Inflation in an Open Economy: A Case Study of the Philippines

Ichiro Otani

doi:10.5089/9781451969382.024.A005

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Inflation in an Open Economy: A Case Study of the Philippines

Author: Mr. Ichiro Otani

Publication Date:: 01 Jan 1975

eISBN:: 9781451969382

Language:: English

Keywords:: SP; inflation equation; increase imports; goods price; inflow of imports; adjustment coefficient; Inflation; Export prices; Monetary base; Import prices; Imports

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As price increases have accelerated in a number of countries in the past few years, there has been active discussion of imported inflation in open economies. Several theoretical studies on the subject have appeared,1 but few empirical studies have been made. It has been argued in particular country cases that the recent acceleration of inflation is due largely to external rather than to domestic factors. However, without adequate empirical work, the validity of this argument remains open to question.

Abstract

As price increases have accelerated in a number of countries in the past few years, there has been active discussion of imported inflation in open economies. Several theoretical studies on the subject have appeared,¹ but few empirical studies have been made. It has been argued in particular country cases that the recent acceleration of inflation is due largely to external rather than to domestic factors. However, without adequate empirical work, the validity of this argument remains open to question.

The purpose of this study is to build on the recent theoretical work on imported inflation in an attempt to fill the gap caused by the lack of empirical analysis. Section I deals with the theoretical framework, as applied to the Philippines. In Section II, the model is tested, and a quantification of imported inflation, as well as other sources of inflation, is attempted. Section III summarizes the findings.

I. A Theoretical Framework

specification of the model

The basic model developed in this section is an extension of the macroeconomic models developed by Laidler (1972) and Turnovsky and Kaspura (1974). However, it differs from the Turnovsky and Kaspura model in the relationship it postulates between changes in real output and the price level. Turnovsky and Kaspura assume that the supply of goods and services adjusts to changes in aggregate demand. In the model used here, a quantity theory of money is incorporated to describe explicitly aggregate demand, aggregate supply, and the price adjustment that would clear both the money and the goods markets. Laidler’s (1972) approach to this relationship is essentially the same but not as explicit, since his model does not indicate the exact mechanism through which a change in the money stock would influence the price level.

Some important simplifying assumptions are made. The first is the usual “small country” assumption—that is, the prices of Philippine exports and imports are assumed to be determined in the world market. Second, the model is a short-run flow equilibrium model. The short-run flow equilibrium can be viewed as a temporary state which the system must pass through in the process of achieving a long-run equilibrium. Therefore, it may well be a disequilibrium state compared with the long-run equilibrium position in which both the flow and stock demand are equal to the supplies. The behavioral equations will, therefore, be expressed as adjustment functions.

The model contains three behavioral equations—describing the adjustment process in real cash balances, prices (or output),² and the inflow of imports—and three identity equations—the money supply at the end of the period, the average stock of money during the period, and the general price level (a weighted average of the price indices for domestically produced and consumed goods, exports, and imports).

Real cash balances

The money demand function is the conventional one, containing real income and the expected rate of inflation as explanatory variables. This function usually includes an interest rate variable to represent the opportunity cost of holding money. However, since the concept of broad money is used, and since there is no significant capital market in the Philippines, as in many other less developed countries, the expected rate of increase in the general price level seems to be the best proxy variable for the opportunity cost of holding money.

The desired stock of real money balances is formulated as follows:

\begin{matrix} log {(\frac{M *}{P})}_{t}^{d} = a_{1} + b_{1} log Y_{t} + c_{1} {P^{e}}_{t} + u_{t} & (1) \end{matrix}

where M* is the average stock of nominal money; P is the general price level; Y_t is the level of real income,³ P^e_t is the expected rate of inflation, and u_t is a random variable which is assumed to be normally and independently distributed with zero mean and constant variance; a₁ is a constant, and b₁ and c₁ are parameters which are expected to have the following signs:

b_{1 > 0; c_{1} < 0.}

The expected rate of inflation (P^e_t) is assumed to be generated by an adaptive expectation hypothesis of the following form:

Δ P e_{t} \equiv P e_{t} - P e_{t - 1} \equiv δ (Ṗ_{t - 1} - P e_{t - 1})

where Ṗ_t is the actual rate of inflation in terms of the general price level; δ is the adjustment coefficient and 0 < δ ≤ 1—that is, the adjustment in the expectation in the current period is a function of the gap between the actual and the expected rate of inflation in the previous period. Thus.

{P^{e}}_{t} = Σ_{i = 0}^{\infty} δ {(1 - δ)}^{i} {\dot{P}}_{t - i - 1} .

Hence, the expected rate of inflation can be treated as a predetermined variable in this model.

It is further assumed that the public is unable to adjust its stock of real money balances instantaneously to the desired level, but can do so only partly within a given period. Thus, this relationship is expressed as:

\begin{matrix} Δ \log {(\frac{M *}{P})}_{t} = α [\log {(\frac{M *}{P})}_{t}^{d} - \log {(\frac{M *}{P})}_{t - 1}] & (2) \end{matrix}

where

Δ \log {(\frac{M *}{P})}_{t} = \log {(\frac{M *}{P})}_{t} - \log {(\frac{M *}{P})}_{t - 1}

and α is the adjustment coefficient lying between zero and unity. Substitution of equation (1) in equation (2) yields:

\begin{matrix} Δ log {(\frac{M *}{P})}_{t} = α a_{1} + α b_{1} log Y_{t} + α c_{1} {P^{e}}_{t} - α log {(\frac{M *}{P})}_{t - 1} + α u_{t} & (3) \end{matrix}

General price level

The general price index is a weighted average of the prices of domestically produced and consumed goods and local prices of exports and imports. It is assumed that the local prices of these traded goods are determined by world market prices and the exchange rate. Equation (4) shows the definition of the general price index.

\begin{matrix} P_{t} \equiv a_{2} {Pd}_{t} + b_{2} {Px}_{t} + c_{2} {Pz}_{t} & (4) \end{matrix}

where a₂, b₂, c₂ = weights distributed according to expenditures; a₂ + b₂ + c₂ = 1; Pd_t represents the prices of domestically produced and consumed goods (that is, of nontraded goods); Px_t represents the local prices of exports; and Pz_t represents the local prices of imports.

Relationship between money, income, and the price of nontraded goods

Suppose that the supply of money is increased beyond the level which the public wishes to hold, given the existing level of real income (output) and the price level. It is well known that in a closed economy this condition of an excess supply of money could lead to an increase in prices and/or an increase in real income (output). In the present model of an open economy, it is assumed that both prices and output of domestic goods can rise as the excess supply of money is created in the economy, and that they in turn increase imports, as import prices fall relative to the prices of the nontraded goods. It can be shown that in a very simple form, the rate of change in the prices of output is a function of the gap (in log) between the short-run equilibrium level of output and the “normal” (long-run) level of output.⁴ Thus, this relationship can be expressed as follows:

\begin{matrix} Δ log {Pd}_{t} = b_{3} (log Y_{t} - log {\bar{Y}}_{t}) & (5) \end{matrix}

where Y_t is the actual supply of output, Ȳ_t is the “normal” level of output, which is increasing at a constant rate over time,⁵ and b₃ can be interpreted as the slope of the supply schedule. As b₃ approaches zero, the short-run supply elasticity with respect to prices is so large that the short-run output can increase beyond the normal level with little increase in prices. Since the actual rate of inflation is influenced by factors other than the gap between the short-run output and the normal level of output, a more realistic specification is necessary. By including the expected rate of inflation and higher costs of inputs, such as imported raw materials, the inflation equation can be modified as follows:

\begin{matrix} Δ log {Pd}_{t} = a_{2} + b_{3} (log Y_{t} - log {\bar{Y}}_{t} + c_{3} {P^{e}}_{t} + d_{3} Δ log {Pz}_{t} + v_{t}) & (6) \end{matrix}

The coefficients in this equation are expected to have the following signs: a₃ ≷ 0, b₃ > 0, c₃ > 0, and d₃ > 0. Note that v_t is a random error term, like u_t in equation (1).

This equation is very similar to those developed by Laidler (1972) and Turnovsky and Kaspura (1974) and is used by many researchers investigating price determination in an open economy.

Imports

The demand for imports is specified as a function of the actual level of income and relative prices, i.e., the ratio of the prices of domestic goods to that of imports.

\begin{matrix} log {Z^{d}}_{t} = a_{4} + b_{4} log Y_{t} + c_{4} log {(\frac{Pd}{Pz})}_{t} + w_{t} & (7) \end{matrix}

where Z_t is the volume of imports, and w_t is a random error term. Both b₄ and c₄ are expected to have positive signs. It is further assumed that even though the world supply schedule for a small country such as the Philippines is infinitely elastic with respect to prices determined in the world market, the country is not able to import all it wishes within a given period, because of various factors. Importers must go through certain administrative procedures to obtain licenses for imports, and international transportation of goods takes time. Therefore, it is hypothesized that only a part of the desired level of imports will arrive within a given period. The change in imports in a given period is then a function of the gap between the desired level of imports in the current period and the actual level of imports in the previous period.⁶

\begin{matrix} Δ log Z_{t} = λ (log {Z^{d}}_{t} - log Z_{t - 1}) & (8) \end{matrix}

where λ is the adjustment coefficient, and lies between zero and unity. Substituting equation (7) in equation (8) yields the following:

\begin{matrix} Δ log Z_{t} = λ a_{4} + λ b_{4} log Y_{t} + λ c_{4} log {(\frac{Pd}{Pz})}_{t} - λ log Z_{t - 1} + λ w_{t} & (9) \end{matrix}

Average money stock and changes in the money stock

The average stock of money during a period is defined as a simple arithmetic mean of the stocks at the end of the previous period and at the end of the current period. The change in the stock of money during the period is defined as the sum of changes in the domestic factors affecting the money stock and in foreign factors. These relationships are expressed in equations (10) and (11).

\begin{matrix} {M^{*}}_{t} \equiv 0.5 (M_{t} + M_{t - 1}) & (10) \end{matrix}

\begin{matrix} Δ M_{t} \equiv Δ C_{t} + X_{t} {Px}_{t} - Z_{t} {Pz}_{t} + Δ {Kf}_{t} & (11) \end{matrix}

where M*_t, Z_t are as defined earlier; M_t is the actual supply of nominal money at the end of the period; C is the domestic credit of the banking system, and is exogenously determined by the monetary authorities; X_t is the volume of exports which is dependent on foreign factors alone; and Kf_t is the net capital stock owned by foreigners in the Philippines, not counting for this purpose the net foreign assets of the Philippine banking system, and is assumed to be exogenously controlled by the government authorities. The expression X_t Px_t – Z_t Pz_t + ΔKf_t then represents the change in the net foreign assets of the banking system.

Thus, the model contains six endogenous variables: Y, M*, M, P, Pd, and Z; and seven exogenous variables: P^e, Px, Pz, Ȳ, C, X, and Kf. A summary of the model is given in Table 1.

Table 1.

Structural Relationships of the Model

the effects of imported inflation

In the model used here imported inflation can arise in two ways: (1) inflation arising from an increase in the world market prices of exports, and (2) inflation arising from higher world market prices of imports. Depending on the case, inflation will be transmitted to the domestic economy through different channels and in different degrees. Therefore, it may be useful to trace each channel briefly.

Effects of higher export prices

The initial impact of higher export prices would be felt in the general price level and the balance of payments. Since export prices are a component of the general price index, their rise will be reflected in an increase in the general price level. At the same time, the higher prices may, and most likely will, bring about an increase in export receipts, thus increasing the stock of money in a short run. The directions of the secondary and final effects are difficult to determine, even though the channel of transmission is quite clear. They depend on the relevant elasticities.

Suppose that higher export prices lead initially to an increase in real cash balances. The initial increase in real cash balances may be greater or less than the level which the public wishes to hold, given the level of real income (output). Let us suppose that real cash balances increase beyond the desired level. Since there is an excess supply of real cash balances, the level of output would have to increase in order to clear the money market. Suppose that the necessary higher level of output exceeds the normal level of output, which is increasing over time at a constant rate; then, domestic prices will increase. As the level of output and the domestic price level both increase, the inflow of imports also increases. This in turn offsets the initial improvement in the balance of payments position and the initial increase in the stock of money. If the offset is less than full, the equilibrium levels of money stock, output, prices, and imports will all be higher than the previous levels. If the offset is more than full, the equilibrium level of money stock will be lower, while those of output and prices may be higher or lower than the previous ones.

Effects of higher import prices

There are three channels through which the impact of higher import prices will be transmitted initially. First, unless the price elasticity of the demand for imports is more than unity, import payments rise. Second, the cost of imported materials for domestic production will increase, exerting upward pressure on the prices of domestically produced goods. Third, the general price level will rise, since import prices are a component of it.

Since the initial decline in the money stock indicates an excess supply of goods and since the normal level of output is increasing over time, the negative gap between the short-run output and the normal level of output will become larger. This in turn exerts a downward pressure on domestic prices (and thus on the general price level) and offsets the direct effects of an increase in import prices. The final price level of domestic goods may be higher or lower than the initial level. The new equilibrium level of output may or may not be greater than the previous one, depending on the elasticity of money stock with respect to import prices.

II. Empirical Study

The structural parameters of the behavioral equations can now be estimated. The short-run effects of imported inflation and of other changes in the relevant exogenous variables will then be analyzed. Similar analyses in steady-state conditions will also be discussed.

estimation

Since the model is nonlinear (but linear in parameters) and the system is simultaneous, equations (i), (iii), and (iv) in Table 1 are estimated by the two-stage least-squares method,⁷ using annual data for the period 1950–73. The results are given in Table 2, and the actual and fitted values are plotted in Chart 1.

Table 2.

Estimates of Behavioral Equations¹

^¹Figures in parentheses are t-ratios. Durbin-Watson statistics should not be taken at face value for well-known reasons.

For estimating the behavioral equations, the lagged value of the rate of inflation in terms of the general price level was used as a proxy for the expected rate of inflation. This is based on the assumption that the adjustment coefficient of the adaptive expectation hypothesis is unity.⁸

In the real cash balance equation (i′) in Table 2, all coefficients have the expected signs. The adjustment coefficient indicates that it would take, ceteris paribus, about two years before the actual level of real cash balances adjusted to 95 per cent of the desired level. The so-called long-run income elasticity is estimated to be about 1.46; this is consistent with a declining trend in income velocity, which fell to about 3 in the 1970s from about 4 in the early 1950s. The coefficient of P^e_t indicates that the absolute value of elasticity increases as the expected rate of inflation rises, with the result that the higher the expected rate of inflation, the greater the proportionate decline in the demand for real cash balances.⁹ Chart 1 shows that the estimated equation traces major swings quite well, even though it misses some of the minor changes.

The inflation equation (iii′) in Table 2 contains a lagged variable of the actual rate of inflation on the same grounds as were discussed in the case of equation (i′). The coefficients of P^e_t and Δlog Pz_t have the right signs and are highly significant. The estimated coefficient of the term (log Y_t – log Ȳ_t) is found to be less significant but still has the right sign. The initial impact elasticity of domestic inflation with respect to import price increases is found to be about 0.6, while with respect to the above-normal output condition and the expected rate of inflation it is about 0.2 and 0.3, respectively. The constant term, an effect of the time trend, is insignificant and can be regarded as zero. The estimated equation performs better in tracing price changes than the real cash balance equation does for its changes. However, it does not pinpoint the swings of minor magnitude with precision.

The import flow adjustment equation (iv′) also has the right signs for the estimated coefficients. The coefficient of the lagged import volume indicates that the adjustment coefficient is 0.68; this implies that about 70 per cent of the gap between the desired level of imports demanded in the current period and the actual level of imports in the previous period is adjusted within one year, and that it would take about three years before 95 per cent of the gap is closed. The long-run income and price elasticities are found to be about 1.5 and 0.9, respectively. An inspection of the fitted and actual values in Chart 1 indicates that the import equation performs as well in tracking movements of the dependent variables as does the equation for the rate of inflation and changes in real cash balances. However, we should not conclude from this observation that the model as a whole performs as well. The general performance of the model will be discussed in the following section.

Simulation

In order to examine how well the model as a whole traces actual movements in the economy, a simulation exercise was carried out by making use of the reduced form of the structural equations, together with the estimated coefficients. Since the system is nonlinear, a linear approximation of the system in terms of growth rates of the variables was obtained in the following matrix form:¹⁰

A Y = B X

where A is a 6 X 6 coefficient matrix for endogenous variables whose row vector is Y’ = (Ṁ^*, Ṗ, Ẏ, Ṗd, Ṁ, Ż), and B is a 6 × 13 coefficient matrix for the predetermined variables whose row vector is X’ = (Ẋ, Ṗx, Ṗz, $\dot{\bar{Y}}$ , Ċ, ΔP^e, Ṁ^*_t-1, Ṗ_t-1, Ṗd_t-1, Ṗz_t-1, Ṁ_t-1, Ż_t-1 1). All the variables are the same as described earlier, and the dot (·) represents percentage changes in the variable. The reduced form matrix obtained from the estimated structural equations, together with the identity equations, is shown in Table 3.¹¹

Table 3.

Reduced Form Linear Approximation of the Nonlinear System¹

^¹All the figures represent elasticities of endogenous variables with respect to predetermined variables, except for ΔP^e; + 0 represents a small positive number; and -0 represents a small negative number.

Table 3.

Reduced Form Linear Approximation of the Nonlinear System¹

Endogenous Variables	Predetermined Variables
Endogenous Variables	Ẋ	Ṗx	Ṗz	$\dot{\bar{Y}}$	Ċ	ΔP^e	Ṁ^{ -1}*	Ṗ_-1	Ṗd_-1	Ṗz_-1	Ṁ_-1	Ż_-1	1
Ṁ^*	0.24	0.27	–0.08	+0	0.43	–0.07	0.04	–0.04	–0.01	0.01	0.37	–0.08	–0.02
Ṗ	0.03	0.16	0.51	–0.13	0.05	0.22	–0.01	0.01	0.62	–0.38	0.04	–0.01	–0
Ẏ	0.18	0.09	–0.48	0.11	0.32	+0	–0.01	0.10	–0.52	0.32	0.18	–0.06	–0.02
Ṗ_d	0.04	0.02	0.52	–0.19	0.07	0.32	–0.02	0.02	0.89	–0.55	0.06	–0.01	–0
Ṁ	0.45	0.51	–0.14	+o	0.82	–0.12	0.07	–0.07	–0.02	0.01	–0.05	–0.16	–0.04
Ż	0.20	0.10	–0.77	–0.01	0.36	0.20	–0.11	0.11	0.03	–0.02	0.30	0.25	–0.02

Table 3.

Reduced Form Linear Approximation of the Nonlinear System¹

Endogenous Variables	Predetermined Variables
Endogenous Variables	Ẋ	Ṗx	Ṗz	$\dot{\bar{Y}}$	Ċ	ΔP^e	Ṁ^{ -1}*	Ṗ_-1	Ṗd_-1	Ṗz_-1	Ṁ_-1	Ż_-1	1
Ṁ^*	0.24	0.27	–0.08	+0	0.43	–0.07	0.04	–0.04	–0.01	0.01	0.37	–0.08	–0.02
Ṗ	0.03	0.16	0.51	–0.13	0.05	0.22	–0.01	0.01	0.62	–0.38	0.04	–0.01	–0
Ẏ	0.18	0.09	–0.48	0.11	0.32	+0	–0.01	0.10	–0.52	0.32	0.18	–0.06	–0.02
Ṗ_d	0.04	0.02	0.52	–0.19	0.07	0.32	–0.02	0.02	0.89	–0.55	0.06	–0.01	–0
Ṁ	0.45	0.51	–0.14	+o	0.82	–0.12	0.07	–0.07	–0.02	0.01	–0.05	–0.16	–0.04
Ż	0.20	0.10	–0.77	–0.01	0.36	0.20	–0.11	0.11	0.03	–0.02	0.30	0.25	–0.02

The method of simulation is to multiply the coefficient matrix by the vector of the actual values of all the predetermined variables; the results represent estimated values of all the endogenous variables. Charts 2 through 4 show the actual and simulated values of the endogenous variables in terms of percentage changes for the period 1951–73.

Chart 2 shows that the model traces reasonably well the major changes in the rate of inflation in the early 1950s and late 1960s through the 1970s, even though it misses some turning points of minor magnitude.¹² The model performs better in explaining the rate of inflation in terms of the general wholesale price index than in terms of prices of domestic goods. This is to be expected, since the general wholesale price index contains export and import prices as its components, while the equation for prices of domestic goods contains import prices as a cost-push factor.

Chart 3 shows that the model traces changes in the average stock of money very well, especially since 1960, but that it tends to exaggerate the changes in the 1950s. The model’s performance in explaining changes in the money stock on a year-end basis is generally similar. However, estimated changes tend to be more exaggerated in the case of year-end money stocks than in the case of average stocks. The poor performance in the 1950s seems to have been caused by the assumption of the constant ratio of nominal value of imports to money stock and nominal value of exports to money stock (lagged by one period), which tended to have more variation in the 1950s than in the 1960s.

Chart 4 shows that the model performs poorly in explaining the real sector of the economy; this was to be expected, since the model was designed to explain imported inflation. Thus, the model appears to perform quite satisfactorily in explaining inflation.

Short-run analysis

The effects of an increase in export quantum due to higher world demand is shown in the first column of Table 3. As expected, it has a very small effect on prices (the elasticities being 0.03 for the general price level and 0.04 for domestic goods prices). However, it has a considerable impact on the money stock, whose elasticity is estimated to be 0.45 (the average stock of money having an elasticity of 0.24). To a lesser extent, a higher export quantum also tends to increase output and the volume of imports, whose elasticities are estimated to be 0.18 and 0.20, respectively.

A rise in export prices has the same effect on endogenous variables as does export quantum, insofar as the direction of impact is concerned, but the magnitudes are quite different. General prices are affected with an elasticity of 0.16 (roughly the same magnitude as the weight attached to export prices for computing the general price index), but the prices of domestic goods are barely affected (the elasticity being 0.02). The rise in export prices also increases output, which, together with the rise in domestic goods prices, increases the demand for, and thus the inflow of, imports. The impact of an increase in export prices on the stock of money is found to be roughly the same as that of an increase in export quantum.

The effects of higher import prices depend not only upon the rate of increase, but also on the magnitude of changes in the rate. The elasticities of Ṗz_t and Ṗz_t-1 in Table 3 can be rearranged in the following way:

Suppose that import prices increased by 10 per cent in the current year after having been stable in the previous two years (Ṗz_t = 10, Ṗz_t-1 = 0). Both the general price index and domestic prices would increase by about 5 per cent; real output and inflow of imports would decline by about 5 and 8 per cent, respectively. It is interesting to note that even though the short-term direct price elasticity of imports is about 0.7 (a 1 per cent rise in the import price leading to a 0.7 per cent decline in the import flow), the total impact elasticity, allowing for changes in endogenous variables, such as domestic prices and output, is estimated to be about 0.8. The rise in the magnitude of the elasticity is mainly due to the negative feedback effect on imports of a decline in output. Since the price elasticity of imports is less than unity, a rise in import prices leads to an increase in import payments and, ceteris paribus, causes a decline in the stock of money.

A rise in the long-run output contributes to an increase in the short-run output, with an elasticity of 0.11, and leads to a decline in prices. The increase in output raises the demand for imports, but a decline in prices of domestic goods offsets this in large part, so that the inflow of imports declines only slightly and the stock of money increases only slightly.

An increase in the domestic credit of the banking system raises the stock of money significantly (an elasticity of 0.82). At the same time, it encourages an increase in imports and domestic production (with elasticities of 0.36 and 0.32, respectively). The impact of credit expansion on prices is found to be rather small, a 10 per cent increase in domestic credit leading to a 0.5 per cent rise in the general price level and a 0.7 per cent increase in the prices of domestic goods. This small impact of domestic credit expansion is due primarily to price rigidity in the economy or to a price elastic short-run supply schedule, the elasticity being estimated at about 5.¹³ However, the interpretation should be treated with caution and it should not be concluded from this finding that any rate of credit expansion would lead to a higher growth rate of output. As pointed out in footnote 4, credit expansion leading to increased demand for output beyond the full employment limit would result in an increase in prices only. Also, the model’s poor performance in tracing changes in output makes it difficult to ascertain the true elasticity of the supply schedule.

In the 1960s, the Philippines experienced a moderate rate of inflation (always less than 10 per cent per annum) in terms of the general wholesale price index, as well as in terms of domestically produced and consumed goods. However, the rate of inflation accelerated quite rapidly in the 1970s. Table 4 shows that, in general, purely external factors¹⁴ exerted an upward pressure during the 1960s, except in 1967 and 1968, while domestic factors exerted a small downward pressure in most years. In 1970, the average exchange rate of the peso per U. S. dollar increased by about 60 per cent, and the depreciation is estimated to have contributed a 15 per cent increase in the prices of domestically produced and consumed goods in that year. The effect of domestic factors and the lagged endogenous variables in 1970 was estimated to be a slight reduction in the prices of domestic goods in that year. However, the rate of inflation in 1971 was largely explained by the lagged effects of the past inflation, among other variables.

Table 4.

Factors Affecting Inflation¹

^¹In percentage points.

^²In terms of wholesale price index of domestically produced and consumed goods.

^³Effects of X, Px, and Pz.

^⁴Effects of Ȳ and C.

Table 4.

Factors Affecting Inflation¹

		Contribution of
Year	Rate of Inflation²	External factors³	Lagged endogenous variables	Domestic factors⁴	Residuals
1951	9.5	12.3	2.1	–0.4	–4.5
1952	–6.2	–6.0	1.6	–0.5	–1.3
1953	–2.0	–2.7	–6.3	–0.3	7.3
1954	–5.2	–1.4	3.8	–0.3	–7.3
1955	–1.4	–2.4	–4.8	0.6	5.2
1956	1.9	4.6	2.4	–0.3	–4.8
1957	3.9	2.5	–0.2	0.9	0.7
1958	2.4	2.1	1.7	–0.5	–0.9
1959	–1.8	4.4	0.5	–0.5	–6.2
1960	4.8	3.5	–6.2	–1.0	8.5
1961	4.7	2.8	2.6	1.1	–1.8
1962	2.0	5.1	2.6	–0.2	–5.5
1963	8.4	4.2	–2.5	0.7	6.0
1964	6.8	0.8	7.5	—	–1.5
1965	2.5	1.0	4.5	–0.6	–2.4
1966	5.7	1.2	1.6	–0.1	3.0
1967	2.3	—	6.4	0.4	–4.5
1968	1.4	–0.6	2.2	–0.3	0.1
1969	1.7	1.6	2.0	—	–1.9
1970	19.7	16.1	—	–0.3	3.9
1971	16.7	7.1	11.4	–0.3	–1.5
1972	11.6	3.9	7.5	—	0.2
1973	16.6	14.0	6.7	—	–4.1

^¹In percentage points.

^²In terms of wholesale price index of domestically produced and consumed goods.

^³Effects of X, Px, and Pz.

^⁴Effects of Ȳ and C.

Table 4.

Factors Affecting Inflation¹

		Contribution of
Year	Rate of Inflation²	External factors³	Lagged endogenous variables	Domestic factors⁴	Residuals
1951	9.5	12.3	2.1	–0.4	–4.5
1952	–6.2	–6.0	1.6	–0.5	–1.3
1953	–2.0	–2.7	–6.3	–0.3	7.3
1954	–5.2	–1.4	3.8	–0.3	–7.3
1955	–1.4	–2.4	–4.8	0.6	5.2
1956	1.9	4.6	2.4	–0.3	–4.8
1957	3.9	2.5	–0.2	0.9	0.7
1958	2.4	2.1	1.7	–0.5	–0.9
1959	–1.8	4.4	0.5	–0.5	–6.2
1960	4.8	3.5	–6.2	–1.0	8.5
1961	4.7	2.8	2.6	1.1	–1.8
1962	2.0	5.1	2.6	–0.2	–5.5
1963	8.4	4.2	–2.5	0.7	6.0
1964	6.8	0.8	7.5	—	–1.5
1965	2.5	1.0	4.5	–0.6	–2.4
1966	5.7	1.2	1.6	–0.1	3.0
1967	2.3	—	6.4	0.4	–4.5
1968	1.4	–0.6	2.2	–0.3	0.1
1969	1.7	1.6	2.0	—	–1.9
1970	19.7	16.1	—	–0.3	3.9
1971	16.7	7.1	11.4	–0.3	–1.5
1972	11.6	3.9	7.5	—	0.2
1973	16.6	14.0	6.7	—	–4.1

^¹In percentage points.

^²In terms of wholesale price index of domestically produced and consumed goods.

^³Effects of X, Px, and Pz.

^⁴Effects of Ȳ and C.

The sharp acceleration in the rate of inflation in 1973 was due largely to purely external factors, although the lagged independent variables also exerted a substantial upward push. Domestic factors are seen to have exerted no pressure on prices in that year.

Long-run analysis

The short-run analysis in the previous section was limited by the difficulty in successfully delineating the effects of external and domestic factors on inflation. This was mainly due to the inclusion in the model of the lagged independent variables. However, this difficulty will be greatly reduced in long-run analysis, since the system reaches a dynamic equilibrium in the long run.¹⁵ For this purpose, let us assume that the system has reached a steady-state equilibrium. More specifically, the following assumptions are made:

(1) The rate of inflation is constant for both the general wholesale price index and the prices of domestically produced and consumed goods.

(2) The world rate of inflation is constant and uniform for all traded goods; that is, the rate of increases in the price of exports and imports in the world market is the same (Ṗx_t = Ṗz_t).

(3) Exports increase at a constant rate.

(4) Domestic credit increases at a constant rate.

These assumptions also imply that:

(5) Actual and long-run output grow at the same constant rate—Ẏ_t = ${\dot{\bar{Y}}}_{t}$ , and the rate of growth in the average stock of money and the end-of-year stock of money is the same—Ṁ^*_t = Ṁ_t.

(6) There is no change in the expected rate of inflation—ΔP^e_t = 0.

Under these assumptions, the system of equations shown in Table 1, together with the estimated structural parameters and their reduced form, will be as follows:

\begin{matrix} {\dot{M}}_{t} - {\dot{P}}_{t} = 1.46 {\dot{\bar{Y}}}_{t} & (1') \end{matrix}

\begin{matrix} {\dot{P}}_{t} - 0.694 \dot{P} d_{t} = 0.294 \dot{P} z_{t} & (2') \end{matrix}

\begin{matrix} 0.68 {\dot{Z}}_{t} - 0.61 \dot{P} d_{t} = 0.99 \dot{\bar{Y}} - 0.61 \dot{P} z_{t} & (4') \end{matrix}

\begin{matrix} 0.95 {\dot{M}}_{t} + 0.6 {\dot{Z}}_{t} = {\dot{C}}_{t} + 0.55 {\dot{X}}_{t} - 0.05 \dot{P} z_{t} - 0.05 & (6') \end{matrix}

The first column of Table 5 indicates that autonomous economic growth, ceteris paribus, leads to a decline in prices, both in the general price level and in that of domestically produced and consumed goods with elasticities of –1.3 and –1.9, respectively. This decline also reduces imports. As a result, the stock of money increases; this, together with the decline in prices, satisfies the public’s increased need for real cash balances.

Table 5.

Reduced Form of the Steady-State Model

Table 5.

Reduced Form of the Steady-State Model

Endogenous Variables	Exogenous Variables
Endogenous Variables	${\dot{\bar{Y}}}_{t}$	Ṗx_t and Ṗz_t	Ẋ_t	Ċ_t	1
Ṁ_t	0.1	0.42	0.32	0.58	–0.03
Ṗ_t	–1.3	0.42	0.32	0.58	–0.03
Ṗd_t	–1.9	0.17	0.46	0.84	–0.04
Ż_t	–0.2	–0.74	0.41	0.75	–0.04

Table 5.

Reduced Form of the Steady-State Model

Endogenous Variables	Exogenous Variables
Endogenous Variables	${\dot{\bar{Y}}}_{t}$	Ṗx_t and Ṗz_t	Ẋ_t	Ċ_t	1
Ṁ_t	0.1	0.42	0.32	0.58	–0.03
Ṗ_t	–1.3	0.42	0.32	0.58	–0.03
Ṗd_t	–1.9	0.17	0.46	0.84	–0.04
Ż_t	–0.2	–0.74	0.41	0.75	–0.04

World inflation, ceteris paribus, leads to domestic inflation, with elasticities of less than unity. Therefore, the prices of domestic goods decline relative to those of imported goods, and imports decline as well. The rate of increase in the money stock is found to be equal to the rate of increase in the general price level; therefore, real cash balances remain unchanged.

The growth of exports leads to increases in both the general price level and the prices of domestic goods. It also increases imports and the stock of money. Domestic credit expansion also raises the stock of money, prices, and imports.

III. Concluding Remarks

The purpose of this study has been to extend and test a model of inflation in an open economy in the spirit of Laidler (1972), McCallum (1973), and Turnovsky and Kaspura (1974). The estimated behavioral equations of the model generally describe movements in the demand for real cash balances, output, prices, and imports in the Philippines during 1951–73. The model as a whole traced rates of inflation and changes in the money stock quite well, but traced changes in output and imports poorly. This was not unexpected, since the model is designed to investigate inflation rather than the real sector.

Because of the inclusion of lagged endogenous variables in this model, it was difficult to separate clearly the effects of domestic and external factors on the price level in the short run. However, it appears that in most years before 1973, external factors played a small role in the price increases that occurred in the Philippines. In contrast, the large price increase in 1973 was attributable mainly to external factors, and the inflation of that year was thus largely imported.

Under long-run steady-state conditions, credit expansion appears to play no part in influencing real output,¹⁶ but it increases prices and imports considerably. However, these implications of credit expansion for output, prices, and imports in the steady-state condition should be interpreted cautiously, since the present study is not based on a growth model.

APPENDIX: Derivation and Approximation of the Nonlinear System

This Appendix provides a brief summary of the derivation of the linear approximation of the nonlinear system that is used in the text. The dot (·) and delta (Δ) represent the percentage change and the first difference.

Estimated Demand Function for Money

The first difference in equation (i′) after transformation (Table 2) is:

\dot{M} *_{t} - {\dot{P}}_{t} = 1.21 {\dot{Y}}_{t} - 0.29 Δ P e_{t} + 0.17 \dot{M} *_{t - 1} - 0.17 {\dot{P}}_{t - 1}

General Price Index

Equation (ii) of Table 1 can be rewritten as:

\frac{Δ P}{P} = a_{2} \frac{Pd}{Pd} \frac{Pd}{P} + b_{2} \frac{Δ Px}{Px} \frac{Px}{P} + c_{2} \frac{Δ Pz}{Pz} \frac{Pz}{P}

where a₂ = 0.694, b₂ = 0.157, and c₂ = 0.149.

Pd/P, Px/P, and Pz/P are variables in a strict sense. However, for the period considered in this study, it remained remarkably stable; standard deviations of these ratios are shown below.

Thus, the mean values are used as constant parameters.

Domestic Price Equation

The first difference of equation (iii′) of Table 2 is:

\dot{P} d_{t} - \dot{P} d_{t - 1} = 0.21 ({\dot{Y}}_{t} - \dot{{\bar{Y}}_{t}}) + 0.32 Δ {P^{e}}_{t} + 0.62 (\dot{P} z_{t} - \dot{P} z_{t - 1})

Import Equation

The first difference of equation (iv’) of Table 2 is:

{\dot{Z}}_{t} = 0.99 {\dot{Y}}_{t} + 0.61 \dot{P} d_{t} - 0.61 \dot{P} z_{t} + 0.32 {\dot{Z}}_{t - 1}

Average Money Stock

Equation (v) of Table 1 can be rewritten as follows:

\frac{Δ M^{*}}{{M^{*}}_{t}} = 0.5 \frac{Δ M_{t}}{M_{t}} \cdot \frac{M_{t}}{{M^{*}}_{t}} + 0.5 \frac{Δ M_{t - 1}}{M_{t - 1}} \frac{M_{t - 1}}{{M^{*}}_{t}}

For the period considered in this study, the mean and standard deviation of the ratios Mt/M^*_t, and M_t-1/M*_t are shown below.

Therefore, these mean values are treated as constant parameters.

Change in the Stock of Money

Equation (vi) of Table 1 can be rewritten as follows:

\frac{Δ M_{t}}{M_{t}} = \frac{Δ C_{t}}{C_{t}} \frac{C_{t}}{M_{t}} + \frac{X_{t} {Px}_{t}}{M_{t}} - \frac{Z_{t} {Pz}_{t}}{M_{t}} + \frac{Δ {Kf}_{t}}{{Kf}_{t}} \frac{{Kf}_{t}}{M_{t}} .

Let X_tPx_t/M_t = W_t. Then Ẇ_t = Ẋ_t + Ṗx_t - Ṁ_t.

Since W_t = (1 + Ẇ_t)β, where β = (XPx/M)_t-1 then

\frac{X_{t} {Px}_{t}}{M_{t}} = (1 + {\dot{X}}_{t} + \dot{P} x_{t} - {\dot{M}}_{t}) β .

Similarly,

\frac{Z_{t} {Pz}_{t}}{M_{t}} = (1 + {\dot{Z}}_{t} + \dot{P} z_{t} - {\dot{M}}_{t}) γ

where γ = (ZPz/M)_t-1.

Let $α = \frac{C_{t}}{M_{t}} and δ = \frac{{Kf}_{t}}{M_{t}}$ .

\frac{Δ M_{t}}{M_{t}} = {\dot{M}}_{t} = α {\dot{C}}_{t} + (1 + {\dot{X}}_{t} + \dot{P} x_{t} - {\dot{M}}_{t}) β - (1 + {\dot{Z}}_{t} + \dot{P} z_{t} - {\dot{M}}_{t}) γ + δ \dot{K} f_{t} .

The mean and standard deviation of these ratios are shown below.

The value of δ is not obtainable due to lack of data, but it is assumed to be very small or negligible.

The reduced form result of all these transformed equations as an approximation of the nonlinear system is expressed in the matrix form in Table 3.

Data Description

The data used in this study were obtained from the Data Fund of the International Monetary Fund.

BIBLIOGRAPHY

Amemiya, Takeshi, “The Non-Linear Two-Stage Least-Squares Estimator,” Journal of Econometrics, Vol. 2 (September 1974), pp. 105–10.
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Cagan, P., “The Monetary Dynamics of Hyper-inflation,” in Studies in the Quantity Theory of Money, edited by Milton Friedman (University of Chicago Press, 1956), pp. 25–117.
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Edgerton, David L., “Some Properties of Two-Stage Least Squares as Applied to Non-Linear Models,” International Economic Review, Vol. 13 (February 1972), pp. 26–32.
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Friedman, Milton, A Theoretical Framework for Monetary Analysis (National Bureau of Economic Research, New York, 1971), a study based on two papers: “A Theoretical Framework for Monetary Analysis,” and “A Monetary Theory of Nominal Income,” which appeared in the Journal of Political Economy, Vol. 78 (March/April 1970), pp. 193–238, and Vol. 79 (March/April 1971), pp. 323–37, respectively.
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Harberger, Arnold C., “Some Notes on Inflation,” in Inflation and Growth in Latin America, edited by Werner Baer and Isaac Kerstenetzky (Homewood, Ill., 1964), pp. 319–51.
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Kelijian, Harry H., “Two-Stage Least Squares and Econometric Systems Linear in Parameters but Non-Linear in Endogenous Variables,” Journal of the American Statistical Association, Vol. 66 (June 1971), pp. 373–74.
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Khan, Mohsin S., “Experiments with a Monetary Model for the Venezuelan Economy,” Staff Papers, Vol. 21 (July 1974), pp. 389–413.
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Laidler, David E., “Price and Output Fluctuations in an Open Economy” (unpublished, December 1972).
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Laidler, David E., “Simultaneous Fluctuations in Prices and Output—A Business Cycle Approach,” Económica, Vol. 40 (new series) (February 1973), pp. 60–72.
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Laidler, David E., “The Influence of Money on Real Income and Inflation: A Simple Model with Some Empirical Tests for the United States, 1953–72,” Manchester School of Economics and Social Studies, Vol. 41 (December 1973), pp. 367–95.
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McCallum, B. T., “Friedman’s Missing Equation: Another Approach,” Manchester School of Economics and Social Studies, Vol. 41 (September 1973), pp. 311–28.
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Mundell, Robert A., Monetary Theory: Inflation, Interest and Growth in the World Economy (Pacific Palisades, California, 1971).
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Parkin, J. M., “Inflation, the Balance of Payments, Domestic Credit Expansion and Exchange Rate Adjustments” in National Monetary Policies and the International Financial System, edited by Robert Z. Aliber (University of Chicago Press, 1974), pp. 49–63.
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Shinkai, Yoichi, “A Model of Imported Inflation,” Journal of Political Economy, Vol. 81 (July/August 1973), pp. 962–71.
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Silveira, Antonio M., “The Demand for Money: The Evidence from a Brazilian Economy,” Journal of Money, Credit, and Banking, Vol. 5, Part 1 (February 1973), pp. 113–40.
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Toyoda, Toshihisa, “Price Expectations and the Short-Run and Long-Run Phillips Curves in Japan, 1956–68,” Review of Economics and Statistics, Vol. 54 (August 1972), pp. 267–74.
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Turnovsky, S. J., and André Kaspura, “An Analysis of Imported Inflation in a Short-Run Macro-Economic Model,” Canadian Journal of Economics, Vol. 7 (August 1974), pp. 355–80.
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Mr. Otani, an economist in the Asian Department, is a graduate of the University of California at Berkeley and the University of Minnesota. In addition to colleagues in the Fund, the author is indebted to Professor Findlay of Columbia University for his helpful comments. However, the author is solely responsible for the views expressed.

For example, see Harberger (1964), Mundell (1971), Laidler (1972), Shinkai (1973), Parkin (1974), and Turnovsky and Kaspura (1974).

Friedman (1971) shows that adjustment functions in prices and output are mutually dependent. Therefore, one is a mirror image of the other.

Y_t can be regarded as the level of income that will clear the money market, given the real cash balances. See McCallum (1973) for a similar application.

The concept of “normal output” used in this study differs from the concept of full-employment output in that it takes into account the fact that the elasticity of output in an economy begins to decline considerably before full employment is reached. Thus, we postulate a zone in which both output and prices rise in response to an increase in demand. The concept of “normal output” relates to the lower boundary of this zone while that of full employment relates to the upper boundary. An increase in demand beyond this upper boundary does not bring forth increased output but results in an increase in prices only.

The rationale for this specification is as follows. Assume that the “normal” (long-run) level of output is dependent on the Cobb-Douglas type of production function, whose factors of production, capital, and labor grow at a constant rate over time: that is, Ȳ_t = A₀K^β_t L^(1-β)_t

$\begin{array}{l} w h e r e & K_{t} = K_{0} e^{a t} a n d L_{t} = L_{0} e^{b t} . \\ T h e r e f o r e, & {\bar{Y}}_{t} = B_{0} e^{(α β + b (1 - β)) t} \\ w h e r e & B_{0} = A_{0} . K_{0} . L_{0}, \end{array}$

and accordingly Ȳ_t is a function of the time trend alone. Actual level of output (Y_t) can deviate from the normal level of output (Ȳ_t) when the real interest rate or wage rates deviate from trend value of the respective variable. Since the nominal interest and wage rates can be reasonably assumed to be fixed institutionally in most of the less developed countries, such as the Philippines, the actual output can increase beyond the normal level of output only if an increase in the prices make the real interest or wage rates less than the trend values that are consistent with the normal level of output.

This type of specification is also adopted by Khan (1974).

Since all the behavioral equations satisfy the order condition for identifiability, the two-stage least-squares method modified for the nonlinear system can be shown to yield a consistent estimator. See Edgerton (1972). See also Kelijian (1971) and Amemiya (1974) for the property of two-stage least-squares used to estimate a model with nonlinear variables but linear parameters.

Recall that ΔP^e_t ≡ P^e_t - P^e_t-1 = δ(Ṗ_t-1 - P^e_t-1). Therefore, if δ = 1, P^e_t = Ṗ_t-1. The validity of this assumption in an annual model is supported by a number of studies. See, for example, Toyoda (1972) and Silveira (1973).

This interpretation is consistent with Cagan’s (1956) specification of the demand function.

The detailed derivation of the linear system in growth rates is shown in the Appendix. Kf is neglected, since the share of Kf in the stock of money would be very small or negligible.

The reduced form matrix is obtained by A^-1B.

Laidler (1973) experienced similar results in his study of inflation in the U. S. economy.

This is a reciprocal of the estimated coefficient for (log Y_t - log Ȳ_t). This magnitude is considerably smaller than that estimated for the schedule in the United States by McCallum (1973), who estimates it to be about 25, while the coefficient of (log Y_t - log Ȳ_t) is about 0.04.

This excludes the effects of the depreciation of the peso in the early 1960s and 1970s.

It can be shown that a 6 × 6 matrix (say, H) of reduced form coefficients of the lagged endogenous variable converges to 0 in the long run— $lim_{t \to δ} H^{t} = 0.$ In our case, H^t ≃ 0 when t = 40.

See assumption (5) above under Long-run analysis. Because of this assumption, the implication of credit expansion for the long run is somewhat biased.

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IMF Staff papers: Volume 22 No. 3

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1975: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969382

ISSN:: 1020-7635

Pages:: 292

DOI:: https://doi.org/10.5089/9781451969382.024

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Philippines: Percentage Change in Real Cash Balances, Domestic Prices, and Imports

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Philippines: Actual and Simulated Percentage Rate of Inflation

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Philippines: Actual and Simulated Percentage Change in Money Stock

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Philippines: Actual and Simulated Percentage Change in Output and Imports

	Mean	Standard Deviation
Pd/P	1.00	0.016
Px/P	0.938	0.078
Pz/P	1.00	0.053

	Mean	Standard Deviation
Pd/P	1.00	0.016
Px/P	0.938	0.078
Pz/P	1.00	0.053

	Mean	Standard Deviation
M_t/M_t*	1.06	0.039
M_t-1/M_t*	0.94	0.039

	Mean	Standard Deviation
M_t/M_t*	1.06	0.039
M_t-1/M_t*	0.94	0.039

YN	=	nominal gross domestic product
P	=	general price level (wholesale prices)
Pd	=	wholesale price index of domestically produced and consumed goods
Px	=	wholesale price index of exports
Pz	=	wholesale price index of imports
P^e	=	expected rate of inflation in terms of P (=Ṗ_t-1)
Mz	=	nominal value of imports in national income account
Xn	=	nominal value of exports in national income account
M	=	stock of total liquidity
NFA	=	net foreign assets of the banking system
C	=	domestic credit of the banking system
Y	=	YN/P
Z	=	Mz/Pz
X	=	Xn/Px
ΔKf	=	ΔNFA -Xn + Mz
Ȳ	=	trend value of Y (obtained by a regression of the following form Ȳ = Ae^gt)
M*	=	(M + M_t-1)/2

(i′)	$\begin{matrix} Δ \log {(\frac{M }{P})}_{t} = \underset{(- 3.92)}{- 4.77} + \underset{(4.01)}{1.21} \log Y_{t} \underset{(- 2.73)}{- 0.29} {P^{e}}_{t} \underset{(- 3.94)}{- 0.83} \log {(\frac{M }{P})}_{t - 1} \\ \begin{matrix} {\bar{R}}^{2} = 0.34 & D - W = 1.05 \end{matrix} \end{matrix}$
(iii′)	$\begin{matrix} Δ \log {Pd}_{t} = \underset{(- 0.04)}{- 0.004} + \underset{(1.00)}{0.21} (\log Y_{t} - \log {\bar{Y}}_{t}) + \underset{(6.69)}{0.32} {P^{e}}_{t} + \underset{(6.25)}{0.62} Δ \log {Pz}_{t} \\ \begin{matrix} {\bar{R}}_{2} = 0.77 & D - W = 1.97 \end{matrix} \end{matrix}$
(iv′)	$\begin{matrix} Δ \log Z_{t} = \underset{(- 2.78)}{- 4.27} + \underset{(3.51)}{0.99} \log Y_{t} + \underset{(0.78)}{0.61} \log {(\underset{Pz}{Pd})}_{t} \underset{(- 3.69)}{- 0.68} \log Z_{t - 1} \\ \begin{matrix} {\bar{R}}_{2} = 0.42 & D - W = 1.54 \end{matrix} \end{matrix}$

(i′)	$\begin{matrix} Δ \log {(\frac{M }{P})}_{t} = \underset{(- 3.92)}{- 4.77} + \underset{(4.01)}{1.21} \log Y_{t} \underset{(- 2.73)}{- 0.29} {P^{e}}_{t} \underset{(- 3.94)}{- 0.83} \log {(\frac{M }{P})}_{t - 1} \\ \begin{matrix} {\bar{R}}^{2} = 0.34 & D - W = 1.05 \end{matrix} \end{matrix}$
(iii′)	$\begin{matrix} Δ \log {Pd}_{t} = \underset{(- 0.04)}{- 0.004} + \underset{(1.00)}{0.21} (\log Y_{t} - \log {\bar{Y}}_{t}) + \underset{(6.69)}{0.32} {P^{e}}_{t} + \underset{(6.25)}{0.62} Δ \log {Pz}_{t} \\ \begin{matrix} {\bar{R}}_{2} = 0.77 & D - W = 1.97 \end{matrix} \end{matrix}$
(iv′)	$\begin{matrix} Δ \log Z_{t} = \underset{(- 2.78)}{- 4.27} + \underset{(3.51)}{0.99} \log Y_{t} + \underset{(0.78)}{0.61} \log {(\underset{Pz}{Pd})}_{t} \underset{(- 3.69)}{- 0.68} \log Z_{t - 1} \\ \begin{matrix} {\bar{R}}_{2} = 0.42 & D - W = 1.54 \end{matrix} \end{matrix}$

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Abstract

I. A Theoretical Framework

specification of the model

Real cash balances

General price level

Relationship between money, income, and the price of nontraded goods

Imports

Average money stock and changes in the money stock

the effects of imported inflation

Effects of higher export prices

Effects of higher import prices

II. Empirical Study

estimation

Simulation

Short-run analysis

Long-run analysis

III. Concluding Remarks

APPENDIX: Derivation and Approximation of the Nonlinear System

Estimated Demand Function for Money

General Price Index

Domestic Price Equation

Import Equation

Average Money Stock

Change in the Stock of Money

Data Description

BIBLIOGRAPHY

Same Series

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