Applied general equilibrium.
A Classical - Keynesian - Schumpeterian approach.
Oscar DE-JUAN
University of Castilla – La Mancha
Conference on Economic Growth and Distribution
Luca, 16-18 June 2004
------------------------Address: Facultad de Ciencias Económicas y Empresariales
02071 Albacete (España)
e-mail: oscar.dejuan@uclm.es
Abstract.
This paper sets the basis for a computable applied general equilibrium model
(AGE), useful for policy evaluation and growth analysis. It is rooted on
Classical, Keynesian and Schumpeterian traditions which seem naturally fitted
for the purpose. Classical Political Economy was concerned with the analysis
of the processes of production, distribution, consumption and accumulation (that
brings about economic growth). The social accounting matrix (SAM) of section
2 is a fair reflection of this scheme, while the AGE model of the next two
sections is supposed to explain the systems of prices and quantities there
embedded. Reading vertically the first block we get the Sraffian prices of
production than can also be expressed as Post-Keynesian administered prices.
Reading horizontally we obtain the level and composition of output as a multiple
of autonomous demand. This is nothing but Keynes’s principle of effective
demand, where ‘animal spirits’ have been replaced by Schumpeterian
innovative firms.
De-Juan: A Clakesch applied general equilibrium model
1
1. Introduction.
This paper presents the basic traits of a computable applied general equilibrium
model. AGE models, to abridge, explain the system of prices and quantities
embedded in the flows of production, distribution, consumption and
accumulation embedded in a social accounting matrix (SAM). Once the
parameters have been computed by different techniques (‘calibration’ being one
of them) the model becomes a useful instrument for policy evaluation, impact
analysis and the like. They allow us to compute the effects on the level and
composition of output, employment or income distribution, associated to a
variety of scenarios:
- Major public expenditures like the European funds for regional
development, which affect both the demand side and the supply side
(productivity and costs).
- Fiscal reforms, like the introduction of a tax or the substitution of the
system for funding pensions.
- Industrial and innovation policies that try to foster a particular sector.
- Change in monetary policy or changes in international financial markets
leading to a major shift of interest rates and exchange rates.
- Energy shock that drills up the price of oil.
- Effects of a major technical innovation like the diffusion of information
and communication technologies.
Our model, that is dynamic by nature, is aimed at explaining the sources and
effects of economic growth. Which industries have played the role of
locomotives? How much has productivity increased and what have been the
required transformations in the capital/output ratio, the capital/labour ratio and
the types of labour employed?
AGE models has been a successful branch of Neoclassical economics
since the early nineties: Kehoe & Kehoe (1994), Ginsburgh & Keyzer (2002),
Kehoe, Srinivas & Whalley (2004) 1. The basis, no matter the heroic
assumptions introduced to make the model computable by calibration, is
Walrasian general equilibrium (Walras, 1871-74).
Starting from given
preferences, technology and endowments of capital and labour, the model
determines the market clearing prices. Both production and consumption are
represented by Cobb-Douglas functions that admit substitution of factors in
production and substitution of goods in consumption. The real wage, the
interest rate (identified with the rate of profit) and relative prices will change until
the size and composition of output is such that warrants full employment, full
capacity and utility maximization.
AGE models can be built from different perspectives. Pyatt and Round
(1979, 1985), Pyatt (1992) used the information contained in a SAM to derive
fixed-priced multipliers useful for policy analysis. Neoclassical AGE tend to see
these multipliers as a first step towards flexi-price models. We shall see,
however, that for certain purposes the assumption of fixed prices is a more
realistic one. Many years ago von Neumann (1945-46) studied how relative
1
In the Appendix of Ginsburgh& Keyzer, there is an introduction to GAMS software, which is the
technique generally used for calibration.
De-Juan: A Clakesch applied general equilibrium model
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quantities and prices should be for the economy to achieve its potential rate of
growth. The model does not describe the actual dynamics of capitalist
economies, but it highlights certain equilibrium conditions and limits, that we
shall take into account. Post-Keynesians have developed stock-flow models
where financial variables influence the performance of the real sector (Godley,
2004). Although in this paper we focus on the real sector of the economy, we
shall leave room for financial variables so that they can be used in other
studies. The Cambridge Multisectoral Model (Barker & Petterson, 1987) was a
successful combination of input-output techniques and econometrics, that we
consider better than mere ‘calibration’ from the data of a SAM. Gibson &
Seventer (2000) have developed recently a ‘structuralist’ AGE model
comparable to the neoclassical one but allowing for unemployed resources. All
of these models provide useful ideas. The model we are going to present here
is based, however, in three major traditions in Economics: Classical, Keynesian
and Schumpeterian. Let’s call it ‘Clakesch – AGE model’.
Any model is particularly well suited for certain purposes. If we were
asked to explain welfare gains we should refer the reader to the Neoclassical
models derived from Walras and Pareto. But whenever we are asked to
analyse the dynamics of a demand-constrained system, or to evaluate the
impact of economic policies on output, employment and distribution, our
Clakesch-AGE has competitive advantages. It is like playing at home a math of
European football in a field designed for that purpose. Neoclassical AGE
practitioners seem to play American football in a European football pitch. They
are so many and so talented players, that one can expect some interesting
results. It is our contention, however, that with the same effort the results would
have been much more successful in a Clakesch -AGE model.
The scheme of the paper is as follows. In section 2 we present the basic
SAM suggested by the United Nations (1993). This SAM (and, indeed, the
whole system of national accounts), reflects faithfully the processes of
production, distribution, consumption and accumulation, envisaged in Classical
Political Economy. In section 3 we decipher the Classical-Sraffian prices of
production embedded in the first vertical block of the SAM (i.e. in the inputoutput table by industries). In parallel we explain distributive variables and the
general price level. In section 4 we read horizontally the SAM to figure out the
quantity system. The super-multiplier we derive from a compact SAM will allow
us to compute the level of composition of output associated to a particular
vector of autonomous demand. This is nothing but Keynes’s and Kalecki’s
‘principle of effective demand’ (Keynes, 1936; Kalecki, 1971). Schumpeter
(1912) fills the vector of autonomous demand and explains why and how it
moves forward. By launching into new goods, new processes and new markets
(exports included here), the innovative firms become the driving force of the
system and the ordinary vehicle of technical change. This approach makes
clear that the locomotives of the economy are located in particular industries
and backs the need of a disaggregated analysis of the economy following the
paths opened by Leontief’s (Dietzenbacher & Lahr, 2004) and Stone’s (1981).
In the last section we summarize the peculiarities of our Clakesch – AGE model
contrasting them with the Neoclassical one.
De-Juan: A Clakesch applied general equilibrium model
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2. A social accounting matrix for a growing economy.
Social accounting matrices (SAM) reflect the transactions (accounts) between
activities, factors and institutions. The advantage of SAM over other national
accounting techniques is that they present in full detail the production,
distribution and expenditure relationships among a huge number of agents.
The United Nations Statistics Division (1993) grants researchers freedom to
design a SAM in the way most convenient for their specific purposes. The basic
scheme they suggest fits perfectly our purposes. In this section we shall remind
this scheme justifying a handful of personal options.
A) Activities as industries producing goods.
We identify industries with goods. This assumption does not deny the
possibility of joint production. It simply implies the possibility to obtain a
symmetric matrix for inter-industry transactions (, in Table 1), where the
number of columns (industries) coincides with the number of rows (goods).
Disaggregation by industries should be as large as possible. According to their
economic nature, we should separate four groups: (1) intermediate goods and
services (energy, raw materials, industrial goods, services to enterprises…); (2)
fixed capital goods by type (big infra-structures, structures, equipment, industrial
vehicles and houses); (3) goods and services for final consumption classified by
function (food, clothing, personal services,…); (4) collective services provided
by government.
B) Factors of production and primary distribution of income.
In Classical Political Economy, labour is the only factor of production, properly
speaking. It receives incomes according to the wage stipulated in the labour
contract. Working with a SAM, it is easy to introduce different types of
employees each one receiving a specific kind of income. The rest of value
added constitutes an “operating surplus”, attached to the firms until it is
“redistributed” into taxes, interest payments, rents, dividends, reserves and
depreciation allowances. 2
C) Institutions and expenditures.
a. Non financial corporations or “firms” (F). They accumulate reserves
and decide investment. To simplify notation, we can identify them with
industries (1, 2 … n), which add up to F.
2
Capital depreciation is a difficult issue to tackle with. The best account differentiates capital
goods by type and age, using the scheme of “joint production” (Lager, 1997). A simpler
alternative supposes that capital goods are replaced after a period (different in each industry
and for each commodity). To provide for such replacement, firms retain ‘depreciation
allowances’ purchasing financial assets. There is still a simplest alternative that we are going to
use in this paper only for the purpose to alleviate the exposition. We add up intermediate
consumption and fixed capital consumption. We are imagining that firms devote a portion of
labour and goods to repair fixed capital.
De-Juan: A Clakesch applied general equilibrium model
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b. Financial institutions (B). They relate agents with capacity to finance
and agents in need of finance. The key distinction separates “monetary
financial institutions” (the banking sector) and “non-monetary financial
institutions” (mutual and pension funds). To abridge we shall refer to
both as B.
c. Households (H). For our purposes it is convenient to differentiate
households according to their income source and expenditure patterns.
H1 would represent, for instance, households of non-qualified workers,
whose income is rather low and devoted entirely to consumption. H2
stands for households of qualified workers with medium incomes, most of
them consumed in a basket that includes luxury goods. H3 for households
of managers, self-employed, property income recipients; a substantial
part of such incomes is supposed to be saved; in their consumption
basket, luxury goods are quite important.
Hp for households of
pensioners and other transfers recipients, whose expenditure patterns
are similar to H1.
d. Government (G). By means of taxes and transfers, it pays a key role in
the redistribution of income. It is also conceived as an ‘industry’ providing
free social services.
e. Rest of the world (RW). A useful classification would distinguish
between foreign countries with our same currency (rest of Europe) and
foreign countries with a different currency (rest of the world, Europe
excluded). The exchange rate is defined as e = dollars / euro. An
appreciation of the euro would be reflected in an increase in e.
D) Accounts.
The flows among industries, factors and institutions are classified (according to
the economic nature) in the following accounts.
a. Production account. The traditional input-output table is included in the
first block of Table 1. The rows inform about the sale of outputs; the
columns about the purchase of inputs. ‘Value added’, i.e. payment to the
primary factors of production, makes the balance.
b. Income or current account. Rows in the second block inform about the
origin of incomes (distribution of primary incomes and redistribution).
Columns indicate the allocation of disposable income into final
consumption and savings.
c. Accumulation or capital account. With the savings and transfers of
capital (rows in third block), firms finance their investments separated by
industries and types of capital goods. Households invest in houses.
d. Finance account. It informs about the flows of funds from creditors to
debtors (usually intermediated by banks). To simplify the making of Table
1, we have grouped them into a single row with positive figures for
borrowing and negative figures for lending. We distinguish five types of
financial assets: FA1: cash and bank deposits; FA2: bills; FA3: bonds
(medium and long term); FA4: equities; FA5: bank loans.
e. Balance of payments with the rest of the world. Transaction with the
rest of the world (current, capital and finance) are gathered in the last
vertical block. The inflow of foreign currency (exports of goods and
services, for instance) bear a positive sing. The outflow of foreign
De-Juan: A Clakesch applied general equilibrium model
5
currency associated to imports, loans from the rest of the world and so
on, are treated as negative. 3
E) Satellite accounts (and complementary information).
The combination of flows and stocks improves the usefulness of a Sam. The
following ‘balances’ or ‘stocks tables’ will proof to be very convenient.
a. Tables gathering informations about total population (by age, sex and
level of studies), working population, etc.
b. Labour matrix (L) with so many columns as industries and so many rows
as types of labour (non qualified labour, qualified labour, managers…).
c. Fixed capital matrix (K) with so many columns as industries and so many
rows as capital goods (big infra-estructures, structures, equipment,
industrial vehicles, houses). At the time of gathering the information it
would be convenient to specify the degree of capacity utilization of the
capital installed.
d. Balance sheet of outstanding financial assets (FA1 to FA5). The most
liquid ones are identified with ‘money’ (FA1=M3). The most illiquid ones
(bonds and equities) represent certain rights upon the real capital of the
economy (our table K).
3.Prices and distribution in a capitalist economy.
Competition forces firms to introduce the best available techniques, to use
capacity at the optimal level and to adjust prices to the production costs (which
includes a normal and general profit rate on the value of capital invested).
Sraffa (1960), inspired in the Classical-Marxian tradition, built the system of
equations leading to such prices. He proves, that given technology and the real
wage, we can determine a unique vector of relative prices (in terms of a chosen
numeraire) and the general rate of profit. Before expounded the price equations
let us comment on the ‘givens’, i.e. technology and the real wage.
A) Technology. Our production functions are directly taken from the first
vertical block of the SAM that corresponds to an input-output table (IOT). They
are Leontief’s production functions with constant technical coefficients.
Entrepreneurs are free to choose among different techniques, but, once the
choice has been done, they cannot combine at will inputs and factors of
production. Constant returns to scale are also assumed. In the short run, as a
mechanism of adjustment to demand fluctuations, entrepreneurs may change
the degree of capacity utilization (capital / output ratio). But using capital more
hours a day implies hiring extra labour, so the degree of mechanization (capital
/ labour ratio) remains constant. Technology is materialized in the following
sets of data.
The ‘rest of the world sector’ is traditionally represented by a column for exports and a row for
imports (and the like). The advantage of row-column system is that it follows the same
accounting principles as the rest of accounts and it makes easier the treatment of tariffs. The
advantage of the column system is that it simplifies the presentation of the SAM and allows
seeing the balance of payments at a glance. Tariffs would be included in the price of imports
and in the current account (payments from the rest of the world to government).
3
De-Juan: A Clakesch applied general equilibrium model
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(a) A matrix of intermediate goods coefficients: A    qˆ 1 . This is a square
matrix n·n, n being the number of industries. 4 We can separate domestic
from imported intermediate tables (d, m) and compute two different
matrices of technical coefficients (Ad, Am). 5 Let ˆ be a diagonal matrix
indicating the percentages of imports for each good. These percentages
reflect price elasticity of imports and are bound to change with the ratio
domestic price / international price. Our previous matrix A can be
segmented in two: Am  A·ˆ and Ad  AI   .
(b) A rectangular matrix of labour coefficients: l  L  qˆ 1 . The matrix has so
many columns as industries and so many rows as types of labour.
(c) A rectangular matrix of capital coefficients: k  K  qˆ 1 , with so many rows
as capital goods. Note that these figures reflect the normal or desired
capital / output coefficients.
B) Distribution.
Workers consider as a social conquest the real wage achieved in the past (wr).
In the yearly wage agreements, trade unions will try to consolidate it, fixing the
nominal wage (w) such that: wt=wt-1+, ( being the expected or targeted
inflation for year t). Historically, the real wage has risen pari passu with
productivity, so we can expect that trade unions will claim for further increases
in the nominal wage proportional to productivity gains. Tensions in the labour
market (reflected by percent deviations of the employment rate () from its
conventional value) will encourage trade unions to demand further increases in
nominal wages. 6
[1]
wt  wt 1    f (ˆ )  f ' (ˆ )
In the previous equation wt refers to the nominal wage in year t for the basic
labour category (let say, ‘non qualified labour’). Other types of labour will earn a
4
To make easier our presentation, we shall assume that the information supporting the IOT
allows us to separate prices and quantities. The first industry, for instance, produces 5 million
tones of cereal, each tone worth 8.000 euros. If one tone compost (industry 2) worth 10,000
euros is required for that purpose, the technical coefficient a21 will be 1/5=0,2. In practice we
just know that the gross output of industry 1 amounts to 4,000 million euros. If we divide all the
cells in the first column of  by 4,000 we obtain technical coefficients in value terms, for
instance a’21 = 10,000/8,000 = 1,25. All the formulas would be similar, although they apply to
different physical units. By construction, at time 0 all the prices would be 1. They do not refer,
however, to 1 tone of cereal, 1 tone of iron and 1 machine, but to an imprecise numbers of
tones and machines.
5
IOT of European countries usually separate import from other European countries (in euros)
and imports from the rest of the world (in dollars). This is the type of information that best fits
our purposes. The price of imports should include tariffs and all types of taxes.
6
Alternatively, we could refer (changing the sign) to deviations from the conventional
unemployment rate. Notice that there is not a ‘natural’ employment or unemployment rate
marking a long period equilibrium. It is just an historical position that is bound to change with
aggregate demand fluctuations.
De-Juan: A Clakesch applied general equilibrium model
7
multiple of it, a multiple that is supposed to be constant except for the periods
where there are excesses or shortages of a particular type of labour.
The rate of profit is obtained in parallel to the prices of production.
Relative prices vary, precisely, to make possible that the ‘representative’ firm of
each industry obtains the normal rate of profit on the capital advanced (r). 7 The
interest rate is another distributive variable. For our purposes (analysis of the
economy of a country or region within Europe) both the interest rate and the
exchange rate can be taken as given. 8
C) Prices of production, administered prices and inflation.
Now we are in conditions to derive the Sraffian system of prices of production
corresponding to a competitive capitalist economy. It results form a vertical
reading of the matrices of direct coefficients. 9 The price of production of any
commodity appears can be presented as a multiple of the unit labour cost,
although it is a complex multiplier that mixes technical and distributive variables.
[2]
p  p·A  wr ·l  r·( p·k )  wr ·l ·I  A  r·k 
1
Post-Keynesian economists have a preference for administered prices.
Entrepreneurs set prices marking-up primary costs, expressed in monetary
units (w, for nominal wage, instead of wr). The rate of profit on fixed capital (r)
7
We assume that only fix capital is properly advanced. Intermediate consumption and wages
are paid regularly out of sales proceeds. By ‘representative’ firms we mean the one using the
best available technology. Probably a handful of innovative firms are using more productive
technologies protected by patents and the like. A bulk of firms may be using old-fashioned
technology until they replace capital or quit the industry. Note, that whenever we compute
technological coefficients by calibration from IOT, we refer to the average technology in the
industry.
8
Note that in the treatment of the rate of profit and interest rate we depart from Sraffian
tradition. The equations of prices of production, after choosing the numeraire, have one degree
of freedom; it can be either the real wage or the rate of profit. Sraffa (1960) starts the book
referring to the first one. But he shifts later on to the second variable, saying that the rate of
profit (identified with the interest rate) is a ‘pure number’ that can be defined without reference
to any numeraire. Pivetti (1991) justifies such an option. In our opinion, there is no problem with
the real wage and there are negative implications associated to the second one: it implies the
identification of the rate of profit and the rate of interest. Following the Classical-Marxian
tradition (usually well summarized by Kalecki) we accept their mutual independence. There is
not such a thing as a ‘long run real interest rate’, determined by the rate of profit; but neither can
we expect that the rate of profit will follow the movements of the rate of interest. We can simply
refer to the ‘conventional interest rate’, the one that has ruled in the past and is expected to rule
in the future. Such convention can be influenced by a persistent monetary policy by the Central
Bank, who sets the interest rate in money markets. For studies centered in the European
economy, the interest rate should be an endogenous variable related to the conventional rate,
the base rate fixed by Central Bank and the tensions in the financial markets. The exchange
rate would be another variable to take into account and should be explained in parallel to
interest rates.
9
Taxes and tariffs can be added (to this and the following formulas) by multiplying the relevant
distributive variables by (1+t).
De-Juan: A Clakesch applied general equilibrium model
8
is substituted by a profit margin or mark-up on circulating capital, which appears
as a diagonal matrix <I+b>.10 We have also separated domestic and imported
intermediate goods. 11 Both formulas are legitimate and compatible provided the
mark-up depends on the sectoral degree of mechanization. The higher the
capital / labour ratio, the higher has to be the sectoral mark-up on circulating
capital in order to get a normal rate of profit on fixed capital. In a capitalist
economy long term mark-ups are forged by competition and the divergence
among them can be taken as given for the usual time span of input-output
tables (five years).
Marks up may be sensible to the degree of capacity
utilization, but here we are interested in the basic structure of administered
prices (pa) that consider the average mark-up over the cycle (b).
[3]
pa   pa Ad  pm ·Am  w·l · I  b
The use of administered prices has practical advantages. First, they
provide a way to skip the fixed capital matrix: when it exists, is not very reliable.
Second, it provides a formula to figure out the general level of prices (P). In the
preceding formula we have just to substitute l by l’= total labour / final output;
and Am by A’m = value of imports / final output. The mark-up b’ would be the
share of profits in income.
[4]
P  ( p m ·Am'  w·l ' )·(1  b' )
Inflation is a cost-push phenomenon. It may reflect a pure distributive
conflict (higher economic power exercised by trade unions, domestic
entrepreneurs and international providers of row materials) or demand
pressures in a fast growing economy (a transient phenomenon that could be
endogeneized in our model). The dynamics of the price level can be
represented by the following equation:
[5]
Pˆ    ˆ  ˆ  bˆ
Inflation has a trend element, which nowadays can be safely identified with the
rate targeted by the Central Bank (). If nominal wages rise at a rate   ˆ ,
inflation expectations will be confirmed ( P̂   ). Inflation will be higher than
targeted in the following cases. (a) the increase of nominal wages exceeds the
previous rate: ˆ  wˆ  (  ˆ ) is positive; (b) the euro cost of imports
rises( ˆ  0 ), either because the dollar price of imports increases or the euro
depreciates; (c) the aggregate mark-up rises (b > 0).
D) Market prices and demand.
10
11
We shall represent diagonal matrices by angular brackets or a circumflex.
The value in euros of imported row materials (and the like) is pm·Am, where pm= $pm /e (e defined as
dollars per euro).
De-Juan: A Clakesch applied general equilibrium model
9
So far we have just considered supply forces. Markets prices are supposed to
reflect both supply and demand. In principle, excesses of demand will push
prices up. But this is a transient phenomenon since higher prices and profits in
industry j will attract investments, production will rise cancelling out the
excesses of demand for commodity j, relative prices will return to the long run
equilibrium determined by production costs. This is the theoretical scheme. In
practice only a handful of primary products (oil and row materials, in particular)
are sensitive to demand, as Post-Keynesians have repeatedly showed after
Sylos-Labini (1957). Such prices are determined abroad and are taken as data
in our model. In an advanced industrial economy, the bulk of industries are
prepared to accommodate demand shocks piling inventories and adjusting
capacity utilization. In services there is not such a possibility but the risk of
loosing customers by continuous changes in prices has convinced
entrepreneurs to maintain prices in their long run equilibrium, marked by costs
of production.12 We can take for sure –a key conclusion for our purposes– that
in an advanced industrial economy relative prices are not influenced by the
ordinary ups and downs of demand.
4. Output and growth in a demand-constrained system.
In section 3 we have seen that a vertical reading of the first block of the
SAM leads to the Sraffian system of prices of production or to Post-Keynesian
administered prices. We can expect that competition in a capitalist economy
will enforce such prices. In a similar vein, a horizontal reading of the SAM
would provide us with a system of quantities. It was implicit in the Classical
equations (Kurz and Salvadori, 1998; Nell, 1998, 2004). And it was the core of
von Neumann (1945-46) general equilibrium. Both models provide useful hints
for understanding certain equilibrium conditions and certain limits. 13 But they
do not describe properly the working of a capitalist economy that it is supposed
to be a demand constrained system. According to the Keynesian principle of
effective demand, the equilibrium level of output at a given moment does not
depend on the productive capacities of the economy but on the expected
demand at normal prices (Keynes, 1936; Kalecki, 1971; Kornai, 1979). It can
be expressed as a multiple of the autonomous demand expected for the period
under consideration. In the simplest Keynesian model, the multiplicand is
identified with investment, and the multiplier with the inverse of the propensity to
save. After an increase in investment expenditures, output will growth until the
savings stemming from the new incomes match the new investments: S=I.
In this section we are going to translate the principle of effective demand
to a multisectorial growing economy. Our first task is to separate autonomous
from induced demand, in order to endogeneize the second kind of flows and
derive a ‘super-multiplier’. Autonomous demand is independent of income.
Their main elements are identified in the last column of Table 2: exports,
12
13
NeoKeynesian literature explains this phenomenon under the heading of ‘menu costs’.
A couple of examples will suffice. (1) The growth of the system is limited by the basic input
whose production is growing more slowly. (2) The golden rule is achieved when the rate of
growth and the rate of profit coincide.
De-Juan: A Clakesch applied general equilibrium model
10
government real expenditures, modernization investment, private expenditures
financed out of current or capital transfers. To make possible the expected
increases in autonomous demand, firms are supposed to demand intermediate
goods, to hire labourers (who will consume a significant proportion of their new
incomes) and to purchase new capital goods to expand capacity. Production
will adjust to aggregate demand (autonomous plus induced). It will rise until the
new ‘uncommitted incomes’ ( = incomes not devoted systematically to
consumption or expansionary investment) match the value of autonomous
demand (Z). Table 3 makes clear such process emphasizing that it is Z which
determines . A brief review of the components of aggregate demand will
illuminate some points.
Table 2
Table 3
A) Autonomous demand.
(a) Exports. For small open economies, exports constitute the main element of
autonomous demand. Exports are supposed to depend on the rate of growth of
the international economy and the exchange rate.
Both variables are
exogenous to our model. But there are a couple of endogenous determinants:
the relative prices of tradable goods and the general level of prices. Any AGE
model is supposed to introduce the price elasticity of exports and imports. In
our Clakesch model this is the single most important link between prices and
quantities.
(b) Government expenditures. Public consumption and public investment are
policy instruments and, for this reason, autonomous. The same can be said
about current and capital government transfers that feed autonomous private
expenditures (whether for consumption or investment). Autonomous means
independent of current income. Such expenditures, however, are influenced by
other variables determined by the model or that can be figured out with the
information provided by the SAM and satellite accounts (population by age,
unemployment rate, etc.).
(c) Modernization investment. Innovative entrepreneurs compete (or try to
escape from competition) by introducing new goods either for consumption or
for investment. The new capital goods are the ordinary vehicle of technical
change, although it may take several years to perceive their effects. Let’s call
‘modernization investment’ the expenditures involved in the the production of
these new goods. Schumpeter (1912) made clear that innovations usually
come out in clusters and that new products call for complementary ones, at the
time they displace old-fashioned substitutes (‘creative destruction’). The
diffusion of new products follows usually a ‘logistic curve’. After the introduction
of the product, demand accelerates; latter it decelerates and even stagnates
when the market becomes saturated. Among the determinants of innovation
and modernization investment we should consider competitive pressures,
physical capital, human capital and other facilities. Financial conditions do also
matter, by speeding up or slowing down the implementation of investment
De-Juan: A Clakesch applied general equilibrium model
11
decisions. In the next section we shall refer briefly to changes in interest rates.
Let us comment here on the importance of differential profits rates. A higher
than normal profit rate (ri>r) provides a stimulus for investment and allows
funding it in a non-risky way (i.e. out of profits). External finance becomes also
more accessible since funds can be raised in better conditions.
B) Induced demand.
(a) Induced or expansionary investment. Firms expand capacity so that the
expected increases in demand are matched efficiently, i.e. using capacity at the
desired degree (expressed by the equality between the actual capital (output
ratio (kt) and the desired one (k). Investment will be k times the expected
increased in demand, to which production adjust. For the economy as a whole
we get: I=k·g·Y. This is the well-known accelerator principle. 14 Expression [6]
presents the basic steps we should cover to obtain domestic induced
investment.
I i"  k · g · q
[6]
I i'  I  E k ·I i"
~
I i  I  h·i ·I i'
I i ,d  I   ·I i
Some observations will help understanding the preceding equations.
1. In our disaggregated economy [k] is a matrix with so many columns as
industries and so many rows as capital goods.
Net output (Y) is
replaced by a diagonal matrix of sectoral total outputs <q>, whose
expected rates of growth appear also as a diagonal matrix <g>. The
combination of these three matrices provides us the basic investment
decision (I”) formalized in the first equation of [6].
2. By construction, the driving force of the economy lies in the expected
rates of growth of autonomous demand (column vector gz). Firms,
however, cannot predict changes in gz, they rely in the path of growth of
demand for their products (g). In doing so, excesses of capacity
(negative or positive) are bound to occur (Ek) any time there is a variation
in gz. They should be subtracted form I” as it is indicated in the second
equation (and explained in De Juan 2004).
3. The accelerator should be flexibilized by distinguishing between
investment decisions and investment expenditures. The first ones are
based on the conventional rate of interest (i*), the one that has ruled in
the past and is supposed to continue in the foreseeable future. Temporal
deviations may speed up investment expenditures (if negatives) or slow
them down (if positives). Investment decisions may be altered by the
~
~
term h·i , being i  (i  i * ) / i * and h a positive parameter (apparently
quite small).
14
As far as we know there are not many attempts to endogeneize investment in a multisectoral
model. Leontief (1970) and Lager (1997) are the exceptions, although their objectives are
different from ours.
De-Juan: A Clakesch applied general equilibrium model
12
4. In impact analysis we are not concerned with total expenditures but with
domestic ones. To obtain induced domestic investment (Ii,d) we should
pre-multiply Ii by the diagonal matrix <I->. , as we know, indicates the
proportion imported for each commodity. Such proportion reflects the
price elasticity of imports and will vary with the real exchange rate.
(b) Induced consumption. In The General Theory, Keynes assumed that the
bulk of private consumption depends on household disposable income. The
hypothesis was verified at that time and has been ratified ever since. In the
second half of the 20th century the propensity to consume of households has
been quite high and stable. Kalecki contributed to the discussion suggesting
that the aggregate propensity to consume was a weighted average of the
propensities of different income groups. Our SAM allows us to present different
social groups, each one characterized by a particular propensity to consume
and a particular consumption basket. De-Juan, Cadarso & Córcoles (1994)
presents an induced domestic consumption matrix (Cid) that, once more, we
shall approach in several steps.
[7]
Ci nn 
Ci ' nn  DC nh · PC hh ·VAhn
I  VAT nn ·DC nh · PC hh · I  T y ·VA  TR hn
hh
C id  I   ·C i
Our point of departure is the matrix of value added or primary incomes
[VA] with so many rows as income groups (h) and so many columns as
industries (n). Pre-multiplying by <PC> we obtain the incomes systematically
consumed. In the diagonal of <PC> we find the consumption propensities of
the different income groups. [DC] indicates the distribution of consumption
expenditures among goods. 15 It is a rectangular matrix with n rows (each one
for any consumption product), and h columns (each one for each social group).
By construction, any column of [DC] adds up to 1.
In the first equation in [7] we have abstracted from transfers and taxes.
In the second equation we introduce current transfers (TR) and income taxes
(Ty) to obtain disposable income. To express consumption in ‘base prices’ (as
the rest of the SAM), we discount the value added tax (VAT). In the last
equation we pre-multiply the previous result by <I-> in order to get domestic
induced consumption. .
Our model is prepared to introduce the influence of prices in the
distribution of consumption among different goods, the influence of interest rate
on the propensities to consume (or save) and wealth effects. We are not going
to do so because empirically these new variables add very little. Cambridge
multisectoral model has shown that linear expenditure functions, similar to the
15
Information about propensities to consume and expenditure patterns can be obtained from
family budget statistics. The problem is that the consumption functions of such statistics do not
coincide with the consumption goods contemplated in input – output tables. A bridge is
necessary to join both statistics. Econometrics will help to fill up certain gaps.
De-Juan: A Clakesch applied general equilibrium model
13
ones we have used here, explain consumption better than any other. (Barker &
Petterson, 1987, following Stone’s suggestions). Changes in prices might affect
the substitution in consumption between, let’s say, two types of meat, but not
between food and dressing, that is the level we are considering in a SAM.
C) Multipliers.
At this moment we are in conditions to determine the equilibrium level of output
corresponding to a vector of autonomous demand (Zt) and the super-multiplier
that captures induced consumption and induced investment. First we obtain
the enlarged interindustry transaction table (*), adding up the tables of
intermediate consumptions (d), final induced consumption (Cid) and final
induced investment (Iid). Second, we divide the cells of each column by the
total output of the industry to obtain the enlarged matrix of coefficients (A*d).
Third we compute a Leontief’s inverse to obtain MQ.
[8]
*d   d  Ci ,d  I i ,d
[9]
Ad*  *d ·qˆ 1
[10]
MQ  I  Ad*


1
MQ is the multiplier of total output. Like Miyazawa-Maseegui (1963) and
Kurz (1992) it ties together the Classical and Keynesian traditions. Like Hicks
(1950) it adds up induced consumption and induced investment. And like Pyat
and Round (1979) it is derived from a SAM and presented in a disaggregated
fashion.16 Each column of the super-multiplier matrix informs us about the
direct and indirect effects of a unitary expansion of industry j over the output of
all the industries that provide resources to j. The provision may be in a direct or
indirect way, and the “resources” are defined in the broadest sense so to
include intermediate goods, final consumption goods of new hired workers, and
fixed capital goods to expand capacity at the required rate.
Economists are generally less interested in total output (that includes
intermediate goods) than in final output (Y), income (VA) or employment (L).
Table 4 explains how to obtain the corresponding super-multipliers MY, MV,
ML. 17
Table 4
16
The format is not similar. Traditional input-output multipliers and SAM multipliers are built
adding up additional columns and rows to the original transaction matrix. Our enlargement
consists in increasing the values of the cells of the original n·n matrix.
17
The formulas, as they appear, compute the effects on gross final output and gross income.
To obtain the multipliers of net output and income, we should have previously endogeneized
depreciation.
De-Juan: A Clakesch applied general equilibrium model
14
D) Theory of output and policy evaluation.
One of the fundamental issues of Economics is the explanation of the level and
composition of output in a given moment (t) and its growth. Given the vector of
autonomous demand (and its rate of growth) and once the super-multiplier has
been computed, the answer is straightforward. With reference to total output
we can write:
[11]

q t  I  A*

1
·Z t  MQ·Z t .
qt  MQ·Z t  MQ·g z ·Z t
The same scheme may be useful for policy evaluation. If we are asked
about the effects of European structural funds on a country and a period (not
necessarily a year), we have to consider the second equation and change the
elements of vector Z where public expenditure impinges on. Usually the
impact on autonomous demand requires a previous analysis. Unemployment
benefits, for instance, will rise private autonomous consumption distributed
among consumption goods following a specific pattern. Certain reforms may
modify both the multiplicand and the multiplier. Think in a reduction of tariffs.
Exports (an important element of Z) will rise according to price elasticity. But
imports will also rise, at the expenses of domestic demand. A change in  and
the multiplier seems unavoidable. In the case of major reforms the general
level of prices and relative prices may be affected, which would oblige us to a
second round of computations. Imagine, for instance, a complete abolition of
tariffs when the country joins a free trade association. Imagine that exports rise
much more than imports and push capacity far above the normal level, causing
a rise in the general level of prices. Inflation usually conveys a real appreciation
of the exchange rate so in the second round we should compute the effects of a
fall in exports and a rise of imports. Trade liberalization also implies a rise in
productivity that affects relative prices. All these effects can be analysed by a
Clakesch - AGE models and treated in different scenarios.
5. Conclusions (by way of contrast).
In this paper we have developed an applied general equilibrium model, rooted
on the Classical, Keynesian and Schumpeterian traditions, as an alternative to
the Neoclassical paradigm developed in the early nineties. A direct contrast
between them may help a deeper understanding of both of them. Table 5
shows the different sets of data. It is obvious that our model needs more
information from outside. This apparent weakness may become a strength,
since it grants more degrees of freedom and allows the researcher to introduce
institutional and historical or ‘path dependent’ variables. The system may
operate for different levels of wages (real and nominal), rates of interest,
exchange rates, inflation rates … The ones which have ruled in the past may
become ‘conventional’ and influence economic behaviour. (Of course they may
also change and agents should adapt to the new outcomes).
De-Juan: A Clakesch applied general equilibrium model
15
Table 5
The differences in the data, are a reflection of the different conceptions
about the working of a capitalist economy and the meaning of economic
equilibrium. Neoclassical AGE models, not less than Walras seminal book, are
supply constrained and static in nature. They take as given certain endowments
of capital and labour and solve for the prices that warrant full capacity and full
employment in the production of the set of goods which maximizes consumers’
utility. Prices are ‘market clearing’ and ‘efficient’. Our Clakesch model is
interested in the dynamics of a demand-constrained system. The vector of
autonomous demand emerges as the driving force of output and employment.
Although in the preceding table it is just one element of autonomous demand, it
influences, loosely, the others. It is, indeed, the main vehicle of technical
change, which brings about productivity gains and, later on, real wage
increases. The effects from the demand side are not less important. A cluster
of innovations with important diffusion and dragging effects (the last ones
captured by the super-multiplier) will bring about a long wave of prosperity.
When the market for new products becomes saturated, and no other
innovations take the relay, we can expect a big recession.
Relative prices play a crucial role in both models. While the Neoclassical
model focuses on allocation of given resources; the Clakesch model
emphasizes dynamic issue related to innovation and technical change. The
innovative sectors enjoying higher rates of return will attract new savings until
competence establish the new set of prices of production. Market prices may
help to restore the equilibrium after a shift of demand from commodity a to b. In
our advanced economies, however, technology makes possible and desirable
the adjustment via quantities instead of prices. Firms willing to increase their
market-share in industry b and the mass of profits associated to such
expansion, will react as follows. In the short run they will math the growing
demand by depleting inventories and pushing up the degree of capacity
utilization. Later on they will expand capacity via investment. The contrary will
happen in industry a. Eventually, the excesses of demand may disappear;
markets will clear and firms will get the normal, uniform rate of profit. 18
Being capacity utilization the basic mechanism of short-term
adjustments, we can expect that most of the time the ratio capital / output will be
above or below the normal or desired position. But since it affects profitability,
firms will try at any moment (via investment) to adjust capacity. It is in this
sense that we refer to long-period equilibrium. It will be effectively achieved if
the rate of growth of autonomous demand remains constant for a sufficient time.
Unemployment, on the contrary, does not affect firms’ profitability and can
endure for good. We can refer to a ‘historical’ rate of unemployment, but there
is nothing ‘natural’ in it. The rate may be halved in a couple of years if
autonomous demand resumes at a higher rate of growth.
18
Walrasian prices warrant the same results. But this is not the case in Neoclassical AGE
models. In the way prices equations stand, there is no warranty that (after a change in wages,
taxes or demand) the new prices ensure a uniform rate of profit.
De-Juan: A Clakesch applied general equilibrium model
16
These hypothesis justify the super-multiplier proposed in section 5 as a
tool for policy evaluation and growth analysis. The results will disappoint
economists trained in Neoclassical AGE models. They started with social
accounting matrices and the fixed-price multipliers derived from them (Pyat &
Round 1979, 1985). But this was only a first step. Soon they shifted to AGE
models where prices are flexible and have an impact on the quantities supplied
and demanded. Are we pretending to go back to fixed-price multipliers? The
answer is ‘not’ and ‘yes’ at the same time. For sure our Clakesch model is
prepared to answer the traditional questions of flexi-price multipliers. A
Clakesch model is also prepared to account for price effects, wealth effects and
the like linked to an expansion or contraction in demand. In the same way that
we have allowed substitution between domestic and foreign goods, we could
consider substitution among factors of production and consumption goods. But
are they possible and are they important in practice? Once fixed capital has
been installed, will entrepreneurs alter the numbers of workers attached to any
machine after a wage increase? Will consumers alter the allocation of income
between, let say, food and clothing, when relative prices change? In our
opinion, these questions have to be answered in the negative. If so, the fixedprice super-multiplier is not a weakness but a sensible way to approach
economic reality in advanced capitalist economies.
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De-Juan: A Clakesch applied general equilibrium model
PRODUCTION
(Input / output)
INCOME
distribution /
consumption
ACCUMULATION
(Savings /
investment)
FINANCE
(+ , -)
total
1
2
...
n
W
R
F
H
G
1,
2...
F
H
G
B
FA1
FA2
FA3
FA4
18
PRODUCTION
(Input / output)
Table 1: Basic SAM
INCOME
(distr/consumption)
ACCUMULATION
Savings/ investment
1, 2, ......................n
W, R; F; H; G
1, 2...; F; H; G; B
Intermediate
Consumption

Value Added
Final Consumption
Final Investment
C
I
VA
Total inputs, T1
Property income,
Current Transfers
Taxes
TR
REST WORLD
(+ , -)
total
+Exports
- Imports
X’
Total
output
T1
Prop. income RW,
Cur. Transfers RW
Taxes (from+, to -)
TRw
T2
T3
Savings
Capital Transfers
Cap. Transfers RW
(from+, to -)
S
TRk
TRk,w
T2
Net Lending
(borrowing +; lend.-)
FF
T3
Net lending RW
(lend +; borrow -)
FFw
T’4
T4
De-Juan: A Clakesch applied general equilibrium model
19
Table 2: Induced and autonomous elements in a SAM
PRODUCTION
SALES
Intermediate
Consumption
AUTONOMOUS
INDUCED
INDUCED
DEMAND
CONSUMPTION INVESTMENT
Induced
Consumption
Induced
Investment
Exports
Gov. C & I.
Modernization I
INCOME
Distributed
Value Added
Income Taxes
Property income,
Current Transfers
 Autonomous C
SAVINGS
Savings
of firms
Savings
of H & G.
Capital Transfers
 Autonomous I
Table 3. A compact SAM that bears the super-multiplier.
INDUCED
INCOMES
UNCOMMITTED
INCOMES
1
2
.
.
n
INDUCED
DEMAND
1, 2, ........................................... n
AUTONOMOUS
DEMAND
Λ*
Z
Intermediate consumption.
Induced final consumption.
Induced final investment.
Exports
Government C & I
Private autonomous C & I.
Modernization Investment
Σ
(ZΣ)
De-Juan: A Clakesch applied general equilibrium model
20
Table 4: Super-multipliers
Multiplier of
Total Output
Multiplier of
Final Output
Multiplier of
Income (VA)
Multiplier of
Employment

MQ  I  Ad*


MV  v·I  A 
MY  I  Ad · I  Ad*
* 1
d

 d  *d  Ad*
1
ML  l · I  Ad*

1

1
We subtract from MQ intermediate consumption.
v is a rectangular matrix with so many rows as
primary factors (wages of non qualified labour,
wages of qualified labour, profits…)
l is a rectangular matrix with so many rows as
types of labour.
Table 5: Data in Neoclassical and Clakesch AGE models
Neoclassical – AGE model
Clakesch –AGE model
Endowements (K, L).
Technology
(malleable production functions)
Technology
(Fixed coefficients, but capital/output
ratio may adjust to demand fluctuations)
Individual preferences
(malleable consumption functions)
Expenditure patterns of social groups
Distribution (wr)
Autonomous demand (gz).