The Inflation Process

The price level, P, is defined as a geometric average of the price of nontraded goods, P^N, and the price of traded goods, P^T:

with δ measuring the share of traded goods in total expenditure. Taking log differences of equation (1) yields

with Δ denoting the first-difference operator.

Since the economy considered is “small,” the world price of traded goods, Q, is exogenously given and its rate of change in domestic currency is determined by the world rate of inflation, Δlog Q. a weighted average of the rate of change of the official exchange rate, ?log e_t, and the rate of change of the parallel rate, Δlog b_t:

where θ, assumed constant in the short run, denotes the proportion of trade carried through official channels.⁶ The rationale for considering a weighted average of both exchange rates to determine the domestic price of tradable goods is that trade takes place at both the official exchange rate (through official channels) and the parallel market rate (through smuggling). However, in most countries where foreign exchange rationing by the banking system is prevalent, the officially fixed exchange rate is not relevant for the determination of market prices of traded goods. It only measures the rents captured by those (usually the government and a small group of importers) to whom foreign exchange is made available at the official rate. This suggests that the weight attached to the parallel market rate in equation (2) above should be significantly greater than the share of smuggling in total trade, and that econometric estimates of θ should be close to zero and not statistically significant. As shown below, the latter implication is indeed supported by the empirical results.

Since an excess supply of money implies an excess demand for both traded and nontraded goods, by assuming that the excess demand for nontraded goods varies with excess demand throughout the economy, one can postulate the following equation for the rate of change of the prices of nontraded goods:

where m = M/P denotes the real money stock (M denoting the nominal stock of money), m^d is the demand for real cash balances (explained below), and ${\pi }_{t+1/t}\equiv \mathrm{\Delta }\log P_{t+1/t}^a$ is the expectation of the rate of inflation for period t + 1 formed at period t. The coefficient Ф₁, measures the degree to which the prices of nontradable goods move with the expected future level of domestic inflation, and Ф denotes the elasticity of non-traded goods prices to the excess supply of real money balances.⁷ Firms adjust the price of nontradable goods with respect to the price of all goods sold and exchanged in the economy. Accordingly, expected general inflation rather than the expected percentage change in the price index for home goods appears on the right-hand side of equation (3).

Substituting equations (2) and (3) in (1′) yields an expression for the rate of domestic inflation as a function of world inflation, changes in the official and parallel exchange rates, expected inflation, and the rate of ex ante disequilibrium in the money market:

If all goods are traded—that is, δ = 1—then the last two terms in equation (4) disappear, so that the domestic rate of inflation is pegged to the world rate at a composite exchange rate. Also, in the long run the money market is in equilibrium and expected and actual rates of price increase are equal, so that domestic prices grow at the same rate as the rate of change in prices of traded goods (expressed in domestic currency at a composite exchange rate) only if δ/[l—(1 - δ)Ф₁] = 1; that is, if Ф₁ = l.

Parallel Market for Foreign Exchange

The parallel market exchange rate is determined by the interactions between the supply of and the demand for foreign currency in that market. Following Lizondo (1987) and Kharas and Pinto (1989), the model provides a proper distinction between the role of stocks and flows in the behavior of the parallel market exchange rate. The flow market for foreign currency arises out of illegal cross-border transactions in goods and services. The stock of foreign currency is held as part of a diversified portfolio, and is determined by an equilibrium condition akin to that in an asset market.

The flow supply of foreign currency in the parallel market results from the overinvoicing of imports and underinvoicing of exports, the degree of which is assumed to depend on the level of the spread between the official and parallel exchange rates. Formally, the flow supply function can be written as⁸

The flow demand for foreign currency in the parallel market—that is, the demand for foreign currency as a medium of exchange for current account transactions—arises because the monetary authorities cannot satisfy total demand (for legal and illegal transactions) at the official exchange rate. Such demand, denoted by Δlog C^d_t, is positively correlated with overall economic activity (measured by the level of real income) and the deviation of domestic prices from foreign prices, valued at the parallel exchange rate:

The net rate of addition to the stock of foreign currency in private agents’ portfolios, Δlog F_t, is therefore given by

where F denotes total foreign currency holdings by the public.

The portfolio component of foreign currency demand in the parallel market is, as emphasized in the currency substitution literature (see Calvo and Rodriguez (1977) and Ramirez-Rojás (1985)), positively related to the expected rate of return derived by holding this asset and negatively related to the expected rate of return derived from holding alternative assets (domestic currency in this context). The opportunity cost of holding foreign currency is given by the rate of return on domestic money, which is equal to minus the expected domestic inflation rate, ${\pi }_{t/t-1}\equiv \mathrm{\Delta }\log P_{t/t-1}^a$, assuming that expectations are formed at period t—1 for period t. The return from holding foreign money as an asset can be written as the difference between the expected rate of depreciation in the parallel market, $\mathrm{\Delta }\log b_{t/t-1}^a$ and the expected rate of world inflation, $\mathrm{\Delta }\log Q_{t/t-1}^a$ assuming that agents are concerned about the external purchasing power of their holdings of foreign currency. Assuming homogeneity in wealth, equilibrium in the stock market for foreign currency is given by

where

The quantity M_t+b_tF_t measures nominal financial wealth of the public, with foreign currency holdings valued at the parallel market exchange rate.

Using, as an approximation

where 0<τ< 1, equation (8) can be rewritten as

Taking first differences of (9), substituting in (7), and using (5) and (6) yields the following solution for the parallel market exchange rate:⁹

where Ω = 1 + c₁ + c₂ ³0.

Equation (7) indicates that the parallel market rate is positively related to the rate of growth of domestic money supply, the official exchange rate, real output, relative prices, and changes in the expected rates of return on foreign and domestic currencies. The coefficient of the official exchange rate variable will be higher, the higher is the elasticity of (flow) supply of foreign exchange in the parallel market and the lower is the elasticity of (flow) demand for foreign currency in that market.

A higher level of economic activity, a rise in the level of domestic prices relative to foreign prices, or an increase in the rate of change of the expected rate of return on foreign currency holdings will increase the unofficial demand for foreign currency, and this will entail a depreciation of the parallel market exchange rate. A rise in the stock of domestic currency at t, for given expectations, implies a depreciation of the parallel market rate in order to restore portfolio equilibrium.

For given prices and expectations, a devaluation of the official rate reduces on impact the exchange rate differential and therefore the incentive to underinvoice exports and overinvoice imports. The fall in (flow) supply of foreign exchange requires a depreciation of the parallel rate to maintain equilibrium, and this, in turn, reduces (flow) demand, offsetting, in part, the initial upward effect on the free exchange rate. In the short run the parallel rate always depreciates by less than the official rate (since c_t/Ω < 1), so that the exchange rate differential falls. In the long run, however, with Δπ_t/t-1 = Δρ_t/t-1 = 0, the parallel rate depreciates in the same proportion as the official exchange rate, if γ₂ → 0.

The model thus predicts that if relative prices have a negligible effect on the flow demand for foreign currency, there will be an initial fall in the parallel market premium¹⁰ following a devaluation of the official exchange rate and a gradual increase thereafter, leading ultimately to a one-to-one correspondence between the increase in the official and parallel exchange rates. For this long-run neutrality to hold, the statistical estimate of γ₂ must be close to zero and the sum of the estimated coefficients on log b_t-1 and log e_t must be close to unity, a restriction whose validity will be examined in the next section.

The Money Market and Official Reserves

Actual holdings of real money balances m = M/P are assumed to adjust with a lag to the difference between (the logarithm of) desired holdings, m^d, in the current period and (the logarithm of) actual holdings at the end of the previous period. This partial adjustment mechanism can be described as

where v denotes the speed of adjustment.

The demand for real balances is specified as a function of real output, the expected rate of inflation, and the difference between the expected rate of depreciation of the domestic currency in the parallel market and expected world inflation, expectations being formed for period (conditional on information available at t— 1:

The expected inflation rate measures the opportunity cost of money holdings in terms of domestic real assets. As discussed above, foreign exchange is bought and sold in the unofficial market, in part because the public desires to alter the composition of its money holdings. This implies that the expected rate of depreciation of the domestic currency in the parallel market, net of foreign inflation, influences the demand for domestic money. The coefficient of the variable ρ_t/t-1 is expected to be negative. When expectations of a depreciation of the parallel exchange rate are revised upwards, for example, the expected return from holding foreign currency increases and agents tend to substitute foreign money for domestic cash balances as the opportunity cost of holding domestic money rises. This leads to a reduction in the demand for domestic currency in real terms.

From the money supply identity, changes in the stock of money—broadly defined to include currency in circulation, demand deposits, and savings and time deposits—are equal to the sum of changes in net foreign assets of the consolidated banking system, R, and changes in net domestic assets, L:

This relationship can be log-linearized around the sample means and expressed in terms of the rate of change of variables in real terms as

where $k_2=(\stackrel{-}{R}/\stackrel{-}{M})$ and $k_3=(\stackrel{-}{L}/\stackrel{-}{M})$ are, respectively, ratios of the sample means of net foreign assets and net domestic assets to the money supply, lagged by one period.

Substituting equation (11) in (14) and rearranging terms yields an equation that expresses the “required” rate of change of net foreign assets in real terms as a function of monetary imbalances and the rate of change of the real stock of domestic assets:

For a given rate of growth of domestic credit in real terms, equation (15) indicates that in a fixed exchange rate economy, changes in the stock of net foreign assets should occur as long as there is an ex ante disequilibrium between supply and demand in the money market, as emphasized in the monetary approach to the balance of payments (see Frenkel and Mussa (1985) and Wilford (1986)). However, if foreign exchange controls are in place, equation (15) cannot be used to explain actual changes in foreign reserves. To do so, the mechanism by which exchange restrictions are enforced must first be specified. A sensible approach is to modify the model of import restrictions developed by Hemphill (1974), and used subsequently by Lipschitz (1984) and Sundararajan (1986).¹¹ The authorities are assumed to choose the rate at which the banking system can allocate changes in the real stock of foreign exchange, Δlog(R/P)^p_t, so as to minimize the cost of deviations from the “required” rate of change, Δlog(R/P)^r_t as well as the cost of deviations from a “targeted” rate of change of net reserves, Δlog(R/P)^*_t A compromise between these potentially conflictive objectives is reached through a linear allocation scheme:

where 0 ≤ ω ≤ 1 denotes the trade-off parameter. In the standard monetary model, reserves adjust fully to equilibrate current supply and demand in the official exchange market, so that ω = 0. If, on the contrary, it is assumed that the authorities are only concerned about their reserve growth target, then ω = 1. More generally, the above equation indicates that the higher the targeted value of the rate of change of net reserves is, the higher is the allowed increase in reserves by the banking system. Similarly, a rise in the required rate of change of international reserves for balance of payments equilibrium translates into an increase proportional to 1—ω in the rate of change of net foreign assets held by the banking system. Therefore, in the general case where 0 < ω < 1, the assumed behavior of the authorities prevents full equilibrium through reserves adjustment in the official foreign exchange market. The coefficient ω can be conveniently regarded as an implicit measure of the degree of rationing.

In the context of an annual model, changes in the actual rate of growth of international reserves can be assumed to adjust rapidly (within a year) to changes in the rate of growth of allocated external assets, so that Δlog (R/P)_t = Δlog (R/P)^p_t. The targeted rate of growth of net external reserves in real terms is assumed to depend linearly on the level of net foreign assets at t—1:

Equation (17) indicates that the higher is the real level of reserves at t—1, the lower the desired rate of increase for period t. Substituting (15) and (17) into (16) yields

Since k₂ and k₃ are determined from the sample, and since the coefficient v can be estimated separately (see below), a simple test of the foreign exchange rationing scheme outlined above can be implemented by recovering the parameter ω from the regression coefficients in equation (18). The higher this estimate is, the higher the emphasis the authorities put on their reserve target. Conversely, the lower this estimate is, the lower the degree of rationing, or the higher the degree of adjustment between current supply and demand in the official market for foreign exchange.

Real Output

The growth rate of real output is assumed to depend on the lagged deviation of actual output from normal capacity level (treated as exogenous), on the excess stock of real money balances, and on the budget deficit:

with G denoting nominal government expenditure, and T, nominal fiscal revenues. The first term on the right-hand side of equation (19)—the so-called output gap—represents the extent to which producers adjust output to changes in their desired supply. This term implies that when actual output is low relative to normal production capacity, y, its growth rate tends to rise. The second term captures the spillover effects of monetary disequilibrium on output. An excess supply of money induces output effects in the short run, as agents in their attempt to adjust money balances to equilibrium level change their spending and their holdings of financial assets.¹² The third term reflects the effects of fiscal policy on activity. Budget deficits are assumed to have a positive effect on output behavior.¹³ In the long run output is equal to its capacity level, the money market is in equilibrium, and government spending equals fiscal revenues, so that the steady-state growth rate of output is equal to δ₁.

Government Sector

Nominal government expenditure, G, is assumed to be exogenous. Nominal government revenues, T, are specified as a log-linear function of nominal income:

Finally, since money is the only domestic financial asset, the government budget deficit cannot be financed by the public. Rather, it is financed by external borrowing and by domestic borrowing from the central bank. The change in net domestic assets of the banking system is therefore equal to changes in the stock of credit to the private sector, ΔL^p—assumed to be exogenous—plus changes in net credit to the government, which are determined by the budget deficit net of foreign financing (consisting of loans and grants), ΔF^g:

The complete structural model is shown in summary form in Table 2; the variables are defined in Table 3.

Table 2.

Equations of the Model

Table 2.

Equations of the Model

Money demand

$\log m_t^d={\alpha }_0+{\alpha }_1\log y_t-{\alpha }_2{\pi }_{t/t-1}-{\alpha }_3{\rho }_{t/t-1}$

Real output

$\mathrm{\Delta }\log y_t={\Delta }_1-{\Delta }_2\log (y_{t-1}/{\stackrel{-}{y}}_{t-1})+{\Delta }_3[\log m_{t-1}-\log m_t^d]+{\Delta }_4\mathrm{\Delta }\log (G_t/T_t)$

Inflation rate

$\mathrm{\Delta }\log P_t=\theta \Delta \mathrm{\Delta }\log e_t+(1-\tau )\Delta \mathrm{\Delta }\log b_t+\Delta \mathrm{\Delta }\log Q_t+(1-\Delta ){\mathrm{\Phi }}_1{\pi }_{t+1/t}+(1-\Delta ){\mathrm{\Phi }}_2[\log m_{t-1}-\log m_t^d]$

Net foreign assets

$\mathrm{\Delta }\log {(R/P)}_t=[(1-\Omega )k_1/k_2-\Omega k_0]+(1-\Omega )v/k_2[\log m_t^d-\log m_{t-1}]-(1-\Omega )k_3/k_2\mathrm{\Delta }\log (L/P{)}_t-\Omega \lambda \log (R/P{)}_{t-1}$

Parallel market exchange rate

$\log b_t=(1/\mathrm{\Omega })[({\gamma }_0-c_0)+\log b_{t-1}+\mathrm{\Delta }\log M_t+{\mu }_1/(1-\tau )\mathrm{\Delta }{\pi }_{t/t-1}+{\mu }_2/(1-\tau )\mathrm{\Delta }{\rho }_{t/t-1}+{\gamma }_1\log y_t+c_1\log e_t+{\gamma }_2\log (P_t/Q_t)]$

Government revenues

$\log T_t={\beta }_0+{\beta }_1[\log y_t+\log P_t]$

Money supply

$M_t=L_t+R_t$

Domestic credit

$L_t=L_{t-1}+\mathrm{\Delta }{L}_t^p+G_t-T_t-\mathrm{\Delta }{F}_t^g$

Real money balances

$m_t\equiv M_t/P_t$

View Table

Table 2.

Equations of the Model

Money demand

$\log m_t^d={\alpha }_0+{\alpha }_1\log y_t-{\alpha }_2{\pi }_{t/t-1}-{\alpha }_3{\rho }_{t/t-1}$

Real output

$\mathrm{\Delta }\log y_t={\Delta }_1-{\Delta }_2\log (y_{t-1}/{\stackrel{-}{y}}_{t-1})+{\Delta }_3[\log m_{t-1}-\log m_t^d]+{\Delta }_4\mathrm{\Delta }\log (G_t/T_t)$

Inflation rate

$\mathrm{\Delta }\log P_t=\theta \Delta \mathrm{\Delta }\log e_t+(1-\tau )\Delta \mathrm{\Delta }\log b_t+\Delta \mathrm{\Delta }\log Q_t+(1-\Delta ){\mathrm{\Phi }}_1{\pi }_{t+1/t}+(1-\Delta ){\mathrm{\Phi }}_2[\log m_{t-1}-\log m_t^d]$

Net foreign assets

$\mathrm{\Delta }\log {(R/P)}_t=[(1-\Omega )k_1/k_2-\Omega k_0]+(1-\Omega )v/k_2[\log m_t^d-\log m_{t-1}]-(1-\Omega )k_3/k_2\mathrm{\Delta }\log (L/P{)}_t-\Omega \lambda \log (R/P{)}_{t-1}$

Parallel market exchange rate

$\log b_t=(1/\mathrm{\Omega })[({\gamma }_0-c_0)+\log b_{t-1}+\mathrm{\Delta }\log M_t+{\mu }_1/(1-\tau )\mathrm{\Delta }{\pi }_{t/t-1}+{\mu }_2/(1-\tau )\mathrm{\Delta }{\rho }_{t/t-1}+{\gamma }_1\log y_t+c_1\log e_t+{\gamma }_2\log (P_t/Q_t)]$

Government revenues

$\log T_t={\beta }_0+{\beta }_1[\log y_t+\log P_t]$

Money supply

$M_t=L_t+R_t$

Domestic credit

$L_t=L_{t-1}+\mathrm{\Delta }{L}_t^p+G_t-T_t-\mathrm{\Delta }{F}_t^g$

Real money balances

$m_t\equiv M_t/P_t$

Table 3.

Definition of Variables

Table 3.

Definition of Variables

Δ	First-difference operator
b	Parallel market exchange rate
Δlog bat/t-1	Expected rate of depreciation of the parallel market exchange rate, formed at period t—1 for period t
e	Official exchange rate (exogenous)
ΔFg	Foreign financing (including loans and grants) of the budget deficit (exogenous)
G	Nominal government expenditure (exogenous)
L	Domestic credit of the consolidated banking system
LP	Domestic credit to the private sector (exogenous)
M	Nominal money stock
m ≡ M/P	Real money balances
P	Domestic cost of living index
PN	Price index of nontradable goods
PT	Domestic price of tradable goods
πt/t-1	Expected rate of inflation, formed at period t—1 for period t; πt/t-1 ≡ Δlog Pat/t-1
πt+1/1	Expected rate of inflation, formed at period t for period t + 1; πt+1/t ≡ Δlog Pat+1/t
Q	World price of tradable goods (exogenous)
Δlog Qat/t-1	Expected rate of world inflation, formed at period t—1 for period t
R	Net foreign assets, consolidated banking system
ρt/t-1	Expected rate of return on the foreign currency, formed at t - 1 for t; ρt/t-1 ≡ Δlog bat/t-1 - Δlog Qat/t-1
T	Fiscal revenues
y	Real domestic output
Ӯ	Capacity level of real domestic output (exogenous)

View Table

Table 3.

Definition of Variables

Δ	First-difference operator
b	Parallel market exchange rate
Δlog bat/t-1	Expected rate of depreciation of the parallel market exchange rate, formed at period t—1 for period t
e	Official exchange rate (exogenous)
ΔFg	Foreign financing (including loans and grants) of the budget deficit (exogenous)
G	Nominal government expenditure (exogenous)
L	Domestic credit of the consolidated banking system
LP	Domestic credit to the private sector (exogenous)
M	Nominal money stock
m ≡ M/P	Real money balances
P	Domestic cost of living index
PN	Price index of nontradable goods
PT	Domestic price of tradable goods
πt/t-1	Expected rate of inflation, formed at period t—1 for period t; πt/t-1 ≡ Δlog Pat/t-1
πt+1/1	Expected rate of inflation, formed at period t for period t + 1; πt+1/t ≡ Δlog Pat+1/t
Q	World price of tradable goods (exogenous)
Δlog Qat/t-1	Expected rate of world inflation, formed at period t—1 for period t
R	Net foreign assets, consolidated banking system
ρt/t-1	Expected rate of return on the foreign currency, formed at t - 1 for t; ρt/t-1 ≡ Δlog bat/t-1 - Δlog Qat/t-1
T	Fiscal revenues
y	Real domestic output
Ӯ	Capacity level of real domestic output (exogenous)