and the l-r-1 rmtris. The cstimtts are available on request.

* /3 and

r’-

‘i?

because lagged unemployment

A. P. Thirlwail, Rcgiorrai urremploymen~in G.B.

?h5

Forecasts for more than one period ahcad would involve, of coumc, using generated values of the lagged endogenous variables. We reserve this for forecasting outside the sample period usirig predicted values of the exogcnms variables. There are a number oferror measures that can be used in comparing the predicted with the actual values of the endogenous variables. Two commonly used ones are the mean absolute error and the root mean square error. The mean absolute error is perhaps easiest to interpret and is the measure used here. In practice, the different error measures tend to be highly correlated with each other. An assessment of the forecasting accuracy of any model must necessarily be subjective, depending on expectations and the use to which the forecasts are to be put. In the present c se, the errors are not unduly large, varying between 10 and 20 percent of the mean rate of unemployment in the different regions. Moreover there is not much to choose between the forecasts using the twostage least squares structural estimates and the ordinary least squares structural estimates. In some regions the OLS estimates give a lower mean absolute error, and in other regions the two-stage estimates give the best forecastirrg performance. 6. The direct (&ted) reduced farm using eq. (18) Estimation of the reduced form directly by okinary least squares gives the minimum residual va.riance but not necessarily the most satisfactory parameter estimates for forecasting outside the sample. Indeed, the presumption is that efficiency is lost in fitting the reduced form directly by ignoring the structural information of the system. The mean absolute error of the within-sample forecasts can be expected to be lower than the forecasting errors reported in table 3, but the outside-sample forecasts may be worse. In this section, the Table 3 Within-sample forecasting performance of the solved reduced form model., 1951-1972. .__ __ _. .._ _.__ __._ ._.._ -.-.--_ -_-._ “.__.._ ._... _..._. Criterion of forecasting performance

South East

South West

Midlands

North West

_. .__ -.

North

Scotland

Wales

Great. Britain

0.572

0.390

0.697

0.416

.

Sohed reduced form using OLS structural estimates

Mean absolute error _.. .

0.225

0.769

0.474

0.313 ..-

_.

_. ._. -

_

0.574

0.652

---.-. .

Sohed reduced form using 2SLS structural e:rt.‘nrates

Mean absolute error _ _-. F

0.356

0.8%

0.319

0.321

0.509

0.621

._.

..-

..- _.__._ _._ .___.___..__~__ ~. -- ---- ..-_ -_ _ ___ ______

__ _~

_. _.__.._____

_._ _ ___.~ _

._---.

R2

._~___._^_

Rho

--~ _...- _

1.859

2.240

1.985

0.978

0.974

1.764

- 0.035

-0.167

0.049.

0.113

__.~._.... - .-__--

0.965

e-957

.--__

D.W.

--

iterative techkque), 1951-1972.

_ ____ ._______. - .___. P-

.,- ._-

V,SE-0.252 Ftsk +0.324 VcMID-0.112 VINW s-O.277 V,N+0.364 Vtscor-0.059 VtWAL (0.108) (0,129) (0.089) (0.108) (0.111) (0.130) (0.145)

l.JISE = 1.627-0.496

--.--. --..

-0.086 U,-1se+0.265 Ut-1sw+0.328 U,_,“‘D+0.054 Ut_INW+0.026 U,_1N-0.130 U+lsco= (0.142) (0.084) (0.067) (0.071) (0,085) (0.036) - 0.059 C&_lWAL (0.058) (2) &SW = 2.638-0.516 V+O.849 V,sb +00.496 V~“‘Fi0.012 V,NW-0.320 V1y+0.571 V~SmT-0.262 VCWAL (O.lb5) (0,136) (0.165) (0.198) (0.201) (0.170) (0.222) - 1.152 U,_1SE+0.736 Ur_1sW+0.843 U,_1M’D-0.119 L’~_1Nw-0.060 Cf+IN-0.027 Ul_IsCoT (0.217) (o:?Y;, (0.128) (0.103) (8.109) (0.130) +0.014 U+IWAL (0.088) (3) LyD = G.976-0.215 VtsE--0.342 V,sw+0.317 VIM’D-0m295 V,Nw-0.046 V,“+0.187 V,SCoT~0.048 VtWAL (0.153) (0.183) (0.126) (0.153) @.i57) (0.186) (0.205) -0.138 L/~-~Se+0.072 Ut_1sw-tl.293 U+1M’LP-0.270 frL TNW-Q.022 U,_,N+0.012 U,_rxoT (0.201) (0.119) (0.096) (0.101) (0.121) (0.052) -0.061 Ut_lWAL (0.082) (4) tJtNW = 1.450- 0.598 Vtse- 0.027 V,sw+ 0.497 VtMID - 0.643 VtNw+ 0.073 V,” + 0.191 C’tsco++ 0.033 VtWAL (0.173) (0.207) (0.142) (0.178) (0.210) (0.232) (0,173) 0.380 Up-~SE-00.004 Ut-1sw+0,523 U,_1M’D+0.548 U,_1NW+0.006 Ur_,N+0.032 Ut_ISCoT (0.227) (0.134) (0.108) (0.136) (0.114) (0.058) -0.036 Ut_*WAL (0.092)

(I)

___.

~..-_

Table 4 Direct reduced firm by ordinary least squares (with adjustment for serial corrdation using Cochrane-Orcutt

.

A.P. Thirlwa!l, Regional unemployment in G.B.

d I

5 d I

I

d

5 d

3

o\l 0

A.P. ?‘hirlwall, Regiooral uttemployment ,QIG.B.

368

direct reduced form equations, and the within-sample forecasts, are presented (tables 4 and 5, respectively). Later, the dircci reduced form model is used to make c:ontlitior,aI forecasts for 1973. These are then compared with the conditional forecasts from the solved redlxced form. The direct reduced form is estimated by ordinary lea.st squares using the Cochr;me--0rcutt iterative technique to adjust for serial correlation. It can be seen from table 4 that the coefficient estimates look very reasonable from an economic point of view. The sig;ls on all the ‘own’ vacancy rates are negative with the exceptii>n of the Midlands region. Some of the coefficients are not statistically signii,cant at the 0.95 confidence level, but in thle presence of multiccsllinearity there is no ?-As for rejecting the variables from t’heequatitins. The direct reduced fcrm also shows some interesting interi-e$o;lal linkages. In the sovth, labour would seem to be fair!y mobile between the two broad regions of the South F.ast and South West. ‘Unemployment in the South East falls in response to both an increase in labour dt:mand in the South East and in the South West. Likewise, labour demand in the South East affects unemployment in the South West. Unemployment in several other regions also appears to be linked to the demand for labour in the South East and South West. Table 5 Within-sample forecasting performance of the direct reduced form model, 1951-1972. __

_ -. _.

Criterion of forecasting performance ._____-_.--_.

__. _. _ - ~__

__-.-._.-_.-. _-_-__-

South East ____--

South west

0.069

0.113

.

-.-- ---.---I

Midlands North West -_-_- -.._I_

..__.

---- --..-- ..--. --

North - __.__._~_.

-..- ..---_I

Scotland

_..- -,-.--.--.^

Wales

_ _-___ ._.-__- _________

Great Britain __

Mean absolute CITOT - -. - .

- -----~

iI.

-_.-. ---.----_-.

0.109 -

.-.--_

0.174 --.

0.163

_.._~ - - .---_

0.155

0.090

---- _-._--_. .__.__-.__-.-

There are two possible explanations for this apparent link. One iC &at there is a genuine response of the r,lnemployed in regions outside the south to employment opportunities in the south. The other is that the vacancy rates for the South East and South West are standing as a proxy for national demand conditions with which unemployment in all regions is closely associated. It is impossible here to distinguish between these two hypotheses. It zan be seen from table 5 above that the witbTn-sample forecasting performance of the direct reduced form model is extrem?! v good. There is no region in which the mean absolute error is gloater than 0.2 percentage points, or more than 8 percent of the mean rate of unemployment. Whether the model provides good outside-sample forecasts depends on the stability of the structure of the model. Preliminary testing showed that the structure of the model is not stabIe enough for the outside-sample forecasts

A. F. Thirlwali, Regional uncmploymen~ in G.B.

369

to be as good as the within-sample forecasts, but which of the ti:,rez versions of the model perform better is an empirical question. A comparison of table 5 and tabie 3 might suggest that the direct reduc(:d form will give better conditional outside-sample forecasts than the solved reduced form. Strictly speaking, however, for the reasons mentioned earlier, this cannot be said with any confidence; one must simply compare performance. For comparison of the models, outside-sample forecasts arc made for the 4 quarters of 1973, using the parameter estimates of the model for 1951 to 197’2. The outside-sample forecasts, like the within-sample forecasts, are essential:ly one-period ahead forecasts using known values of the lagged endogenous vari~b’tes. The mean absolute errors reported are averages of each af the four quarters of 1973, The re.
Table 6 Outside-sample forecasting performance of the mo.!el estimated over the period 1951-1972,and predicting for 1973. Criterion of forecasting performance

South East

South West

Midlands North West

North Scotland Wales

Wved reduced form using OLS structural estimates

Mean absolute error ____

.___ -___

0.22 --.-...

1.30

_.-_-_

0.45

.- - ----_-_-_~__--

0.47 __.___

1 .oa

0.52

0.88

-__-____-._-I_.__

Solved reduced form using 2SLS structural estimates

Mean absolute error _ ____

0.60

1.50

____.__.__.____ .__-__..-.-._-. _ _

0.55 ._

0.67 __ ____. ..-..-..-.

0.80 ~._._ -._...__

1.28 I_____,_.

____

1.30 __

__

Direct reduced form with adjustment for serial correlation

Mean absolute error ._.__.._._.._-

0.32 _._.. -_. ,_. -- _

0.80 .-

0.22 . -- .--

0.15

0.80

_. _ _._,.__ . . _ .._.----

0.52 ..-, __.._..._ ._

0.65 _

...^._

In general, the outside-sample forecasting performance of the solved reduced form is inferior to that of the direct reduced form. The solved reduced form using 2SLS structural estimates is consistently inferior, while the solved reduced form using C&S structural estimates forecasts better in only two out of the seven regions. Without further refinement of the model, and without further outside-sample forecasting, it was decided to use the direct reduced form to make ‘tue oatside-sample forecasts wing predicted values of the predetermined variables.

370

A.P. Tltirl;vall,Regional unemploymentin G.B.

The direct reduced form model will also be used for solving for the pattern of regional demand (as measured by vacancies]) to equalise regional unemployment rates. 8. E-x-anteforecasts using predicted values of the predeterminedvariabEes To make forecasts of the futarc: requires some method of forecasting the predetermined variables, which in the direct reduced form consist of regional vac;incy rates and regional unemployment rates lagged by one period. Two problems. immediately arise. First, how do we predict vacancy rates; and secondly, how dc we treat endogenous variables lagged one period in multiperiod forecasting? Strictly speaking, unemployment lagged one period can only be known one period ahead. For forecasting more than one period ahead, lagged unemployment rates are really not predetermined variables at all, but endogenous. It is not clear what to do about this problem. One possibility would be to extend the period of the lagged endogenous variables, but this would involve altering the structure of the model. Another possibility would be to make forecasts period by period taking the generated values of unemp?oyment in the current period as the lagged value of unemployment for predicting unemployrtY=n
A.P. Thirlwall, Regional urlemployment in G.B.

371

six quarters. Despite the fact that the areas covered by the Electricity Boards are not always the same as the Standard regions,7 some interesting correlations did emerge. The most significant correlation in most regions is between the vacancy rate and electricity consumption two quarters back. From what knowledge there is of employment-output relationsh:ps, the lag between changes in the demand for labour and electricity consumption might be expected to be roughly of the order of 6 months and this is confirmed by tlhe data. The equations used for forecasting vacancies are given in table 7, where ET,‘Ec and E’ stand for total, commercial and industrial electricity consumption, respectively, and where consumption is measured in millions of units (t values in brackets). up

to

Table 7 The correJation between vacancy rates and electricity consumption, 1951-1972. . _ .-.-

VtSE = 1.018 + 0.000229 Et _ 2c (6.2) VSW = 0,988+0.00167 E+ 2c I

KM = c/DNW= V

=

KW = vts

=

(3.0) 0.820+0.000041 E,-tr (3.7) 0.800+O.OOOo68& 2.r (3.1) 0.32O-tO.OOO24 Et_ 2T (4.0 0.360+0.00Of4 El_ 2T (4.0) 0.330f0.00045 E,- 2’ (3.8) . _.

r2 = 0.329

v2 = 0.219 r2 = 0.148 Y2= 0.110 r2 = 0.178 ?J = 0.169 r2 = 0.330 .- -....---__-

The two-period lag allows us to forecast up to two quarters ahead without indulging in the dubious process of extrapolating the exogeneous variables, but the forecast for the second quarter ahead must use generated values of the lagged endogeneous variables from the first-quarter forecast. What errors this introduces into the second-quarter-ahead forecast is hard to say, but the forecasts and forecasting errors can be compared with those using known values of the predetermined variables. The forecasts for the first two quarters of 1973, ;The London and Central, South Eastern, Southern and Eastern Area Boards were aggregated to form an area close in coverage to the South East region; the Midiands,*East Midlar& and Yorkshire Area Boards were amalgamated to form an area cIose to the Mldiands region; South Wales and Merseyside and North Wales cvere aggregated to form an area approximating to Wales; the Scottish Area Boards were amalgamated to L:over Scotland; the North Ea.st Area &xud was assumed to approximate to the North Region, and the South West and North West Area Boards were assumed to approximate to the South West and North West regions, respectively.

372

A.

P. Thirlwall, R~gionul unemployment ii1 G. B.

based’on

the structure of the model estimated over the period 195 i--1972, are shown in table 8. The mean errors for the first two quarters of 1973 are in some regions h&l=r than-the mean errors using known values of the predetermined values in 1913 and sometimes lower.8 In general it appears that very little forecasting accuracy is lost using predicted values of the predetermined variables, and in one or two cases (presumably where the structure has changed quite sharply) some fGrecasting accuracy is gained. Overall, it cannot be concluded that the model is of little use unless the predetermined variables are known. Table 8 Forecasts of unemployment outside the sample using predicted values of the pmletermined variables; 19%1972. __ __.-_ __._-__-.---_-----... . . .._M-..--_.-_ ..-_-.-.__ -~- ____ . .__.._-. South East ___

1st

-_

__. _

South west

~.._ -.-... ..-. -.-.~--

----

Midlands

North West

---. -~ -.- --.---^

-

North -

Scotland Wales

- --.. -- .------.----

-.-.---..-----

True Predicted

1.9 1.9

3.1 2.7

3.0 2.5

4.3 4.0

5.5 5.4

5.7 5.3

4.4 4.4

Error

0

0.4

0.5

0.3

0.1

0.4

0

1.6 1.4

2.5 2.1

2.4 2.1

4.8 4.4

4.8 4.2

3.8 3.5

0.2

0.4

0.3

3.7 3.2 -0.5

0.4

0.6

0.3

0.40

13.40

0.25

0.50

0.15

quarter

True Predicted 2nd quarter -_ En-or Mean error __

___.. ._. .__.

0.10 _

0.40 -

._ . _

-. _. _.___.__..

. . ._... .._..

.___ _____ __.

.__ ___

Whether the errors reported in table 8 imply a good or bad forecasting performance is largely a matter of subjective judgement. One possible test of usefulness is to compare the errors with the errors derived from the naive hypothesis that unemployment in the current quarter will be the same as in the last quarter. On this test the mean errors are as follows : South East (0.2) ; South West (0.35); Midlands (P.4); North West (0.35); North (0.55); Scotland (0.55); and Wales (0.5). Compared with the naive hypothesis, the model performs ‘worse’ in the North West and South West but better in the other five regions. It is a little worrying that the forecasts in two regions should give inferior predictions to the assumption that unemployment will be the same in the fiuture as in the past; on the other hand, it is comforting that ahe model performs better than such a naive prediction in five regions out of the seven. Before becoming unduly pessimistic or optimistic, however, we shall have to subject the model to much raore extensive testing outside the sample period. ‘Appamtly main model.

the side relation to predict vacancies is more stable than the structure of the

373

9, The pattern of demand to equalise regional unemploymentrates Given the forecasting performance of the direct reduced form model, the estimates in table 4 are used to obtain some idea of the pattern of demanc , as rzeasured by regional vacancy rates, that would be required to equalisc regional unemployment rates in the ‘general equilibrium’ framework outlined. An unemployment rate of 2 percent is assumed for each region. This has been the average rate of unemployment in Great Britain over the sample period. To sofve for the pattern of vacancies that would equalise the U”s at 2 percent, set

Thus gives a new matrix Y = x*X*, where n* is now of dimension m x finand X* is of dimension VIx T. Hence X* = n*-’ Y gives the values of V’ which equalise unemployment in each region at 2 percent. The results obtained. are shown in table 9, in comparison with the average vacancy rates which have actually prevailed over the sample period. Table 9 Required vacancy rates to equalise regional unemploymcn t rates at 2 percent. _____._,____,^__-___-__-

Required V’s Region __._ ._...._.__ __.____^ _..__ ____. -0.34 South East 1.52 South West 0.76 Midlands 2.95 North West 1.95 North I.55 Scotland 2.57 Wales __-_...

.,. - _ _ _. ._.__- -..-. - -

--I-.

--

.-

__

__...__

-

_.._..

.._.

.

.

Actual V’s (Average 1951-1972) - _._.-..___-.--__

-. .-...

1.50 1.40 1.42 1.13 0.80 0.75 0.98 .--

The results show that the pattern of demand required to equal&e region& unempIoyment rates, as measured by vacancy rates, is the reverse of that which has prevailed in the past. The regions with the highest vacancy rates over the period require the least demand pressure to achieve 2 percent unemploymeni, whereas those with the lowest vacancy rates require the greatest demand pressure. The North West and W;ijes in particular seem to require a very high pressure of demand, as measukd by vacancies, for unemployment to be 2 percent. The differential demand pressure required for the equaiisation of uncruployment rates is a reflection of three main factors; firstly, differences in the amount of unemployment in regions which exists independent of the pressure of demand; secondly, differences in the responsiveness of unemployment to demand within the region, and thirdly, differences in the repercussions th:it demand in one region has on others. We know from (other str:dies? however, [Thirlwali (1969), Cheshire (1973)], that the rate of unemployment which i,

A.P. Thirlwail, Regional unemployment

374

irt G.B.

independent of the pressure of demand does not differ markedly between regions and that the sensitivity of unemployment to demand is, if anything, higher in high unemployment regions than in low unemployment regions. It wculd seem, therefore, t:hat the differential pattern of vacancies outlined in table 9 is mainly a reflection of interregional labour demand relations. In the South East region, for example, the fact that the pressure of demand would apparently have to be such that l-he vacancy rate is negative is almost certainly due to the strong repercussions that extra labour demand outside the south would have on the demand for labour in the south because of the quantity of inputs ‘the north purchases from the south. On the other hand, the feedback effects of the south on the north are probably much less. All this leads to the conclusion that if a yeally serious attempt is to be made to equalise unemployment rates between regions, and unemployment in the north is to be reduced without creating labour shortages in the south, labour demand must be severely curtailed in the south while the :north is expanded. The differential demand pattern between regions to equalise unemployment is substantially different from that indicated if each region is taken in isolation without considering interregional linkages and the repercussilans that the expansion of demand in one region has on others. In a way, the regional demand problem is more serious than appears on the surface in the sense that to equalise unemployment it would not only be necessary to raise dem;snd in the north to the level in the south, but in excess of the level in the south becacse the north apparently makes much heavier demands on the south than the south does on the north. This is not LLnew conclusion by any mean,s. Casual empiricism has suggested this conclusion for years. This study, however, provides strong empirical evidence to support the conclusion and gives some measure of the demand expansion required in the north and of the demand restraint required in the south. References Cheshire, P., 1973, R.egional unemployment difl‘erences in Great Britain (Cambridge University Press, London). Christ, r.. 1966, Econometric models and methods (Wiley, New Yfvk). Cochrarle ‘D. and G.H. Orcutt, 1949, Application of least squarcx regression to relationships containrng auto correlated error terms, Journal of the American Statistical Association, Mar&. i-air, R . l970, The estimation of simultaneous equatiarl models with lagged er,dogenous variabitrs and first order serially correlated errors, ECorli;*Kv::i;a, M:I~. Fair, R., 1971, A s h o rt -run forecasting model of thr s. Ii g#Ii*-rl. 1 Stiiteh ~conc~my (I3.C. f-leath, LeGig

on).

Harris, C-P. and A.P. Thirlwall, 1968, 1nterregior;aI uariatk 1s in cqclicril sensitivity to unemployment in the U.K., Bulletin of the Oxford Institute o’ tconomic!; and Statistics, Feb. Thirlwali, k-P., 1966, Regional unemployment as a cyclical p: ,cnomenon, Scottish Journal of PolitiG4 Ectinon\!~, June. Thirhvall, A.P., 196O,Types of unemployment with special reference to non dcrnand - Deficient unemployment in Great Britain, Scottnsh Journal of Political Economy, Feb. Thirlwall, A.P., 1974, Regional economic disparities and regional policy in the European Economic Community, Urban Studies, Feb.