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Chapter 13Empirical Models

of Stabilization

© Pierre-Richard Agénor and Peter J. Montiel

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Central macroeconomic policy challenge: how to achieve stabilization and adjustment while minimizing the cost measured in terms of real income.

In the past, this refered to reducing inflation and improving the current account while avoiding short-run income losses arising from deficient aggregate demand.

Recently, disappointing medium-term growth experience of many developing countries has turned attention to the maintenance or reactivation of the economy's long-run growth momentum.

In this chapter, analytical tools available to address interaction among stabilization, adjustment, and growth in practical developing-country applications are examined.

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Short-run macroeconomic models assume that productive capacity is exogenous.

In contrast, the study of the interaction between stabilization and growth requires the specification of medium-term models.

Two essential features of these models: Productive capacity is treated as endogenously

determined. Explain the rate of accumulation of productive factors

and the rate of change in total factor productivity as functions of the current and expected future values of macroeconomic variables and policy instruments.

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Interaction among stabilization, adjustment, and growth in medium-term models is:

Given the predetermined values of total factor productivity and stock of productive factors, economy's short-run equilibrium simultaneously determines output, employment, price level, the current account, and rate of net investment in new productive factors.

Rate of net investment determines the stock of productive factors in the next period, which together with updated values of total factor productivity determine the next period's level of productive capacity.

Thus, growth of productive capacity between this period and the next depends on characteristics of this period's short-run equilibrium, rate of net investment generated in that equilibrium.

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Four types of models: “Bank-Fund” models, “gap” models, macroeconometric models, and computable general equilibrium models.

Success of such models in shedding light on the interactions between stabilization and growth in developing countries depends on three features: Specification of determinants of productive capacity. Description of the forces determining the rate of

accumulation of productive assets and total factor productivity.

Quality of the model's description of the economy's short-run equilibrium.

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Bank-Fund Models. Three-Gap Model. Macroeconomic Models. Computable General Equilibrium Models.

Bank-Fund Models

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The IMF Financial Programming Model. The World Bank RMSM Model. A Simple Bank-Fund Model.

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The IMF Financial Programming Model

IMF provides advice to developing countries on macroeconomic policy.

The Fund extends financial support to stabilization programs that meet certain criteria: they must be consistent with the principles set out in the

institution's articles of agreement; offer a convincing prospect of repayment.

This assistance is conditioned on the borrowing country's compliance with a set of quantitative policy performance criteria drawn up in consultation with the Fund and embodied in a financial program.

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Design of such a program and specification of such criteria rely on “financial programming.”

Simplest financial programming model determines the magnitude of domestic credit expansion required to achieve a desired balance-of-payments target under a predetermined exchange rate.

Balance sheet identity for the banking system,

M = D + ER,

E: nominal exchange rate;

D: credit to the nonbank sector;

R: claims on foreigners;

M: monetary liabilities.

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R and M are endogenous and D is an exogenous policy variable under the control of the monetary authorities.

Velocity:

= Y/M,

Y: nominal GDP. Money market is required to be in flow equilibrium:

M = -1Y - -1Y-1.

Assume: nominal exchange rate and velocity are both constant and that nominal output is exogenous.

-1

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Model can be solved for the change in the stock of international reserves R as a function of and Y, as well as of the monetary policy instrument D:

ER = -1Y - D.

Given a target value for the change in reserves and projections for and Y, required expansion in the stock of credit can be derived from

D = -1Y - ER. Expanded version (“Polak model”) makes nominal

output endogenous (Polak, 1957).

(4)

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Balance-of-payments identity

R = X - (Y-1+Y) + F, 0 < < 1.

X - (Y-1+Y): net exports.

X: autonomous component of net exports.

F: exogenous net capital inflows. Figure 13.1: interaction between the money-market

equilibrium condition (4) and the balance of payments identity (6) in determining nominal income and the balance of payments.

(4) is positively sloped MM locus, while (6) is negatively sloped locus RR.

E: equilibrium values of the balance of payments and change in nominal income.

(6)

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Figure 13.1The Polak Model

E

R

MM

RR

y

R*

y*

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Increase in the rate of expansion of credit causes the balance of payments to deteriorate and nominal income to rise.

Increase in exogenous receipts of foreign exchange improves the balance of payments and raise nominal income.

“Polak” financial programming model can be given “classical” closure (solved for the domestic price

level, taking real output as exogenous); “Keynesian” closure (solved for changes in real

output, taking the price level as given).

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The World Bank RMSM Model IMF financial programming model:

Short-run model of stabilization and adjustment. “Adjustment” refers to the balance of payments. “Stabilization” refers to the price level in classical

mode and to real output in Keynesian mode. It contains no aggregate production function and

does not determine capacity output. World Bank's Revised Minimum Standard Model

(RMSM): model of capacity output. Used to generate macroeconomic projections in country

economic reports at the Bank.

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Emphasis in RMSM: ascertaining whether the domestic and external financing available to a particular country is adequate to achieve a target for economic growth.

Key analytical feature of RMSM: link between financing and capacity growth.

(6): interpreting Y as real output, if autonomous net exports are taken to be exogenous (X = X), the economy's growth is determined by the volume of external financing F - R.

RMSM is then used to calculate the volume of domestic saving required to sustain this increment to output.

Assume fixed-coefficients Harrod-Domar production function in capital and labor, with capital taken to be the scarce factor.

~

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Increase in capacity requires domestic investment

I = Y,

: incremental capital/output ratio (ICOR).

(7)

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Letting C and S denote domestic consumption and saving, we can use the national income accounting identity

I = (Y - C) + (Y - X),

and the definition of savings

S = Y - C,

to find the volume of domestic saving required to achieve a given increment to productive capacity:

S = X - Y-1 + (-)Y.

S is an increasing function of Y, since is a number in the neighborhood of 3-4, while is a fraction.

~

~

(8)

(9)

(10)

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With saving itself linearly related to output in Keynesian fashion,

S = SA + sY, 0 < s < 1.

Resulting framework can be used to derive the level of autonomous saving required to sustain an increment to capacity output:

SA = X - Y-1 + [ - ( + s)]Y.

(11)

(12)~

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A Simple Bank-Fund Model The model can be used in a variety of ways, with the

“financing needs” mode described above being the most common.

With R and Y exogenous, while F and S are endogenous, the model is solved in “financing needs” mode.

With R bounded from below, F and S exogenous, Y endogenous, and (8) setting a minimum value for investment, the model is solved in “two-gap” mode.

Alternative application of the RMSM is to combine it with the financial programming model to derive a simple Fund-Bank model of adjustment and growth.

Assume: Y is real output and SA is exogenous.

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(12) can be solved for the rate of capacity growth Y. Growth of productive capacity is determined in

neoclassical fashion by availability of saving (domestic and foreign, via SA

and X); productivity of investment, given by .

This capacity growth rate can be fed into the Polak model given by (4) and (6).

Since Y is now interpreted as real output, and (4) involves nominal income, it must be rewritten as

ER = -1[(P-1 + P)Y + Y-1P] - D,

P: domestic price level.

(13)

~

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Resulting model can be solved in two ways: If capital inflows are exogenous and the domestic price

level is endogenous, (6) yields the balance of payments R and (13) the domestic price level.

If the domestic price level is exogenous and capital inflows are endogenous, (13) yields the balance of payments and (6) the level of capital inflows.

Three-Gap Models

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“Financing gap” method incorporated in the RMSM is the most venerable approach to the projection of real output growth in developing countries.

“Gap” models are close contenders. “Two-gap” models focus on foreign exchange and

domestic saving as alternative constraints on growth, date back to Chenery and Strout (1966).

“Three-gap” models includes also fiscal gap.

Bacha (1990): Foreign exchange availability is linked

directly to the rate of growth of productive capacity; indirectly to the level of actual real output.

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ICOR relationship described in (7) is retained, but investment now is assumed to require imported capital goods:

Z = I, 0 < < 1,

Z: level of capital goods imports. From (14) and the balance-of-payments identity:

I = (1/)[X + (F - J)],

X: level of exports net of other imports;

J: sum of external debt service, transfers, and changes in foreign exchange reserves.

Suppose that X is subject to the upper bound X*, determined by external demand.

(15)

(14)

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Then (15) becomes the inequality

I (1/)[X* + (F - J)],

which represents the “foreign exchange” constraint on investment, and thus, by (7), on capacity growth.

“Savings” constraint is derived as follows: from the balance-of-payments and national income accounting identities (6) and (8), we have

I = Y - C - G - (F - J),

G: government spending.

(16)

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Defining private saving as Sp = Y - - C, where is government net tax revenue, the previous equation becomes

I = Sp + ( - G) - (F - J).

Sp is an increasing function of output and is bounded above by private saving at full capacity output, Sp, taking private consumption to be exogenous; noting that Y is bounded above by full-capacity

output. This means that I is also bounded from above, so that

I Sp + ( - G) - (F - J),

which represents the saving constraint on investment.

~

~ (17)

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To derive the “fiscal constraint,” assume that base money is the only financial asset available for the private sector, so that private sector's budget constraint can be written as

Sp - Ip = M/P,

Ip: private investment;

M: stock of base money. Change in M is assumed to be given by

M = M(, ), 0 < < 1,

: rate of inflation;

: “propensity to hoard.”

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In this case, all foreign capital flows accrue to the government, and the budget constraint of the consolidated public sector can be written as

Ig = M(, ) + ( - G) + (F - J),

Ig: public investment. Total investment:

I = Ip + Ig.

(20)

(21)

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Assume: private and public investment are complements, so that private investment is bounded above by the level of public investment:

Ip k*Ig,

k*: ratio of private to public capital in the composite capital stock.

From (20) to (22), fiscal constraint on total investment takes the form

I (1 + k*)[M(, ) + ( - G) + (F - J)].

(22)

(23)

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This model simultaneously determines the level of output, the current account, the rate of growth of productive capacity, and the rate of inflation.

Focus of “gap” models is on the implications for such variables of alternative levels of foreign financing (F -J).

Figure 13.2: illustrate the mechanisms at work. Central endogenous variable I is plotted against (F -J). (16) and (17) are plotted as the loci FF and SS,

representing the foreign exchange and saving constraints.

Slope of SS is unity, as can be verified from (17), while that of FF is 1/, which is greater than unity, since is a fraction.

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Figure 13.2The Three-Gap Model

F

F

S

S

G

G

I

(1/m)x*

0 F - J)' F - J

I'

(1+k*)[H(,) + ( - g)]

S + ( - g) ~p

Source: Adapted from Bacha (1990, p. 291).

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Relative positions of the two curves rely on the assumption that (1/)X* < S + ( - G).

Hatched areas beneath the curves represent the feasible regions for I.

If net foreign inflows are (F -J)’, both constraints are binding and investment is I’.

To the left of (F - J)’, foreign exchange constraint binds.

Investment is determined by foreign exchange availability.

Economy will suffer from Keynesian excess capacity since investment will therefore be less than the level

that would satisfy (17) as an equality; since the other components of aggregate demand

are fixed.

~

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Actual output will be given by

Y = C + (1-)Ic + X*,

Ic: actual constrainted level of investment. If (F - J) exceeds (F - J)’, economy will be

constrained by domestic saving. Investment will now be determined along SS, and

output will be at full capacity. Slack variable in this case is net exports, which are

squeezed by domestic demand and are given by

X = Y* - C + (1-)Is,

Is: savings-constrained level of investment.

(25)

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This part of the analysis reproduces the two-gap model of Chenery and Strout.

How does the ``fiscal gap'' fit in? Inequality (25) is represented by an area bounded

above by a locus GG with slope 1 + k* and vertical intercept (1 + k*)[M(, ) + ( - G)].

Quantity 1 + k* may be greater or less than 1/, so GG may be steeper or flatter than FF.

Curves GG and SS have the same slope. But, their relative heights depend on the values of and

k*. Although the private sector budget constraint (18)

implies that Sp > M(, ) as long as Ip is positive, the difference between Sp and M(, ) decreases with .

~~

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Thus a larger value of raises the height of GG relative to SS.

Larger value of k* has a similar effect. Incorporate the fiscal constraint in the model: treat as

an endogenous variable that ensures that (23) holds as an equality.

In this case, the role of the fiscal constraint is merely to determine the rate of inflation.

Given the value of I, (21) and (22) holding as an equality would determine the levels of Ip and Ig, and given the latter, (23) holding as an equality would determine .

Endogenous changes in move GG to intersect whichever of the two other loci happens to be binding at a point directly above the relevant value of (F - J).

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Increase in (F - J) would increase the rate of capacity growth by raising I, reduce the rate of inflation by permitting the

government to finance itself externally, rather than through the inflation tax.

If is an exogenous policy variable, GG serves as an independent constraint.

If the fiscal constraint does not bind k is the slack variable; given I and Ig, private investment Ip is determined,

and the actual value of k implied by Ip and Ig may be smaller than k*.

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If fiscal constraint binds, increase in (F - J) increases capacity growth, because receipt of foreign financing results in higher public investment, which in turn induces more private investment.

Actual level of output will rise, through Keynesian demand effects emanating from higher levels of both private and public investment.

This brings the economy closer to full capacity utilization, and net exports will fall.

Macroeconomic Models

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Problems related to models considered in Section 1: Omit substantial amount of economic structure and

behavior. They are deficient as medium-term models both

because of their specification of the determinants of productive

capacity; rate of accumulation of productive factors.

Production function is of the fixed-coefficients Harrod-Domar type.

They do not contain an independent investment function describing the behavior of agents who actually make the decision to accumulate productive factors.

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Investment in physical capital is treated as a residual. Bank-Fund model treats investment as determined

by the available saving; three-gap model derives it residually from saving,

foreign exchange availability, or the government budget, depending on which is the binding constraint.

To analyze complicated dynamic macroeconomic phenomena, macroeconometric models are used.

This section provides a brief overview of the structure of “representative” macroeconometric models for developing countries.

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Structure of Production. Aggregate Supply. Aggregate Demand.

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Structure of Production Majority of macroeconometric models for developing

countries have been built along the lines of the Mundell-Fleming production structure.

Economy specializes in the production of a single home good, which is an imperfect substitute for the foreign good.

Domestically produced good can be either consumed at home or exported.

Domestic residents consume both the home good and the foreign good.

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Aggregate Supply Family of models dubbed RMSM-X retains the constant

ICOR assumption. Capacity output is specified as a function of capital K,

labor N, and an imported intermediate good O:

Y = F(N, O; K),

with standard neoclassical properties. Empirically, this function is given a Cobb-Douglas or

CES form. Capital stock is predetermined in the short run and

grows endogenously as the result of net investment.

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Both the level of total factor productivity and the labor force grow exogenously.

Imported intermediate goods are available from the world market in infinitely elastic supply at an exogenous foreign-currency price.

Determination of the domestic-currency price of the home good depends on how the supply side of the economy is modeled in the short run.

In the simplest macroeconometric models, the supply side is described along Keynesian fix-price or classical flex-price lines.

Keynesian version has no dynamics arising from the expansion of productive capacity, since it takes output to be entirely demand driven.

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Classical version: continuous full employment is assumed; output of the home good is determined by the

inherited capital stock, the size of the labor force, and the price of the imported intermediate good;

short-run supply behavior is depicted via a variable mark-up price equation.

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Price of the home good is taken to be determined by unit costs plus a mark-up factor that depends on the rate of capacity utilization in the economy:

P = P(w, PO, Y/Yc),

w: nominal wage;

Yc: capacity output;

PO: domestic-currency price of the imported intermediate good.

Short-run aggregate supply curve is an upward-sloping function of level of real output, and it is displaced vertically by changes in w or in PO.

+ + +(27)

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In (27) w and Yc are predetermined, while Y and P are solved out simultaneously.

Price of imported intermediate goods depends only on their exogenous foreign-currency price and the exchange rate.

Behavior of nominal wages is based on an expectations-augmented Phillips curve:

Ns: labor force;

a: expected inflation rate;

N(): actual employment.

ww

= [N(Y, K, PO)

Ns, a]

+ + +

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Most common approach to the modeling of expectations formation in macroeconometric models for developing countries has been the use of adaptive expectations.

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Aggregate Demand Demand side of macroeconometric models for

developing countries tends to have an IS-LM flavor with ad hoc adjustments of behavioral relationships.

“IS” side: Set of determinants of consumption includes

disposable income Ydisp, real interest rate r, and some type of real wealth variable a = A/P:

C = C(Ydisp, r, a), 0 < C/Ydisp < 1.

There is no particular consensus on the specification of private consumption behavior, and the specifications range.

+ +-(29)

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A is a predetermined variable that evolves over time in response to private saving, derived from substituting (29) in the private sector's budget constraint.

Set of determinants of private investment spending includes real output, a cost of capital term q, and lagged capital stock:

I = I(y, q, K-1).

Problems related to investment functions: omission of forward-looking variables; failure to account for the likely irreversibility of

investment in physical capital.

+ - -

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Some structural aspects of potential significance for understanding capital accumulation in developing nations are not dealt with in the investment functions: effect on investment of the existence of an external

debt overhang; role of complementary factors such as infrastructure,

human capital, and imported inputs; role of financial repression.

Treatment of the trade sector: Exports are determined by foreign income and the

relative price of the home good. Imports depend on the same relative price as well as

on domestic real GDP.

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Some models include a measure of foreign reserve availability in the import demand function to capture the intensity of rationing in official foreign exchange market.

“LM” side: Institutional disaggregation includes the central bank

and the deposit money banks. The central bank's balance sheet is at the heart of the

financial sector, with the change in its liabilities linked to changes in its assets.

Demand for money depends on real GDP and a domestic nominal interest rate.

Careful modeling of financial repression and informal markets are not found in macroeconometric models.

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Common treatment of capital mobility leaves foreign interest rates out of domestic asset demand functions, taking capital flows to be exogenous.

Both specification of domestic financial markets and their interactions with world capital markets play important roles in determination of cost of capital.

Result: macroeconometric models fall short of providing a suitable framework for the analysis of the interactions among stabilization, adjustment, and growth.

Computable General Equilibrium Models

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Economy-wide modeling approach for developing countries is the construction of computable general equilibrium (CGE) models.

CGE models are applied microeconomic models, designed to study issues such as the effects on resource allocation and income distribution of various types of external shocks or policy interventions.

Key distinction between CGE models and macroeconometric models: level of aggregation assumed for both goods and factors.

CGE models are highly disaggregated on both their demand and supply sides.

On the supply side: Contain a large number of distinct production activities

and factors of production.

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Supply of imports is disaggregated into different types of commodities that can be purchased on the world market.

Profit-maximizing behavior by firms generates sectoral supply functions for individual domestically produced commodities and demand functions for various types of factors.

On the demand side: Different types of households are distinguished by the

nature of their ownership of factors of production. Utility maximization by individual classes of households

generates demand for domestic and foreign goods, and supply functions for different types of factors.

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World demand for domestic goods exhibit different price elasticities for different goods, permitting the domestic economy to exercise market power over some commodities.

Relative price adjustments play a central role.

Distinction between macroeconometric models and traditional CGE realted to their dynamic properties.

CGE models are oriented to the solution of period-by-period comparative-statics exercises.

Since CGE models represent actual economies, macroeconomic phenomena of an explicitly intertemporal nature appears.

But, these phenomena are modeled in rudimentary fashion.

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Private households are assumed to save a fixed fraction of their incomes.

Public consumption is exogenous. Investment is often either exogenous or determined by

saving rate. Implications of these assumptions:

with households not spending all of their income each period;

with independent investment and public consumption decisions;

CGE models require a period-by-period macroeconomic mechanism to reconcile aggregate saving and investment (“closure” rule).

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Dewatripont and Michel (1987) classify potential closures into four types: Keynesian, Johansenian, Kaldorian, classical.

Sensitivity of numerical results to the particular choice of a closure rule is not always clear, and may vary depending on the issue at hand.

None of these mechanisms leaves traditional CGE models well suited to the analysis of the links among stabilization, adjustment, and growth.

Reason: all of them have the effect of leaving investment exogenous or determined by saving.

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Addressing links between stabilization and growth requires the inclusion of an independent investment function, that responds endogenously to current and expected future macroeconomic variables.

Since these intertemporal links are omitted, dynamics in traditional CGE models are too simple to capture interactions among stabilization, adjustment, and growth.

Walrasian problem solved each period is static. Recently, CGE models have begun to incorporate more

sophisticated macroeconomic relationships: “New structuralist'' CGE models in Taylor (1990), “micro-macro” models patterned after Bourguignon et

al. (1992),

incorporate traditional macroeconomic relationships.

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This modification brings recent CGE models close to “dependent economy” macroeconomic simulation models.

Although these innovations enrich the macro dynamics exhibited by CGE models, the macroeconomics of these models remain relatively simple.

In contrast to the static optimizing behavior assumed for within-period sectoral supply and demand functions, dynamic behavior is left rather simple and ad hoc.

Intertemporal optimization on the part of either households or firms based on forward-looking expectations remain absent.

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Appendix: The Khan-Knight Monetary Disequilibrium

Model Figure 13.3.

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Figure 13.3Logical Structure of the Khan-Knight Model

Endogenous variables

Demand for money Expected inflation rate

Domestic inflation rateForeign inflation rateReal output

Taxes

Imports

Exports

Current account

Net foreign assets

Capital flows

Money supply

Government spending

Fiscal deficit

Private sector credit

Total domestic credit