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Chapter 3Behavioral Functions

© Pierre-Richard Agénor and Peter J. Montiel

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Consumption and Saving. Private Investment. The Demand for Money. Aggregate Supply Functions.

Consumption and Saving

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Consumption Smoothing. Length of Planning Horizon and Liquidity Constraints. Effects of Interest Rate Changes on Savings. Public and Private Consumption.

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Importance of consumption: Private consumption represents the largest component

of aggregate demand. Domestic investment in developing countries is

generally financed by domestic saving, and private consumption is an important determinant of it.

Since current account deficit is equal to domestic investment minus domestic saving, private consumption behavior is central to the external adjustment process.

Standard model of household consumption: Representative household devises a consumption plan

by maximizing utility over its lifetime, subject to an intertemporal budget constraint.

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With additively separable utility and no uncertainty, the household maximizes lifetime utility:

u(·): concave period utility function;

c: real consumption;

: constant rate of time preferences.

V = t = 0

T u(ct)

(1+)t(1)

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Assuming constant real interest rate r, V is maximized by choosing a path of consumption {c} subject to

a0: household’s initial wealth;

y: disposable factor income.

t = 0

T u(ct)

(1+r )t a0

+

t = 0

T yt

(1+r )t

Tt = 0

(2)

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(3): allocation of consumption across periods must be such that an extra unit of consumption makes the same contribution to lifetime utility no matter to period.

Consumption path that solves the household's optimizing problem satisfies Equation (3), (2) holds as an equality.

(3) determines the rate of growth of consumption. (2) determines the initial level of consumption.

First-order condition for an optimum is given by the Euler equation:

u(ct)1 + r

, t = 1,…,T - 1.u(ct+1) = 1 + (3)

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Implications: Households will tend to smooth consumption, so

consumption will not be tied to current income. Effect of changes in income on current consumption

depends on when such changes take place; how long they are expected to last.

No prediction about the effects of changes in r on consumption: Substitution effect tends to depress current

consumption. Income effect tends to increase it. Net effect on consumption of a change in r depends

on the relative strength of these two effects.

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Application of this theory in developing countries raises four issues:

Whether households can effectively smooth consumption which depends on access to unconstrained borrowing and lending.

Effective length of planning horizons. Empirical determination of the effects of r changes on

consumption. Effects of fiscal policy on private consumption.

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Why is household consumption behavior different in developing countries? (Gersovitz (1988) and Deaton (1989)):

1) Households tend to have different demographic structures: Individual household tends to be larger; More generations live together, sharing resources.

Implications: If resources are shared among the several generations

within the household, there is no need for “hump'' saving to finance retirement.

With pooled resources, the household provides insurance for individuals against risk.

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Developing-country households provide a closer approximation to the “dynastic” household of Barro (1974).

2) Household incomes in the developing world are more uncertain.

Reasons: share of agricultural incomes; macroeconomic instability arising from both external

shocks and domestic macroeconomic policy shocks. Since this uncertainty cannot be diversified away by risk

pooling within the household, precautionary saving is more important in developing countries.

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3) Many households in developing countries operate at near-subsistence income levels.

This strengthens the motive for consumption smoothing.

4) Developing-country households' need to cope with the implications of financial repression.

Thus, consumption smoothing may be restricted to transfer resources across time by inability to borrow against future earnings very low real returns on current saving.

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Consumption SmoothingEvidence on consumption smoothing in developing

countries: This evidence comes from tests of the permanent

income hypothesis (PIH). These tests effectively consist of estimating regression:

c = a0 + a1yp + a2(y–yp) + u,

c: real per-capita consumption,

yp: real per-capita permanent income,

y: current per-capita real income,

u: disturbance term.

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Results indicate that income decomposition matters. That is propensity to consume out of yp exceeds

propensity to consume out of y. These results are consistent with the consumption-

smoothing hypothesis. But elasticity of c with respect to yp is not found to be

unity, nor is the propensity to consume out of y found to be zero.

Thus, the strict form of the PIH is not often supported by the data in developing nations.

Second type of evidence emerges from cross-country studies of saving behavior.

If “hump” saving over the life cycle is important, countries experiencing rapid growth in per-capita incomes should exhibit high saving rates.

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Evidence suggests that consumption smoothing over the life cycle may be important.

Third type of evidence has to do with responses to income shocks.

Changes in the terms of trade have been large in many developing countries.

Bevan et al. (1993): effects of the 1976-1979 coffee boom on farmers in Kenya.

Increase in coffee prices was passed on to small growers, who thus experienced a windfall in income.

This windfall was understood to be temporary and saved (consumption smoothing).

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Length of Planning Horizon and Liquidity Constraints

Evidence suggests that planning horizons extend beyond a single period and some households are able to move resources intertemporally.

This evidence is consistent with Deaton's suggestion that the “dynastic family” construct is more relevant in the developing world.

Measured incidence of liquidity constraints is substantially greater in developing countries.

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Corbo and Schmidt-Hebbel (1991): Variables measuring liquidity constraints are added

significantly to aggregate consumption equations. This result suggests two groups of consumers:

those who smooth consumption over time; those whose consumption is limited by current

resources.

Haque and Montiel (1989): Point estimates of the share of total consumption

accounted for by households that simply spend their current incomes.

For fourteen of their sixteen countries the estimated share exceeded 20%.

These are larger than the typical estimate of 0.1 for the United States.

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Effects of Interest Rate Changes on Savings

Some authors have found evidence of positive interest rate effects on saving in developing countries, but estimated effects are small.

Fry (1996): Sample of fourteen Asian developing countries over the

period 1961-1983. 1% increase in the real deposit rate increased the

saving rate by about 0.1%. Giovaninni (1985) and Schmidt-Hebbel et al. (1992)

have failed to detect a statistically significant positive interest rate effect.

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Standard Lucas critique and data related problems make the results difficult to interpret.

Alternative: estimate the intertemporal elasticity of substitution directly.

If utility function exhibits constant relative risk aversion, (3) will relate the rate of growth of consumption to the difference between the r and , with a factor of proportionality equal to the intertemporal elasticity of substitution.

Estimation of the Euler equation can thus yield an estimate of the intertemporal elasticity of substitution.

This approach estimates a “deep” parameter directly and relies on consumption data.

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Giovaninni (1985) finds statistically significant intertemporal elasticity of substitution (averaging about 0.5) in only 5 out of 15 cases.

Rossi (1988): Allows for liquidity constraints and direct substitutability

between private and public consumption. He found larger estimates of the intertemporal elasticity

of substitution. But these were too small to say that changes in real

interest rates affect consumption.

Ogaki, Ostry and Reinhart (1996): Estimate effects of real interest rates on saving. Intertemporal elasticity of substitution varies with the

level of wealth.

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They find that sensitivity of saving to the interest rates rises with the level of income.

In low-income countries, estimates of the intertemporal elasticity of substitution are low.

Range of estimated values for the intertemporal elasticity of substitution is large: from 0.05 to 0.6.

Even the highest estimates remain small, so effect of changes in interest rates on saving is weak.

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Public and Private Consumption

Could public consumption be a direct substitute for private consumption in developing countries?

McDonald (1983) finds results consistent with this view. Karras (1994) suggests that private and public

consumption expenditure are complementary rather than substitutes.

Private Investment

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Specification Issues. Determinants of Private Investment: The Evidence.

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Why investment is important? It determines the rate of accumulation of physical

capital and is thus an important factor in the growth of productive capacity.

Because it is a forward-looking activity with irreversible aspects, it is a volatile component of aggregate demand.

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Specification Issues Empirical investment functions for industrial countries

have relied on either a “stock” or a “flow” approach. Under the stock approach: Price of installed capital is pk. Given a discount rate and rate of depreciation , the

rental price of capital is = ( + )pk. Flow profit function:

(k) = py[k, n(w/p, k)] – wn(w/p, k),

p: price of output;

w: nominal wage;

n(·): level of employment.

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Optimal capital stock k* satisfies

(k*) = .

Given an initial capital stock k0, net investment

represents a gradual adjustment of the actual to the desired capital stock.

Gross investment is derived by adding to this an amount of replacement investment that is proportional to the initial capital stock.

Under flow model: Convex function h(I): total cost of achieving the level of

gross investment I.

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If the firm's objective is to maximize the present value V(k) of its profits (k) net of the costs of investment ph(I), then at each period rate of I must satisfy

h(I*) = q/p,q = dV(k)/dk : marginal value of installed capital at the current period;

q/p: marginal value of “Tobin's q” (ratio of the value of installed capital to its replacement cost).

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Determinants of investment in stock version: expected future values of aggregate demand; user cost of capital; wage rate; initial capital stock.

Determinants of investment in flow version: marginal value of Tobin's q; parameters of the adjustment-cost function.

Modification of standard industrial-country investment theory is required in developing country analysis:

Investment functions are heavily dependent on institutional environment in financial system; but equity markets are absent and prevalence of financial repression is prevalent in the developing world.

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Imported capital goods are important in the developing world; so foreign exchange rationing, and cost of foreign exchange may be important determinants of private investment behavior.

Role of imported intermediate goods are important; so specification of relative factor prices in empirical investment functions cannot be restricted to the wage rate and user cost of capital: Domestic-currency price and availability of such

goods must be also taken into consideration. Servén (1990b): long-run effect of a real devaluation

on private capital formation is ambiguous. It depends on the effect of the real depreciation on

the import content of capital goods.

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Existence of a debt overhang in many countries: possibility that confiscatory future taxation will be used to finance future debt service may need to be reflected in the specification of private investment behavior.

Large role of the public capital stock suggests the need to incorporate complementarity-substitutability relationships between public and private capital into private investment decisions: Public sector investment crowds out private

investment expenditure if it uses scarce physical and financial resources that would otherwise be available to the private sector.

Public investment to maintain or expand infrastructure and provision of public goods are complementary to private investment.

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Macroeconomic instability and resulting uncertainty may have a large influence on private investment: There will be a tendency to delay irreversible

investment in the face of uncertainty. Delay involves trading off the returns from investing

now against the gains from being able to make a more informed decision in the future.

Servén (1996): interactions between instability, irreversibility, and uncertainty played a significant role in the poor investment performance of sub-Saharan Africa.

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Determinants of Private Investment: The Evidence

Rama (1993): Thirty-one studies conducted over the period 1972-1992.

Problems: All of them are vulnerable to the Lucas critique. Moreover, many of them employ ad hoc investment

functions. Treatment of expectations is often rudimentary. In several cases the dependent variable is total, rather

than private, investment. Data are typically annual, and the available time series

are often very short.

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Estimating techniques do not always handle simultaneity problems.

Conclusions of the evidence: Aggregate demand plays an important role driving

private investment (consistent with “flexible accelerator” specification).

Relative factor prices enter the stock version of the theoretical investment function; but little information is available on effects of financial variables on private capital formation through user cost of capital in developing countries.

Credit variables have a statistically significant coefficient with the expected sign.

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Indicators of foreign exchange availability tended to behave as expected.

Seven out of eleven studies found a positive role for the public capital stock. When a distinction is made between infrastructural

and other types of public investment, more significant results are obtained (Blejer and Khan (1984)).

Results are consistent with the hypothesis that infrastructural investment is complementary to

private investment, increases in other types of government investment

crowd out the private sector. Indicators of macroeconomic instability of various types

have significant negative effects on private investment.

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Rodrik (1991): uncertainty on the part of economic agents regarding the government's future intentions affects investment behavior.

Larraín and Vergara (1993): real exchange-rate variability has an adverse effect on private capital formation.

Cardoso (1993) and Bleaney and Greenaway (1993a): fluctuations in the terms of trade affect private investment.

Fitzgerald et al. (1994), Greene and Villanueva (1991), Oshikoya (1994), and Schmidt-Hebbel and Muller (1992): significant negative effect of the debt output ratio on investment.

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Cohen (1993): stock of debt itself does not have a significant influence on investment, but that debt service may have crowded out investment.

The Demand for Money

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Conventional Money Demand Models. Currency Substitution and the Demand for Money.

Domestic- and Foreign-Currency Deposits. Currency Substituton: The Evidence.

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Conventional Money Demand Models

Conventional models of money demand in developing countries include real income as a scale variable; rate of inflation as an opportunity cost variable.

Reasons for why domestic interest rates are excluded. Alternative financial assets are assumed not to be

available. Government regulations imply that such rates display

little variation over time.

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Early studies that introduced nominal interest rates in money demand functions met with little success.

Some recent studies have found a significant effect of interest rates on money demand in developing nations where financial markets have reached a relatively high degree of diversification; began to operate with relative freedom from

government intervention and regulations. Statistically significant effects of interest rate variables on

the demand for real money balances. Arrau et al. (1995), José Rossi (1989) for Brazil; Reinhart and Végh (1995) for Argentina, Chile, and

Uruguay.

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Foreign interest rate can be relevant opportunity cost of holding domestic monetary assets. Hoffman and Tahiri (1994) for Morocco; Calvo and Mendoza (1996) for Mexico.

Limitation: ignore interest rate in informal credit markets as a relevant opportunity cost of holding cash.

This neglect may explain why early studies using official interest rates were not very successful.

Van Wijnbergen (1982): informal-market interest rate had a significant effect on the demand for time deposits in Korea.

Problem: lack of adequate time series information on informal interest rates in most countries.

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Exclude interest rates and assume a partial adjustment mechanism of actual to desired levels.

Conventional money demand function:

lnm = a0 + a1 ln y - a2+k + (1-) lnm-1 + u,

m: real money balances;

y: real income;

+k: expected inflation rate for k periods ahead;

u: disturbance term;

0 < < 1 : speed of adjustment.

a (8)

a

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Estimation of (8) raises econometric issues related to simultaneity, the choice of proxy variables for expectations, and so on.

Two-step estimation approach: Estimate the long-run determinants of the demand for

money using cointegration techniques. “General-to-specific” approach is used to specify the

short-run dynamics of money demand. Asilis et al. (1993) for Bolivia, Domowitz and Elbadawi

(1987) for Sudan, and Ahumada (1992) for Argentina.

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Advantages of this approach: provides richer specification of the short-run

dynamics; better predictions of the short-run behavior of real

money holdings. Problems:

Long-run parameter estimates do not vary significantly from those derived by less sophisticated techniques.

Excessively long lags in estimated money demand equations.

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Currency Substitution and the Demand for Money

Currency substitution: foreign currency substitutes for domestic money as a store of value, unit of account, and medium of exchange.

This has become a pervasive phenomenon in many developing countries.

What does the degree of currency substitution depend on?

Assets denominated in domestic currency cannot provide an efficient hedge over time in countries where inflation is high;

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opportunities for portfolio diversification are limited; ceilings on domestic interest rates are present.

Degree of currency substitution is higher when there are low transactions costs of switching from domestic-

currency assets to foreign-currency assets; uncertainty about social and political developments; fear of expropriation of assets denominated in

domestic currency; potential need to leave the country.

Existence of informal markets facilitates transactions in foreign exchange may reinforce the substitution between domestic- and foreign-currency assets.

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Domestic- and Foreign-Currency Deposits

Figure 3.1: evolution of foreign-currency-dominated deposits in Egypt and Indonesia.

Short- and long-run consequences of an increase in the holdings of foreign currency (Agénor and Khan, 1996).

Short run effects: Rise in foreign-currency deposits held abroad is

equivalent to a capital outflow. This can have destabilizing effects on

domestic interest rates; exchange rate; international reserves.

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Source: International Monetary Fund.

Figure 3.1aForeign Currency Deposits Held in Domestic Banks

1981q1 1983q1 1985q1 1987q1 1989q1 1991q1 1993q1 1995q1 1997q1

10

15

20

25

30

35

40

45

50 Egypt (As a percentage of the narrow money stock)

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Source: International Monetary Fund.

Figure 3.1bForeign Currency Deposits Held in Domestic Banks

1981q1

1983q1

1985q1

1987q1

1989q1

1991q1

1993q1

15

20

25

30

35 Indonesia (As a percentage of banks' demand, time and savings deposits)

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Outflow may create a shortage of liquidity in the domestic banking system.

This puts upward pressure on domestic interest rates. Outflow depreciates the domestic currency under a

floating exchange-rate regime. If the government is committed to defending a particular

exchange rate, it would deplete its reserves. Residents increase transfers abroad by foreseeing

devaluation and higher inflation or the imposition of exchange controls when a country faces possibility of a balance-of-payments crisis; immediate corrective policy action is not taken.

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Consequently, funds are shifted abroad, accelerating the erosion of official reserves and precipitating the crisis.

Long run effects: They are seen if the resources are permanently lost by

the home country. Reduction in available resources to finance domestic

investment leads in the short run to a reduction in activity; in the long run to a decline in the rate of capital

formation, thus in the country's growth rate. Reduction in government's ability to tax all the income

earned by its residents.

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Thus, there is an increased need to borrow from abroad; domestic monetary financing (higher long-run inflation

rate).

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To capture the effect of currency substitution, researchers introduce interest rate differential between domestic and foreign

interest rates, or if it is not available; expected rate of depreciation of the exchange rate.

Expected rate of exchange-rate depreciation is proxied by actual rate of depreciation of the exchange rate; deviations from purchasing power parity, with foreign

prices valued at the parallel market rate (Blejer, 1978);

Currency Substitution: The Evidence

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Ramírez-Rojas (1985): differential between the domestic and foreign

inflation rates for Argentina and Mexico; 3-month future price of the U.S. dollar in pesos for

Mexico; differential between the domestic interest rate paid

on deposits denominated in domestic currency for Uruguay;

domestic interest rate paid on foreign-currency deposits for Uruguay;

rate of depreciation of the black market rate

augmented with the foreign inflation rate Phylaktis and

Taylor (1993).

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Evidence supports the existence of significant currency substitution effects in many developing countries.

Some studies use data on domestic foreign-currency deposits.

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Regression equation takes the form:

ln (M/EF) = a0 - a1a + …

+ (1-) ln (M/EF)-1+u,

M and F: domestic and foreign currency holdings;

E: exchange rate;

a: expected rate of depreciation;

u: disturbance term;

0 < <1: speed of adjustment. (9) relates the currency ratio

inversely to expected rate of depreciation; to lagged values of the currency ratio.

(9)

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Inclusion of the inflation rate as an additional regressor is avoided due to the high degree of collinearity between inflation and the rate of depreciation.

Domestic-foreign interest rate differential is sometimes included in the studies of the countries for which data on domestic market-determined rates are available.

Calvo and Végh (1996): (9) tests existence of a dollarization phenomenon rather than currency substitution.

Reason: it does not capture the role of foreign-currency holdings as a medium of exchange.

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In some studies, data on foreign currency deposits held domestically are supplemented by available information on monetary assets held overseas.

Savastano (1992) uses data on foreign-currency deposits both at home and abroad in the United States in his study of currency substitution in Latin America.

In their study of dollarization in Argentina, Kamin and Ericsson (1993) use an estimate of the stock of dollars circulating in that country.

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Agénor and Khan (1996): Data on deposits held abroad by residents of developing

countries and estimate a dynamic, forward-looking model of currency substitution.

Model is developed in two steps. Desired composition of currency holdings is derived

from an optimizing model of household behavior. Actual currency holdings are then determined in a

multiperiod, costs-of-adjustment framework. Complete solution of the model leads to an empirical

specification that incorporates both backward- and forward-looking elements.

Important feature: it does not require information on the domestic interest rate.

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Empirical evidence: foreign interest rate expected rate of depreciation of the parallel market

exchange rate

are important in the choice between domestic money balances and overseas foreign-currency deposits.

Aggregate Supply Functions

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Cross-Regime Tests. Within-Regime Tests. An Assessment of the Evidence.

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Controversy: “New classical” macroeconomics, featuring the Lucas

“surprise” supply function, versus Keynesian “sticky wage” formulations as empirical

approximations to short-run supply behavior. Degree of stickiness of wages and prices depends on

institutional structure of labor markets. Taylor (1980): staggered, overlapping multiperiod wage

contracts cause sticky nominal wages. Corden (1989): less-organized labor markets in

developing countries make Keynesian nominal wage stickiness less likely to be observed.

It may be more feasible to characterize labor markets in developing countries as auction markets.

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Then the Lucas “surprise” short-run aggregate supply function may be relevant for developing countries.

This function postulates a positive relation between output and unexpected movements in prices.

In the Lucas model, workers cannot infer the aggregate price level based on contemporaneously available information.

Policy ineffectiveness proposition in new classical macroeconomics requires the use of rational expectations on the part of economic agents.

Relevance of this mechanism for the formation of expectations has been questioned for developing countries.

Reason: scarcity of information.

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Relevance for developing countries of the policy neutrality proposition associated with new classical macroeconomics and the Lucas supply function.

Tests of the neutrality proposition for developing countries have taken two forms.

Cross-regime tests: empirical plausibility of the “surprise” supply function itself using cross-sectional evidence, following the approach of Lucas (1973).

Within-regime tests: power of anticipated aggregate demand policy to affect the deviation of actual real output from its capacity level, following Barro (1978).

They use time series data for individual countries.

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Cross-Regime Tests If agents know

true distribution of relative prices, average price level, their own selling price

when formulating supply decisions, they face an inference problem.

Reason: their supply choice depends on the unobservable relative price of what they sell.

Optimal forecast of the aggregate price level: weighted average of the price they observe and the mean of the aggregate price level distribution.

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The more variable the nominal demand in the economy, the more agents will interpret an observed increase in their own selling prices as a change in the aggregate price level rather than in relative prices.

Thus, the smaller will be their supply response. “Surprise” supply function:

y = y + (p–pa) + (L)y-1,

y: actual output;

y: “normal” output;

p: actual price level;

pa: expected price level;

: decreasing function of the variance of aggregate demand.

~

~

(10)

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In more unstable aggregate demand regimes, the short-run aggregate supply function will be steeper in the price-output space.

Lucas (1973): small size of in Argentina and Paraguay provided his only two volatile observations.

Williams and Baumann (1986) use nonparametric methods and found significantly different from zero correlation.

Ram (1984) used extended country group and supported the predictions of Lucas's model.

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Jung (1985): Refined Lucas's test by noting that the slope of the

aggregate supply curve in Lucas's model depends on variance of nominal income, but also variance of relative prices, responsiveness of supply to unanticipated changes in

relative prices. Thus, tests tests need to examine the partial correlation

between nominal income variance and the slope of the supply curve.

He found a negative partial correlation. This result is consistent with Lucas's formulation, but the

relationship was statistically weaker for developing.  

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Limitation: these tests do not discriminate among competing hypotheses.

To obtain more definitive results, it is necessary to use a test that can discriminate between these competing models of short-run supply behavior.

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Within-Regime Tests This empirical testing of the Lucas supply function

satisfies this criterion. This test estimates the reduced-form output equation

emerging from a model that incorporates the function as its description of short-run supply behavior (Barro, 1978).

Adding to the supply function (10) an aggregate demand function:

y = (m-p) + Z, > 0,

m: logarithm of the nominal money supply;

Z: vector of other variables that affect aggregate demand.

(11)

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This yields a reduced-form equation for y:

y = y + a1(m-ma) + a2 (Z-Za) + a3(L)y-1,

ma and Za: expected values of m and Z. (12): only unanticipated changes in m and Z can cause y

to deviate from its full-capacity level. This is in contrast to the “sticky wage” Keynesian

formulation. Policy ineffectiveness proposition follows from (12). Reason: systematic aggregate demand policy would be

foreseen by economic agents who know the rule. Thus, it would be incapable of generating unanticipated

changes in m or Z.

(12)~

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Test of the model against the Keynesian alternative involves estimating (12) determining whether anticipated changes in m and Z

add explanatory power to the regression (12) after the unanticipated components have been included.

Because these tests require the specification of anticipated changes in m and Z, the rule governing the behavior of these variables must be estimated jointly with (12).

Because m is a policy variable, and if policy variables are included in Z, these rules imply stable policy regimes.

These tests are therefore within-regime tests of the “surprise” supply function.

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Tests represent joint tests of the “surprise” supply function and the assumed expectations mechanism.

Barro (1979a): link between money growth and output in Mexico, but no strong links in either Brazil or Colombia.

Hanson (1980): Statistically significant small effects of unanticipated

money growth on output in Brazil, Chile, Colombia, Mexico, and Peru.

Different processes explained money growth in different countries.

Not test for the importance of the anticipated unanticipated distinction.

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Edwards (1983): Takes into account the role of fiscal deficits in causing

money growth. Significant effects of money growth (anticipated or not) in

only three of nine Latin American countries.

Canarella and Pollard (1989): Significant effect of unanticipated money growth on real

output, and negative effect on the price level. Significant negative relationship between unanticipated

money growth and its predictability.

Sheehey (1986): More comprehensive set of predictors for monetary

policy.

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His results were not supportive of the Lucas supply function.

Weak negative association between the variance of unanticipated money growth and the effect of unanticipated money on output.

This raises questions about the strength of the cross-regime evidence.

Choudhary and Parai (1991): Estimated reduced-form output equations including

contemporaneous and lagged terms in both unanticipated and anticipated money.

Tested exclusion restrictions on the anticipated money terms.

Found anticipated money had effect.

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Chopra (1985): Estimated a reduced-form price level equation using

aggregate demand as the policy variable. Keynesian formulation: this equation would

contain lagged prices, impose equal coefficients on anticipated and

unanticipated aggregate demand components. Lucas formulation excludes lagged prices and require a

unitary coefficient on anticipated movements in aggregate demand.

Restrictions imposed by the Lucas formulation were consistent with the estimated parameters in 3 out of 13 cases.

In 6 cases these restrictions were rejected in favor of the Keynesian alternative.

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An Assessment of the Evidence Although the cross-regime tests support the Lucas

supply function in developing countries, such tests do not necessarily discriminate against a Keynesian alternative.

Within-regime tests have not always been applied in that way.

Where they have applied, the Keynesian alternative is not easily rejected in developing countries.

Evidence is weak for two reasons: Geographic coverage of this research has been quite

limited, focused on Latin America. Existing within-regime tests use simple “representative”

industrial-country macroeconomic models.

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If the relevant developing-country model is different, then the reduced-form output equation will be misspecified.

Example: if capital mobility is high, anticipated or unanticipated money should not enter a

reduced-form output regression in a “new classical” model,

but fiscal policy and foreign interest rates should. Failure of several of the studies may reflect high capital

mobility not failure of “surprise” supply function. Conclusion: Keynesian features could be defended if

models were generalized to yield reduced-form output equations nesting both classical and Keynesian hypotheses.

AppendixUncertainty, Irreversibility,

and Investment:A Simple Example

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Effects of uncertainty and irreversibility on investment. Risk-neutral firm must decide whether to invest in an

irreversible project at the purchase cost pK in period t = 0. If investment takes place at the beginning of period t = 0,

it will yield a known return of R0 at the end of the period, and then an uncertain return R in every future period.

Given the information available at t = 0, expected value of the future return is E0R.

Net present value of anticipated return stream of cash flows associated with the project is

V0 -pK + (1+r)-iE0 R,R0

(1+r) i=0

(1+r)1

+ [ ]2

r: discount rate.

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V0 -pK +R0 + E0R/r

(1+r)

Rearranging this:

Applying a conventional net present value criterion would suggest that the firm should invest as long as V0 > 0:

rpK: user cost of capital. If investment were fully reversible, then the future would not

matter. Then optimal decision rule: invest today as long as R0 -

rpK > 0.

R0 - rpK +E0R - rpK

r> 0, (A2)

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Irreversibility requires taking into account the difference between expected return and user cost of capital as well.

Although (A2) can hold in an ex ante sense, ex post it may not.

Reason: there is a nonzero probability that in a future period R-rpK < 0.

Thus, firm may be “locked in” an unprofitable venture. Therefore, it has incentives to delay investment in order

to learn more about the factors affecting future return.

How does uncertainty affect (A2)? Consider the case that firm knows for sure that

uncertainty will vanish in t = 1 and that the project's returns for t > 1 will remain constant.

Firm decides not to invest at all today and to invest next period if and only if the realized return exceeds rpK.

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In that case, net present value of the anticipated stream of cash flows will be given by

V1 Pr(R > rpK)

(1+r)-iE0(R | R > rpK)-pK

(1+r) i=0

(1+r)1

+ [ ]2

{ }Pr(R > rpK): probability that the project's return exceeds the cost of capital;

E0(R | R > rpK): expected value of R, conditional on the project's return exceeding the cost of capital.

Comparing the above strategy with the previous case can be done by calculating

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Comparing the above strategy with the previous case can be done by calculating

- (R0-rpK) }

V1 - V0 = (1+r)1

Pr(R > rpK)E0(rpK - R | R rpK)

r{

Firm is better off investing today if V1 - V0 < 0, a condition can be written as

Pr(R rpK)

E0(rpK - R | R rpK)r

(R0 - rpK) >

(A3)

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This equation compares cost of waiting (R0 - rpK), with value of waiting (R rpK).

Expected present value of the mistake is measured by the right-hand side of (A3): mistake is made with probability Pr (R rpK); its expected per-period size, given today's information,

is E0(rpK - R | R rpK); because it accrues every period into the indefinite

future, it has to be multiplied by 1/r to transform it to present value terms.

It pays to invest immediately only if cost of waiting outweighs value of waiting.

Implication of (A3): possibility that in the future R may exceed rpK has no effect on the investment threshold and thus no effect on the decision to invest today.

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Reason for this asymmetry: option to wait has no value in states in which investing would have indeed been the right decision.

This option value of waiting is given by

= max(V1 - V0, 0).

Another implication: increase in the spread of the distribution of future returns that raises the likelihood of “bad” outcomes will raise the critical threshold that the marginal

productivity of capital must reach; thus tend to depress investment.