- Email: [email protected]
The Southampton econometric model
The Southampton Econometric Model
David F. Heathfield Four reasons are offered for presenting a paper on a now dehct model. First it was one of the very few attempts to construct a large-scale econometric model of the UK. Second, is its monetary sector few modei of that vintage had such a sector and, unlike modern models, its monetary sector was strictly Keynesian. Third is the explicit modelling of output and price equations. And fourth is the treatment of disequilibrium. Disequilibrium arises through the incompatibility of plans: total demand, for example, may exceed total supply and pro&s may be exceptionally high or unsustainably low. The rest of the paper gives a fuller account of the role of these disequilibrium terms in the explanation of price and output changes. Lists of equations and working papers are attached. Keywords:Economic model; Supply side; Disequilibrium
The author is with the Department of Economics, The University, University Road, Highfield, Southampton So9 5NH, UK. ri
manuscript received 2 September
The Southampton Econometric Model Building Unit was set up in 1965 with a grant from the SSRC (UK) and ran for 12 years until 1977 when the grant was withdrawn. The principal aim of the Unit was to construct an econometric model which could be used to test economic theory. It was not therefore an exercise in forecasting (although of course one way of assessing economic theory is on its ability to forecast) and was not in competition with time series models. We were, however, interested in policy prescriptions. Improving economic theory should lead to better economic advice being given to policymakers. But it was also argued that economic theory alone was of limited use in formulating policy since it yields so little guidance as to the size (or in some cases even the sign) of the parameters of the model and this information is vital for policymaking. The empirical side of the modelling was therefore aimed at testing and quantifying economic theory. Though no longer operational, the model building exercise is, for perhaps four reasons, still of interest today. First, the aims of the unit were unique and perhaps over-ambitious and hold lessons for those who now argue for small, or even single equation, economic and time series models. Second its monetary sector, due to D. C. Rowan, marked it out from both its contemporaries (which had no monetary sector) and from its modem counterparts by being purely Keynesian. Third is the specification of explicit supply decision and price decision equations of firms. This is a departure from the usual Keynesian assumptions that output passively follows demand and that prices follow costs, and bears directly on the ‘supply side’ emphasis now being given to economic theory and economic policy. Fourth is the treatment of disequilibrium market clearing is not assumed and indeed persistent disequilibrium in some markets will influence price and supply decisions. This paper therefore deals largely with the real sector of the Southampton Econometric Model (SEM) and particularly its supply decision equation and its treatment of disequilibrium. The monetary sector is briefly outlined and a list of equations is attached. The specification of SEM offered here derives largely from that outlined by Pearce [3] with some modifications described by Heathfield and Pearce [l]. A note on the data period The terms long run, short run and medium term seem to be designed to
108
0284-88W84/010108-18
$03.00@ 198q Butterworth &Co (Publishers) Ltd
77w Southamptvn
Economcbic hknid: D. F. IhthjWd
indicate the reliable range of various forecasting models and at the same time to indicate the kind of simplifying assumptions adopted by the model builder. Short-run models achieve some simplicity by treating high inertia variables as constants. They typically use quarterly or even monthly data and are best suited to behavioural equations associated with a short decision period. Long-run models use annual data and consequently have a somewhat restricted view of low inertia variables. Neither of these forms of simplification was compatible with our aims and hence SEM was specified in quarterly periods but at the same time did not exclude the possibility of endogenous ‘structural’ change. In the equations which follow, the time subscripts refer to quarters as if they were aggregate decision periods. This together with the underlying causal chain, gives SEM an appearance of recursiveness.
The red sector of the model We begin with the basic accounting identity that home supply plus imports equals home ‘demand plus exports, plus inventory change, plus valuation adjustments. The valuation adjustment or adjustment to factor costs absorbs those taxes imposed between buyers and sellers. Thus:
Z?(f)+ S(f) - D=(t)+ DG(t)
+ D”(t)
+ H(t)
+ dy(t)
- A(t)
(1)
where = quantity of home supply at ex-works prices during the period 90) P(t) = quantity of imports at exdocks prices D%) = consumers’ expenditure at retail prices DG(t) = public authorities current expenditure (PACE) at buyers’ prices = gross domestic fixed capital formation at buyers’ prices 5;; = change in inventories at buyers’ prices ox(t) = UK exports at FOB prices A(t) = adjustment to factor costs This identity is highly aggregative. It distinguished only one type of commodity, two types of suppliers and five types of demanders. Disaggregating this single commodity group into various subgroups of commodities is essentially different from further disaggregation of suppliers or demanders. It is the disaggregation of the single commodity group which sets SEM in the multisector class. We may write, for each subgroup of commodities, an identity similar to Identity (1) in that what is produced or imported of that subgroup must go somewhere, but since commodities may be used in the production of commodities a sixth element of demand, industrial demand, must appear on the demand side. This kind of demand is-of course netted out in the aggregate form. One further change in the identity was necessary. Part of the change in value of each commodity group between the producer or importer on the one hand and the final buyers on the other is the value added by the distributive trades. This value-added had to be allocated to its own commodity group and hence had to be deducted from the demand side of every non-distributive group of commodities. This is more fully treated elsewhere (21. For the moment we can regard it as a valuation problem and treat it as we treated the adjustment to factor cost term. ECXMMIC
MODEUW3
January 1984
108
‘I&
&uthamptonEwm
Mod& D. F. Hmthfi& The disaggregated identity, using the subscript i to denote the commodity group, is then:
SF(t) + ST(f) = Of(t) + D?(t) + D:(t) + D?(f) + D:(f) + D!(t) - A&) - A;(r)
(2)
where #(t) = industrial demand for the eh commodity as a single use intermediate input A;(f) = distributive margin on the final sales of the i’h commodity The nature and degree of this disaggregation was to some extent at choice. In his original specification Pearce [4] distinguished between traded and non-traded goods, but this distinction was simply not possible with the data then available. Already then we were obliged to compromise between the requirements of theory and the availability of data. Nevertheless the scheme of disaggregation chosen may have been such that some classes were more traded than others and hence it may still have been possible to investigate the effects of changing their relative prices. It will be evident from Identity (2) that the same scheme of disaggregation must apply to each element in the identity. It was also the case that each element is subject to its own specific classification in the published data. For example, home supply by the Standard Industrial Classification (SIC), imports and exports by the Standard International Trade Classification (revised or unrevised) (SITC), inventories by another and fixed capital formation by yet another. Such a rich variety of classifications is no doubt considered useful for sector studies where, for example, consumer demand requires categories which are regarded as homogeneous by the consumer, and production decisions require categories which are homogeneous in the eyes of the producer. But for an integrated model these separate classifications had, at some stage, to be reducible to a common classification. We found that the only classification into which the others may be transformed was the SIC. This was principally due to the impossibility of reclassifying factors of production into anything other than the SIC. Having decided upon a classification for our disaggregation it remained to specify the extent or degree of disaggregation. This was largely a matter of balancing the rather ill-defined benefits against the equally ill-defined costs. The greater the degree of disaggregation the easier it was to transform other classifications into the common one and more could have been said about the structure of the economy. On the other hand the published data became less reliable beyond a certain level of disaggregation and the amount of work, like the number of equations, grew at a more than proportionate rate. As a first step we decided upon a 14 sector classification thus:
110
Industry
1958 SIC heading
Agricultural forestry and fishing Mining and quarrying Food, drink and tobacco Chemical and allied industries Metal manufacture Engineering and allied industries
I II III IV V VI, VII, VIII and IX
ECONOMC MCNELUM
January 1984
l7u Southampton Econolncaic Model:
D. F. Heuthjkld
X,XIandXII XIII, XIV, XV and XVI XVII XVIII
Textile, leather and clothing Other manufacturing Construction Gas, electricity and water Services Public administration (including ownership of dwellings) Non-competing imports Sales by final buyers
This included every commodity encountered in the UK and was a ‘typical product’ classification. That is, any commodity, whether home produced or imported, was allocated to that SIC sector which would have typically produced it had it been produced in the UK. Those commodities not typically produced in the UK (eg citrus fruits and tobacco) were allocated to the non-competing import sector. This scheme of disaggregation was not immutable1 and there was a case for separating mineral oil refining from other chemicals and for separating wholesale and retail trades from other services, but for the moment we consider only 14 sectors. (For a description of these various classification transformations see Southampton Discussion Papers Series Sl-$20 and NSl-NW a list of titles is attached.) Apart from this disaggregation, by type of commodity, the demand side was also further disaggregated. The notion of a single representative consumer was retained in the sense that we did not distinguish between different so&-economic groups. This clearly ruled out the possibility of investigating the effects of changing income distribution, but the amount of work involved was beyond our resources, Government current expenditure remained a single element of demand as did exports but this latter (like imports) may well have been better treated if disaggregated according to country of destination (origin). Part of the total demand for fixed capital formation was by the public authorities (on capital account) and this was treated separately. The remaining fixed capital formation was demanded solely by industry as were single-use intermediates and inventories. These three industrial demands were further disaggregated between 14 separate industry groups using the same classification as was used for the 14 commodity groups. This yielded the input-output matrix, the incremental fixed capital stock matrix and the incremental inventory matrix. The identity became:
s:(t) + S?(t) = (14)
Of(t)
(14)
+ @(f)
(14)
+ D?(t) +
(14)
li $w (14 x 15)
(14)
+ (14 x 14)
(14 x 14)
(14)
(14)
where a single subscript denotes the commodity group and a double subscript denotes first the commodity and second the industrial demander.
‘Analternative scheme of diiggregation attached to the Appendix. ECONOMY lWDEW#W
is
The figures in parentheses indicate the number of categories within each term and imply that 700 quantity variables have to be generated and explained. This 700 is, however, purely notional. Many of the categories did not exist. For example there were no industrial demands for ‘public
January 1984
111
mesowthampton Ecouromcnic Model:
D. F. Heathfiid
administration’ and ‘noncompeting imports’ demanded neither singleuse intermediates nor fixed capital. Nevertheless the number of variables remaining was quite substantial. Diiuilibrium The next stage was to formulate equations for each quantity variable. We confined our attention to four types of equation; the first three of which are well known. (i) Behavioural equations which represent the behaviour of an identifiable decision taker with regard to a variable over which he has control and those variables which influence his behaviour with respect to that variable. (ii) Technological, institutional and quasi-legal relationships such as production functions and the liquidity ratio of commercial banks. (iii) Identities, which simply permit a useful shorthand. The fourth type of equation, which might be called a data generating equation, did not appear in the model, but used economic theory to generate the data not available from official sources. The theory used for this purpose could not subsequently be tested against model data. Decision equations are usually derived by assuming some form of maximizing behaviour subject to certain constraints. Some of these constraints will be known by the decision taker and hence may properly and directly influence his decision. Other constraints will be less clearly known and yet others will be completely unforeseeable. Imperfect knowledge of constraints may lead decision takers to formulate plans which are either achieved but in retrospect are sub-optimal or which turn out to be unattainable. This latter means that what was originally planned at the beginning of the decision period differs from the actual outcome during the decision period. Differences such as these we called unplanned behaviour. The existence of unplanned behaviour means that our data, which described actual behaviour, were no longer suitable for testing those equations which referred to planned behaviour. Either the data had to be separated out into planned and unplanned elements or the behavioural equations had to be modified to include both planned and unplanned behaviour. We adopted a little of each of these solutions. Unforeseeable events, such as strikes, severe winters and intemational crises, can be introduced into what would otherwise be planned behavioural equations by using dummy variables. Let us call the outcome of these hybrid planned and unplanned equations the ‘predicted value’ of a variable. There remained one further constraint which seemed to us different in kind from those already mentioned and it was central to the specification of SEM. Our accounting identities clearly held ex post but there was no mechanism for ensuring that they also held ex ante. Even when predicted values were used there remained the possibility of incompatibility between the various decision takers. Many other models ignore this ex antelex post distinction and use the identities to generate some quantity variables. Modem monetarist models assume market clearing with supply side dominant hence they ignore demand; older Keynesians assumed goods markets clear with demand side dominant hence they ignore supply. Both are ways of avoiding difficulties but also miss some important aspects of a free enterprise economy. 112
EcoNGlmcMoDEuJN
G January 19B4
The Southampton Econontctric Model:
D. F. Huzdfkld
Unplanned activity which arose from incompatibility seemed to us to differ from that arising from other unforeseen events. Whereas, for example, a severe winter may throw one off course, the course remains unchanged. But unplanned activity arising from incompatibility requires a change of course; a change of course which is designed to achieve compatibility. Furthermore there seemed to be no short cut way of allowing for this unplanned activity in estimating the behavioural equations. It was necessary to know the size and sign of the disequilibrium term and how it is allocated among decision takers. The use of dummy variables or stock adjustment models in place of this compatibility constraint relies on fairly restrictive assumptions which we did not wish to make. In SEM the size of the disequilibrium term was determined by the residual of the identities. The allocation of this term among the various elements in the identity was the subject of a number of suggestions but the simplest, following Keynes, was to assume that inventory holders absorb all this unplanned activity. This we argued, is, in part, precisely what inventories are for. The identification of disequilibrium with unplanned inventory changes promoted the stockbuilding equation from a rather minor element of demand to a central role in SEM. If, as we supposed, inventories are held to absorb differences between supply and demand then it is reasonable to suppose that unplanned changes in inventories provide decision takers with some indication of the incompatibility between them. Thus, it is partly by reacting to unplanned inventory changes that the decision takers seek to avoid persistent incompatibility. The disequilibrium term is therefore one of the principal driving forces in the model. Confining unplanned activity to inventory holders and the use of dummy variables to represent some unforeseen events solved the problem of generating observations of each of our ‘predicted’ quantity variables except inventories. Any difference between what we have called ‘predicted values’ and actual values was (save in the case of inventories), by assumption, an unsystematic error term. Observations of inventories however comprised the ‘predicted value’ plus an unplanned element plus an error term. For the period over which we had observations of inventories we could find the disequilibrium term by simply subtracting predicted inventories from actual inventories. Thus, work using the disequilibrium term could proceed without first having to estimate every element in the identity. This also meant that the disequilibrium term did not have to absorb the errors in the other (non-inventory) predicted values. If the disequilibrium term was found from the identity then any error in the predicted value of any variable would appear in the residual. Outside the sample period, where we had no observations of inventories, it was of course necessary to generate the disequilibrium term from the identity.
Home supply, prices and inventories These three items were treated together because we believed them to be interrelated decisions of a single decision taker. We first set out the decision making process and then we consider problems involved due to SEM’s system of disaggregation. We assumed that at the beginning of each decision period (in our case one quarter) the entrepreneur sets a price and output for the coming 6coNoMKz MOOEUNG
January 1984
118
The So~ton
Euwwme@ic MO&:
I
Figure 1. Average costs, average revenues and price/output combinations.
D. F. He&jkld period. There are clearly other variables which he controls (eg wage rates and advertising) but we limited ourselves to investigating his output and price decisions. We further assumed that he was aware of the shape of his average cost curve and of the fact that increasing his prices would, ceteris puribus, cause demand for his product to fall. He was not aware of the actual shape or position of his demand curve nor was he aware of the position of his cost curve. The cost curve shifted due to exogenous (to the entrepreneur) changes in factor prices and the demand curve shifted due to (again exogenous to the entrepreneur) changes in other prices, incomes, tastes etc. Some of these shifts would be predictable by the entrepreneur (for example paid holidays and Christmas spending) and he could moderate his output and prices accordingly. For the rest we assumed that the entrepreneur would leave production and prices unchanged until he received some indication from the market that he has misestimated demand or until he received some indication from his accountant that he has misjudged his costs. The former could be perceived through his inventory changes and the latter through his profit figures. Apart from the equilibrium positions there were four possible outcomes. (i) Excess profits positive and unplanned inventories positive. This implied that his current prices/output combination was above both the average revenue curve and the average cost curve. (ii) Excess profits positive and unplanned inventories negative. This implied that his current price/output combination was above his average cost curve but below his average revenue curve. (iii) Excess profits negative and unplanned inventories negative. He was below both the average cost and the average revenue curves. (iv) Excess profits negative and unplanned inventories positive. .He was below the average cost curve but above the average revenue curve. The four positions are shown diagrammatically in Figure 1. We assumed that he would always try to be on the average revenue curve so as to suffer no unplanned inventory changes, and that he would want always to be above (or at least on) his average cost curve so as to suffer no losses. Being above his average cost curve did not, however, necessarily provoke change. We further assumed that when faced with the alternative of altering either output or price he preferred to alter output. This was because of the costs of price changes and his uncertainty about their effect on the market. As he approached capacity, changes in output gave way to changes in prices. Thus in position (i) he would reduce output or reduce prices; (ii) he would increase output or increase prices; (iii) he would increase price; and (iv) he would reduce output. This implied that his reaction to unplanned inventories and excess profits depended upon the combination of the two and hence we needed four equations to ‘explain’ changes in output and changes in prices the choice of equation depending upon the nature of his disequilibrium. Thus our equations became:*
We made no allowance in these equations for any constraint on the entrepreneur due to money capital limits perhaps today this omission is rather more important than it -seemed in the halcyon days when inflation was not a probkm.
111
AS;(t) = olt + lo; + o&+(t - 1) + Q Afl+(t - 1)1 + 14 + ar7z:i+(t - 1) + arsA 4-(t - 1)1 + IdO + @ ni(t - 1) + art,,A G+(t - l)/ ECONOMIC MODEUJNG January 1984
The Southampton Ectnwmebic Model: +
Ia;:
+
a13
+ (Kg2
a11 Jci(t -
-
1)
+
arl2LI C’-(t
1) - K,(t - 1))
-
D. F. Hcrrdrficld
111
(4)
where A$‘(0 are t
0) n*Y(0 W’(t) Ar-(t)
= change in gross output at constant prices = constant = time = excess profits (positive) in money terms. = excess profits (negative) in money terms = unplanned inventory changes (positive) in constant price terms = unplanned inventory changes (negative) in constant price terms
and G(t) L(0
= optimum capital usage capacity term ) = actual capital usage
The square brackets go to zero if either variable within goes to zero. An exactly equivalent equation was used for price change except of course the parameters will differ.
The monetary sector A great deal of work was done on this sector and some of that work is reported by Rowan and O’Brien ($61. We did not in fact integrate the real and monetary sectors although, as they developed, the links between them became apparent and there was no obvious incompatibility. Because of this almost independent development and because so much work had been done in the monetary sector any detailed description of that sector merits a paper of its own. (This is true also of course of the econometric work and the data generation and handling techniques which were developed). Nevertheless because of the rise in monetary theory and its introduction into many erstwhile Keynesian models a brief outline of the monetary sector and its links with the real sector may be helpfully included here. The monetary sector comprised three subsections of: (i) the central authorities (defined as the Bank of England and the Treasury); (ii) the commercial banking sector; and (iii) a composition of non-bank financial intermediaries, corporate enterprises and households. The approach used was basically Keynesian with the assumed equality between the supply of and the demand for moneyresulting in a rate of interest - in this case at the equity rate. This rate together with the administered bank rate formed the basis of a structure of interest rates comprising those two, the rate on Consols and the rate on Treasury Bills. This structure was determined by the difference between the portfolio of assets supplied and that demanded so that equilibrium was brought about by compensating movements in interest rates. The supply of money was determined in part by the liquidity base of the commercial banking system and its multiplier. The liquidity base was in turn determined by the monetary base, the non-banking public’s ECONOMY MODEUJW January 1984
1lS
The Southampton Ecommeic
Model:
D. F. Hcorhfild demand for currency and special deposits. The public’s demand for currency was determined by transaction needs which in turn depended upon the money value of GNP. Thus the real sector intruded upon the monetary sector. The monetary base and special deposits were instruments through which the central authorities achieved their targets. These targets may be in the real sector or the monetary sector but were taken to be: (i) (ii) (iii) (iv) (v)
the level of registered unemployed; the rate of change of aggregate price level; the balance of payments; the rate of growth of real GNP; and an orderly market for government debt.
The first four of these represent ways in which the real sector (via the central authorities reaction function) influenced the monetary sector. The ways in which the monetary sector affected the real sector at various points may be summed up as: (i) changes in interest determining capital gains which enter the consumer demand equations; (ii) changes in interest rates affecting the incomes of interest receivers; (iii) changesin interest rates affecting the cost of capital particularly in the dwelling sector; and (iv) changes in bank advances which enter consumer demand equations.
A commentary To translate a conceptual framework based upon economic theory into a system of equations with each variable designated so as to correspond with some identified data series was no small task, particularly when the number of series called for was something in excess of 1500. Matching an econometric model to published data is a process which involves both experiment and compromise. Where no published data existed it was easiest to modify the model. But this frequently implied abandonment of the economic theory which it was our object to test. The alternative, which whenever possible we tried to adopt, was to attempt to construct the missing series by reference to raw data, by manipulation of published information or by the application of economic theory itself. The cost of this alternative was high. Specially constructed series had to be subjected to tests for consistency and accuracy and the value of alternative procedures compared. Furthermore the use of specially constructed series complicated the problem of updating very much more than proportionately. Quite apart from the obvious difficulty of estimating any such system of equations and of displaying the results in some readily comprehensible way, it became clear that any comprehensive model of the economy required its own specific system of national accounts. These enormous data difficulties and the very long-term pay-off period for a model of this kind eventually led to its demise. That is not to say that the project was either a mistake or a failure.
The equations It is not our intention, nor would it be possible in a paper of this length, to derive each set of equations by closely reasoned argument. What we 116
ECONOMY MODEUJNG January1984
The Southampton Econometric
Model: D. F. Heathjkld
have tried to do is to provide a clearly specified set of equations and to stress the constraints on them due to the need for overall consistency.
SEM - a listing of equations The basic accounting indent@ g(t) + SF(?) a D?(t) + D?(t) + D?(t) + i +
f:
D{{t) + i
qj(t)
0$(f) - A,(t) - A;(t)
(1)
The consumers expenditure equation
wo - W)~
_
(1
_
A)
w -
V - W(t) PRO) 6
_
(1
A)
1))
1
1
W - CW - 1) PR(t - 1)
PR(t - 1)
Wf)
+ 8
_
CG(t - 1) -CW - (1 - A)
+ p [HP(t) -
mt -
PR(t - 1)
PRO)
+
1) -
1
(1 - A) HP(t - 1)) BA(t - 1)
BA(f) -[I Wf)
PR(t - 1)
+ rl {PR(f) - PR(f - 1)) _ (1 _ h) {PR(t - 1) - PR(t - 2)) PR(t - 1)
+ v
-pm -
PR(t - 2)
(1 - IL)
PR(f)
PM(t - 1) PR(f - 1)
I+
e(f) - (1 - k)e(f - 1)
(t 1
1 J
(2)
The inputloutput coefficient determining equation Uij(f)= %+%
pj
1) +
zpfli i
[ Indushial
January 1984
41
+
a,?
(3)
demand for single use intermediates
q(t> * F
ECONOMiC IWOELUM
2
a2t
%,Cf> $CO
(4) 117
The Soathampton Ecronomcnic Model:
D. F. Heathfield Industrial demand for investment in plant and machinery
~pnst) =
or0 +
K~tA)
F
d.[OO
h(t - i) +
+
- K,(t - i)} + F oj n’(t
- i)]
&&j(t
- j) +
ff3ppw
(5)
+
(6)
Outputlcapital ratio of plant and machinery Y*(T) = Yo+ZZ
t=T K,(t - 1) _R f$ Kn(t - 1) +O
s=O K,(t)
K,(t)
ar,K,(t) + ar2t
An equation similar to Equation (6) is used to explain changes in capital/labour ratios. Industrial investment in buildings and works L(t)
= Mpm(t
+ 1) -
aroluspm(Ol + ~z&vW
(7)
Industrial investment in vehicles
%SW
Z”(f) = a(J + -
L(t)
+ w + ML(f)
(8)
Registered unemployment equation
(9)
RU(t) = oc + arlU(t)
lndustrial employment equation [L$L$(t
AL,,(t) = aAl,
- 1) - L$.L$(t
- 2)]
[L$L,d(t - 1) - L:L,d(t - 2)]
WJ)
Non-wage labour cost equation NWLCi(t) = [NHZ(t) + SETi(
L&t)
(11)
Wage costs of self-employed equation
w;;(t)
= [w,(t)
wci(t)
+
x
niT(t)l
wxo + ~iT”‘O)l
(12)
Import equation (goods) AS?(t) = a,, + cqAc(t
X
-
‘)f~2[(~)i(t-l)-(~)i(t-2)]
s?(t - 1) + ar3[Kti(t - 1) - K+,(t - l)]
(13)
Non-competing imports equation is similar to Equation (13) but without the price or capacity terms. lt8
ECONOMIC MODELLIM
January 1984
l7u Southampton Economuric Model: D. F. Heath@&
Import equation (services) ASr(t) = cq,+ QAS”‘(f) + Ap(t)]
+ asAY,
(14)
Export equation (goods) AH(t) = oro+ a~A$(t) + a&‘f(t) - f’!‘(t)] ti(t - 1)
(15)
Industry basic hourly wage rate equation W,(t) - Wi(t 7 1) =
W(t) - W(t - 1)
wi(t - 1)
[ x
X
1)
W(t L$L$t
-
1
1) - L$L$(t - 2)
[
Ld,L$i(t - 2)
1
L,dLd,(t - 2)
1
L,“Ld,(t - 1) - L,dLd,(t - 2 J
(16)
Aggregate supply of man hours equation L”,(t) L”,(t) = ocl + cv1t + ar28 +
a3
L&t)
+
a4 F(t)
+a~RA+a!(jsLA
(17)
Wage cost equation W,,(t) = CQ+ a1 LNut(t) +
a2 Ldf)
Lui(r)
+ a3 wi(t)
(18)
Aggregate employment equation AL,(t)
= CQ + ar,[L,d(t) Ld,(t) - L,d(t - 1) Ld,(t - I)1 + lxz[Lf(t - 1) Ld,(t - 1) - Ld,(t - 2) L,d(t - 2)] +
a3 z?U(t)
(19)
Aggregate unemployment equation AU(t) = AL;(t) - AL,(t)
(20)
Supply of new labour equation LS,(t)-ar,+ar,t+cuzZ?A+or3SLA
(21)
Distribution margins on consumer goods di(t) = Cyl+ a$ + cW# + QTt(t) + @t(t) + ~7fw) + %a EcoNo#Bc MOOEUNG
January 1984
+ %Vi(t) (22)
119
l%e souduunptonEconometricModel:
D. F. H~athfkld Home suppry decision equation
AS:(f) = aIt + [4, + @-Ii’-(t - 1) + ~Afl+(t - l)] + [& + ar,l-Ii+(t- 1) + arsAc-(t - l)] + [& + @-I,(t - 1) .+ cw,oAG+(t- l)] + [CY:+ culJIi(t - 1) + curzA$‘-(t - l)] + ar@*,(t - 1) - K& - l)]
(23)
Home ex-works price decision As Equation (23) but with A*(f) as the dependent variable. Planned inventory level equation P(t) = Q + cy&(t) + a2t
(24)
This equation is applied to finished goods, work in progress, raw
material and fuel and distribution sector separately. ProfiB equation IlT n SfPi - C P&‘aji - W&‘piyi - T i
(29
Aggregate hourly basic wage rate equation
wo -
W(t - 1)
W(t - 1) + oI
2
= are + arQ.#:Ls,- L,dLd(t - 1)
ww) - PNt - l)l
(26)
PI?(t - 1)
Import price equation r(t)
= obp~(f) x ER(f) + orIT
+ ar2DY(t)
(27)
Export price equation pi”(r) = ar,Pi”(r)x I%(t) + CYST(t)
(28)
Variables treated as exogenous to the model
(i) (ii) (iii) (iv) (v) (vi) (vii) 120
All government expenditure; Investment in dwellings; International capital flows; Tax rates and subsidies; Exchange rate; Exports of services; Sales by final buyers. ECONOMIC MODELUNG January 1984
fh Usting
i9bhampton Econom
tricModel: D. F. Heathj%ld
of variables used supply of r* commodity by home producer valued at constant wholesale prices supply of I* commodity from overseas valued at constant ex docks prices consumer demand for commodity constant retail prices
i valued at
government demand for commodity i valued at constant ex works/ex docks prices ti
=
Df
= UK demand for fixed capital of eh type valued at
industrial demand for single used intermediates of type i values at constant ex works/ex docks prices constant buyers prices
M
=
Df
= home demand for additions to inventories of the P”
overseas demand for I* commodity valued at constant UK export prices commodity valued at constant supply prices
VAi + V-A.:
= valuation adjustment to reduce all valuations used in
the identity to wholesale prices (ie includes distribution margins and some taxes)
IEcOMMC
PRi
retail price of P commodity
PR
aggregate retail price
1
rate of depreciation of stocks of consumer durables
Y
disposable income
EX
consumers expenditures which are exogenously determined valued at current retail prices
W
current value of wealth
CG
capital gains
HP
proxy for hiie purchase controls
BA
bank advances
PM
marginal price of the gas, electricity and water sector
a
seasonal dummy
e
error term
aii
input output coefficient
P
wholesale price
t
time
&pm
investment in plant and machinery by the r* home sector measured at constant buyers price
K*m
stock of plant and machinery currently held by ?” industry measured at 1958 replacement cost
MODELUNG January 1984
121
The Southampton Econornbc
Model: D. F. Heathfkld
KL
=
desired capital usage in the 8” industry
Klli
=
actual capital usage in the z* industry
nT
=c
total profits earned in the z6 industry
p*
=
buyers price of plant and machinery
L.IBW
=
investment in buildings and works by the zti industry valued at constant buyers prices
K.#BW
=
stock of buildings and works held by the r* industry valued at 1958 replacement cost
=
investment in vehicles by the I* industry valued at constant buyers prices
=
world price of i commodity (in dollars)
=
UK taxes (excluding purchase taxes) on imported commodity i
Iiv
DT
X
UK
c
=
UK taxes on UK exports of commodity i
ER
z
exchange rate (f/$)
4
=
percentage mark up by distributors of consumers goodsoftypei
Ti
=
Ri
=
Vi
X
Di
=
purchase tax (implicit rate) on consumer goods of type i abnormal sales of consumer goods of type i (constant retail price value) current ex dock value of imports of i divided by current ex dock/ex works price value of all i sold to consumers retail price maintenance dummy
=
normal hours
SET
=
Selective Employment Tax
NHI
=
National Health Insurance
=
demand for labour stock
=
demand for labour hours
=
supply of labour stock
2=
supply of labour hours
TL
=
standard rate of income tax
RA
z
retirement age
SLA
P
school leaving age
D
P
resale price maintenance dummy
I”
=
unplanned inventories
P
=
planned inventories
LNH
L”, Ld, Ls, L”,
122
duty on imported commodity i
ECONOMIC MODELUNG January 1984
The Sothampton
Econometric Model: D. F. Heathjkld
References D. F. Heathfield and I. F. Pearce, ‘A view of the Southampton Econometric Model of the UK and its Trading Partners’, in A. G. Renton, ed, Modelfing the Economy, Heirtern-, London, 1974. D. F. Heathfield and G. J. Evans, ‘Distribution margins in the UK: a quarterly analysis’, Applied Economics, NQ. 3,197l. I. F. Pearce, ‘The Southampton Econometric Model of the UK and its trading partners’, in K. Hilton and D. F. Heathfield, eds, The Economerric Study of the United Kingdom, Macmillan, London, 1970. I. F. Pearce, ‘The problem of the balance of payments’, Znrernational Economic Reuiew, January l%l. D. C. Rowan, ‘The monetary sector of the Southampton Econometric Model’, in K. Hilton and D. F. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. D. C. Rowan and R. J. O’Brien, ‘Expectations, the interest rate structure and debt policy’, in K. Hilton and D. F. Heathfield, eds, The Econometric Study of the United Kingdom, Macmihan, London, 1970.
Appendix New SEM dkggregation
A
L M 0 P Q R S T
scheme
A Agiicufuuc. forestry and fishing B Construction partof c chcmicais D Publicadministration E Engineering Food manufacturing partof F GaS partof w
9 14
andpartof 7 -
partof s DartOf 0 partof w M partof c part of s Extraction part of Q R Other manufacturing Services and water partsof Sand W Textiles, leather and T clothing Distribution Coal mining Electricity Metal manufacture Mineral oil refining Transport
u V
sales by final buyers Alcoholicdrink and
Z
tobacco Total, all industries
partof
6 3
part of 15 1 4 partof 6 2 16 12 partof 7and13 part of 15 8
11
Z
Reconstruction of former SEM scheme New scheme
A B C -
A B c+o D
D
EcoNoIHlc
MOOUUNG
E F+V M -
Q
Q+K
R S T U W Z
R S + H + P (less water) T U G + L(plur water) Z
10
U partof F
Fermer SBM
E F M N
January 1984
Relationship with CSO scheme New SEM 1 2
K 0 G L C+R E+M T A F V
3
4 5n113 6 8
9
10 11 12 14
Q
B H+S P
:i Relation to SIC (IWS) New SEM
SIC
A B C
Order1 GrderKX Grders IV and V, except mlh 262 123
The Southampton Econometric Model: D. F. Heathjkld D E F G H K L M 0 : R S T U V
Order KKVII Orders VII to XII Order III (excluding mlh’s 231,239, and 240) mlh 601 Order XXIII mlh 101 mlh 602 Order VI mlh 262 Order XXII Order II, except mlh 101 Orders XIII to XIX Orders XXIV to XXVI, mlh 603 Orders XIII to XV mlh’s 231, 239 and 240
Source papers Sl s2 s3 S4 S5 S6
S7 S8 s9 SlO Sll s12 s13 s14
s15 S16 s17 S18 s19 s20
Statistical sources for international trade sectorgeneral, K. Hilton. Estimation of consumers’ expenditure by industry, K. Hilton. The estimation of imports, exports, etc by industry, K. Hilton and D. Heathfield. Industrial classification of consumers’ expenditure, K. Hilton. Industrial classification of public authorities’ current expenditure, K. Hilton and D. Heathfield. Industrial classification of supply of fixed capital formation and stockbuilding (plus amendment), K. Hilton and D. Heathfield. Industrial classification of imports, exports and re-exports, D. Heathfield. Gross output at current prices by industry, K. Hilton and D. Heathfield. Distribution margins and intermediate products, D. Heathfield. Price indices of industrial inputs and outputs, K. Hilton and D. Heathfield. Weights used for the index of import prices, R. Hall. Consumers’ expenditure, G. Evans. Data specification and processing - labour sector, G. Evans. Index of import prices (gross of duty) (incorporating Sll -weights used for the index of import price), R. Hall. Corporate data, C. T. Stromback. An econometric model of the UK and its trading partners, A. Harrison. Estimates of expected demand: a note (plus supplement), P. K. Trivedi. Unduplicated quarterly gross output at current prices, R. Chang. Taxation - amendments to the data bank, J. D. Byers, I. F. Pearce, P. Smith, C. T. Stromback. The cost of capital, G. Anderson, P. K. Trivedi.
Series ‘A’ - application papers A.1 A.2
A.3 A.4
A.5
A.6
A.7
A.8
A.9
A.10
Some notes on consumer expenditure functions for the UK, D. Tumham, K. Hilton and D. Crossfield. Short-run consumption functions for the United Kingdom, K. Hilton and D. Crossfield, in K. Hilton and D. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. Evidence on the quantity theory in the United Kingdom, K. Hilton. Aggregate quarterly dividend behaviour in the United Kingdom, G. R. Fisher, in K. Hilton and D. HeathfIeld, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. Expectations, the interest rate structure and debt policy, D. C. Rowan and R. O’Brien, in modified form in K. Hilton and D. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. Capital and capacity utilisation in the United Kingdom, K. Hilton, Discussion Paper 7003, Bulletin of Oxford University Instituteof Statistics, Vo132, No 3, 1970. Distribution margins in the United Kingdom - a quarterly analysis, D. Heathfield, Discussion Paper 7007, Applied Economics, October 1971. A generalised approach to Stone’s model for aggregate consumption expenditure, M. S. Common, Discussion Paper 7008, to be published in shortened form in Manchester School. Planned stockholding: evidence from British company data, K. Hilton and D. Cornelius, Discussion Paper 7201. The demand for current account deposits, D. Rowan, Discussion Paper 7204.
!Se.ries‘T’ - theory papers T.l T.2 T.3 T.4
T.5
T.6
T.7
Some notes on the Southampton model, I. F. Pearce. A system of relationships for the Southampton model, I. F. Pearce. The application of the Brookings’ model dwelling sector to United Kingdom data, T. Espenshade. The Southampton Econometric Model of United Kingdom and its trading partners (First report on the SEM), I. F. Pearce, in modified form in K. Hilton and D. Heathfield, eds, The Econometric Study of The United Kingdom, Macmillan, London, 1970. The monetary sector of the Southampton Econometric Model, D. C. Rowan, in K. Hilton and D. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. The treatment of goods and services in the real sector of the Southampton Econometric Model (Second report on the SEM), D. Heathfield. A view of the Southampton Econometric Model, D. Heathfield and I. F. Pearce.
ECONOMICMODELUNGJanuary 1984
The Southampton Ewnometric Model: D. F. Heathjield
Series ‘M’ - method papers M.2 M.3 MA
MS
On the asymptotic significance of ratio estimates, R. O’Brien and K. Hilton. The stability of linear time series relationships, R. O’Brien. Serial correlation in econometric models, R. O’Brien, in K. Hilton and D. Heathfield, eds, The Economem’c Study of the United Kingdom, Macmillan, London, 1970. The Bayesian analysis of partial adjustment models, R. O’Brien.
New source papers NSl Employment series (El), P. Smith. NS2 Wholesale (home sales) price index, S. P. Chakra“arty. NS3 Exports, C. J. Stromback.
ECONOMC MODEWNG January 1984
NS4 Income from employment, P. Smith. NS5 Taxes on expenditure less subsidies, C. J. Stromback. NS6 Consumer’s expenditure, T. Harrison. NS7 Earnings, hours and wage rates, P. Smith. NS8 Interindustry conversions, T. Harrison.
Southampton discussion papers in economics and econometrics No 7505 Input-output in the Southampton Econometric Model of the United Kingdom and its trading partners, S. P. Chakravarty, E. R. Chang, D. F. Heathfield, A. Ingham. No 7601 Some preliminary simulation experiments with the labour-wage-price sector of the Southampton Econometric Model, P. Smith.
125
David F. Heathfield Four reasons are offered for presenting a paper on a now dehct model. First it was one of the very few attempts to construct a large-scale econometric model of the UK. Second, is its monetary sector few modei of that vintage had such a sector and, unlike modern models, its monetary sector was strictly Keynesian. Third is the explicit modelling of output and price equations. And fourth is the treatment of disequilibrium. Disequilibrium arises through the incompatibility of plans: total demand, for example, may exceed total supply and pro&s may be exceptionally high or unsustainably low. The rest of the paper gives a fuller account of the role of these disequilibrium terms in the explanation of price and output changes. Lists of equations and working papers are attached. Keywords:Economic model; Supply side; Disequilibrium
The author is with the Department of Economics, The University, University Road, Highfield, Southampton So9 5NH, UK. ri
manuscript received 2 September
The Southampton Econometric Model Building Unit was set up in 1965 with a grant from the SSRC (UK) and ran for 12 years until 1977 when the grant was withdrawn. The principal aim of the Unit was to construct an econometric model which could be used to test economic theory. It was not therefore an exercise in forecasting (although of course one way of assessing economic theory is on its ability to forecast) and was not in competition with time series models. We were, however, interested in policy prescriptions. Improving economic theory should lead to better economic advice being given to policymakers. But it was also argued that economic theory alone was of limited use in formulating policy since it yields so little guidance as to the size (or in some cases even the sign) of the parameters of the model and this information is vital for policymaking. The empirical side of the modelling was therefore aimed at testing and quantifying economic theory. Though no longer operational, the model building exercise is, for perhaps four reasons, still of interest today. First, the aims of the unit were unique and perhaps over-ambitious and hold lessons for those who now argue for small, or even single equation, economic and time series models. Second its monetary sector, due to D. C. Rowan, marked it out from both its contemporaries (which had no monetary sector) and from its modem counterparts by being purely Keynesian. Third is the specification of explicit supply decision and price decision equations of firms. This is a departure from the usual Keynesian assumptions that output passively follows demand and that prices follow costs, and bears directly on the ‘supply side’ emphasis now being given to economic theory and economic policy. Fourth is the treatment of disequilibrium market clearing is not assumed and indeed persistent disequilibrium in some markets will influence price and supply decisions. This paper therefore deals largely with the real sector of the Southampton Econometric Model (SEM) and particularly its supply decision equation and its treatment of disequilibrium. The monetary sector is briefly outlined and a list of equations is attached. The specification of SEM offered here derives largely from that outlined by Pearce [3] with some modifications described by Heathfield and Pearce [l]. A note on the data period The terms long run, short run and medium term seem to be designed to
108
0284-88W84/010108-18
$03.00@ 198q Butterworth &Co (Publishers) Ltd
77w Southamptvn
Economcbic hknid: D. F. IhthjWd
indicate the reliable range of various forecasting models and at the same time to indicate the kind of simplifying assumptions adopted by the model builder. Short-run models achieve some simplicity by treating high inertia variables as constants. They typically use quarterly or even monthly data and are best suited to behavioural equations associated with a short decision period. Long-run models use annual data and consequently have a somewhat restricted view of low inertia variables. Neither of these forms of simplification was compatible with our aims and hence SEM was specified in quarterly periods but at the same time did not exclude the possibility of endogenous ‘structural’ change. In the equations which follow, the time subscripts refer to quarters as if they were aggregate decision periods. This together with the underlying causal chain, gives SEM an appearance of recursiveness.
The red sector of the model We begin with the basic accounting identity that home supply plus imports equals home ‘demand plus exports, plus inventory change, plus valuation adjustments. The valuation adjustment or adjustment to factor costs absorbs those taxes imposed between buyers and sellers. Thus:
Z?(f)+ S(f) - D=(t)+ DG(t)
+ D”(t)
+ H(t)
+ dy(t)
- A(t)
(1)
where = quantity of home supply at ex-works prices during the period 90) P(t) = quantity of imports at exdocks prices D%) = consumers’ expenditure at retail prices DG(t) = public authorities current expenditure (PACE) at buyers’ prices = gross domestic fixed capital formation at buyers’ prices 5;; = change in inventories at buyers’ prices ox(t) = UK exports at FOB prices A(t) = adjustment to factor costs This identity is highly aggregative. It distinguished only one type of commodity, two types of suppliers and five types of demanders. Disaggregating this single commodity group into various subgroups of commodities is essentially different from further disaggregation of suppliers or demanders. It is the disaggregation of the single commodity group which sets SEM in the multisector class. We may write, for each subgroup of commodities, an identity similar to Identity (1) in that what is produced or imported of that subgroup must go somewhere, but since commodities may be used in the production of commodities a sixth element of demand, industrial demand, must appear on the demand side. This kind of demand is-of course netted out in the aggregate form. One further change in the identity was necessary. Part of the change in value of each commodity group between the producer or importer on the one hand and the final buyers on the other is the value added by the distributive trades. This value-added had to be allocated to its own commodity group and hence had to be deducted from the demand side of every non-distributive group of commodities. This is more fully treated elsewhere (21. For the moment we can regard it as a valuation problem and treat it as we treated the adjustment to factor cost term. ECXMMIC
MODEUW3
January 1984
108
‘I&
&uthamptonEwm
Mod& D. F. Hmthfi& The disaggregated identity, using the subscript i to denote the commodity group, is then:
SF(t) + ST(f) = Of(t) + D?(t) + D:(t) + D?(f) + D:(f) + D!(t) - A&) - A;(r)
(2)
where #(t) = industrial demand for the eh commodity as a single use intermediate input A;(f) = distributive margin on the final sales of the i’h commodity The nature and degree of this disaggregation was to some extent at choice. In his original specification Pearce [4] distinguished between traded and non-traded goods, but this distinction was simply not possible with the data then available. Already then we were obliged to compromise between the requirements of theory and the availability of data. Nevertheless the scheme of disaggregation chosen may have been such that some classes were more traded than others and hence it may still have been possible to investigate the effects of changing their relative prices. It will be evident from Identity (2) that the same scheme of disaggregation must apply to each element in the identity. It was also the case that each element is subject to its own specific classification in the published data. For example, home supply by the Standard Industrial Classification (SIC), imports and exports by the Standard International Trade Classification (revised or unrevised) (SITC), inventories by another and fixed capital formation by yet another. Such a rich variety of classifications is no doubt considered useful for sector studies where, for example, consumer demand requires categories which are regarded as homogeneous by the consumer, and production decisions require categories which are homogeneous in the eyes of the producer. But for an integrated model these separate classifications had, at some stage, to be reducible to a common classification. We found that the only classification into which the others may be transformed was the SIC. This was principally due to the impossibility of reclassifying factors of production into anything other than the SIC. Having decided upon a classification for our disaggregation it remained to specify the extent or degree of disaggregation. This was largely a matter of balancing the rather ill-defined benefits against the equally ill-defined costs. The greater the degree of disaggregation the easier it was to transform other classifications into the common one and more could have been said about the structure of the economy. On the other hand the published data became less reliable beyond a certain level of disaggregation and the amount of work, like the number of equations, grew at a more than proportionate rate. As a first step we decided upon a 14 sector classification thus:
110
Industry
1958 SIC heading
Agricultural forestry and fishing Mining and quarrying Food, drink and tobacco Chemical and allied industries Metal manufacture Engineering and allied industries
I II III IV V VI, VII, VIII and IX
ECONOMC MCNELUM
January 1984
l7u Southampton Econolncaic Model:
D. F. Heuthjkld
X,XIandXII XIII, XIV, XV and XVI XVII XVIII
Textile, leather and clothing Other manufacturing Construction Gas, electricity and water Services Public administration (including ownership of dwellings) Non-competing imports Sales by final buyers
This included every commodity encountered in the UK and was a ‘typical product’ classification. That is, any commodity, whether home produced or imported, was allocated to that SIC sector which would have typically produced it had it been produced in the UK. Those commodities not typically produced in the UK (eg citrus fruits and tobacco) were allocated to the non-competing import sector. This scheme of disaggregation was not immutable1 and there was a case for separating mineral oil refining from other chemicals and for separating wholesale and retail trades from other services, but for the moment we consider only 14 sectors. (For a description of these various classification transformations see Southampton Discussion Papers Series Sl-$20 and NSl-NW a list of titles is attached.) Apart from this disaggregation, by type of commodity, the demand side was also further disaggregated. The notion of a single representative consumer was retained in the sense that we did not distinguish between different so&-economic groups. This clearly ruled out the possibility of investigating the effects of changing income distribution, but the amount of work involved was beyond our resources, Government current expenditure remained a single element of demand as did exports but this latter (like imports) may well have been better treated if disaggregated according to country of destination (origin). Part of the total demand for fixed capital formation was by the public authorities (on capital account) and this was treated separately. The remaining fixed capital formation was demanded solely by industry as were single-use intermediates and inventories. These three industrial demands were further disaggregated between 14 separate industry groups using the same classification as was used for the 14 commodity groups. This yielded the input-output matrix, the incremental fixed capital stock matrix and the incremental inventory matrix. The identity became:
s:(t) + S?(t) = (14)
Of(t)
(14)
+ @(f)
(14)
+ D?(t) +
(14)
li $w (14 x 15)
(14)
+ (14 x 14)
(14 x 14)
(14)
(14)
where a single subscript denotes the commodity group and a double subscript denotes first the commodity and second the industrial demander.
‘Analternative scheme of diiggregation attached to the Appendix. ECONOMY lWDEW#W
is
The figures in parentheses indicate the number of categories within each term and imply that 700 quantity variables have to be generated and explained. This 700 is, however, purely notional. Many of the categories did not exist. For example there were no industrial demands for ‘public
January 1984
111
mesowthampton Ecouromcnic Model:
D. F. Heathfiid
administration’ and ‘noncompeting imports’ demanded neither singleuse intermediates nor fixed capital. Nevertheless the number of variables remaining was quite substantial. Diiuilibrium The next stage was to formulate equations for each quantity variable. We confined our attention to four types of equation; the first three of which are well known. (i) Behavioural equations which represent the behaviour of an identifiable decision taker with regard to a variable over which he has control and those variables which influence his behaviour with respect to that variable. (ii) Technological, institutional and quasi-legal relationships such as production functions and the liquidity ratio of commercial banks. (iii) Identities, which simply permit a useful shorthand. The fourth type of equation, which might be called a data generating equation, did not appear in the model, but used economic theory to generate the data not available from official sources. The theory used for this purpose could not subsequently be tested against model data. Decision equations are usually derived by assuming some form of maximizing behaviour subject to certain constraints. Some of these constraints will be known by the decision taker and hence may properly and directly influence his decision. Other constraints will be less clearly known and yet others will be completely unforeseeable. Imperfect knowledge of constraints may lead decision takers to formulate plans which are either achieved but in retrospect are sub-optimal or which turn out to be unattainable. This latter means that what was originally planned at the beginning of the decision period differs from the actual outcome during the decision period. Differences such as these we called unplanned behaviour. The existence of unplanned behaviour means that our data, which described actual behaviour, were no longer suitable for testing those equations which referred to planned behaviour. Either the data had to be separated out into planned and unplanned elements or the behavioural equations had to be modified to include both planned and unplanned behaviour. We adopted a little of each of these solutions. Unforeseeable events, such as strikes, severe winters and intemational crises, can be introduced into what would otherwise be planned behavioural equations by using dummy variables. Let us call the outcome of these hybrid planned and unplanned equations the ‘predicted value’ of a variable. There remained one further constraint which seemed to us different in kind from those already mentioned and it was central to the specification of SEM. Our accounting identities clearly held ex post but there was no mechanism for ensuring that they also held ex ante. Even when predicted values were used there remained the possibility of incompatibility between the various decision takers. Many other models ignore this ex antelex post distinction and use the identities to generate some quantity variables. Modem monetarist models assume market clearing with supply side dominant hence they ignore demand; older Keynesians assumed goods markets clear with demand side dominant hence they ignore supply. Both are ways of avoiding difficulties but also miss some important aspects of a free enterprise economy. 112
EcoNGlmcMoDEuJN
G January 19B4
The Southampton Econontctric Model:
D. F. Huzdfkld
Unplanned activity which arose from incompatibility seemed to us to differ from that arising from other unforeseen events. Whereas, for example, a severe winter may throw one off course, the course remains unchanged. But unplanned activity arising from incompatibility requires a change of course; a change of course which is designed to achieve compatibility. Furthermore there seemed to be no short cut way of allowing for this unplanned activity in estimating the behavioural equations. It was necessary to know the size and sign of the disequilibrium term and how it is allocated among decision takers. The use of dummy variables or stock adjustment models in place of this compatibility constraint relies on fairly restrictive assumptions which we did not wish to make. In SEM the size of the disequilibrium term was determined by the residual of the identities. The allocation of this term among the various elements in the identity was the subject of a number of suggestions but the simplest, following Keynes, was to assume that inventory holders absorb all this unplanned activity. This we argued, is, in part, precisely what inventories are for. The identification of disequilibrium with unplanned inventory changes promoted the stockbuilding equation from a rather minor element of demand to a central role in SEM. If, as we supposed, inventories are held to absorb differences between supply and demand then it is reasonable to suppose that unplanned changes in inventories provide decision takers with some indication of the incompatibility between them. Thus, it is partly by reacting to unplanned inventory changes that the decision takers seek to avoid persistent incompatibility. The disequilibrium term is therefore one of the principal driving forces in the model. Confining unplanned activity to inventory holders and the use of dummy variables to represent some unforeseen events solved the problem of generating observations of each of our ‘predicted’ quantity variables except inventories. Any difference between what we have called ‘predicted values’ and actual values was (save in the case of inventories), by assumption, an unsystematic error term. Observations of inventories however comprised the ‘predicted value’ plus an unplanned element plus an error term. For the period over which we had observations of inventories we could find the disequilibrium term by simply subtracting predicted inventories from actual inventories. Thus, work using the disequilibrium term could proceed without first having to estimate every element in the identity. This also meant that the disequilibrium term did not have to absorb the errors in the other (non-inventory) predicted values. If the disequilibrium term was found from the identity then any error in the predicted value of any variable would appear in the residual. Outside the sample period, where we had no observations of inventories, it was of course necessary to generate the disequilibrium term from the identity.
Home supply, prices and inventories These three items were treated together because we believed them to be interrelated decisions of a single decision taker. We first set out the decision making process and then we consider problems involved due to SEM’s system of disaggregation. We assumed that at the beginning of each decision period (in our case one quarter) the entrepreneur sets a price and output for the coming 6coNoMKz MOOEUNG
January 1984
118
The So~ton
Euwwme@ic MO&:
I
Figure 1. Average costs, average revenues and price/output combinations.
D. F. He&jkld period. There are clearly other variables which he controls (eg wage rates and advertising) but we limited ourselves to investigating his output and price decisions. We further assumed that he was aware of the shape of his average cost curve and of the fact that increasing his prices would, ceteris puribus, cause demand for his product to fall. He was not aware of the actual shape or position of his demand curve nor was he aware of the position of his cost curve. The cost curve shifted due to exogenous (to the entrepreneur) changes in factor prices and the demand curve shifted due to (again exogenous to the entrepreneur) changes in other prices, incomes, tastes etc. Some of these shifts would be predictable by the entrepreneur (for example paid holidays and Christmas spending) and he could moderate his output and prices accordingly. For the rest we assumed that the entrepreneur would leave production and prices unchanged until he received some indication from the market that he has misestimated demand or until he received some indication from his accountant that he has misjudged his costs. The former could be perceived through his inventory changes and the latter through his profit figures. Apart from the equilibrium positions there were four possible outcomes. (i) Excess profits positive and unplanned inventories positive. This implied that his current prices/output combination was above both the average revenue curve and the average cost curve. (ii) Excess profits positive and unplanned inventories negative. This implied that his current price/output combination was above his average cost curve but below his average revenue curve. (iii) Excess profits negative and unplanned inventories negative. He was below both the average cost and the average revenue curves. (iv) Excess profits negative and unplanned inventories positive. .He was below the average cost curve but above the average revenue curve. The four positions are shown diagrammatically in Figure 1. We assumed that he would always try to be on the average revenue curve so as to suffer no unplanned inventory changes, and that he would want always to be above (or at least on) his average cost curve so as to suffer no losses. Being above his average cost curve did not, however, necessarily provoke change. We further assumed that when faced with the alternative of altering either output or price he preferred to alter output. This was because of the costs of price changes and his uncertainty about their effect on the market. As he approached capacity, changes in output gave way to changes in prices. Thus in position (i) he would reduce output or reduce prices; (ii) he would increase output or increase prices; (iii) he would increase price; and (iv) he would reduce output. This implied that his reaction to unplanned inventories and excess profits depended upon the combination of the two and hence we needed four equations to ‘explain’ changes in output and changes in prices the choice of equation depending upon the nature of his disequilibrium. Thus our equations became:*
We made no allowance in these equations for any constraint on the entrepreneur due to money capital limits perhaps today this omission is rather more important than it -seemed in the halcyon days when inflation was not a probkm.
111
AS;(t) = olt + lo; + o&+(t - 1) + Q Afl+(t - 1)1 + 14 + ar7z:i+(t - 1) + arsA 4-(t - 1)1 + IdO + @ ni(t - 1) + art,,A G+(t - l)/ ECONOMIC MODEUJNG January 1984
The Southampton Ectnwmebic Model: +
Ia;:
+
a13
+ (Kg2
a11 Jci(t -
-
1)
+
arl2LI C’-(t
1) - K,(t - 1))
-
D. F. Hcrrdrficld
111
(4)
where A$‘(0 are t
0) n*Y(0 W’(t) Ar-(t)
= change in gross output at constant prices = constant = time = excess profits (positive) in money terms. = excess profits (negative) in money terms = unplanned inventory changes (positive) in constant price terms = unplanned inventory changes (negative) in constant price terms
and G(t) L(0
= optimum capital usage capacity term ) = actual capital usage
The square brackets go to zero if either variable within goes to zero. An exactly equivalent equation was used for price change except of course the parameters will differ.
The monetary sector A great deal of work was done on this sector and some of that work is reported by Rowan and O’Brien ($61. We did not in fact integrate the real and monetary sectors although, as they developed, the links between them became apparent and there was no obvious incompatibility. Because of this almost independent development and because so much work had been done in the monetary sector any detailed description of that sector merits a paper of its own. (This is true also of course of the econometric work and the data generation and handling techniques which were developed). Nevertheless because of the rise in monetary theory and its introduction into many erstwhile Keynesian models a brief outline of the monetary sector and its links with the real sector may be helpfully included here. The monetary sector comprised three subsections of: (i) the central authorities (defined as the Bank of England and the Treasury); (ii) the commercial banking sector; and (iii) a composition of non-bank financial intermediaries, corporate enterprises and households. The approach used was basically Keynesian with the assumed equality between the supply of and the demand for moneyresulting in a rate of interest - in this case at the equity rate. This rate together with the administered bank rate formed the basis of a structure of interest rates comprising those two, the rate on Consols and the rate on Treasury Bills. This structure was determined by the difference between the portfolio of assets supplied and that demanded so that equilibrium was brought about by compensating movements in interest rates. The supply of money was determined in part by the liquidity base of the commercial banking system and its multiplier. The liquidity base was in turn determined by the monetary base, the non-banking public’s ECONOMY MODEUJW January 1984
1lS
The Southampton Ecommeic
Model:
D. F. Hcorhfild demand for currency and special deposits. The public’s demand for currency was determined by transaction needs which in turn depended upon the money value of GNP. Thus the real sector intruded upon the monetary sector. The monetary base and special deposits were instruments through which the central authorities achieved their targets. These targets may be in the real sector or the monetary sector but were taken to be: (i) (ii) (iii) (iv) (v)
the level of registered unemployed; the rate of change of aggregate price level; the balance of payments; the rate of growth of real GNP; and an orderly market for government debt.
The first four of these represent ways in which the real sector (via the central authorities reaction function) influenced the monetary sector. The ways in which the monetary sector affected the real sector at various points may be summed up as: (i) changes in interest determining capital gains which enter the consumer demand equations; (ii) changes in interest rates affecting the incomes of interest receivers; (iii) changesin interest rates affecting the cost of capital particularly in the dwelling sector; and (iv) changes in bank advances which enter consumer demand equations.
A commentary To translate a conceptual framework based upon economic theory into a system of equations with each variable designated so as to correspond with some identified data series was no small task, particularly when the number of series called for was something in excess of 1500. Matching an econometric model to published data is a process which involves both experiment and compromise. Where no published data existed it was easiest to modify the model. But this frequently implied abandonment of the economic theory which it was our object to test. The alternative, which whenever possible we tried to adopt, was to attempt to construct the missing series by reference to raw data, by manipulation of published information or by the application of economic theory itself. The cost of this alternative was high. Specially constructed series had to be subjected to tests for consistency and accuracy and the value of alternative procedures compared. Furthermore the use of specially constructed series complicated the problem of updating very much more than proportionately. Quite apart from the obvious difficulty of estimating any such system of equations and of displaying the results in some readily comprehensible way, it became clear that any comprehensive model of the economy required its own specific system of national accounts. These enormous data difficulties and the very long-term pay-off period for a model of this kind eventually led to its demise. That is not to say that the project was either a mistake or a failure.
The equations It is not our intention, nor would it be possible in a paper of this length, to derive each set of equations by closely reasoned argument. What we 116
ECONOMY MODEUJNG January1984
The Southampton Econometric
Model: D. F. Heathjkld
have tried to do is to provide a clearly specified set of equations and to stress the constraints on them due to the need for overall consistency.
SEM - a listing of equations The basic accounting indent@ g(t) + SF(?) a D?(t) + D?(t) + D?(t) + i +
f:
D{{t) + i
qj(t)
0$(f) - A,(t) - A;(t)
(1)
The consumers expenditure equation
wo - W)~
_
(1
_
A)
w -
V - W(t) PRO) 6
_
(1
A)
1))
1
1
W - CW - 1) PR(t - 1)
PR(t - 1)
Wf)
+ 8
_
CG(t - 1) -CW - (1 - A)
+ p [HP(t) -
mt -
PR(t - 1)
PRO)
+
1) -
1
(1 - A) HP(t - 1)) BA(t - 1)
BA(f) -[I Wf)
PR(t - 1)
+ rl {PR(f) - PR(f - 1)) _ (1 _ h) {PR(t - 1) - PR(t - 2)) PR(t - 1)
+ v
-pm -
PR(t - 2)
(1 - IL)
PR(f)
PM(t - 1) PR(f - 1)
I+
e(f) - (1 - k)e(f - 1)
(t 1
1 J
(2)
The inputloutput coefficient determining equation Uij(f)= %+%
pj
1) +
zpfli i
[ Indushial
January 1984
41
+
a,?
(3)
demand for single use intermediates
q(t> * F
ECONOMiC IWOELUM
2
a2t
%,Cf> $CO
(4) 117
The Soathampton Ecronomcnic Model:
D. F. Heathfield Industrial demand for investment in plant and machinery
~pnst) =
or0 +
K~tA)
F
d.[OO
h(t - i) +
+
- K,(t - i)} + F oj n’(t
- i)]
&&j(t
- j) +
ff3ppw
(5)
+
(6)
Outputlcapital ratio of plant and machinery Y*(T) = Yo+ZZ
t=T K,(t - 1) _R f$ Kn(t - 1) +O
s=O K,(t)
K,(t)
ar,K,(t) + ar2t
An equation similar to Equation (6) is used to explain changes in capital/labour ratios. Industrial investment in buildings and works L(t)
= Mpm(t
+ 1) -
aroluspm(Ol + ~z&vW
(7)
Industrial investment in vehicles
%SW
Z”(f) = a(J + -
L(t)
+ w + ML(f)
(8)
Registered unemployment equation
(9)
RU(t) = oc + arlU(t)
lndustrial employment equation [L$L$(t
AL,,(t) = aAl,
- 1) - L$.L$(t
- 2)]
[L$L,d(t - 1) - L:L,d(t - 2)]
WJ)
Non-wage labour cost equation NWLCi(t) = [NHZ(t) + SETi(
L&t)
(11)
Wage costs of self-employed equation
w;;(t)
= [w,(t)
wci(t)
+
x
niT(t)l
wxo + ~iT”‘O)l
(12)
Import equation (goods) AS?(t) = a,, + cqAc(t
X
-
‘)f~2[(~)i(t-l)-(~)i(t-2)]
s?(t - 1) + ar3[Kti(t - 1) - K+,(t - l)]
(13)
Non-competing imports equation is similar to Equation (13) but without the price or capacity terms. lt8
ECONOMIC MODELLIM
January 1984
l7u Southampton Economuric Model: D. F. Heath@&
Import equation (services) ASr(t) = cq,+ QAS”‘(f) + Ap(t)]
+ asAY,
(14)
Export equation (goods) AH(t) = oro+ a~A$(t) + a&‘f(t) - f’!‘(t)] ti(t - 1)
(15)
Industry basic hourly wage rate equation W,(t) - Wi(t 7 1) =
W(t) - W(t - 1)
wi(t - 1)
[ x
X
1)
W(t L$L$t
-
1
1) - L$L$(t - 2)
[
Ld,L$i(t - 2)
1
L,dLd,(t - 2)
1
L,“Ld,(t - 1) - L,dLd,(t - 2 J
(16)
Aggregate supply of man hours equation L”,(t) L”,(t) = ocl + cv1t + ar28 +
a3
L&t)
+
a4 F(t)
+a~RA+a!(jsLA
(17)
Wage cost equation W,,(t) = CQ+ a1 LNut(t) +
a2 Ldf)
Lui(r)
+ a3 wi(t)
(18)
Aggregate employment equation AL,(t)
= CQ + ar,[L,d(t) Ld,(t) - L,d(t - 1) Ld,(t - I)1 + lxz[Lf(t - 1) Ld,(t - 1) - Ld,(t - 2) L,d(t - 2)] +
a3 z?U(t)
(19)
Aggregate unemployment equation AU(t) = AL;(t) - AL,(t)
(20)
Supply of new labour equation LS,(t)-ar,+ar,t+cuzZ?A+or3SLA
(21)
Distribution margins on consumer goods di(t) = Cyl+ a$ + cW# + QTt(t) + @t(t) + ~7fw) + %a EcoNo#Bc MOOEUNG
January 1984
+ %Vi(t) (22)
119
l%e souduunptonEconometricModel:
D. F. H~athfkld Home suppry decision equation
AS:(f) = aIt + [4, + @-Ii’-(t - 1) + ~Afl+(t - l)] + [& + ar,l-Ii+(t- 1) + arsAc-(t - l)] + [& + @-I,(t - 1) .+ cw,oAG+(t- l)] + [CY:+ culJIi(t - 1) + curzA$‘-(t - l)] + ar@*,(t - 1) - K& - l)]
(23)
Home ex-works price decision As Equation (23) but with A*(f) as the dependent variable. Planned inventory level equation P(t) = Q + cy&(t) + a2t
(24)
This equation is applied to finished goods, work in progress, raw
material and fuel and distribution sector separately. ProfiB equation IlT n SfPi - C P&‘aji - W&‘piyi - T i
(29
Aggregate hourly basic wage rate equation
wo -
W(t - 1)
W(t - 1) + oI
2
= are + arQ.#:Ls,- L,dLd(t - 1)
ww) - PNt - l)l
(26)
PI?(t - 1)
Import price equation r(t)
= obp~(f) x ER(f) + orIT
+ ar2DY(t)
(27)
Export price equation pi”(r) = ar,Pi”(r)x I%(t) + CYST(t)
(28)
Variables treated as exogenous to the model
(i) (ii) (iii) (iv) (v) (vi) (vii) 120
All government expenditure; Investment in dwellings; International capital flows; Tax rates and subsidies; Exchange rate; Exports of services; Sales by final buyers. ECONOMIC MODELUNG January 1984
fh Usting
i9bhampton Econom
tricModel: D. F. Heathj%ld
of variables used supply of r* commodity by home producer valued at constant wholesale prices supply of I* commodity from overseas valued at constant ex docks prices consumer demand for commodity constant retail prices
i valued at
government demand for commodity i valued at constant ex works/ex docks prices ti
=
Df
= UK demand for fixed capital of eh type valued at
industrial demand for single used intermediates of type i values at constant ex works/ex docks prices constant buyers prices
M
=
Df
= home demand for additions to inventories of the P”
overseas demand for I* commodity valued at constant UK export prices commodity valued at constant supply prices
VAi + V-A.:
= valuation adjustment to reduce all valuations used in
the identity to wholesale prices (ie includes distribution margins and some taxes)
IEcOMMC
PRi
retail price of P commodity
PR
aggregate retail price
1
rate of depreciation of stocks of consumer durables
Y
disposable income
EX
consumers expenditures which are exogenously determined valued at current retail prices
W
current value of wealth
CG
capital gains
HP
proxy for hiie purchase controls
BA
bank advances
PM
marginal price of the gas, electricity and water sector
a
seasonal dummy
e
error term
aii
input output coefficient
P
wholesale price
t
time
&pm
investment in plant and machinery by the r* home sector measured at constant buyers price
K*m
stock of plant and machinery currently held by ?” industry measured at 1958 replacement cost
MODELUNG January 1984
121
The Southampton Econornbc
Model: D. F. Heathfkld
KL
=
desired capital usage in the 8” industry
Klli
=
actual capital usage in the z* industry
nT
=c
total profits earned in the z6 industry
p*
=
buyers price of plant and machinery
L.IBW
=
investment in buildings and works by the zti industry valued at constant buyers prices
K.#BW
=
stock of buildings and works held by the r* industry valued at 1958 replacement cost
=
investment in vehicles by the I* industry valued at constant buyers prices
=
world price of i commodity (in dollars)
=
UK taxes (excluding purchase taxes) on imported commodity i
Iiv
DT
X
UK
c
=
UK taxes on UK exports of commodity i
ER
z
exchange rate (f/$)
4
=
percentage mark up by distributors of consumers goodsoftypei
Ti
=
Ri
=
Vi
X
Di
=
purchase tax (implicit rate) on consumer goods of type i abnormal sales of consumer goods of type i (constant retail price value) current ex dock value of imports of i divided by current ex dock/ex works price value of all i sold to consumers retail price maintenance dummy
=
normal hours
SET
=
Selective Employment Tax
NHI
=
National Health Insurance
=
demand for labour stock
=
demand for labour hours
=
supply of labour stock
2=
supply of labour hours
TL
=
standard rate of income tax
RA
z
retirement age
SLA
P
school leaving age
D
P
resale price maintenance dummy
I”
=
unplanned inventories
P
=
planned inventories
LNH
L”, Ld, Ls, L”,
122
duty on imported commodity i
ECONOMIC MODELUNG January 1984
The Sothampton
Econometric Model: D. F. Heathjkld
References D. F. Heathfield and I. F. Pearce, ‘A view of the Southampton Econometric Model of the UK and its Trading Partners’, in A. G. Renton, ed, Modelfing the Economy, Heirtern-, London, 1974. D. F. Heathfield and G. J. Evans, ‘Distribution margins in the UK: a quarterly analysis’, Applied Economics, NQ. 3,197l. I. F. Pearce, ‘The Southampton Econometric Model of the UK and its trading partners’, in K. Hilton and D. F. Heathfield, eds, The Economerric Study of the United Kingdom, Macmillan, London, 1970. I. F. Pearce, ‘The problem of the balance of payments’, Znrernational Economic Reuiew, January l%l. D. C. Rowan, ‘The monetary sector of the Southampton Econometric Model’, in K. Hilton and D. F. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. D. C. Rowan and R. J. O’Brien, ‘Expectations, the interest rate structure and debt policy’, in K. Hilton and D. F. Heathfield, eds, The Econometric Study of the United Kingdom, Macmihan, London, 1970.
Appendix New SEM dkggregation
A
L M 0 P Q R S T
scheme
A Agiicufuuc. forestry and fishing B Construction partof c chcmicais D Publicadministration E Engineering Food manufacturing partof F GaS partof w
9 14
andpartof 7 -
partof s DartOf 0 partof w M partof c part of s Extraction part of Q R Other manufacturing Services and water partsof Sand W Textiles, leather and T clothing Distribution Coal mining Electricity Metal manufacture Mineral oil refining Transport
u V
sales by final buyers Alcoholicdrink and
Z
tobacco Total, all industries
partof
6 3
part of 15 1 4 partof 6 2 16 12 partof 7and13 part of 15 8
11
Z
Reconstruction of former SEM scheme New scheme
A B C -
A B c+o D
D
EcoNoIHlc
MOOUUNG
E F+V M -
Q
Q+K
R S T U W Z
R S + H + P (less water) T U G + L(plur water) Z
10
U partof F
Fermer SBM
E F M N
January 1984
Relationship with CSO scheme New SEM 1 2
K 0 G L C+R E+M T A F V
3
4 5n113 6 8
9
10 11 12 14
Q
B H+S P
:i Relation to SIC (IWS) New SEM
SIC
A B C
Order1 GrderKX Grders IV and V, except mlh 262 123
The Southampton Econometric Model: D. F. Heathjkld D E F G H K L M 0 : R S T U V
Order KKVII Orders VII to XII Order III (excluding mlh’s 231,239, and 240) mlh 601 Order XXIII mlh 101 mlh 602 Order VI mlh 262 Order XXII Order II, except mlh 101 Orders XIII to XIX Orders XXIV to XXVI, mlh 603 Orders XIII to XV mlh’s 231, 239 and 240
Source papers Sl s2 s3 S4 S5 S6
S7 S8 s9 SlO Sll s12 s13 s14
s15 S16 s17 S18 s19 s20
Statistical sources for international trade sectorgeneral, K. Hilton. Estimation of consumers’ expenditure by industry, K. Hilton. The estimation of imports, exports, etc by industry, K. Hilton and D. Heathfield. Industrial classification of consumers’ expenditure, K. Hilton. Industrial classification of public authorities’ current expenditure, K. Hilton and D. Heathfield. Industrial classification of supply of fixed capital formation and stockbuilding (plus amendment), K. Hilton and D. Heathfield. Industrial classification of imports, exports and re-exports, D. Heathfield. Gross output at current prices by industry, K. Hilton and D. Heathfield. Distribution margins and intermediate products, D. Heathfield. Price indices of industrial inputs and outputs, K. Hilton and D. Heathfield. Weights used for the index of import prices, R. Hall. Consumers’ expenditure, G. Evans. Data specification and processing - labour sector, G. Evans. Index of import prices (gross of duty) (incorporating Sll -weights used for the index of import price), R. Hall. Corporate data, C. T. Stromback. An econometric model of the UK and its trading partners, A. Harrison. Estimates of expected demand: a note (plus supplement), P. K. Trivedi. Unduplicated quarterly gross output at current prices, R. Chang. Taxation - amendments to the data bank, J. D. Byers, I. F. Pearce, P. Smith, C. T. Stromback. The cost of capital, G. Anderson, P. K. Trivedi.
Series ‘A’ - application papers A.1 A.2
A.3 A.4
A.5
A.6
A.7
A.8
A.9
A.10
Some notes on consumer expenditure functions for the UK, D. Tumham, K. Hilton and D. Crossfield. Short-run consumption functions for the United Kingdom, K. Hilton and D. Crossfield, in K. Hilton and D. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. Evidence on the quantity theory in the United Kingdom, K. Hilton. Aggregate quarterly dividend behaviour in the United Kingdom, G. R. Fisher, in K. Hilton and D. HeathfIeld, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. Expectations, the interest rate structure and debt policy, D. C. Rowan and R. O’Brien, in modified form in K. Hilton and D. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. Capital and capacity utilisation in the United Kingdom, K. Hilton, Discussion Paper 7003, Bulletin of Oxford University Instituteof Statistics, Vo132, No 3, 1970. Distribution margins in the United Kingdom - a quarterly analysis, D. Heathfield, Discussion Paper 7007, Applied Economics, October 1971. A generalised approach to Stone’s model for aggregate consumption expenditure, M. S. Common, Discussion Paper 7008, to be published in shortened form in Manchester School. Planned stockholding: evidence from British company data, K. Hilton and D. Cornelius, Discussion Paper 7201. The demand for current account deposits, D. Rowan, Discussion Paper 7204.
!Se.ries‘T’ - theory papers T.l T.2 T.3 T.4
T.5
T.6
T.7
Some notes on the Southampton model, I. F. Pearce. A system of relationships for the Southampton model, I. F. Pearce. The application of the Brookings’ model dwelling sector to United Kingdom data, T. Espenshade. The Southampton Econometric Model of United Kingdom and its trading partners (First report on the SEM), I. F. Pearce, in modified form in K. Hilton and D. Heathfield, eds, The Econometric Study of The United Kingdom, Macmillan, London, 1970. The monetary sector of the Southampton Econometric Model, D. C. Rowan, in K. Hilton and D. Heathfield, eds, The Econometric Study of the United Kingdom, Macmillan, London, 1970. The treatment of goods and services in the real sector of the Southampton Econometric Model (Second report on the SEM), D. Heathfield. A view of the Southampton Econometric Model, D. Heathfield and I. F. Pearce.
ECONOMICMODELUNGJanuary 1984
The Southampton Ewnometric Model: D. F. Heathjield
Series ‘M’ - method papers M.2 M.3 MA
MS
On the asymptotic significance of ratio estimates, R. O’Brien and K. Hilton. The stability of linear time series relationships, R. O’Brien. Serial correlation in econometric models, R. O’Brien, in K. Hilton and D. Heathfield, eds, The Economem’c Study of the United Kingdom, Macmillan, London, 1970. The Bayesian analysis of partial adjustment models, R. O’Brien.
New source papers NSl Employment series (El), P. Smith. NS2 Wholesale (home sales) price index, S. P. Chakra“arty. NS3 Exports, C. J. Stromback.
ECONOMC MODEWNG January 1984
NS4 Income from employment, P. Smith. NS5 Taxes on expenditure less subsidies, C. J. Stromback. NS6 Consumer’s expenditure, T. Harrison. NS7 Earnings, hours and wage rates, P. Smith. NS8 Interindustry conversions, T. Harrison.
Southampton discussion papers in economics and econometrics No 7505 Input-output in the Southampton Econometric Model of the United Kingdom and its trading partners, S. P. Chakravarty, E. R. Chang, D. F. Heathfield, A. Ingham. No 7601 Some preliminary simulation experiments with the labour-wage-price sector of the Southampton Econometric Model, P. Smith.
125