Production—demand adjustment in Norwegian manufacturing

Production-demand adjustment in Norwegian manufacturing A quarterly error correction model Erik Biorn and Hilde Olsen In this paper, we specify a general error correction equation for seasonally unadjusted data, with an arbitrary number of regressors. Special attention is paid to the specification of trend and seasonal filters, which hare proved to be of importance when using seasonally unadjusted quarterly data. Within this framework, the adjustment of production to demand in a stockbuihlin 9 sector is analysed. We hare specified an output decision equation with three explanatory variables, capacity, demand and stock imbalance. The model is estimated on Norwegian quarterly national accounts data by means of a non-linear least squares algorithm. Experiences from simtdation exercises are also reported, illustrating the dynamic tracking as well as the dynamic behat,iour of the model. Ke)'words: Macroccononlic models, Norway; in empirical models of the behaviour of an economy in the short run eg quarterly models, the treatment of the output decisions of firms plays a crucial role. It is an empirical htct that in several sectors, notably in manufacturing, the time path of output from a sector over the business cycle often departs substantially from the time path of demand directed towards the sector. The counterpart to these deviations is variations in stock formation, in empirical work such short-run deviations are frequently analysed by means of stock adjustment models of the standard textbook type or simple generalizations of it (see eg Rowley and Trivedi [ 14] Chapter 2.2 and Feldstein and Auerbach [5]). In this paper we take a different approach. Using the "error correction" formulation as our point of departure (see Sargan [ 15], and Hendry, Pagan and Sargan [ 10] pp 1048-1049), we propose an econometric framework for analysing the adjustment of production to demand on the basis of quarterly data from a stockholding sector. The original error correction model, which is a one-period adjustment model, hits some deficiencies when applied to seasonally unadjusted

Erik Biorn is with the Department of Economics, University of Oslo. Oslo, Norway and Hilde Olsen is with the Ministry of Finance, Oslo. Norway. The research was carried out while the authors were at the Central Bureau of Statistics, Oslo. Norway. Final manuscript received26 August 1988.

Error correction nlodel

quarterly data and in this paper we use a generalized version of it. The paper is organized as follows. First, we specify a general quarterly error correction (QEC) equation for seasonally unadjusted data, with an arbitrary number of regressors (second section). It is an extension of the model in Biorn and Olsen [3], with specific attention paid to the trend and seasonal filters. Next, this general model formulation is accommodated to an output decision equation with three explanatory variables, capacity, demand, and stock imbalance (third section). After a brief presentation of the data, which are aggregates for Norwegian manufacturing (fourth section) and of the estimation procedure, which is a combined grid search, non-linear least squares procedure (fifth section), the empirical results are reported. We focus on the one hand on the coetlicicnt estimates, goodness of fit and dynamic tracking of alternative QEC equations (sixth section) and on the other on the dynamic behaviour of the model when exposed to sustained or temporary shifts in its exogenous variables ie capacity and demand (seventh section). The final section offers some concluding remarks.

A general quarterly error correction equation for seasonally unadjusted data The basic model Consider first the case where economic theory postulates a linear static relationship to hold in the long run between the variables Y and X~ . . . . . Xr:

0264-9993/89/020189-14 $03.00 ~ 1989 Butterworth & Co (Publishers) Ltd

189

Production-demand adjustment in Norwegian manufacturino: E. Biorn and H. OIsen •

r=flo + ~ fl, X, "'

(1)

a , r , = a r ; = r ; - rf_,

The quarterly observations on these variables do not satisfy this static relationship, but we assume that their behaviour in the short run can be represented by a process correcting - according to servomechanistic control principles - short-run deviations from a steady state path, given by (1). This mechanism will be formalized as an error correction (EC) process. Since the quarterly data are seasonally unadjusted, we use a generalization, denoted as a quarterly error correction (QEC) process (discussed, for the case with one X variable, in Biorn and Olsen [ 3 ] ) rather than the one-period version of the EC process (Sargan [ 15], Hendry and Richard [11] pp 130-131 and Hendry, Pagan, and Sargan [10] pp 1048-1049). In the present paper, this QEC process is extended to an arbitrary number of X variables and specified in terms of seasonally adjusted values of the variables involved. The seasonal adjustment procedure is integrated in the model structure. The error correction equation is K

[I-,(L)]rf= y

rt = r;_,

a,[l-,(L)]X~

+~/p(L) Ito +,~ lt, Xf;- Yf +,:, (2) where 7 is a constant between 0 and I, p ( L ) = p t L + p , L 2 + . . . is a polynomial in the lag operator L, t: is a zero mean, white noise disturbance, the subscript t is the time index and the superscript S denotes a seasonally adjusted variable. The coefficients of p(L) are assumed to add to unity ie p( I ) = Pt + P2 + . . . . 1. This polynomial will be denoted as the trend filter polynomial, and we can accordingly interpret

etc. Extending the error correction to four quarters (one yeart, we get p ( L ) = L"tie r: = rf_,

A* V,,= a , Yf = r f - Y L , etc. To show that (2) can be interpreted as an error correction equation, it is convenient, using (3)-(6), to rewrite it as K

~,a*X,,-;'{Yt-Yt*}+~,

A'Y,= ~

where Y** is the steady state, or target value of Y in quarter t, defined by (I) ie K

r,** = flo + ~ / t , x ? ,

(8)

i~l

Equation (7) says the following. For given trend values ie for given values of Y,* and Y,**, a departure of X, from its trend will induce a departure of Y from its trend by a, units. If the trends do not satisfy the steady state path (8), there will be an error correction, so that ifthe trend in Yexceeds its long-run target( Y,* > Y,**), the difference will have a negative effect on the adjustment of Y. If the trend value of Y is below its target ( Y,* < Y,**), the discrepancy will affect Y positively. The speed of adjustment is represented by 7. The trend departure of Y is the net result of two effects: the trend departure of the Xs and the trend error correction. The seasonal filter, It(L) = #o + ii t L + #2 LZ + .... is assumed to be the same for all variables ie

Ys, = # ( L ) Y , Y * =p(L)Y~, "

(7)

i=I

(9)

(3)

X s =#(L)X.

i= l..... K

(lO)

and

X~, = p ( L ) X s

i = 1. . . . . K

(4)

as trend values of Y, and X,, and A*Yt = Yts - Y* = [I - p ( L ) ] Y

s

where Y, and X , are the values of Y and X~ observed in quarter t. The filter is mean preserving ie its coefficients add to unity, lL(l) = lq + #2 + . . . . 1. Inserting (9) and (I0) in (2), we get the QEC equation expressed in terms of the observed values:

(5) K

A*Xu = X s - X,*, = [I - p ( L ) ] X s

i=! ..... K (6)

~(L)[I-p(L)]Y,=~

~,u(L)[!-p(L)]X.

- Tp( L )#( L ) t Yt - 1 ~ 1 f l i X . ] as detrended values of these variables. In the simple one-period (quarter) EC model, we have p ( L ) = L ie

190

+ "/flo + e,

( 11 )

E C O N O M I C M O D E L L I N G April 1989

Production-demand adjustment in Norwegian rnanufacturiny: E. Biorn and H. OIsen The trend and seasonal f i h e r s

l a ( L ) p ( L ) = ~ ( l + L + LZ + L 3)

In the empirical applications, the seasonal adjustment filter is specified as the one sided, unweighted, four quarter, moving average operator

x ( p t L + p 4 L 4 - p t p a L ~) = }[Pt( L + L2 + L3) + (Pl + P4) L4

+p.L(I - pt)(L~ + L6 + L 7) p(L) =~(1 + L + L2 + L3)

(12)

ie all of its coefficients are a priori given. The trend polynomial is parametrized as p(L)= plL + p~L4- plp4L s

(13)

where Pt and P.L are parameters between 0 and 1 at least one of them being equal to 1. The latter restriction is needed to ensure that p( 1 ) = Pt + P.L - PtP.t = 1 and implies that the detrending operation (5)-(6) contains a full differencing over either one or four quarters (or both). Stated equivalently: the trend operator defines either the value of the variable lagged one quarter plus a fraction p., of the quarterly increase realized one year

(15)

- p , p 4 L s]

In the general case the combined filters will both define autoregressive processes of order 8. If p t = I, terms of order !, 2, 3, 5, 6, and 7 will vanish from p(L)[ I - p(L)] and terms of order 5, 6, and 7 will vanish from p ( L ) p ( L ) . No term will vanish ifp,~ = 1 in the general case. The variety of lag patterns inherent in this specification is illustrated by the following examples. If ,o.~ = 1. p ~ = 0, the composite polynomials are p ( L ) [ l - p ( L ) ] = I ( I + L + L z +/_,3)(I - L"~)

= ~ [ ( I - L"L) + ( L -

L ~)

+(LZ-L")+(I?-LT)]

ago:

which defines the average annual increase over the last four quarters

p ( L ) = L + p.LL~( I - L)

or the value lagged one year plus a fraction Pt of the annual increase realized one quarter ago: p ( L ) = L "~ + p l l . ( I

I t ( L ) I , ( L ) = ~(L 4 + L .~ + l~,' + / 7 )

which defines the annual average lagged four quarters p, = I, P4 = 0 implies

-- L 4)

When applied to a variable which follows a linear trend ie Z, = A + Bt these two specifications of the trend filter give

p(L)[i -p(L)]

= I ( I + L + L2 +/_.3)(! - L)

=I(~ -L'*) which defines the average quarterly increase over the last four quarters, while

p ( L ) Z , = A + B(t - 1 + pa)

and

p ( L } p ( L ) = t4(L + L 2 + L 3 + L 4')

4 + 4p~)

p(L)Z, = A + B(t-

defines the annual average lagged one quarter, while l'Jl = P4 = 1 leads to

ic the filtered values will lag l - p 4 and 4 ( 1 - P t ) quarters behind the original values respectively. Written out, the composite detrending-seasonal filter polynomial and the composite trend-seasonal filter polynomial implied by (12) and ( ! 3) are respectively

x(I-ptL)(I-p.L

4)

-

+

which defines one quarter of second annual difference,

which defines the annual average lagged one quarter plus the average of the quarterly increase lagged four quarters.

=¼[! + ( i - p t ) ( L + L2 + L 3) -- (Pt

=I(I-L'~) 2

p ( L ) p ( L ) = t [ L + L" + L 3 + L~ + ( L 4 - Ls)]

2 + L 3)

p(L)[I-p(L)]=t(I+L+L

p(L)[I-p(L)]=~t(I+L+LZ+L3)(I-L)(I-L'*)

P.~) L'~ Quarterly error correction versus cointegration

p.t(I -- p t ) ( L 5 + L6 + L7)

+ p t p . L s]

E C O N O M I C M O D E L L I N G April 1989

(14)

The relationship that exists between error correction models and cointegration has been discussed in recent

191

Production-demand adjustment in Norwegian manufacturing4: E. Biorn and H. Olsen

literature tsee Granger [6.], Granger and Weiss [7.], Hendry ['9.] and Engle and Granger ['4,]1. It is known that the simple one-period error correction model ( ie p( L ) = L) for non-seasonal data (ie/~(L) = 1) usually has a cointegration representation ( Engle and Granger [4.] p 259). Will this also be the case for our more general model? Assume that I'~, X t, . . . . . X r, are integrated of order 1 ie their first differences have a stationary, invertible, ARMA representation (see Engle and Granger [4] p 252). Then y S X s . . . . . . X s, and Y,*. X'~, . . . . . X~., will also be integrated of order I, since they are constructed by application of the linear filters ldL) and plL)(see Harvey ['8.] p 42). Our QEC model, as formalized in (7)-(8), says that

-;. & +

, , x : , - v: = E ~,a*x,,-a*v,+~., i=l

i=1

The righthand side of this expression will then bc integrated of order 0 when ~: is a zero mean, white noise disturbance. This follows from the fact that the dctrending operator I - p(L) always contains the lirst order difl'crcncc operator I - L. If Pt = I, we have

manufacturing sector is sometimes referred to as the stockholding sector. These stocks may act as a buffer between production and demand. Producers may in some periods meet demand by reducing stocks. In other periods they may produce more than necessary to meet actual demand by increasing stocks (see Biorn [1,] Section 2). How can a long-run steady state path be represented with this interpretation of the variables? A balanced expansion (or contraction) can be characterized by equality of production, capacity and demand ie y = r / = D and equality of the actual and the desired stock ie S = S. Since it involves three equations, this expansion path can only be fully represented by means of a multiequation model, including the identity Y = D + AS and equations for supply and demand of the commodity in question. We shall not construct such a model, but 'condense' the long-run expansion path into one equation containing capacity, demand and stock imbalance as joint determinants of the production target. The equation for the production target is K

Y** = ~

fl, X * = a ~ * _ , + ( I - a ) i ) *

i-I

I -

I'(L)

= (I

-

L)(I

-

pal?)

+ b(s%*- s?_,)

If t'4 = I we have I - t,( L)=(

I - I, IL)( I - l?)

=(I-I,~L)(I-L)(I

+ L + L Z + L 3)

Since in both cases the tirst order difference operator is applied to the seasonally adjusted wtriables, A*X~, and A* Y, will bc integrated of order 0. From this wc can conclude that the seasonally adjusted variables y s X~ . . . . . . X'~-, will be cointegrated of order 1, 0, according to the Engle-Granger terminology, under the assumptions made.

The output decision function Theoretical b a c k g r o u n d

We now accommodate the general QEC framework to the specitication of :t short-run output decision function for a stockholding manufacturing sector. The variables assumed to motivate the sector's choice of production scale, Y. are its production capacity, Y, its expected demand, /), and the difference between its desired and actual stock of finished goods, S ' - S. These three variables correspond to X~ in the general model in the previous section. The producers in manufacturing industries often keep considerable stocks of finished products - the

192

(16)

where the asterisks indicate trend values, as in I:,quation (4), and a and h are constants between 0 and I. It may be given the following rationalization. At the beginning of quarter t there is an imbalance between the (trend wdues of the) production capacity and the desired stock, on the one hand, and the (trend values of the) demand and the actual stock, on the other, reflecting decision errors, costs of adjustment, erroneous expectations, etc in previous quarters. Equation (16) represents firms' strategy to eliminate these discrepancies and can be formally derived by minimizing with respect to Y** :t cost function specilied either as A I-Y** - Y*_ t']-" + BE Y** - D,* - C(~,* - S*_ t )-]2 OF ,.IS

tie Y** - ~*- t - C(~* - S*_ , ).]2 + BE Y** - O* ,]'Here A, B and C arc positive constants, C being the share of a stock imbalance which the firm desires to eliminate in one quarter. This cost minimization gives Equation (16) with a = A / ( A + B),b = ( I - a ) C in the first case and a = A / ( A + B), b = a C in the second. Interesting special cases are a = b ~ 0 (ie target value of production equal to trend value of demand, regardless of capacity and stock imbalance) and a = 1, h = 0 (ie

E C O N O M I C M O D E L L I N G April 1989

Production-demand adjustment in Norwegian manufacturin~t: E. Biorn and H. Olsen target value of production equal to trend value of production capacity, regardless of demand and stock imbalance). This interpretation of(16)implies that it does not represent a strict long-run relationship, but rather a medium-term target relation, the corresponding long-run model being characterized by equality between production, capacity and demand and no stock imbalance. The QEC version of the output decision fimction The departures of the (seasonally adjusted) values of capacity, demand and stock imbalance from their trends are assumed to induce a departure of Y from its trend equal to

/~(L)[I - (1 - ?)p(L)] Y, = #(L)[:c - p(L) x ( : c - ?a)] Y,_ 1 +/~(L) x [(1 - , 0 -

p(L)(I - x

- ' / ( l - a))]/), + ~(L)[/~ - p(LX/~ - 7b)] x (g', - S,_ ~) + ~,

(20)

This version of the QEC output decision function will be analysed empirically in the following sections of the paper. Data

K

y. =,,a*x,,=~a*~_, + ( i - ~(),a*t~, i=I

+/~m*(~, - S,_ t)

(17)

where

A* ~,-t = }:'~-t- YT-t = [ I -,o(L)] ~s_ t = ,.(L)[ l - p(L)] t-,

A*/), =/5~ - / ) * = [I - / , ( L)]/5~ = ,u(L)[l - p(L)]/~, a*(s,-

s,_,)=(sf

- sL,)-(s:

- s:_,)

= l,(C)[l - p ( L ) ] ( ~ , - S,_x) Inserting (16) and (17) in (7), we get the QEC output decision function

a* Y,,= ~a* ~_, + ( I - : , ) a * ~ , + l ~ a * ( g , - s , _ , ) - 7[ Y * - a ~ ' ; - t

-( I -a)D7

- b(~* - ST_t )] + t:,

(18)

Inserting the trend and seasonal adjustment filters, (18) can be written in terms of the observed, seasonally unadjusted variables (see ( 1 ! )) as I , ( L ) [ I - p(L)] Y, = l,t(L)[ 1 - p ( L ) ] [ ~ - t

+(!

- ~)/~,

+ fl(~, - S,_, )] - ?p(L)/t(L)[ Y, - a ~ _ , -(1 -a)i~,-b(S,-

S,_t) ] + ~,

or, when collecting terms, as

E C O N O M I C M O D E L L I N G April 1989

(19)

Quarterly data on production ( YL production capacity (~'), demand (D) and stocks of inventories (S), at constant prices in total manufacturing, are used. The data are, with some exceptions to be explained below, taken from the (seasonally unadjusted) Norwegian quarterly national accounts and are an extension of the data base for the quarterly model KVARTS (see Biorn, Jensen and Reymert [2]). The quantity series in the Norwegian national accounts change base year regularly and the quarterly data used in the present investigation are all rebased to 1985 prices at a fairly disaggregated level of sector and commodity classification and are then aggregated to manufacturing totals. The data on capacity, ~', are constructed by using a modified version of the Wharton method which is based on linear trends passing through the peaks of the seasonally adjusted production series. Data on actual stocks of finished goods in this sector, S, are constructed from the quarterly quantity index of stocks, which is based on information on stocks in the major industry groups exclusive of commodities in progress. This index is rebased to be consistent with the changes in stocks recorded in the national accounts. The data on stocks are available from 1972:1 only, which restricts the estimation period. Since the Norwegian quarterly national accounts are based on the SNA commodity-sector approach, they include no information about the demand directed to each specific sector. The demand indicator, D, is constructed indirectly by subtracting the increase in stocks from the production i n t h e sector. Then, since each sector usually produces a multitude ofcommodities, we ignore on the one hand supplementary production taking place in the sector we are considering and on the other supplementary production of its primary commodities in other sectors. The consequence of this simplification may not be too serious because the aggregate manufacturing sector covers most of the stockbuilding activities in the economy. In the

193

Production-demand adjustment in Norwegian manufacturing: E. Biorn and H. OIsen

presentation of the theoretical model we assumed that expected demand (/~) was the relevant variable influencing production decisions. It is, however, unobservable and instead of trying to model the expectation process, we have used actual demand (see Biarn I-1] p 31 ). One interpretation of this formulation may be that the producers have rational expectations. In the Norwegian national accounts (annual as well as quarterly), sources and uses are balanced for each commodity, while our focus is on the stockbuilding of the manufacturing sector which, as mentioned above, produce several commodities, As shown in Biorn [ 1] Section 2.5 and 4.1, this causes some complications because of the discrepancy between the change in stocks as recorded in the quantity index and as recorded in the national accounts. To fulfil the balance equation Y = D + AS we must allocate this discrepancy either to the demand or to the stock component. If we allocated it to demand, this discrepancy would influence production activity. If not, it would simply be an adjustment in the stockbuilding component. As we find the production data in the national accounts most reliable and there is no information on how to distribute this residual, we have allocated it entirely to the stockbuilding component. Desired stocks (5) is an unobservable variable as well. A reason why firms want to hold stocks is to satisfy expected demand. We have, as a simple approximation, assumed proportionality between expected demand and desired stock. To eliminate expected demand we unsuccessfully tried different specifications of the anticipation process and in the empirical version there is no distinction between expected and actual demand. Desired stock is thus estimated by

= kD,

procedure

The output decision function (20), with the trend and seasonal filters (12) and (13) as well as (21) inserted, is linear in (the current and lagged values of) Y, D, ~ and S and non-linear in the eight parameters a, b, k, p~, p,, a, ~, and 8- For given values of k, ~, Pt and p~ it is, however, linear (with no constant term) in a, b, a and /l. The equation is estimated by the non-linear least squares routine NLS in the T R O L L system (see T R O L L [16] ), by means of which we can perform an unconstrained minimization of the sum of squared 194

1"

¢Zt =Q(a,b,~,~,7, k, pt, p,) t=l

where T is the number of observations. If the disturbances are normally distributed, the estimates will be maximum likelihood estimates. The latter property holds strictly if the initial values of Y,(ie those necessary to construct the initial lags) are regarded as fixed, or conditionally on these initial values. Otherwise this iterative procedure will give approximate maximum likelihood estimates (see Harvey 18] pp 121-122). NLS solves this minimization problem iteratively by means of a quasiNewton algorithm (NL2SOL). There is no guarantee that this iterative process will converge to the global minimum of Q. In some cases this was checked by repeating the computation, starting from a different set of initial values of the coefficients; but there was no indication that these values influenced the final result. A simultaneous minimization of Q with respect to all the eight parameters in the model proved, however, to be difficult. A combined grid search-N LS procedure was therefore used. We set either Pt or p, equal to I (cfthe second section) and specified a two-dimensional grid over the 'free" p parameter and k. Then we obtained estimates of the remaining five coefficients conditionally by unconstrained NLS. The final solution is the coefficient set which minimizes Q. For Pt and P4 the search is done over the interval (0.0, !.0), with a step length of 0. I. We had some a priori assumptions about the feasible interval for k and did the search for this parameter over the interval (0.2, 0.7), with a step length of 0.1.

(21)

where k is a factor of proportionality. Proportionality between desired stocks and actual demand may be justified if producers perfectly forecast future demand when they make their decisions about production and stockbuiiding today (rational expectations). Estimation

of residuals:

Empirical applications Coefficient estimates Non-linear least squares estimates of (20), computed by means of the above mentioned grid search procedure, are presented in Table 1. A comparison of the different specifications reveals interesting differences. Consider first the case where both Pt and p,, are set equal to 1, which implies a joint differencing over one and over four quarters (case A). This case gives evidence of a very high degree of adjustment of production to departures of capacity and stock imbalances from their trends, the short-run adjustment coefficient of capacity, ct, being 0.68; the complementary short-run coefficient of demand, ( 1 - ~t), is thus 0.32 a~nd the short-run adjustment coefficient ofstocks excee~ls unity (/~ = 1.07). This overadjustment may be a conse~luence of the fact that we impose a four quarter difference on data which E C O N O M I C M O D E L L I N G April 1989

Production-demand adjustment in Norwegian manufacturing: E. Biorn and H. OIsen Table 1. Production in manufacturing industries, quarterly error correction model million 1985 kroner. Non-linear least squares grid search estimates: estimation period 1975:!-1985:4.'

A el

P,L k a

g2

DW SER

B-L( I )" B-L(4)h B-L(8)"

B I 1

C

D

E

F

G

0 1

1 0

1 0

l 0

l 0

I 0

0.4 - 0.32

0.4 0.20

0.3 0.04

0.5 0.01

0.4 0.24

0.4 1

0.4 0

(-0.94) 0.68

( 1.91 ) 0.44

(0.07) 0.49

(0.04) 0.46

(0.901 0.49

0.50

0.46

(4.62) 0.26

(3.19) 0.25

(3.41 } 0.08

(3.08) 0.37

(3.46) 0.28

(2.90) 0

(3.21) 0

( 1.71 )

(3.38)

(0.341

(1.26)

(1.49)

1.07

0.33

0.40

0.29

0.31

0.34

0.31

( 17.231 0.34

(2.86) 0.94

(2.15) O.15

( 1.731 O.15

(1.72) O. 18

(1.87) 0.00

( 1.851 0.09

(3.451

(5.36)

(1.44)

(1.97)

( 1.461

0.9998 0.38 675.7 27.86 43.70 74.92

0.9999 1.56 375.6 1.70 4.84 12.83

0.9999 1.58 374.1 1.30 3.60 9.40

(2.18) 0.9999

(0.05)

0.9998 1.88 597.4 0.09 8.16 12.15

0.9999 1.63 387.6 1.40 4.67 9.58

0.9999 1.53 378. I 1.93 4.50 10.75

1.54 374.8 1.87 5.18 12.06

• A - E: estimation conditional on/h,/'.t, k: F - G: estimation conditional on 1'1,P.~.k. a, h; t-values in brackets; i, B-L(i) is the Box- Ljung statistic for ith order residual autocorrelation. have already bccn seasonally adjusted by the moving average filter (12). If no stable seasonal components are left in the seasonally adjusted data, this may imply an overdifferencing which is 'compensated' by the trend departure correction. Next consider the alternative with p t equal to 0 and P4 equal to ! (case B). The estimated error correction parameter, 7 = 0.94, indicates that output is adjusted towards its equilibrium value almost instantaneously. This may be a consequence of the existence of a non-linear trend in the data which is not adequately eliminated by taking the four quarter differences. This may indicate that in the present alternative the variables are not cointegrated of order !, as assumed above. The presence of this kind of specification error is supported by the very low value of the D u r b i n Watson statistic and the Box Ljung statistics, indicating significant first, fourth and eighth order autocorrelation. In fact, this is not surprising. The data are already seasonally adjusted and the four quarter differencing implies a redundant elimination of seasonalities which may have serious consequences for the dynamic properties of the disturbance term. The estimation experiments indicate that the best results - both in terms of fit and plausibility of estimates - are obtained by setting p ~equal to 1 and p,, equal to 0 ie by performing a full quarterly but no annual differencing. The alternatives C, D and E are not very different with respect to statistical properties, but on a judgemental basis we prefer alternative E, where k = 0.4, by a slight margin. This implies that the desired stock is 40% of the quarterly demand. In this alternative

E C O N O M I C M O D E L L I N G April 1989

producers seem likely to pay about the same attention to demand as to capacity when adjusting output. The estimate is ~t = 0.49 ie 1 - 0 t = 0.51. Thus in the short run ie in one quarter production adjusts to approximately half of the trend departure both in capacity and in demand. The short-run adjustment coefficient for stocks, It = 0.3 I, indicates that approximately onethird of the trend departure is eliminated. Reasonably, in the short run, the producers must pay much attention to existing capacity because some time is needed either to reduce or expand capacity. In other words, capacity constrains production in the short run. In the long run, however, producers give the two components different priority: a, indicating the effect of capacity on production is estimated to 0.24 ie ( 1 - a) is 0.76, and b, the effect of the stock imbalance, is 0.28, which indicates that the priority given to establish an output level keeping the stock at a level which is necessary to meet demand is somewhat lower in the long than in the short run. In all the above mentioned alternatives the estimates satisfy ,'1 > a, whereas I! may be larger than or less than b. The interpretation of the first inequality is that the effectof the capacity is more important in the short than in the long run, while more attention is paid to demand in the long than in the short run. This conclusion seems to be robust to the dynamic specification of the equation. In the short run, production may be restricted by capacity constraints. On the other hand some time may pass before increased demand has fully influenced production; but in the long run, there is a tendency for producers to give priority to meet demand. It is then possible - via

195

Production-demand adjustment in Norwefian manufacturint,I: E. Biorn and H. Olsen adjustments in other variables eg investment - to adjust the capacity to the level which is necessary to satisfy this demand. We might, somewhat approximately, interpret these findings as indicating that in the short run production is restricted from the supply side and in the long run it is restricted from the demand side of the economy. The estimated error correction parameter is 7 = 0.18 ie only 18% of the discrepancy between actual production and its corresponding long-run equilibrium will be eliminated in one quarter. As mentioned above, desired stocks is an unobservable variable which is assumed to be proportional to actual demand. Because we had problems in estimating all the parameters simultaneously we have used a grid search to estimate k, the proportionality factor. In alternative E, k was equal to 0.4. To indicate the sensitivity of the results with respect to this choice, Table I also includes corresponding results with k set equal to 0.3 and 0,5 (alternatives C and D). The goodness of fit test statistics are virtually unaffected but there are considerable changes in some of the estimates: in particular, the long-run coefficients a and b are changed. The shortrun effect, however, is virtually unchanged. When k is increased and the level of desired stocks is increased relative to demand the estimated long-run effect of stock imbahmces is increased but the long-run capacity effect is not much changed and is in no case signiticantly positive; nor is the error correction parameter mt, ch affected. In the last two alternatives (F and G) the h)ng-run parameters are restricted. From (16) it follows that if both a and b are set equal to 0, the target wdue of production towards which producers attempt to adjust is equal to the trend value of demand ie stock imbahmccs and the degree of capacity utilization plays no role in long-run decisions. The most important change when this restriction is imposed is that the error correction parameter, 7, is reduced from 0.18 to 0.09. Thus, when long-run capacity effects are eliminated, the estimated adjustment to trend imbalances becomes slower than in the unrestricted case. Finally, we have also tried to restrict a to I and b to 0 (case F). This implies that the target value of output coincides with the trend value of production capacity. The main change in the estimates is that the error correction effect disappears (,/= 0). To summarize, there are indications that when the specification of the long-run response is made more rigid, the estimated degree of error correction becomes slower. Because of the numerical problems encountered when estimating all the parameters simultaneously due, inter alia, to collinearity in the data - we have used the grid search procedure with preassigned values of k, Pt and p~ in the above estimation exercises. To 196

check the effect of this simplification, the model is re-estimated with p , treated as a free parameter in alternative E. Its non-linear least squares estimate is - 0 . 2 5 , which is not significantly different from 0. The remaining coefficients were not substantially altered and the main conclusions concerning the short- and long-run adjustments are retained. From this we can conclude that p,, = 0 is no effective restriction, given the available data. Correspondingly, we have reestimated the model in alternative B (and A), treating p t as a free parameter. Its non-linear least squares estimate exceeds 1, conditionally on k and p., = 1. Last, we have re-estimated the model (in both alternative B and E) with k treated as a free parameter, which gave a least squares estimate of about 0.3-0.4. It may be argued that the righthand variables of our regression model ie capacity, demand and stocks of inventories are not predetermined in relation to the output level but jointly determined with it within a larger unspecified simultaneous model. The use of NLS could thus cause the estimated coefficients to suffer from simultaneity bias. To check for this we have re-estimated some of the model variants above by means of the instrumental variables technique. In the T R O L L system this estimation procedure is available only for linear models. Our model is linear in the parameters, conditional on the values of p t, P.~, ;' and k. We set ;,=0.18, which is the NLS estimate in alternative E. With this simplification, the estimates obtained by using instrumental w~riables were not very different from the NLS estimates. Detailed results are reported in Table 2. Tests of dynamic specification To test the stability and the dynamic tracking of the model we have performed some statistical tests. We have specifically tested for the presence of autoregressive residuals. In addition to the Durbin-Watson statistic, the Box-Ljung statistic (see Ljung and Box l"13]) and the goodness of fit F test (see Kiviet ['12]) for higher order autocorrelation are used. The latter is preferable if, as is the case for some of the models, lagged endogenous variables occur as regressors. Then the standard D u r b i n - W a t s o n and the Box-Ljung tests are biased. Since seasonally unadjusted quarterly data are used, fourth order autocorrelation may be of importance. The different tests give quite similar qualitative conclusions. There is in this respect a remarkable difference between the case where Pt --0, p., = 1 and the case where Pt = 1, p., = 0. In the latter case there is no indication of significant fourth order autocorrelation, which indicates that the stable seasonalities are removed (compare alternatives B and C in Table 1). According to the B o x - L j u n g statistic, E C O N O M I C M O D E L L I N G April 1989

Production-demand adjustment in Norwegian manufacturing: E. Biorn and H. Olsen Table 2. correction based on estimates

Pt ,o, k a x b /3 ;' R: DW SER

Production in manufacturing industries, quarterly error model (million 1985 kroner). Comparison of estimates instrumental variables (IV) and non-linear least squares ( N LS) ( 1975 : I - i 985 : 4)? IV b.,

[Vb.d

,N'LSn

1 0 0.4 0.22 (0.86) 0.46 (2.701 0.28 (1.53) 0.36 ( 2.05} 0.18

1 0 0.4 0.26 (0.751 0.42 (2.36D 0.26 (1.40) 0.35 { 1.981 0.18

0.4245 1.43 378.5

0.4117 1.38 385.5

I 0 0.4 0.24 ~0.90) 0.49 13.46~ 0.28 (1.49) 0.31 { 1.721 0.18 {2.181 0.9999 1.54 374.8

• t-values in brackets; ~'lh, 1~.,. k and 7 are tixed parameters in the IV estimation. ,o I, I~L. and k are fixed in the NLS estimation (of altcrnl, tive E in Table II; ' 14 instruments. Lagged values of the variables in the model and of macrovariablcs which are asst, mcd to be influencing the activity, seasonal dummies and strictly exogenous variables, aThe II lirst principal components of the variables in footnote ~. although with more lags. arc used as iflstrtlMents.

there are no first order residual autocorrelations either. When no first order differencing is performed ic whcn Pt = 0 there are, however, strong indications of first order autocorrelation from all the tests we have used. Thus there is obviously a non-linear trend in the data which is not removed by the specified model. When P.t is set to I, there is significant fourth order autocorrelation, indicating overdiffcrencing. As di~usscd above this may indicate that the variables are cointegrated of order higher than 1. The results from the Kiviet test are not presented but are in line with the tests referred to above. Simulation results To test the dynamic behaviour of the different specifications of the QEC equation (201 we have performed some simulation experiments. Both the within sample tracking performance and the dynamic behaviour of the model when a permanent shift in one of the exogenous variables occurs are investigated. The stability of the model is investigated by giving each of its exogenous variables a temporary shock. These simulations are based on a two-equation model, including the output decision function and the identity connecting production, demand and stockbuilding ie Y = D + AS. In this identity the discrepancy between stockbuilding as measured in the national accounts and stockbuilding as measured by the quantity index for stocks is also taken into account. As it is not E C O N O M I C M O D E L L I N G April 1989

clear how this discrepancy should be modelled, we have for simplicity used the series calculated from the historical data. For genuine forecasting purposes this procedure would not be feasible but we may, for instance, use a simple time series model (AR or ARMA) to predict the value of the discrepancy. We have used the two equations for joint simulation of production and stockbuilding, while taking demand as exogenous. More realistic simulation experiments could, of course, have been performed if we had endogenized demand by specifying a demand function. The e x post simulations are carried out for the estimation period 1975 : ! - 1985:4 with the exogenous variables set equal to the values observed and the simulated values substituted for the lagged endogenous variables. In the first period the observed values of the lagged variables are used. Treating the endogenous variables in this way, simulation errors in one period are allowed to influence the forecasting performance in future periods because of the autoregressive structure of the model. The choice of the starting period may affect the forecasting performance since the effect of the initial disturbance will affect all subsequent values of the endogenous variables. The within sample tracking performance of the different alternative specifications in Table I its measured by the relative root mean square error (RRMSE) do not seem to be very different. For the seasonally adjusted production, RRMSE is about 1.4-1.5% in the main alternative (E). For the seasonally unadjusted production variable, the RRMSE is 6.1% ie about four times as large its when measured in terms of the seasonally adjusted data. This illustrates that the smoothing of the data implied by the seasonal adjustment procedure tends to improve the tracking properties of the model to a considerable degree. The specification involving it full four quarter differencing (alternative B) has a different dynamic behaviour. In some periods it fits the historical seasonally adjusted series quite well, in others the simulated and historical data deviate considerably, probably as a consequence of over differencing. The simulation results are presented in Tables 3 and 4. Some of the results are also presented graphically in Figures I-6. The seasonally adjustcd, exogenous variables are shifted one at a time to investigate the process of adjustment towards the new equilibrium. The effect of a permanent shift in demand by 10 billion Norwegian kroner in 1978:i is presented in Table 3, columns I-4. As proportionality between demand and desired stockbuilding is assumed, the increased demand induces an increase in desired stockbuilding which reinforces the expansion towards the new equilibrium. The long-run effects are quite similar in the different models. The new equilibrium level of production 197

Production-demand adjustment in Norwegian manufacturing: E. Biorn and H. Olsen Table 3. Effect on production (million 1985 kroner) o f an increase in demand by a p p r o x i m a t e l y 1 0 0 0 0 million 1985 kroner. Sustainodshifi &om1978:l

T e m p o r a r y s h i ~ in 1 9 7 8 : !

i"

fi ~

iiF

1978:1 2 3 4

1 671 3 673 5875 8 195

1 591 3 488 5587 7820

1575 3 550 5773 8 148

1979:1 2 3 4

8916 9349 9609 9 765

8 550 9032 9 352 9563

1980:1 2 3 4

9 859 9 916 9 949 9 969

1981:1 2 3 4 1982:1 2 3 4

ivd

i"

fi~

Hie

iv d

1 738 3 726 5884 8 154

1 671 2016 2216 2337

1 591 1 910 2114 2249

I 575 1989 2239 2 392

1 738 2003 2173 2286

9039 9581 9904 10088

9 238 9910 10324 10 577

726 436 262 157

735 486 321 213

897 547 325 185

1092 677 417 255

9 702 9 795 9 856 9 896

10 185 10 231 10 344 10 240

10 280 10 157 10 121 10 125

94 57 34 20

141 93 61 41

99 45 13 -5

-298 -124 -37 4

9981 9 989 9993 9996

9923 9940 9952 9 960

10225 10 205 I0 184 10 163

10119 10098 10078 10064

12 7 4 3

27 t8 12 8

-15 -20 --21 - 21

-6 -21 20 -15

9997 9998 9999 9999

9965 9 968 9974 9 972

10143 I0 125 10 109 10(~4

10054 10046 10038 10032

2 I I 0

5 3 2 1

-20 -18 -17 --15

-I0 -8 -7 -6

' i : l'~ = I. P.L = 0 , a =0, h = 0 ( a l t e r n a t i v e G); hii: /h ~ I, l,.~ = 0 , u = 1, h = 0 {alternative F); ~iii: Pt = I. l'+ =O, a. b free (alternative E); diV: Pl = 0 . l~'a = l, (1, h free ( a l t e r n a t i v e B).

Table 4. Effect on production (million 1985 kroner) of an increase in capacity by a p p r o x i m a t e l y II}INHJ million 1985 kroner. Sustained shift from 1978:1

T e m p o r a r y shift in 1978: I

i"

iP

iiV

1978: I 2 3 4

0 1 140 I 825 2 236

0 I 247 2073 2 621

(} I 237 1 971 2 387

1979:1 3 4

2 483 1 491 896 538

2 986 1 983 1 320 881

1980:1 2 3 4

323 194 116 70

1981:1 2 3 4 1982:1 2 3 4

ivd

i"

iP

lip

ivd

0 1 091 1 824 2 314

0 1 140 690 414

0 I 247 832 553

0 1 237 739 420

0 I 091 737 495

2 607 1 469 763 332

2 644 I 225 352 - 181

249 --999 -- 600 --360

368 - 1011 - 668 -442

221 -- I 146 - 711 --434

332 - I 430 - 879 -536

591 399 273 189

76 -70 - 147 - 183

- 502 - 177 -57 -37

- 216 -- 130 -78 -47

-- 292 -- 193 - 128 -84

- 258 -- 147 -78 -36

-- 324 328 121 21

42 25 15 9

133 96 72 56

-

194 190 178 163

-59 -67 -54 -40

-28 - 17 - 10 -6

-56 -37 -24 - 16

- II 4 12 16

-22 -8 13 14

5 3 2 I

46 39 34 31

- 146 - 129 -114 -99

-32 -27 -24 -20

-4 -2 -I -- I

- II -7 -5 -3

17 17 16 15

9 5 4 4

• i: pt = l, ,o.~ = 0 , a = 0 . b = O (alternative G); hii: p~ -- I. P4 = 0 . a = 1. b = 0 (alternative F); "iii: p, = I, p.~ = 0 . a. b free ( a l t e r n a t i v e E); diV: Pt =0, I'.L = 1, a, b frce ( a l t e r n a t i v e B).

198

ECONOMIC

MODELLING

April

1989

Production-demand adjustment in Norwegian manufacturing: E. Biorn and H. Olsen 1.6

11

1.2 9

t, C o

o o~

7

o.s 0.4

o=

._

\

/

o -0.4

- -0.8 1978

I

1979

I

1960

I

1981

I

1982

l

1983

[

I

198q

1

1985

Figure I. Effect on production of a sustained increase in demand by 10 000 million 1985 kroner, P l = 1, p.t = 0, a, b free.

1978

Figure 4. Effect on production of a temporary increase in capacity in 1978:1 by 10000 million 1985 kroner, p, = 1. P4 = 0, a, b free.

2.8

12

2.q C

~2.0

"

o

1o 8

st.

~1.6

-

6 t-

O

: E

c1.2 Q q

r I I I J I I 1979 1980 1981 1982 1983 198q 1985

q

~ 0.6 o o_0.~

p, !

1978

0 I

I

1978

1979

I

1980

1

1981

I

1982

I

1983

I

198q

1985

Figure 2. Effect on production of a sustained increase in capacity by 10000 1985 kroner, Pt = 1,/q4 = 0, a, b free.

I

I

1980

1979

I 1981

I 1982

I 1963

I t96q

1985

Figure 5. Effect on production of a sustained increase in demand by 10000 million 1985 kroner (desired stocks kept fixed), Pl = I, P4 =0, a, b free. 12

2.7 2.q t,¢-

2.1

2,¢

1.8 1.s

co

1.2

~_ O.9

~ o.6 o

0.3

I 1978

0

I 978

I 1979

I 1980

1 1981

1 1982

I 1983

| 1984

198.5

Figure 3. Effect on production of a temporary increase in demand in 1978:1 by 10000 million 1985 kroner, p~ = I, Pa = 0, a, b free seems to have been reached by 1981:1 ie in about three years and most of the effect is exhausted within six to seven quarters. There is a tendency for the models with b set equal to 0 (alternatives F and G in Table 1) ie those in which the producers in the long run are assumed to take no account of stock imbalances when

ECONOMIC MODELLING

April 1989

I 1979

I

I 1980

1981

1 1962

1 1983

I 198q

1985

Figure 6. Effect on production of a synchronized increase in demand and capacity by 10000 million 1985 kroner (desired stocks kept fixed), p, = 1, P4 =0, a, b free. they decide how much to produce, to attain the new production level with a s m o o t h e r adjustment path than when stock imbalance, which is influenced by the expanded demand, is one of the factors motivating production. When b is a free parameter (alternatives B and E) ie when trend departure in stocks is one of the motivating factors, the producers are, in the initial

199

Production-demand adjustment in Norweyian manufacturiny: E. Biorn and H. Olsen

stages, likely to overadjust. This is due to the expansionary effects of increased stock imbalances. When production is too low compared to demand, stocks are too low compared to the desired level. This boosts production beyond actual increased demand. Table 4, columns I-4, gives the corresponding simulation results when the capacity (seasonally adjusted) is permanently increased by 10 billion Norwegian kroner, with demand kept unchanged. In the long run there is thus no incentive to increase production. The effect of the shift is exhausted in about three years ie the time lag is of the same order of magnitude as in the case with the demand stimulus. In the first quarters production increases quite rapidly under the influence of expanded capacity and reaches its peak at about 1979:1 ie after approximately one year. Even if the peak is reached simultaneously in all the alternative specifications, the production effect varies, from approximately 2 500 to 3 000 million Norwegian kroner ie by about 2 5 0 of capacity expansion. Production is then too high compared to demand and this diseqt, ilibrium is stronger than the disequilibrium between production and capacity. This induces a reduction in production until it reaches its initial equilibrium, which is consistent with actual demand. In the alternatives where h is set equal to 0 ie with no production impulses from stock imbalances in the long run there is a smooth adjustment towards the equilibrium level. When a and b are unrestricted production is contracted too strongly; this is conapensatcd by :m increase before the new equilibrium is attained, in periods when production is too high compared with demand, stockbuilding is also too high compared with desired stockbuiiding, which consequently initiates negative production effects. The adjustment towards the equilibrium thus takes the form of dampened oscillations. When a = I (alternative F) ie when the producers try to adjust towards the trend in capacity only, production rises faster and declines later on at a slower speed than in the other formulations. To see how the model behaves when exposed to an exogenous shock we have performed similar simulations where demand and capacity respectively are increased temporarily by 10 billion Norwegian kroner in 1978:1 and set back to their previous value in the next quarter. These results are given in Tables 3 and 4, columns 5-8. Such a demand shock might occur, for instance when a substantial increase in household taxes is announced or put into effect. In this model, the producers do not, however, realize that the shift is temporary. These exercises also indicate that the long-run properties of the models are quite similar and that the initial level of production is re-attained in about 1981:1. The demand shock induces a quite rapid increase in production which attains its peak in 1978:4 200

at about 2 300-2 400 million Norwegian kroner above its initial level. Then there is a substantial drop during 1979 and during 1980 only minor adjustments occur. The only exception from this pattern is the model where Pt = 0 and p~ = 1 (alternative B). In this case, the decrease falls off during 1979 but is reinforced in 1980: I and causes an overstrong downward adjustment of production, which next initiates a compensating increase towards the equilibrium level. Compared with the unrestricted alternatives the adjustment is somewhat slower in the models where b = 0 (G and F), where the trend imbalance in stocks is not motivating production. The temporary shift in capacity initiates an immediate and strong increase in production. Since this is not accompanied by a change in demand, a decline in production begins in the following quarter. In 1979:2 ie one year after the original stimulus there is a sudden and dramatic drop in production which is in this quarter ! 000- I 500 million Norwegian kroner below its equilibrium level. This effect is probably a consequence of the large imbalance between capacity and demand live quarters earlier. This downward overshooting is somewhat slower when b = 0, since in this case there are no negative production impulses from the too high stocks which have accumulated. During tile following quarters there is consequently an increase in production towards the equilibrium level. The alternative Pt = 0 and p.~ = 1 (alternative B) is, however, an exception. Here the overadjustment in 1979:2 is extraordinarily large because of the four quarter differencing and the following catching up, which causes an upward overcompensation in the following quarters. Thus production approaches its new equilibrium through dampened oscillations. In the demand shift experiments reported so far we have retained the assumption that the desired level of stocks changes in proportion to demand ie that producers are assumed to revise their desired level of stocks instantaneously to accord with increased demand. Alternative simulations in which the desired level of the stocks is assumed to be unaffected by the demand shift have also been performed (see Table 5). This is naive behaviour where the producers do not realize that increased demand should imply an increase in desired stocks. When b = 0 ie there is no adjustment of output because of the departure from the long-run trend in desired stocks, production rises smoothly towards its new equilibrium. The adjustment, however, seems to be slower than in the previous case. Even if there were no effect of stock imbalances in the long run, the increased stock imbalances would induce shortrun production impulses. When there ar~ no restrictions on a and b ie when stock imbalances ffave an effect in the long run too, the simulation results seem a bit E C O N O M I C M O D E L L I N G April 1989

P r o d u c t i o n - d e m a n d adjustment in N o r w e y i a n manufacturing: E. Biorn and H. Olsen Table 5. Effects on production (million 1985 kroner) of 1978:1 (desired stocks kept fixed).

a

sustained increase in demand by approximately 10000 million 1985 kroner from

Increased demand

Synchronized increase in demand and capacity

i"

iP

iiF

1978:1 2 3 4

772 1 586 3 073 4966

711 2 569 4 641 6857

947 2 467 4 355 6478

1056 2 588 4 439 6503

772 3 867 6 724 9439

711 5 061 8 787 12 100

947 3 705 6 326 8865

1056 3 680 6 263 8818

1979: I 2 3 4

6329 7 795 8 676 9 205

8455 8 970 9 310 9 535

8 119 9 212 9 946 10 443

8418 9 598 10 320 10 757

I 1 296 l0 778 10 467 10 281

14428 12 936 11 950 I I 298

10726 10681 10 709 10 775

l 1062 10 823 10 672 10 576

1980:1 2 3 4

9523 9713 9 828 9897

9684 9783 9 848 9891

10468 10458 10430 10393

10416 10319 10 336 10396

10 168 10 101 10061 10036

10867 10582 I0 393 10268

10544 10389 10 283 10210

9913 10 142 10 278 10359

1981:1 2 3 4

9938 9963 9978 9986

9919 9938 9951 9959

10352 10312 10274 10239

10315 10244 10 193 10 164

10022 10013 10008 10005

10 186 10 131 10095 10071

10 159 10 122 10096 10077

10256 10 177 10 139 10 123

1982:1

9992 9 995 9997

9964 9 968 9970

10208 10 180 10 155

10 141 10 119 10(X)9

10003 10002 10001

10056 10045 10038

10062 10051 10042

10 109 IO(X)2 10075

9 998

9 972

10 134

10082

IO(XX)

10034

10035

10(X)2

3

3 4

i"

ivd

fib

iiF

iva

• i: th = I, p.L = 0, a = 0, h = 0 (alternative G); hit: I't = 1, p.~ = 0, a = I, h = 0 (alternative F); "iii: lh = I, Pa = O, a, t, free (:alternative E); aiv: Pl =0. P.L = I, a, h free (alternative 11). strange, in the lirst round, the rise in p r o d u c t i o n is sm:dlcr than when stocks too were increased, because of the d i s a p p e a r a n c e of this extra d e m a n d impulse. After a couple of years the rise in p r o d u c t i o n is in fact s t r o n g e r than in the alternative above. This is p r o b a b l y a consequence of the weak e x p a n s i o n a r y effects in the early phase of the recovery. Because of the slower a d j u s t m e n t of p r o d u c t i o n d e m a n d is met by reducing stocks. This causes an increase in the stock i m b a l a n c e s which g r a d u a l l y becomes so large that the p r o d u c t i o n stimulus is s t r o n g e r than in the original d e m a n d shift example. Finally, we have p e r f o r m e d an experiment in which a synchronized increase in d e m a n d and c a p a c i t y by 10 billion 1985 N o r w e g i a n k r o n e r occurs in 1978: 1. The level of stocks desired is kept unaltered in this alternative too. In all the four alternatives e x p a n s i o n implies an o v e r a d j u s t m e n t of p r o d u c t i o n . This effect is most p r o n o u n c e d when a = I i e when p r o d u c e r s adjust o u t p u t o n l y t o w a r d s the long-run trend in capacity. Discrepancies between the actual a n d trend d e m a n d also have e x p a n s i o n a r y effect on p r o d u c t i o n . This causes an o v e r a d j u s t m e n t of p r o d u c t i o n by m o r e than 4 0 0 0 million N o r w e g i a n k r o n e r one y e a r after the expansion. Then, however, the c o n t r a c t i o n a r y effects d o m i n a t e a n d p r o d u c t i o n is adjusted quite fast t o w a r d s the new equilibrium. By the end of 1980

ECONOMIC

MODELLING

April 1989

p r o d u c t i o n has a t t a i n e d a b o u t the same level in all four alternatives.

Conclusion In this p a p e r we have presented an extension o f the q u a r t e r l y e r r o r c o r r e c t i o n model with o n l y one e x o g e n o u s variable to a process including an a r b i t r a r y n u m b e r of e x o g e n o u s variables. This Q E C f r a m e w o r k is a c c o m m o d a t e d to the specification of an o u t p u t decision function for a s t o c k h o l d i n g m a n u f a c t u r i n g sector with three exogenous variables, capacity, d e m a n d a n d stock imbalance. S i m u l a t i o n e x p e r i m e n t s indicate that this model has satisfactory d y n a m i c properties. An interesting extension of the work in this p a p e r would be to build a m u l t i e q u a t i o n model e n d o g e n i z i n g some of the r i g h t h a n d side variables in the o u t p u t decision function by i m p o s i n g s e p a r a t e Q E C processes in each equation. It is not o b v i o u s what d y n a m i c properties such a model w o u l d h'ave. A topic for further research is to investigate the choice of e s t i m a t i o n technique and the s i m u l a t i o n p r o p e r t i e s of such s i m u l t a n e o u s models. References

I E. Biorn, Produksjonstilpasnin# og laqeradferd i industri. En analyse av kvartalsdata, Report no 85/25, Central Bureau of Statistics, Oslo 1985.

201

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