A keynesian macro econometric model of t

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JOURNAL OF APPLIED ECONOMETRICS, VOL. 3 , 1-33 (1988)

A KEYNESIAN MACRO-ECONOMETRIC MODEL OF
THE UK: 1955-1984
MEGHNAD DESAI

London School of Economics

GUGLIELMO WEBER

Universiry College, London

SUMMARY
In this paper we present a small Keynesian macro-economic model in which wage-price determination
is linked to the working of goods and money markets. By explicitly treating the Keynes effect we derive
a general expression for the employment-money supply elasticity, and draw the IS-LM loci in the

employment-interest rate space.
Our empirical specification allows for short-run disequilibrium dynamic adjustments around the static
long-run relations predicted by the theoretical model. By careful use of our specification search strategy
we obtain a statistically sound econometric model, which exhibits sensible long-run properties. A
remarkable finding implied by our estimates is that equilibrium unemployment is negatively affected by
both money supply and incomes policy.

1. INTRODUCTION

In early 1980 the UK government adopted the medium term financial strategy (MTFS). This
was a unique experiment in the adoption of a monetarist policy with published targets for
monetary growth announced several years in advance. The intellectual origins of the policy in
the academic debates about monetarism-both of Friedman and of the new classical varietywere acknowledged. In the hearings held by the Parliamentary Select Committee, at the start
of the policy, evidence given by prominent monetarists among others asserted that the preannouncement of monetary growth targets leads to a fall in the rate of inflation via the
expectations mechanism with a negligible rise in unemployment. (See Desai, 1981a, Chapter 5
for details; also Buiter and Miller, 1981a, 1983.)
Subsequent records have shown that while the rate of inflation did come down, there were
also swift, severe and persistent adverse effects on real economic activity as measured by
unemployment. There have been several studies analysing the reasons for the high unemployment (Layard and Nickell, 1985, being the most frequently cited). But these have concentrated
on the link between unemployment and government expenditure, leaving the monetary

variables out of the picture. Other explanations have concentrated on the exchange rate
dynamics (Buiter and Miller, 1981b, 1983).
In these exercises, whether formally econometric or not, the practice has been to include data
which postdate the adoption of the policy as well as other data. This may not be thought to
be a legitimate exercise, since we may be in a different regime after the adoption of the MTFS:
In this paper we address a different question. Given the information up to the end of 1979,

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0883-7252/88/010001-33$16.50
0 1988 by John Wiley & Sons, Ltd.

Received June 1986
Revised August 1987

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M. DESAI AND G. WEBER

before the formal adoption of MTFS, could one have foreseen that restriction of the money
supply growth would lead to output effects as well as price effects?
Such an exercise requires that we confine our estimation to a sample excluding the years since
the adoption of MTFS. It also requires that we seek a model for the transmission of monetary
influence to the real economy, which is a genuine alternative to the new classical model. This
is because we know what, as of end of 1979, the new classical model predicted. We base our
model of the transmission mechanism on Chapter 19 of the General Theory (Keynes, 1936).
In this chapter the effects of money wage reduction on employment are traced via, inter alia,
the money stock. This is known as the Keynes effect (see Chipman, 1965; Tobin, 1981; and
Sargent, 1979).
Our aim is therefore to construct a small (six endogenous variable) but parsimonious (in
terms of the number of exogenous variables which is nine) macroeconometric model which captures, as far as possible, the ingredients required to answer the question about the likely effects
of money on real economic activity. We have had to make some heroic simplifications. Thus
we take the measure of money stock to be M1 rather than M3. This was because the latter was
much less well-controlled during MTFS than the former, but also because for the Keynes effect

M1 is the more obvious measure. Thus we condense the money supply-PSBR-Real economy
connection out of our model (for the concept of condensed structural form, see Desai, 1981b).
As of 1979, the exchange rate aspects of monetary policy were also quite ignored as perusal
of the Select Committee hearings will show. Thus our model is admittedly weak on this link,
which would have to be modelled if we were to bring the model up to date.
As against these simplifications, we can mention several features which are distinctive to our
exercise. First is, of course, the specification of the Keynes effect as the demand for money
equation. This is an alternative to the Marshallian money demand function usually employed
in deriving the LM curve. In as much as it works via producers’ employment and output decisions, it is a natural complement to the Phillips curve for tracing the transmission effects of
money on unemployment. A second distinctive feature is that we have fully endogenized
unemployment and inflation, as well as interest rates. The new classical models impose a recursive structure on the unemployment inflation system which has been rejected by the data
(Cuddington, 1980; Sargent, 1976). Most other models, for some reason or another, fail to do
justice to the complexity of this interaction (see Desai, 1984a, for a critique).
A third feature of our model is that we do not impose the homogeneity postulate a priori
in our relationships. Variables are specified in nominal terms wherever possible, and the
homogeneity restrictions tested ex post by appropriate test procedures. Thus money wages,
prices, money stock and interest rates appear in nominal terms; only unemployment, real output and labour productivity are in real terms. A fourth feature of our specifications is that we
allow for separation between short-run, transient effects and long-run relationships. This is
done by couching our dynamic specifications in the Sargan-Hendry ECM mode (see Hendry
and Richard, 1982, 1983, but for the pioneering paper, see Sargan, 1964/1984). We are interested in both the short-run effects of nominal variables o n real ones, especially of money

stock on unemployment, and the long-run relationship. Since specification search is a contentious issue in applied econometrics, we shall be explicit in stating the diagnostic tests used to
choose between alternative specifications, and also indicate, wherever relevant, the path taken
from the general to the particular specification. We exploit the systems dynamic properties of
the model by studying the distribution of the eigenvalues of the estimated system to throw light
on the persistence of the effects of exogenous shocks on the endogenous variable.
In Section 2 we set out the theoretical model briefly. The model sticks fairly closely t o Keynes’
model in Chapter 19 of the General Theory, as mentioned above. The econometrically

MACROECONOMETRIC MODEL FOR UK

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estimated model differs in some details from the theoretical model, but this is merely in order
to bring it closer to the empirical data. Our aim was to have a small but dynamic simultaneous
equations model that could be estimated from the hundred-odd observations for
1955.1-1979.4. To this end, some drastic simplifications had to be made. The smallness of the
model allows us to use systems tests for restrictions and for detecting misspecifications.
In Section 4 we compute the impact multipliers for money on the endogenous variables of
our model, as well as discuss the long-run properties of the system. We also investigate the

question of post-sample predictive ability of our model, over a period of 5 additional years
(1980-1984).

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2 . THE THEORETICAL FRAMEWORK

There are four basic endogenous variables in the model: employment ( L ) , the rate of interest
( R ) ,nominal wages ( W ) ,price level ( P ) .In the econometric elaboration we split the price level
into output price ( P y ) and retail price ( P r )and also endogenize the prime cost of output ( F )
as an auxiliary variable.
2.1 Employment

In the Keynes model the level of employment is determined at the intersection of the aggregate
supply curve ( Z ) , and the aggregate demand curve (0).

Employment is decided on the basis
of output that producers expect to sell. Aggregate supply price measures their reservation level
of total revenue for each level of employment. The level of employment for which aggregate
supply price Z is less than or equal to aggregate demand is the short-run employment
equilibrium. Assuming away all aggregation problems, we derive total employment L as
follows.
Let K be a mark-up above prime costs which equal the wage bill
2 = (1 + K)WL = W ( 6 ( L ) , (6'

Then in equilibrium Z

=D
'

> O,+" > 0.

(la)

gives us

L

=

L (D e /W ) ,

where D' is the expected nominal level of aggregate demand and W is the money wage. (For
details of the derivation of (lb) from micro-theory see Desai and Weber, 1986). Aggregate
demand is taken to be sum of consumption and investment. These in turn are taken to be
functions of the wage bill, profits and money balances for consumption and profits and interest
rate for investment. The aim is to keep the model as parsimonious as possible. Profit level in
both these cases is the expected profit level. Thus

D = ciyg + 011 WL + cidI'

+ 013R + 014M-1,

(2)

where Heis expected profits, and M consumers' money balances. The parameters have the

usual expected signs. We simplify ( 2 ) further by solving out He in terms of the wage bill. This
is done via the definition of aggregate supply price already used in deriving (1). Given the one-'
period lag between input and output

n,, 1 = ( P Y ) , ,

1

- ( W L ) ,= K WLI.

(3)

In the Keynesian model, in short-run equilibrium Di+
I = D e , i.e. short-run expectations are

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4

M. DESAl AND G. WEBER

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fulfilled. This allows us t o put H,+I =He.
Thus we have

D = ( Y o+ ((YI + ( Y Z X ) W+L( Y ~+Ra4M-1.

(4)

Putting (1) and (4) together, the Keynesian employment function can be written implicitly as
L

=

L(W, R, M - i ) ,

(5)

where LW < 0, LR < 0 and LM > 0. The employment function is our analogue of the IS curve.
It is downward-sloping in the R,L space as the IS is in the R, Y space.

2.2

Keynes Effect/Money Demand

Producers need money to cover prime costs given by W L , which are incurred before they sell
output. Consumers have money deposits M - in the bank at the beginning of the period. Banks
give loans to producers in proportion to WL. This money is disbursed by the producers to
workers as wages. At the end of the period, consumers (workers and producers) are left with
money balances M which reflect the level of demand and the profit margins. We neglect any
initial money balances producers have, or any interest charges paid to the banks on loans or
paid by the banks t o deposits. The money balance identity is therefore

M = M- I

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+ WL + H W L - I

- ((YO

+ (a1 + a m )WL + a3R + CUM-1)

= ( 1 - ( ~ 4 ) M - 1 +[ I - ( ~ I + ( Y z x ) + xW
BL] - C Y ~ R - ( Y O ,

(6)

where B is the lag operator. The consumer money holding relation is quite passive but as we
see in ( 6 ) not inconsistent with the usual specification. It is the producers who demand money
since they activate the money deposits held by consumers.
The producers’ demand for money is proportional to their prime costs, i.e. the wage bill.
Again we use the simplest specification at this stage and avoid complications such as inventories
etc.

MP = P(WL)t,

(7)

where M D is demand for money, p is a proportionality factor. The money stock is exogenously
determined. Thus at any moment of time there may be more or less M than producers require.
We take it that banks invest such money in the money market. This is a simplification of
Keynes’ speculative motive. It ailows us to introduce the interest rate money supply connection
without introducing rentiers explicitly. Thus
R

=R ( M / M D=
) R(M/pWL).

(8)

Equation (8) thus incorporates Keynes’ version of the demand for money as argued in Chapter
19 of the General Theory. While it is different from the conventional Keynesian money demand
function, note that in equilibrium we get a proportionality between the wage bill and total
money income. If so, (8) could be translated in terms of PY rather than WL.
Equation (8) is our LM equation and in the R,L space it gives us an upward-sloping curve.
Given a level of money wages W and money stock M , equations (5) and (8) determine R and
L . But W is not an exogenous variable in our model. We write a conventional specification, for
W and P as follows

w= W ( L S P, e ) ,

(9)

L s being labour supply and P the workers’ expectations of the price level. For the price level

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MACROECONOMETRIC MODEL FOR UK

Table I. The theoretical model
(5)

(8)
(9)
(10)

L = L ( w,R, M - 1 )
R = R(M/pW L )
w =W ( L . ”P, “ )
P = P(W,L ; K )

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we have already assumed a cost-plus mark-up hypothesis in deriving (1) above, i.e.
P = (1 + x ) ( W / Q )= P ( W , L ; F ) ,

(10)

where Q is labour productivity ( Y / L ) ,Y being real output. The implicit production technology
is that L is the variable factor, I? the fixed capital stock.
Equations (9,(8), (9) and (10) can be solved jointly to characterize the static equilibrium of
the model. In this static equilibrium L = L’, P = P‘. We get
Det = (1 - T I R L ~ L R )-( ~~ P W V N P +
) ( V W L - ~ P L ~ W P ) ( V L WV- R W ~ L R ) ,
ELM = ( ~ L M -~ I L R ) (-~ ypwqwp)/Det,

( 1 1)
(12)

where qy,x is the partial elasticity of y with respect to x and E , , ~the total elasticity. We have
only derived ELM of the various possible expressions since that is the focus of our investigation.
We see that if the labour supply is homogeneous in real wages (i.e. the corresponding Phillips
curve is vertical) q w p = 1 and if there is full cost pricing (stable share of wages in total income)
~ P =
W 1. These two are sufficient for ~ L =
M 0, that is for money to have no impact on the real
economy. ~ R W
is the narrow definition of the Keynes effect (Sargent, 1979, p. 56), whereas ELM
is the broader definition which summarizes the discussion in Chapter 19 of the General Theory.
These parameters are however the long-run (static) equilibrium values to be derived carefully
from the econometric estimates from short-run time-series data.
We take the view that the actual economy is a dynamic disequilibrium realization of the basic
static model. There are many ways in which the static model could be dynamized. We could
explore the adjustments when D‘ # 2 which may also lead to N # N* with implications for the
paths of all our variables. We could model expectations more generally and move away from
the convenient simplification D‘ = D adopted in deriving (15).
Our strategy is not to move futher in the direction of theoretical modelling but to move to
an econometric model. In this econometric exercise we will keep a long-run static equilibrium
in the background as a check on systems properties. The model will be specified as a dynamic
disequilibrium one but designed t o yield a dynamic steady state equilibrium as a first approximation. In the econometric specification we shall take growth rates in Wand P as one set of
variables. For the labour side, we think of the ratio ( L / L ’ ) as denoting the state of the labour
market. Now the change in log ( L / L s ) ,i.e. growth rate in the proportion employed, can be
approximated by the percentage unemployed U , and that, along with the rate of interest R , will
be our other set of variables. In the next section we pass on to the econometric specification.

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3. ECONOMETRIC SPECIFICATIONS
We now come t o the task of econometric specification of the basic relations of our model. We
have four basic equations: (a) the labour demand equation which we will specify in terms of
unemployment; (b) the interest rate equation where we shall augment prime costs by including
cost of imported raw materials; (c) the wage equation which will be specified as a Phillips curve;
and (d) the price equation which is split into a GDP deflator satisfying a cost-plus relation and

6

M. DESAI AND G. WEBER

an auxiliary equation linking retail prices to the GDP deflator. Besides these changes we also
adapt our model t o accommodate the open economy aspects of the UK economy. This involves
netting out imports from effective demand before determining employment. It also means that
the interest rate equation has to incorporate the influence of international variables.
As we adapt a static theoretical model to take care of various complications involved in
empirical modelling, there are likely to be severe problems of specification. Adding extra
variables, specifying lags, modelling the serial correlation structure of errors-all these, though
necessary, are invitations t o making mistakes. We have thus to be very careful to check our
specification at each stage for likely misspecification. It is appropriate at this stage that we say
something about our approach.

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3.1 The Specification Search Strategy

The econometric model we aim to estimate can be written in its most general form as

B(L)Yr + r ( L ) Z r= ~

t

,

(13)

where B ( L ) = X;B;L', r ( L ) = C r k L k are polynomial matrices of appropriate order and L is
the lag operator. As usual Yt and Zt denote endogenous and exogenous variables, and Ur is the
vector of errors.
Most of our specification searches and specification tests were carried out at the singleequation level, though we also use systems tests to check for overidentifying restrictions. Take
therefore the first equation from (13) and write it in the usual form:
-

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Yit= CPij(L)Yjr + Pir(L)Yir-i + &iK(L)ZKr + uir.

(14)

Equation (14) is the first equation of (13). Our problem is to impose appropriate restrictions
on the P v ( L ) ,P l ! ( L ) ,Y ~ K ( L
and
) ensure that u l f does not contain any undetected serial correlation. We wish to impose further homogeneous restrictions on the parameters so that the steady
state of the system, as well as the long-run equilibrium, will have appropriate economic interpretation. Our strategy is to start from a very general specification for (14) and then specialize
it down to a particular form by a careful specification search. As we eliminate 'non-significant'
variables, or add restrictions between parameters, we need to check that we have committed
no specification errors.
To this end we estimated each specification by IV (after some experiments with OLS) and
used the following tests

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3. I . 1 The Sargan Misspecifrcation Test (SC)
Write (14) in terms of T x n vector X , n x 1 vector of parameters a , with y and u being T X 1
y = xa+u.

(15)

Then the IV estimator of a is

G= ( X ' P z X ) - ' X ' Pzy,

where P, = Z ( Z ' Z ) - ' Z ' is the projection matrix and Z T x m, m > n is the set of instruments.
Now Sargan (1964) has shown that

rl = [ (u ' z ) ( z 'z ) - ' ( z ' u ) ] / a 2- x 2 ( m- n )

(16)

is a test of whether any variable from the instrument set had been omitted from (15). In practice

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MACROECONOMETRIC MODEL FOR UK

7

the u in (16) are replaced by computed residuals, and u2 by s2. Apart from omission of significant variables, the null hypothesis could be rejected if the u are serially correlated or some of
the Z are endogenous. In order t o fully exploit the ability of the test to detect various problems
we used it in its T . R 2 form regressing the ti on the 2. Then, we could look at 1 values of
individual Z t o detect an important missing variable. Some small sample corrections were made
to the test (see Kiviet, 1986, for the theory).

The Gallant-Jorgenson Test of Restrictions (GJC)
In going from the general to the specific (Hendry and Richard, 1983), we were imposing
restrictions progressively on an equation to simplify it. A useful test for this purpose is the
Gallant-Jorgenson (1 979) test. This involves computing

3.1.2

rz =

(m- n + g ) -

(m- n ) - X :

(17)

where g is the number of restrictions. For small sample correction, see again Kiviet (1986).

Godfrey Test f o r Serial Correlation (GC)
Godrey (1976) proposed a test for first-order serial correlation of the disturbances which is
asymptotically equivalent to running an autoregressive instrumental variable (AIV) regression
and testing for the non-significance of the autoregressive coefficient (Sargan, 1959). The Godfrey test statistic can be expressed in a TR2 form. Let a variable with an asterisk denote
premultiplication by Pz. Then we have

3.1.3

{3

=

a'a:[a:'(r- P(x*'X*)-'X*')aT]
-'tiT'ti/s2.

(18)

This is the TR2 for the regression of ti on ti: and X * where u1 is the lagged value of u . The
test can be generalized to any order of serial correlation by adding the appropriate tii into the
auxiliary regression.
The Godfrey test cannot discriminate between the AR1 and MA1 hypothesis (Godfrey and
Wickens, 1982). But it belongs to the class of LM tests if the set of instruments 2 is suitably
expanded to take care of, for example, lagged endogenous variables on the RHS. If however
due t o lack of degree of freedom, etc., the 2 matrix cannot be augmented then it is a modified
LM (MLM) test. (Breusch and Godfrey, 1981). Given our approach of starting with a very
general specification we used the Godfrey test in its MLM form at earlier stages of the specification search. Once we were in sight of a parsimonious specification then we went on to enlarge
the 2 vector t o get the full LM properties of the test. Again small sample corrections were made
as before.
3.1.4 Test f o r Predictive Failure
The Chow test is well known in this case but has to be modified since some of the RHS
variables are not exogenous. The appropriate procedure here is to compare the criterion function rl in (16) on the null and on the alternative hypothesis. Let the two periods be of length
T I and TZ and denote 2 1 and 2 2 as the appropriate instrument set ( 2 2 is enlarged to include
one dummy for each observation in the second subsample). The procedure then is to run IV
on the first subsample and compute RSSI. Then enlarge the sample period to TO(=T I + T i )
and run another IV and compute RSSo. For both samples run the residuals on the 2 and compute R 2 (Chow, 1960: Davidson, 1984.) Then the T R 2 form of the Chow test is
(4

=

zyx
zy

TOR;- TOR?(RSSI/RSSo) - x"T,

(19)

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8

M . DESAI AND G . WEBER

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Given these four tests the specification search can be described as follows.
As Figure 1 shows, for each specification the Sargan and Godfrey tests were used to locate
variables which were possibly omitted by mistake and serial correlation. The first-stage IV
estimation was for the sample 1958.1-1979.4. Four observations for 1980 were used to perform
the Chow test. If the specification passed these tests, then the usual simplifications were made
of dropping variables which had low t values. As we got near t o the parsimonious specification
we tested the homogeneous restrictions by the Gallant-Jorgenson method.
All this of course requires an immense amount of computation. Since a major missing
variable also dictated rethinking the theoretical specification, the search had to be restaged in

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GENERAL
SPEC1FICATION

t

IV ESTIMATION
ADD REGRESSORS

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CHOOSE
REGRESSORS TO
BE DROPPED

-

1u

I

YES
IV =
SC =
GC =
CC =
GJ =

ADD I V AND
REESTIMATE

Figure 1 .

Specification search

Instrumental Variables
Sargon Criterion
Godfrey Criterion
Chow Criterion
Gallant and Jorgenson
test

9

MACROECONOMETRIC MODEL FOR UK

light of such revisions. A major revision was dictated to an earlier estimated version when it
was pointed out that our specification did not adequately reflect the open economy aspects on
the output/employment side. This meant that, having arrived after an extensive search at what
we thought was a satisfactory model, it had to be ‘junked’ and a new model formulated with
its own specification search.
At the point where we thought the single-equation search had been satisfactorily concluded,
we obtained 3SLS estimates of the complete set of equations. We tested this model for overidentifying restrictions. If these were rejected then the search went back to the single-equation
stage to locate the likely culprits. When the restrictions were accepted the search for a satisfactory model was complete.
Such a lengthy procedure has to be followed to make sure as far as is possible that no serious
misspecification is left undetected. The procedure is necessary but it is not foolproof. The path
from the most general specification to a specific parsimonious one is not unique, as we often
fourid. The method for locating at the simultaneous estimation stage the variables which may
cause the restrictions to be rejected are also not well developed (see, however, Pagan, 1984).
In applied econometric work a more usual practice is to let the specification search be guided
by considerations of whether individual coefficients have the ‘right’ sign and whether they are
individually statistically significant, i.e. have a t value of around 2. Given a multivariate
dynamic equation this attention to the significance of individual t ratio can be misleading. Our
preference is to rely on the test statistics already discussed. But in as much as our estimated
equation tries to capture the disequilibrium dynamics of actual time-series, we prefer to look
at the economic theoretic significance of the variables by examining the steady-state equilibrium
of the model obtained by setting Axt = AXt-i for all i for each variable x. Further, we work
out the long-run static equilibrium by setting all Axl-i = 0 for all i for each x. It is at this stage
that our econometric estimates correspond to the prior theoretical model which is, as is usual,
static or at least steady-state. This method will be followed below as we discuss individual
equations (Hendry, Pagan and Sargan, 1984).

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3.2 Single-equation Estimates

3.2. I The Unemployment Equation
We have t o adapt ( 5 ) in two ways. First, we have to take account of import demand which
should be netted out of D before it can be equated to Z to derive L . Second, we wish to cast
our estimating equation in terms of unemployment U rather than employment L . The output
measure whose prime cost enters as a deflator of the money supply is not D,but D less imports,
After some experiments with a separate import function we found that our best approach was
to solve out for imports. In empirical terms the last equation turned out to have no price effects,
leaving us with a simple equation. Thus let domestic output be PYY and imports PmIm. Thus

PYY == D - PmIm + X - TAX,
PmIm = mo + ml P r y ,

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where Im is the volume of imports and Pm is the price level of imports. X is exports and TAX
is factor cost adjustment. Substituting these into (la), (lb), we get
WC$=P Y Y = D - PmIm+ X - T A X ,
= (1 f

mi)-’ [ (UO - mo) + ( Q I

+ Q Z K ) WL + ad? + Q ~ M1 +- X-TAX] .

(1c)

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M . DESAI AND G. WEBER

Equation (lc) is then solved out in implicit terms as in (5)

L = L ( W , R , M , Pm,X,TAX).

(54

To bring (5a) in an estimable form, we expand it as
A h L

= 171

A h W + 72 A h R

+ 73 A

+

h M + 74 A h P,,* 75 A h X + 76 Aln TAX,

(5b)

and then use the approximation In(] - x) = - x,
A h L

-

A h L” = AU.

This approximation assumes that L s is a sluggishly changing or constant quantity. This approximation brings the goods side of our model in line with the Phillips curve as well.
Let us illustrate a typical specification arrived at after some search (lower-case variables
indicate logarithms of upper-case ones).
[ 1 - 0 . 7 6 L +0.30L4]A4Ur=O*041 -Oe23A4W+ [0*011-0.019LjA4pm

(5.0)

(11.8)

+ [0*012+ 0.031 L 3
(0.6)

(1.6)

(0.5)

0.005L4] A 4 p y
(0.3)

-

(2.4)

+ [ -0.017
(3.1)

(1.3)

(2.2)

0.001L + O*O08L2]
(0.3)
(1.7)

-

A4(tax-py) - 0.029A4R + 0-039A: p,.- 0.006m - O.277U-9
(2.6)
(2.9)
(0.8)
(3.7)

+ 0*009p,-5 + 0*005p,1~-5.
(1 * 1)

(2.2)

R 2 = 0.955, SC(28) = 44.9, GC(4) = 11 -3, Chow(4) = 21 -75.

(20)

In (20) numbers in parentheses are absolute values of t-ratios. All the variables are listed in
Appendix A, and Appendix B lists the instruments used to estimate each equation. The indirect
tax variable appears in its deflated form In(TAX/P,) = (tax-p,). The export variable X failed
to be significant. As will be seen in other equations as well, our preferred choice for variables
is the A4 form, and a string of lagged level terms is added. These latter terms define the long-run
equilibrium of the equation.
It is clear from the Chow test that (20) performs very badly over 1980, it has serial correlation
and the Sargan criterion (SC) is slightly above the 2 - 5 per cent threshold. It has to be said that,
as far as unemployment is concerned, 1980 is an exceptional year in UK economic history. The
sample mean of U for 19551-1979IV was 0.032 and the actual values for the four quarters
of 1980 were 0.06, 0.067, 0.083 and 0.091, i.e. several times the sample mean.
One way to examine equation (20) is to look at the steady-state version implied by it
A4U = 0.08 - 0-43A4W- 0.016A4pn,+ 0.70A4py - 0.019A4tax - 0.054A4R
(0.5) (2.2)
(2.6)
(2.1)
(2.0)
(2.7)
0.52U-9
(4.8)

-

+ O.018py-5 + 0*009p,n-5- 0.010m.
(1 ‘2)

(2 * 0 )

(204

(0.8)

Equation (20a) assigns a role to wage and price inflation terms as well as import price inflation
and tax changes in determining the growth of unemployment. An additional variable in dynamics
is the change in the rate of interest R which has a strong effect, though with a dubious sign.

zyxwvu
zyxwvut
MACROECONOMETRIC MODEL FOR UK

11

The level terms in (20a) then help us to define the long-run relation.

U = 0.154 + 0 . 0 3 4 ~+ ~0.017pm - 0.020m.
(0.5) (1.1)
(2.2)
(0.8)

It is at this stage that we can talk about ‘right’ signs and ‘wrong’ signs since our theory was
couched in static terms and (20b) is the econometric analogue of the static equation. We see
a very weak influence of the money stock, which in this version is non-significant. We are left
with the influence of the two price levels on unemployment. It may seem that pm has the wrong
sign and that perhaps the correct form would be relative prices, or ( p y - p m ) . We believe that
the sign for pmis correct, and reflects the effect of imported raw materials especially oil pfices
which played such a crucial role in the stagflation of the 1970s (Bruno and Sachs, 1985).
Equations (20), (20a) and (20b) are not our preferred equations. They have been discussed
here to illustrate our method of examining the econometric estimates we obtain. We look for
statistical properties for estimated equations but rely for the economic interpretation on the
steady-state and the long-run versions implicit in the estimated equation.
Our preferred equation is given in Table 11. As with the other main relations of this model,
we list the OLS, IV, 2SLS and 3SLS estimates and the associated test statistics. Given the
peculiarities of 1980 we decided not t o reject this specification on grounds of its failure on the
Chow test. The Godfrey test is certainly better in the IV version, as is the Sargan test. These
worsen a bit with 2SLS but still are perfetly adequate. In the preferred equation money supply
has a small but negative and significant coefficient in the OLS and IV version, though we lose
this at the 2SLS and 3SLS stages. We do, however, have the effect of interest rate on unemployment, which is quite significant, In addition, there are long lags in the dependent variable itself
as well as in py and p,,,. The effect of wage changes is instantaneous and no higher-order lags
or level terms in w enter the equation. The tax term also appears only in difference form rather
than in level form. By inspection we can see that the variables which matter in the long run
are U , p y ,pmand m. The shape of this long run relationship cannot be fully determined until
we have looked at all the endogenous variables in their long run state simultaneously.

zyxwv

zyxwvut
zyxwvutsrq
zyxwv

3.2.2 The Interest Rate Equation
This equation, even more than the one above, embodies the crucial innovative feature of our
analysis. The essence of Keynes effect in our opinion is the impact of money supply through
its role in financing prime costs. Thus instead of looking merely at M / W , as Keynes seems to,
we explicitly look at the ratio of money to prime costs. Although in our equations (7) and (8)
we spoke of M / WL, it is quite clear that at the economy level we have to take into account
costs of imported raw materials. We have therefore constructed a new variable net factor costs
labelled F as the appropriate deflator for M .
A brief word should be said here about the construction of F. Typically we had indices of
earnings and import prices but no continuous time-series on inputs into national income. We
had, however, the 1972 input-output table for UK available, from which we could construct
base period net factor costs. So for this period t = O we had

F = (WoLo+ Pm0Zm0) = Yo(aoW0+ b0Pm0),

(17a)

where Y is real output, a is labour input coefficient (l/Q), and b is the import input coefficient
( I m / Y ) .All the values in (17a) are observable. We then ‘blew’ up the base period costs

zyxwvut
zyxwv

12

M . DESAI AND G . WEBER

zy
zyxwvu
zyxw
zyxwvu
zyxwvutsr
zyxwvuts
Table 11. Unemployment rate equation (1958.1-1979.4)
A4u

OLS

0.13
0.74
-0.29
-0.27
-0.022
0.007
0.038
-0.003
0.017
0.009
-0.019
0.004
-0.017
-0.004
0.008
-0.013
-0.032
0.044

Sargan

x2

corrected x 2
corrected F

Chow

(1.7)
(11.8)
(5.0)
(3.6)
(2.5)
(0-4)
(2-2)
(0.2)
(2.4)
(1.2)
(2.4)
(2.0)
(4.0)
(0.9)
(1-8)

(2.1)
(3.0)
(3.5)

0.12
0.73
-0.25
-0.24
-0.024
0.019
0.036
-0.003
0.015
0.008
-0.018
0.004
-0.017
-0-003
0-009
-0.012
0-024
0.041

(1-7)
(11.5)
(4.5)
(3.3)
(2.7)
(1.0)
(2.1)
(0.2)
(2.2)
(0-9)
(2.1)
(1.8)
(4.0)
(0.8)
(2.3)
(2.0)
(2.1)

(3.1)

52.62
41.86 I x : s

xl

corrected xz
corrected F
Godfrey x 2
corrected xz
corrected F
LM x 2
corrected x 2
corrected F

0.04
0.76
-0.30
-0.28
-0.023
0.012
0.031
-0.005
0.009
0.011

-0.019
0.005
-0.018
-0.001
0-008
-0.006
-0.029
0-039

(0.5)

(11.8)
(5.0)
(3.7)
(2.4)
(0-6)
(1.6)
(0.3)
(1.1)
(1-3)
(2.2)
(2.2)
(3.1)
(0.3)
(1-7)
(0.8)
(2.6)
(2.9)

44.9
1 *60F(2x,70)
27.0
21.75 1'2
5.43F(4,70)
14.37
11-29
2*82F(4,70)

1':

14.65
11.51

3515

2SLS

IV

1.2

-

-0.03 (0.4)
0.80 (14-4)
-0.32 (6.3)
-0.24 (2.9)
-0.024 (2.9)
0.023 (1.2)
0.023 (1.4)
-0.013 (0.2)
0.003 (0.4)
0.016 (1-9)
-0.023 (2.8)
0.006 (2.9)
-0.018 (3.9)
0.002 (0.4)
0.009 (2.2)
+o.ooo (0.0)
-0.024 (2.4)
0.030 (2-6)

Hausman (1 978)
IV-test
(2SLS versus OLS)
x; = 12.12

x j = 8.68 (corr.)
F(7.63) =

1-24

backward and forward from 1972 by using

Equation (17b) is more an economic statistical device than a theoretically perfect measure. We
should ideally like t o observe F, but we do not have that. As far as the labour input is concerned
we approximate uf by indices of real output and total employment (ar= L f / Y t ) .For imports
we have no simple way of separating imported inputs from total imports. We have therefore
had to be satisfied with a constant bo. As far as money measure is concerned, we have taken
this to be M I rather than a broader measure since we are concerned here with money needed
t o finance current production. The measure MI is also more likely to satisfy assumption of controllability than a broader measure. (Details of the measure for the 1955-1980 period are in
Desai and Weber, 1986.)
Our search for the most satisfactory equation went through three phases. At first we specified
a general dynamic form for a linear version of equation (8). In as much as this was in terms

zyxwvut
zyxwvuts
zyxw
zyx
zyx
zyxw
13

MACROECONOMETRIC MODEL FOR UK

of nominal interest rates, to check for non-homogeneity we specified the dependent variable
as the real rate of interest (R - A4pr), where pr is the log of retail prices, but also allowed for
A 4 p r separately as an independent variable. This specification gave us
[ l -0.85L+0.32L3-0*4L4](R-A4pr)=0.17+
[ -0.81 + 0 . 5 4 L - 0 * 0 7 L 3
(6.2)
(2.3)
(2.8)
(1.0)
( 5 . 5 ) (2-1)
(0.6)
+ 0 * 1 8 L 4 ] A 4 p r +[ - 0 * 1 6 + 0 * 0 7 L + O * 0 7 L 2 + 0 . 0 4 L 3 ] A 4 ( m -f ) - 0 . 0 2 ( m (0.8)
(3.5) (1.4)
(1-5)
(1.1)
(1 * 1)

f)-4

(a)

R 2 = 0 . 9 4 , SC(31)=35*65, GC(4)=5*34, C h 0 ~ ( 4 ) = 2 . 1 2 .

While this specification passed the diagnostic tests, it gave a very unsatisfactory steady-state
equation which was
R

= 3.60 - 0.88A4pr

+ 0-34A4(m

(0.3) (0.2)

-

f)

(0.2)

0*49(m- f)-4.
(0.33)

-

(2 1a)

The very low t values in (21a) are a consequence of the fact that the sum of these coefficients
on the left-hand side of (21) is not significantly different from zero.
An attempt was made to amend this by allowing for international aspects. During 1955-1979
the UK went through a fixed exchange rate regime with sterling overvalued for a while and
devalued in 1967, a flexible exchange rate regime after 1973 but some form of exchange control
throughout. Only towards the end of the period was there emerging the prospect of free capital
movements. We specified the sterling dollar exchange rate as an additional variable. While this
variable had some effect in the short run (the coefficient of A4et-1 had a value of 2.8), the
problem of the erratic steady state remained. The reason again was the lag structure on the
dependent variable. The coefficients summed to 0 * 03 and not significantly different from zero.
[ 1 - 0.078L + 0 * 2 5 L 3- 0.50L4] (R - A4pr) = 0.20 + [ -0.88

(6.0)

(1.6)

(3.4)

(6.2)

+037L
(2.4)

0.08L3 + 0.42L4]
(0.3)
(1.8)

-

zyxwvu

A4pr+ [ -0.18 + 0.04L + 0 * 0 8 L 2+ 0.07L4]A4(m - f ) - 0*034(m- f)-4
(4.3) (0.9)
(1.8)
(2.1)
(1 '3)

+ [ -0.047 + 0 * 1 1 3 L ] A 4 e +0.035e-5.
(0.9)

(2.8)

(1.3)

,
R 2 = 0.95, SC(28) = 31 *48, GC(4) = 5 ~ 9 0 Chow(4)

=

3 *63.

The steady-state equation corresponding to (22) is
R = -6.7+0.08A4pr-0.37A4(m(0.2) (0.3)
(0.25)

f ) + 1.09A4e-2.15(rn- f ) - 4 - 1-16e-5
(0.17)
(0-18)
(0.19)

(22a)

It is easy to see that there is not much to choose between (21) and (22). They both pass the
diagnostic tests but they fail to provide us with a satisfactory equilibrium interest rate equation.
They both indicate, however, that it is the nominal interest rate which may be the determined
variable in the money market; homogeneity, i.e. the Fisher effect, is persistently rejected.
In so far as the change in the exchange rate is the return on current account in US dollars
(foreign currencies in general), its significance in (22) may in fact be due to portfolio management by firms either purely of a financial sort or from attempts to choose optimally the timing

14

zyxwvu
zyxwvutsrq
zyxwvuts
zyx
zy
zyxwvu
M . DESAI AND 0.WEBER

of exchanging export proceeds into domestic currency. The exchange rate also, however,
restricts the freedom of monetary authorities, at least on a short-run basis. Thus its presence
in (22) may be due to spillover effects from the (monetary) supply side. These broad speculations led us to respecify (22) by addition of the following variables: (i) covered interest rate
differential (R - R * + A4p* - A4pr) where * denotes US values; (ii) a term ( p * - e - p,)
measuring deviations from purchasing power parity; and (iii) a term in offical reserves both for
periods of fixed exchange rate and for pressures on monetary authorities of any sudden loss
in reserves in periods of fixed exchange rates.
[ I -0.57L+0.26LZ+0.29L4-0.29L5]AR-0.13
+(0.11 -0*18L)A4(p*- e
(5.5)
(2.5)
(2.3)
(3.0)
(0.8)
(2.4) (4.9)

+

-

pr)

r0.28 - 0.28L + O*05L4]A 4 p r + [ - 0.023 - 0*022L4]A40R
(2.4) (2.4)
(1.0)
(4.4)
(2-0)

+ [ -0.13 + 0.09L3+ 0.08L4 + 0.05L5]A4(m
(3.4)

(2.8)

(2-3)

-

(1.5)

f)

0*017(m- f)-4
(0.8)

-

0.07R-4 - 0*016(R - R * + A ~ P *- A4pr)-8.
(0.5)
(0.4)

-

SC(42) = 50.21, Chow(4) = 8.13, GC(49) = 6.08.

(23)

Notice that in (23) we have chosen AR as our dependent variable rather than (R - A4pr) as in
(21) and (22). The new regressors added have mixed performance. The PPP term is highly
significant in its A4 form but the two coefficients are of roughly equal size and opposite sign,
and hence unlikely to matter in the steady state. The official reserves (OR) term performs quite
well and would have a role in the steady state. The covered interest rate differential term
appears in its level form but has a t value of only one. As far as the other variables are concerned their performance is similar to that in the previous equations. Once again the A4prinflation-variable has a zero coefficient in the steady state. We believe this vindicates our decision to specify the interest rate equation in nominal rather than real terms, though it goes
counter to the new classical as well as the neo-Keynesian conventions. The steady state of (23) is

AR =0.19-0.1OA4(p*(0.8) (2.7)

e)-0~01(R*-A4p*)+O~16A4pr-0~051A40R+0~12A4(mf)
(0.4)
(1 -6)
(2.8)
(1 ‘3)

zyxw

It is clear that allowing for the international influences does help us identify the interest rate
relationship better. The exchange rate-corrected rate of US inflation ( p * - e ) now comes in
with the correct sign and a reasonable t value. The UK rate of inflation has a coefficient of only
0.16 and a t value of 1.6. Of the other variables, change in official reserves has a significant
influence. The Keynes effect variables are less important in this specification; nor is the US Real
interest rate significant. The low t values of the two level terms in R are a warning that the longrun static equilibrium level of interest rate remains elusive. Thus the long-run solution to (20) is

R

1.6 - 0.21(m - f )
(0.7) (0.7)

=

+ 0*20R*.

(23b)

(0.3)

Equation (23b) differs from the earlier ones in having R*-the

US interest rate in the long-run

zyxwv
15

MACROECONOMETRIC MODEL FOR UK

zyxwvutsrq

equilibrium. But as before at this single-equation stage, the coefficients of the level terms are
somewhat poorly determined. We seem to have caught the disequilibrium dynamics in interest
movements adequately as our various diagnostics indicate, and with (20a) even the steady-state
equation is adequate but the long-run equilibrium remains elusive. But of course we must also
bear in mind that since we have a simultaneous equation system, we should not speak of longrun equilibrium in each equation separately. We have to look at the set of all the long-run equations of the model together, to work out the equilibrium values of the endogenous variable
simultaneously. We look at this below.
3.2.3. The Wage Equation
The most general form of the Phillips curve contains a number of regressors: inflation
expected and unexpected, unemployment, real wage levels and productivity growth plus
variables describing socio-political conditions in which the wage bargain takes place (Desai,

zyxwvut
zyxwvutsrqp
zyxwvut
zyxwvutsr
zyxwvutsrqp
zyxwv
Table 111. Interest rate equation (1958.1-1979.4)
A4R

OLS

Const
A4R- I
A4R-2
A4R-4
A4R -2
A4(P* - e - P r )
A ~ ( P- e-pr)-l
AP r
A 4 ~ r IA4pr-4
A4OR
A4OR-4
A4(m - f 1
A4(m - f ) - 3
A4(m - f ) - 4
A4(m - f ) - 5
(m-"f-4
R-4
(R - R * + A4e)

Sargan x 2
corrected x 2
corrected F
Chow x 2
corrected x2
corrected F
Godfrey x2
corrected x 2
corrected F
LM x 2
corrected x2
corrected F

0-16
0.61
-0.23
-0.31
0.34
0.11
-0.17
0.16
-0.16
0.03
-0.024
-0.010
-0.10
0-07
0.08
0.04
-0.02
-0.08
-0.05

(1.2)
(6.6)
(2.5)
(2.3)
(3.6)
(3'9)
(6.0)
(1.7)
(1.6)
(0.6)
(5.0)
(2.0)
(3.5)
(2.3)
(2-6)
(1.4)
(1-2)
(0.6)
(1.0)

-

26.73
21.21 ]x:
2.29F(4,73)
-

-

1':

8.81
6.81
1 *70F(4,65)

IV

0.15
0-61
-0.23
-0.30
0.33
0.11
-0.16
0.17
-0.17
0.03
-0.024
-0.009
-0.10
0.07
0.08
0.04
-0.02
-0.07
-0.04

(1.0)

(6.5)
(2.5)
(2.3)
(3.5)
(3.9)
(5.9)
(1-7)
(1.6)
(0-6)
(5.1)
(2.0)
(3-2)
(2.3)
(2.6)
(1.4)
(1.0)
(0.5)
(1.0)

64.03
50-21 ]:'2
1.19F(42,69)
10.24
8.13
2*03F(4,73)
7.86
6-08
1*52F(4,65)
9.21
7.06
1 *76F(4,61)

1':
1':
]Ix:

3515

2SLS

0-15
0.60
-0.25
-0.26
0.28
0-13
-0.19
0.29
-0.28
0.04
-0.021

-0-010

-0.13
0.084
0.079
0-045
-0.019
-0.077
-0.019

0.20 (1.4)

(0.9)
(5.6)
(2.8)
(2.1)
(2.8)
(3.3)

0.55 (6.0)

-0.23 (2.9)
-0.29 (2.6)
0.30 (3.5)
0.12 (3.5)
-0.18 (5.9)
+0.27 (2.7)
-0.29 (2.9)
0.04 (1.0)
- 0 * 0 18( 3 '4)
- 0.008( 1 * 6)
-0.14 (3.9)
0.086(3.1)
0.070(2 '4)
0.048( 1 .7)
- 0.027( 1 '4)
- 0.093(0.8)
0.003(0.1)

(5.5)

(2.5)
(2.5)
(0.8)
(3.4)
(1.7)
(3.2)
(2.6)
(2.4)
(1-4)
(0.9)
(0.5)
(0.4)

42.02
32.95 ];'6
1*26F(26,69)
9-61
7.63 1'2
1.91F(4,73)
9.58
7.41 1.2
1 *85F(4,65)

Hausrnan (1978)
IV-test
(2SLS versus OLS)

x$=

1.85

1.42 (corr.)
F(2,61) = 0-54

,y$ =

16

zyxwvuts
zyxwvu
zy
zyxwvu

M. DESAI AND G. WEBER

zyxwvuts

1984a). We began with a very general formulation of this type before we could simplify it down
to a specific form, such as (OLS estimates)
[ 1 - 0.7521 L ] A4 W I = - 5 753

(9.5)

zyxwvu

+ 0.172A4pr - 0.354U - 0.69A
(1.72)

- 0 * 1 3 2 ( ~ - p r ) - 4 +0.187q-4-0.837
(1.7)
(2.8)
(1 '7)

(1.73)

1 (w -

pr)-4

(6.5)

IPD.

R 2 = 0.868, LM(4) = 4.87, Chow(4) = 5.66. (sample 58.1-80.4)

(24)

In (24) q is the log of the average product of labour (Q = Y / L ) . IPD is a dummy variable for
the incomes policy episodes (for details see Desai, Keil and Wadhwani, 1984). We introduce
a first difference term in real wage A l ( w - p r) in this equation. The logic of introducing real
wage levels in the Phillips curve was argued by Sargan (1 964/ 1984) on the grounds of a desired
real wage target which influences wage bargains. But as inflationary pressures mount, wage
bargains have increasingly incorporated a desired real wage growth based on more recent information. This is the justification of the A I ( w - pr)-4 term.
As a Phillips curve, equation (24) has several interesting features. It has a very simple
dynamic structure; the lags are few and the number of variables is small. The unemployment
variable, although in its most simple form, i.e. current level rather than some nonlinear
transform or moving average of U , is significant. If we examine the steady state we see that
the homogeneity postulate is rejected. We get

zy

3 0090+ 0.652Adpr - 1.39211 - 2'757A 1 (W- pr)-4 - 0 * 5 0 2 (-~pr) - 4
(2.5) (1-9)
(1.4)
(2.5)
(1.5)

A4wt =

+ 0.713q-4
(2.3)

0.344 IPD.
(1 '6)

-

The ratio of the A 4 p r term to the A4w term shows that there is less than full adjustment for
inflation. Such a clawback can have a stabilizing effect on the economy (Desai, 1973). In the
long run, however, equation (24) gives us a real wage/unemployment relationship.

zyxwvu

( ~ - p r ) = 6 . 1 5 7 - 2 . 7 7 3 U + 1.420q.
(2.5) (1.1)
(2.9)

In computing the long run we have set IPD equal to zero as well, because a permanent incomes
policy would imply a different sort of world than the one we are modelling. The interesting
aspect of (24b) is the coefficient of q which implies that the share of wages in income is higher
the higher the productivity, but U damps it down. This view of the long-run relation between
real wages and unemployment is more in line with conflict theory than with the usual macroeconomic interpretation (Goodwin, 1967; Desai, 1973).
One of the problems that an applied econometrician faces is data revision during the time
when he is exploring alternative specifications. When we re-examined (24) in the light of some
revisions which had been made to the data for Uand w i t failed to be robust. We had to resume
our search but did not have to start with a most general specification. We could take'as our
starting point (24). We let the Sargan test signal any omitted variables, and the Godfrey and
Chow tests indicate other grounds for respecification. The Godfrey test kept signalling a serial
correlation of the fourth order. We needed a dummy variable for the 3-day week, and we ended

17

MACROECONOMETRIC MODEL FOR U K

up with a slightly more elaborate version of the Phillips curve than (24):

zyxwv
zyxwv
zy
zyxwv

[l - 0 ~ 8 3 L ] A ~ ~ ~ 0 ~ 5 6 - 0 ~ 1 l ~ - ~ + 0 ~ 1 3 ~ ~ - ~ + 0 ~ 1 4 ~ - ~ - 0 ~ 4 2 A ~ ( ~ (17.1)
(2.3) (2.0)
(2.2)
(2.7)
(4.0)
(2.1)

-0.010 IPD +O*06Apm-2+0.13A1A4R-~
-0. 05Dl.
(3.1)
(2.6)
(1.3)
(3 * 8)

R2 = 0.936,

SC(36) = 44.77, Chow(4) = 5*15(4), GC(4) = 3-72.

(25)

D I is the 3-day week dummy, and plnis import price index. The real surprise is the interest rate
term, whose inclusion was strongly flagged by the Sargan test. The major departure is current
inflation A4pr. As per the former, the presence of A p m and AlA4R probably account for the
departure of A 4 p r from unity. The long-run static relationship is
1.289q-5.70U.
~ ~ 4 . +8 1.17pr+
1
(2.9) (7.9)
(4.0)
(1.3)

In (25a) we have again suppressed the dummies. In many ways (25a) is a superior equation compared to (24b). The coefficients of w , pr and q. ar e unlikely to be significantly different from
each other. So (22a) approximates t o a relationship in the (logarithm of) share of wages in
income, call it X = (w - pr - q ) and unemployment. Taking the common coefficient of w , P r
and q to be 1.15 we get,
X

4.2 - 5.0U.

(25b)

In this form the equation is reminiscent of Goodwin's elegant model of the growth cycle, except
that we have arrived at this juncture by econometric work on quarterly observations and
extracting a long-run relation. Goo