Article

Experiments with a Monetary Model for the Venezuelan Economy

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1974
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This paper outlines the theoretical framework and presents the results of a short-term model constructed for forecasting the Venezuelan economy. The explicit purpose was to provide a relatively simple aggregate demand model that would forecast the behavior of key macro-economic variables in Venezuela and would also show the effects of monetary policy on these variables. Since the model centers on the monetary aspects of income and balance of payments determination, it can be described as a “monetary model.”1

The distinguishing characteristic of the monetary approach reflected in this model is the emphasis on how the money supply affects economic activity. In a closed economy, the money supply (or at least the monetary base) can be regarded as a policy instrument, and the monetary approach focuses on the effect on output and prices of changes in this instrument. In an open economy such as the Venezuelan, however, the money supply (or the monetary base) is no longer determined by policy, because changes in it can be brought about through balance of payments surpluses and deficits. The domestic component of the money stock (domestic credit) then becomes the appropriate instrument of monetary policy. A monetary model thus attempts to analyze two questions in the context of an open economy: (1) What are the effects on aggregate demand of changes in the domestic component of the money supply? and (2) What are the effects of changes in aggregate demand on domestic income and the balance of payments, and thereby the level of reserves?2

The model described in this paper is used to analyze these two questions. It is designed explicitly for forecasting the components of the balance of payments and nominal income, with no attempt to split this latter variable into its components of prices and real output.3 Being specified at a highly aggregate level, containing only nine equations, the model can justifiably be criticized for its inadequacy in explaining or describing the Venezuelan economy. However, since this model aims to provide short-term forecasts, it seems appropriate to maintain a simple framework. Ideally, of course, there should be no conflict between an explanatory model and a forecasting model, because a model that explains an economy well should also forecast well. Unfortunately, this is not necessarily the case in practice, for aggregative simple models tend to outperform larger disaggregated ones (Fair, 1971), especially because smaller models appear to have smaller random errors (Friend and Jones, 1964).

The model specified is a linear one and has been estimated on an annual basis for the period 1950-72. The fact that data on key economic variables, such as gross domestic product, are not available for intervals smaller than one year precluded the construction of a quarterly model. Specifying the model in linear terms, it will be shown, leads to tractable solutions without too great a sacrifice in realism. Generally, the true test of a model (in this particular case, the only test) is its ability to predict the behavior of certain variables. Two types of projections have been made: (1) a simulation of the values of income and the balance of payments over the period 1950-72, and (2) a forecast of the values of all endogenous variables for 1973.

The model is specified in terms of levels of variables rather than changes, except for capital flows, and is autoregressive in nature (using, in part, trend relationships). As a result, there is some concern about the ability of the model to forecast turning points, especially in the case of nominal income forecasts. Calculations are therefore made of the within-sample predictions of changes in nominal income to determine to what extent sharp fluctuations are noted by the model. The results, though indicative, should not be accepted as proof of the ability of the model to forecast turning points ex ante, as it is quite probable that the model does not have such ability. This appears to be a general problem with econometric models, including large-scale ones constructed for the United States (Fair, 1971). Turning points are perhaps better dealt with by utilizing outside information of a subjective nature.

From a narrow view then, it is possible that this model can only provide knowledge of the consistency of forecasts made by more informal, subjective methods, but even this ability is useful. The method of forecasting used here and the judgments of policymakers are not mutually exclusive, since judgments which have to be made about the behavior of exogenous variables will be reflected in the forecasts produced by the model. In fact, both methods should be used together. There is no reason to forecast mechanically, if it is believed that changes from previous trends will take place.

Section I describes the basic model, while Section II summarizes it. The results obtained from estimating the model are discussed in Section III. Section IV shows how the impact multipliers are calculated, and presents both within-sample simulations and forecasts beyond the sample. The concluding section summarizes the results of the paper. The method of estimation is described in the Appendix.

I. Description of the Model

The model specified for Venezuela contains six behavioral relationships—the value of imports, private domestic expenditure (in current prices), government expenditure (in current prices), private short-term capital flows, the demand for money, and the supply of money. There are also three identities—gross domestic product (in current prices), the balance of payments (or the change in the value of international reserves of the Banco Central de Venezuela), and the monetary base. Each of these is discussed in turn.

value of imports

The demand for nominal imports is specified as a linear function of private expenditure in current prices and the price of imports:

where Mt is the value of nominal imports in period t, AEt is aggregate private expenditure in period t, and PMt is the price of imports in period t. The variable ut is used to capture the effects of unexplained random fluctuations;4a0 is a constant and a1 and a2 are the estimated parameters, which would be expected to have the following signs:

a1 > 0; a1 < 0

The reasoning in favor of this type of formulation is that a rise in domestic demand for all goods, including foreign, would lead to an increase in demand for imports (Mundell, 1971; Laffer, 1968) and that a rise in import prices would result in a decrease in demand as imports become more expensive. Generally, domestic prices would also be included in the function on the assumption of substitution between foreign and domestic goods, but such prices have been relatively constant in Venezuela and thus have been excluded.5

As actual imports may adjust to demand with a lag, an adjustment is specified to the effect that imports change in period t according to the difference between demand for imports in period t and the actual value of imports in the previous period:

where ΔMt = MtMt-1 and α is the adjustment coefficient lying between zero and unity. As α approaches unity, the adjustment of actual imports to demand is almost instantaneous (in this case, within a year); as α approaches zero, actual imports are never equal to demand and there is always unsatisfied demand in the market. Within these extremes, the adjustment is asymptotic. The specification of this type of adjustment function introduces an explicit distributed lag into the import relationship. Equation (2) can also be written as:

where ω = 1-α and L is the lag operator, LXt = Xt-1. This is the general form of a distributed lag relationship with geometrically declining weights.

Substituting equation (1) in equation (2) and solving for the value of imports, the estimating equation is derived:

which differs basically from equation (1) because the lagged value of imports appears on the right-hand side of the equation. This new equation is used in the estimation.

private domestic expenditure

In the standard Keynesian model of a closed economy, aggregate private expenditure (consumption plus investment expenditure) depends on the level of income and the rate of interest (on long-term bonds). The familiar IS-LM framework shows the channels through which a change in monetary policy affects expenditure by changing the interest rate and thereby affecting investment expenditure. Rather than introducing a single interest rate, which represents the yield on only one asset, it may be more appropriate to include all liquid assets as a determinant of private expenditure. Since the public has a desired stock of liquid assets (which in Venezuela would be represented mainly by the stock of money), a change in money supply would create an excess demand or supply of this stock of money and this would cause changes in expenditures while the public was attempting to restore or get rid of cash balances to re-establish its desired position. Nominal income also has an impact on expenditures and is thus included in the function.

“Desired” private expenditure is therefore specified as a linear function of nominal income and the stock of money:

where AE*t is aggregate private expenditure (in current prices) in time period t, GDPt is gross domestic product (also in current prices) in period t, and MOt is the stock of cash balances in period t; vt is a random error term.

Since it is assumed that private expenditure will increase as income and the stock of money rise, the parameters are expected to have the following signs:

b1 > 0; b2 > 0.

The liquid assets variable (MO) that is included in equation (4) is defined as “broad money,” comprising currency, demand deposits, and time and savings deposits at commercial banks.

Actual expenditures in period t are assumed to adjust to the difference between desired expenditures in period t and actual expenditures in period t-1:

where β is assumed to fall between zero and unity:

0 < 0 ≤ 1.

Substituting equation (4) in equation (5) to eliminate the unobservable variable (“desired” private expenditure, AE*t) and solving for AEt yields the equation to be estimated:

government expenditure

Since a very large proportion of government revenue in Venezuela is derived from taxes on petroleum exports,6 government expenditure can be related to the value of exports:

where GE*t is desired government expenditure (in current prices) and Xt is the value of exports in time period t; wt is a random error term.

It is expected that government expenditure will rise as the value of exports rises:

c1 > 0.

Since exports are assumed to be determined outside the model, this part of the model is in a strict sense decomposable—that is, it can be treated separately from the rest of the model.

Actual government expenditure is assumed to adjust to the difference between desired expenditure in period t and actual expenditure in period t-1.

By substituting equation (7) in equation (8), eliminating GE*t and solving for GEt, the following equation is obtained:

short-term capital flows

One of the recent problems in Venezuela has been the large inflow of private short-term capital. Over the period 1950-70, short-term capital flows (including net errors and omissions in the balance of payments accounts) came to a net outflow averaging approximately $100 million annually; in 1971 and 1972, there were inflows of $300 million to $400 million. The present model will attempt to explain the movement of private capital in and out of Venezuela during the period 1950-72.

Capital flows are assumed to be a linear function of changes in the Venezuelan interest rate, the foreign interest rate, domestic income, and foreign income. Since most of these capital flows take place between Venezuela and the United States,7 the foreign variables are assumed to be U. S. variables. As 1971 was a special year in terms of speculative movements of capital, a dummy variable is included to capture the sharp inflow into Venezuela for that year:

where ΔKt is private short-term capital inflows (excluding the oil and iron sectors and including net errors and omissions), ΔRVZt is the change in the Venezuelan interest rate, ΔRust is the change in the U. S. prime rate, ΔGDPt is the change in Venezuelan income, and ΔYust is the change in U. S. gross domestic product (in current prices). D1 is a dummy variable taking on a value of one in 1971 and zero otherwise; et is a random error term.

The function states that an increased rate of change in the Venezuelan interest rate and income variable leads to an increased inflow of private capital, while an increase in the rate of change of the corresponding U. S. variables results in an outflow. The theoretical pattern of signs is thus:

d1 > 0; d2 < 0; d3 > 0; d4 < 0.

The coefficient of the dummy variable has a positive sign.

the demand for money

The aggregate demand for money balances is generally specified as a function of income and the cost of holding money. This cost is not a direct cost but an “opportunity cost”; it represents the income that an individual has to give up when he chooses to hold money rather than to hold an interest-yielding asset. As such, this cost can be represented by the interest rate.

In this model, the demand for money is specified as a linear function of the interest rate and a concept defined as “permanent income.” Individuals are assumed to adjust their money holdings to a longer-run concept of what they expect their income to be, rather than to current income:

where PYt is permanent income (in current prices)8 and all other variables are defined as before; d refers to demand. It is expected that

k1 < 0; k2 > 0.

Since the interest rate is assumed to adjust so as to equilibrate the money market, the function is rewritten in inverse form, on the assumption that MOdt = MOt:

where f0=k0k1;f1=1k1;f2=k2k1..

Since k1 < 0 and k2 > 0, the expectation is that f1 < 0 and f2 > 0. The variable zt is a random error term.

the supply of money

The supply of money (MO) is specified basically as a behavioral function of the monetary base (reserve money). It is assumed that the supply of money (broad money, as previously defined) in period t is a linear function of reserve money (RM) in period t, period t-1, period t-2, and so on, following the pattern:

where 0 ≤ λ ≤ 1.

By applying a Koyck transformation to equation (8),9 an estimating equation can be obtained:

where η = εt − λ εt-1.

The variable m1 is the money multiplier and is really a function of variables such as income and the rate of interest (Burger, 1971). In the estimation of equation (13), an implicit assumption is made that m1 is constant. On an annual basis, this multiplier was not strictly constant in Venezuela over the period 1950-72, but it followed a fairly stable trend. It may thus not be too unrealistic to assume constancy in the multiplier for the purposes of this analysis.10

nominal income

The level of GDP in current prices is equal to aggregate nominal private expenditures plus the value of exports, plus nominal government expenditure, and minus the value of imports:

The value of exports is assumed to be exogenous to the model, essentially because petroleum and petroleum products dominate aggregate exports, and the behavior of petroleum volume and prices can be assumed to be exogenous, or at least to be determined by policy in the short run. The volume is determined by supply conditions—for example, the length and life of reserves and the rates of investment and exploitation. Prices (or at least fiscal export values) are determined by government authorities and negotiation (Escobar, 1973).

balance of payments

The balance of payments equation (15) is identically equal to the change in net foreign asset holdings of the banking system:

where NFAt is the net foreign asset holdings of the Banco Central de Venezuela. (The commercial and other banks in Venezuela hold very small amounts of foreign assets.) COBt is a variable that includes on a net basis all items in the balance of payments accounts other than the trade balance and short-term capital flows (as described in short-term capital flows, above).

monetary base (reserve money)

The stock of reserve money (RM) is equal to the stock of net foreign assets plus the stock of net domestic assets of the Banco Central de Venezuela:

where NDAt is the stock of net domestic assets of the Banco Central de Venezuela. This variable includes the net claims of the Banco Central de Venezuela on the Government and on state and commercial banks. NDA represents the basic monetary tool in this model, and monetary policy is assumed to be effected through changes in this variable.

II. Statement of the Model

Comprising the structural equations for imports, private expenditure, government expenditure, short-term capital flows, the rate of interest, and money supply—along with the identities for GDP, the balance of payments, and reserve money—the basic monetary model for Venezuela for the period 1950-7211 may be set forth as follows:

The variables are described below.

endogenous variables12
M=nominal value of imports of goods
AE=private aggregate expenditure, in current prices; generated by the equation AE = GDP - X - GE + M
GE=government expenditure, in current prices
ΔK=net private short-term capital flows, including net errors and omissions but excluding the oil and iron sectors
RVZ=weighted average interest rate charged on loans by commercial banks in Venezuela
MO=money supply, plus quasi-money (demand deposits, plus time and savings deposits)
GDP=gross domestic product, in current prices
ΔNFA=change in net foreign assets of the Banco Central de Venezuela
RM=reserve money
exogenous variables13
PM=price index of unit value of imports (1968 = 100)
X=value of exports, in current prices
ΔRus=change in U. S. prime rate
ΔYus=change in U. S. gross domestic product, in current prices
D1=dummy variable for speculative capital inflows in 1971
PY=permanent nominal gross domestic product, in current prices14
COB=net items in the balance of payments accounts, other than the trade balance, short-term private capital inflows, and net errors and omissions; generated by the equation COB = ΔNFAX + M − ΔK
NDA=net domestic assets of the Banco Central de Venezuela; generated by the equation NDA = RMNFA
Mt-1=imports lagged one year
AEt-1=private expenditure lagged one year
GEt-1=government expenditure lagged one year
RVZt-1=Venezuelan interest rate lagged one year
GDPt-1=gross domestic product lagged one year
MOt-1=money supply lagged one year

The operations for the model can be seen in the accompanying flow chart (Chart 1), which outlines the causal sequence of an expansionary monetary policy (that is, an increase in the stock of net domestic assets of the Banco Central de Venezuela) under the assumption that all other exogenous variables are constant. This process is discussed in a causal sequence only for expository purposes, as the effects actually take place simultaneously.

Chart 1.Flow Chart of Monetary Model for the Venezuelan Economy

An increase in NDA will increase the stock of reserve money (RM), as well as the stock of money balances in the economy (MO), since the multiplier (MULT) is assumed to be constant. This increase in money supply will have two effects; it will increase private expenditure (AE) and lower the rate of interest (RVZ). The increase in private expenditure will raise the level of GDP, but it also will lead to a higher level of imports (M), which in turn will reduce GDP. Assume that there is a rise in GDP and this increases private expenditure further and also generates capital inflows (ΔK). At the same time, however, capital outflows tend to occur because of the lower rate of interest in Venezuela. If these outflows exceed the inflows, then the stock of net foreign assets (NFA) of the Banco Central de Venezuela will decline, and there will also be a further decline because of the rise in imports. As NFA declines, the stock of reserve money will also decline, and the process outlined above will be reversed.

III. Structural Equation Estimates

The model set forth in the preceding section was estimated for the period 1950-72 on an annual basis. The method of estimation, which was full-information maximum likelihood, is described in the Appendix. Table 1 shows the values of the estimated coefficients for each of the six behavioral equations, along with the ratio of each estimated coefficient to its standard error. This ratio can be interpreted as following a “quasi-T” distribution, although it is asymptotic normal. The coefficient of determination (R2) is also calculated for each equation. However, this statistic should be interpreted with care, as its properties are not the same as the R2 calculated in ordinary least squares,15 and it should be viewed only as an information statistic. The standard error (SE) of estimate for each equation is also presented, and the same reservations apply to it. Data definitions and sources have been noted in the preceding section.

Table 1.Structural Equation Estimates1
Imports
Mt=1.254(2.13)+0.188(5.47)AEt0.165(2.76)PMt+0.271(2.02)Mt1R2=0.954SE¯=0.421
Aggregate private expenditure
AEt=2.446(2.01)+0.078(2.05)GDPt+1.339(7.40)MOt+0.352(3.45)AEt1R2=0.984SE¯=1.101
Government expenditure
GEt=0.919(1.65)+0.403(6.09)Xt+0.643(7.40)GEt1R2=0.975SE¯=0.471
Short-term capital flows
ΔKt=0.088(0.10)+0.428(8.87)ΔRVZt0.011(2.14)ΔRust+0.030(1.45)ΔGDPt0.040(1.72)ΔYust+2.659(5.35)D1R2=0.861SE¯=0.211
Rate of interest
RVZt=1.573(0.34)5.500(8.57)MOt+1.556(8.04)PYtR2=0.835SE¯=0.399
Money supply
MOt=1.807(5.23)+2.313(14.27)RMt+0.375(7.10)MOt1R2=0.994SE¯=0.305
Gross domestic product
GDPt = AEt + Xt + GEt - Mt
Balance of payments
ΔNFAt = Xt - Mt + COBt + ΔKt
Reserve money
RMt = NFAt + NDAt

The numbers in parentheses below the coefficients are ratios of the coefficient to its standard error. The coefficient of determination (R2) is also calculated. See text for equations.

The numbers in parentheses below the coefficients are ratios of the coefficient to its standard error. The coefficient of determination (R2) is also calculated. See text for equations.

In the import equation (1), as expected, private expenditure has a positive effect and the price of imports has a negative effect on the level of imports. Both estimated coefficients are significantly different from zero at the 5 per cent level. The size of the expenditure coefficient implies that an increase in private expenditure of, say, 1 million bolívares, would lead to an increase in imports of about 200,000 bolívares. The estimated coefficient of lagged imports has the expected positive sign and is also significantly different from zero at the 5 per cent level. Since this coefficient is (1 - α), the indicated result is α = 0.729; and, although the adjustment of imports is fast, it is not instantaneous. The fit of the equation is good, since about 95 per cent of the variation of nominal imports is explained.

Both nominal GDP and the stock of money appear to exert a positive effect on aggregate private expenditure. The estimated coefficients are significantly different from zero at the 5 per cent level and have the expected signs. A rise in nominal income of 1 million bolívares would increase nominal expenditure by 78,000 bolívares, while a similar rise in the money stock would increase expenditure by almost 1.5 million bolívares. The coefficient of the lagged dependent variable (AEt-1) is also significantly different from zero at the 1 per cent level and has the expected sign. This result implies that the coefficient of adjustment is significantly different from unity and that private expenditure takes about two years to adjust to a desired level. The fit of this equation is good, as R2 is equal to 0.984.

Nominal government expenditure is strongly influenced by the value of exports, as expected. Both of the estimated coefficients are significantly different from zero at the 1 per cent level, and the two variables explain government expenditure very well.

All five estimated coefficients in the short-term capital flow equation have the expected signs. Changes in the Venezuelan interest rate result in large changes in capital flows, and the estimated coefficient is highly significant. Changes in the U. S. prime rate have a much smaller impact, although the coefficient is still significant. Both of the income variables—changes in Venezuelan GDP and changes in U. S. GDP—appear to be statistically insignificant. The dummy variable does yield a coefficient that is significantly different from zero at the 1 per cent level. Given the erratic nature of private capital flows, the 86 per cent variation explained by the equation is very good.

In the money demand equation, the estimated coefficients of the stock of money and permanent income are significant and have the expected negative and positive signs, respectively. The coefficient of the money stock seems unusually large, however, and there appears to be no easy explanation of this. The general fit of this equation is also relatively poor.

The impact of the monetary base on the money supply is positive and fairly strong. The estimated coefficient has a very low standard error, as does the estimated coefficient of lagged money supply. The latter coefficient also has the correct positive sign. The size of the estimated money multiplier is fairly close to the average value of the multiplier over the period. The fit of this equation is exceedingly good, since 99 per cent of the variation in the money stock is explained.

The model in general appears to be well specified. Out of the 17 coefficients estimated, all were found to have the expected signs. With the exception of two (in the capital flow equation), all were statistically significant at least at the 5 per cent level.

IV. Forecasts of the Model

This section presents two sets of forecasts, both within and outside the sample. For this purpose, impact multipliers are first calculated.

impact multipliers

The reduced form of the model, expressing the endogenous variables in terms of the lagged endogenous and exogenous variables, was calculated from the structural equations estimated.16 This is the basic advantage of specifying the equation system so that it has linear variables, and an inverse of the matrix of coefficients can be obtained with relative ease. In dynamic analysis terms, the reduced-form coefficients are called “impact multipliers” and they measure the immediate response of the endogenous variables to changes in the exogenous (policy-determined) variables. From the reduced form of the present model, for example, the immediate effect of a change in monetary policy (through a change in the net domestic asset holdings of the Banco Central de Venezuela) on the mean value of nominal GDP or the mean value of the change in international reserves can easily be determined. These reduced-form equations, however, do not directly determine how the system would behave under continuous impact of changes in exogenous variables.

The reduced form of the model is shown in Table 2.17 It relates the 9 endogenous variables to the 15 exogenous variables. Consider, for example, a rise in the value of exports of 10 million bolívares. According to the model, this would increase imports by 1.5 million bolívares, private expenditure by 9 million bolívares, government expenditure by 4.0 million bolívares, the money stock by 4.8 million bolívares, and GDP by 20.5 million bolívares. It would raise capital inflows by 4 million bolívares and the interest rate by 26.1 per cent, as well as improving the balance of payments and increasing the stock of reserve money by 2.1 million bolívares. Similarly, the model indicates that an increase of 10 million bolívares in net holdings of domestic assets by the Banco Central de Venezuela would increase imports by 1.2 million bolívares, private expenditure by 6.7 million bolívare, the money stock by 4.6 million bolívare, GDP by 5.4 million bolívare, and reserve money by 2.0 million bolívare. Capital outflow of 10.8 million bolívare would occur, and the interest rate would decline by 25.5 per cent. The effect on the balance of payments would be to worsen it by 12 million bolívare.

Table 2.Reduced Form of Model, Relating Endogenous Variables to Exogenous Variables
FunctionConstantMt-1AEt-1GEt-1RVZt-1MOt-1GDPt-1NFAt-1PMPYXΔRusΔYusD1COBNDA
Mt−1.6670.2320.0630.0110.053−0.020−0.0040.125−0.1410.0830.147−0.150−0.004−0.3320.1250.125
AEt−2.198−0.2050.3350.0610.284−0.108−0.0190.6630.1240.4420.880−0.007−0.0261.7630.6630.663
GEt−0.9190.6430.403
ΔKt−2.5500.2880.0750.009−0.4900.1740.002−1.076−0.174−0.0500.4000.0300.003−0.202−1.076−1,076
RVZt−2.4570.7030.157−0.027−1.0920.4140.077−2.552−0.425−0.143−2.6100.0280.102−6.784−2.551−2.551
MOt0.163−0.128−0.0290.0050.199−0.075−0.0140.4640.0770.3090.475−0.005−0.0191.2340.4640.464
GDPt−2.888−0.4380.2720.6920.230−0.0870.0160.5390.2650.3592.049−0.006−0.0211.4320.5390.539
ΔNFAt0.7110.0550.012−0.040−0.2200.1950.006−1.201−0.0330.114−0.2050.002−0.008−0.533−0.201−1.201
RMt0.7110.0550.012−0.002−0.0860.1950.006−0.201−0.033−0.134−0.2050.002−0.008−0.533−0.2010.201

The reduced-form equations in Table 2 are useful mainly for simulation and forecasting. They have been used to simulate the behavior of the GDP and the balance of payments during the period 1950-72 and to make forecasts of all nine endogenous variables for 1973.

simulation of GDP and ΔNFA, 1950-72

From the calculated reduced-form equations in Table 2, a series on nominal GDP and ΔNFA was generated. Howrey and Kelejian (1969) have shown that for validating a model no information beyond that already contained in the reduced-form results can be gained by simulating the model within the sample period and then comparing the actual values with the simulated values, but it is precisely to highlight such comparisons that these experiments were performed. Since the model is not designed for multi-period forecasting, the actual values of the lagged endogenous variables were used as input rather than the generated values.18 Problems of error accumulation are therefore ignored, and the model is made to reflect the actual values of the lagged endogenous variables for each period. Generating these ex post simulations for the sample period provides a measure of goodness-of-fit of the model analogous to the calculation of the R2 in ordinary least squares.

Simulated and actual values of the level of GDP, changes in GDP, and the balance of payments for the period 1950-72 are shown in Charts 2, 3, and 4, respectively. In Chart 2 the simulated values of GDP generally lie very close to the actual values. Chart 3, which plots first differences of the actual and simulated values of GDP, is more informative because it points out the extent of divergence between changes in GDP. Although the model is unable to depict the magnitude of changes with accuracy, it does capture the direction of changes most of the time. The differences between actual and simulated values of the balance of payments (Chart 4) are still more striking, but the direction of change in international reserves is often very close to the simulated values.

Chart 2.Venezuela: Simulated and Actual Values of Gross Domestic Product in Current Prices, 1950-72

Chart 3.Venezuela: Simulated and Actual Changes in Gross Domestic Product in Current Prices, 1950-72

Chart 4.Venezuela: Simulated and Actual Balance of Payments, 1950-72

forecasts of the endogenous variables for 1973

Since the true test of a model is its ability to forecast outside the period of estimation, forecasts were made for the endogenous variables for 1973. Using the notation developed for calculating impact multipliers, forecasts for 1973 were made as:

using the actual values of the lagged endogenous variables (these being the values for 1972) and the forecasted values of the exogenous variables; ỹ and z˜ are therefore the forecasted values of the endogenous and exogenous variables.

For the purposes of projecting the values for 1973 of the nine endogenous variables of the system, it is necessary in the context of the model to have the values for 1972 of imports, private aggregate expenditure, government expenditure, the rate of interest, the net foreign asset holdings of the Banco Central de Venezuela, the supply of money plus quasi-money, and GDP, along with the projected values of the exogenous variables for 1973. These projected values are shown in Table 3.

Table 3.Venezuela: Projections of Exogenous Variables for 1973(Values in billions of bolívare)
Exogenous VariablesForecast for 1973
PM:Import prices (1968 = 100)140.0
X:Value of exports in current prices22.2
ΔRus:Change in U.S. prime rate20.0%
ΔYus:Change in U.S. gross domestic product, in current prices200.0
PY:Permanent nominal gross domestic product, in current prices55.0
COB:Services/long-term capital flows/government−8.2
NDA:Net domestic assets of the Banco Central de Venezuela−2.0

Based on partial data for 1973, import prices have been estimated to rise by 8 per cent over their value in 1972. Permanent income is simply extrapolated, using a 6 per cent rate of growth. Based on volume figures for September 1973 and the price of petroleum and petroleum products in November 1973, exports are estimated to be 36 per cent above their level of 1972. Forecasts of the other variables are based on simple linear extrapolation.

Using the projected values in Table 3, and the values for 1972 of the lagged dependent variables, the forecasts of the endogenous variables were calculated. They are shown in Table 4.

Table 4.Venezuela: Actual Values for 1972 and Forecasts for 1973, Using the Monetary Model(Values in billions of bolívare)
Endogenous VariablesActual

Values for

1972
Forecast

for 1973
Percentage

Change
M:Nominal value of imports10.0812.0920.8
AE:Private aggregate expenditure in current prices41.3950.1821.2
GE:Government expenditure in current prices12.6715.1820.0
ΔK:Short-term private capital flows (including net errors and omissions)0.78−1.54
RVZ:Weighted average interest rate in Venezuela9.10%9.0%−1.1
MO:Money plus quasi-money16.5118.7113.3
GDP:Gross domestic product in current prices62.3075.3821.0
ΔNFA:Change in net foreign assets of the Banco Central de Venezuela0.910.48
RM:Reserve money5.236.2218.9

These forecasts indicate that imports can be expected to grow by over 20 per cent over the previous year. Private and government expenditure should rise by 21 and 20 per cent, respectively. There appears to be an outflow of short-term capital of 1.54 billion bolívare ($366 million), basically because of the easing of the interest rate in Venezuela and an increase in the U. S. prime rate (Table 3). The model does forecast a small decline in the domestic interest rate and an increase of over 13 per cent in the money stock. The level of GDP (in current prices) should reach 75.4 billion bolívare in 1973, representing an increase of 21 per cent. Since independent estimates of real GDP for 1973 predict a rise of about 8 per cent, this last result would imply an increase of 13 per cent in the GDP deflator.

The net international reserves of the Banco Central de Venezuela should increase by 480 million bolívare ($112 million) and reach a level of 7.88 billion bolívare ($1,832 million). Its liabilities (reserve money) are expected to grow in 1973 by 19 per cent over the figure for 1972.

V. Conclusions

The purpose of this study is twofold: (1) to design a model showing how policy action by the monetary authorities in Venezuela affects the GDP and the balance of payments, and (2) to utilize the resulting model for purposes of forecasting certain aggregate variables on a short-term basis. Since the design of the model was strongly influenced by its ability to forecast, it was kept at a very simple aggregative level. This approach assumes that the monetary authorities are interested in the behavior of aggregate indicators rather than disaggregated ones. Important sectors of the economy (notably the petroleum sector) were left unexplained in order to avoid trying to forecast the behavior of the world oil market. However, forecasts of the oil sector, which thus will necessarily be made outside the model, will heavily influence the model’s predictive power.

The results obtained for the model, in terms of both the estimates of the parameters and the simulation experiment, were very good. However, the fact that major changes in the economy would probably make the model less relevant should be kept in mind when using it for forecasting purposes.

The importance of coordinating this model with the judgments of policymakers, as mentioned earlier, must be stressed. Forecasts from this model are crucially dependent on information concerning the behavior of exogenous variables; such information, of course, has to be provided from outside the model. In return, this type of simultaneous model can provide information to policymakers as to the consistency of their projections or judgments about the behavior of economic variables, both endogenous and exogenous.

No particular policy approaches have been considered in this study, such as, for example, how the monetary authorities alter their portfolio of domestic assets. As far as this particular model is concerned, changes in net claims on the Government and on state and commercial banks will all lead to the same effect on the monetary base. This is a necessary simplification, since discussions of what may theoretically be the best or most appropriate way to change the monetary base—through altering reserve requirements or through open market operations—are outside the scope of this study.

APPENDIX: Method of Estimation Used in the Monetary Model for the Venezuelan Economy

The Venezuelan monetary model to be estimated can be written in matrix form as:

where Y is a Txn matrix of T observations on each of the n endogenous variables, X is a Txm matrix of the t observations of the predetermined variables, and U is a Txn matrix of disturbances. The assumptions necessary for the estimation of this sytem are:

(1) Each equation of the model is identified, and the coefficients are normalized so that the elements in the leading diagonal of A are unity, and A is nonsingular.

(2) The elements of X are fixed constants, the lagged values of the dependent variables, or linearly independent stochastic variables.

(3) U is independent and normally distributed N (O, Ω).

The estimator used in this study is full-information maximum likelihood, which requires specification of the whole model and utilizes all a priori restrictions on the system to estimate all the structural coefficients simultaneously by maximizing the likelihood function.

subject to the parameters A, B, and Ω.

This estimator is consistent and best asymptotic normal; even when the third assumption is removed, this estimator, although no longer maximum likelihood, is still consistent and asymptotically efficient. The only other estimator that utilizes all a priori restrictions on the model is three-stage least squares, which is generally as asymptotically efficient as full-information maximum likelihood, the difference being of the second order only; and when the latter is best asymptotic normal, so also is three-stage least squares. Since full-information maximum likelihood uses more information than limited-information maximum likelihood, it is more efficient asymptotically. Further, since limited-information maximum likelihood has the same asymptotic efficiency as two-stage least squares, full-information maximum likelihood is more efficient than two-stage least squares. Three-stage least squares is at least as asymptotically efficient as two-stage least squares.

On the basis of asymptotic theory, therefore, full-information maximum likelihood appears to be the best estimator. In addition to the maximum likelihood estimates made in this study, two-stage least squares and three-stage least squares estimates were also found.

The computer programs used in estimating under the system are entitled simul and predic. simul estimates by two-stage, three-stage and full-information maximum likelihood; it allows linear restrictions to be placed on the coefficients and calculates the reduced form. Predic is used to forecast both within and outside the sample period. Both programs are written by C. R. Wymer and adapted for the Burroughs system by N. Arya and Mohsin Khan of the Fund staff.

Prior to estimating the complete model, each equation was checked by using ordinary least squares. Tests were made for specification and, related to this, for autocorrelation. Since there was no serious problem with autocorrelation, no attempt was made to correct for this.

BIBLIOGRAPHY

Mr. Khan, an economist in the Financial Studies Division of the Research Department, holds degrees from the London School of Economics and Columbia University. In addition to colleagues in the Fund, the author is greatly indebted to G. Escobar, Bernardo Ferrán, and J. P. Perez-Castillo for their comments and suggestions.

This present model, a direct descendant of the Polak model (1957), is thus to be distinguished from the models constructed by the United Nations Conference on Trade and Development (1972) and by J. P. Perez-Castillo and others (1963).

For a complete exposition see Johnson (1972) and Robichek (1971).

This oversimplification is facilitated by the historical stability of domestic prices in Venezuela.

For the purpose of estimation, u is assumed to be normal, independent, with zero mean and constant variance.

In preliminary estimates domestic prices were included and found to have no statistical influence on imports. A price series on domestic production of importables is not available.

For an analysis of the system of fiscal export values, see Escobar (1973).

In fact, the series on private short-term capital flows is calculated on the basis of changes in Venezuelan deposits in U.S. banks.

The derivation of PY is shown in Section II.

Lagging equation (12) by one period, multiplying by X, and subtracting from equation (12).

For an investigation of the money supply process and the behavior of the multiplier in Venezuela, see Khatkhate and others (1973).

For the lagged values of the variables, 1949-71.

Data for M, GE, K, and RVZ were derived from the Banco Central de Venezuela, Anexo Estadístico (1971-72) and La Economía Venezolana en los Ultimos Treinta Años (1971); data for MO, ΔNFA, and RM were derived from the International Monetary Fund, International Financial Statistics; data for GDP were derived from International Financial Statistics and Anexo Estadístico.

Data for PM and ΔYus were derived from the International Monetary Fund, International Financial Statistics; data for X were derived from the Banco Central de Venezuela, Anexo Estadístico (1971-72) and La Economía Venezolana en los Ultimos Treinta Aíos (1971); data for ΔRus were derived from the Federal Reserve Bulletin of the Federal Reserve System.

This series was calculated by using the formula:

PYt = a GDPt + (1 - a) (1 + g) PYt-1

The value for g was set at 0.04, the average growth rate in Venezuela. Various values of a were used in equation (5) of the model to determine when the standard error was minimized. The value of a which achieved this minimum was 0.1. The series used was therefore:

PYt = 0.1 GDPt + (0.9) (1.04) PYt-1

First, it is not bounded (0, 1) but (−∞, 1) so that small values are not an indication of a poor fit; and, second, its distribution is not a straightforward F.

This is more efficient than directly estimating the reduced form (Kmenta, 1971).

The general linear model of Section I, containing G structural equations, can be written as:

where yt is a G-component vector of endogenous variables, zt is a K-component vector of exogenous variables (including lagged endogenous variables) and Ut is a G-component vector of error terms. B and Γ are G X G and G X K matrices of structural parameters. The reduced form of equation (26) is:
where Π = − B-1Γ.

Naturally, this latter approach would have been a more stringent test of the model—when simulated values of endogenous variables in one period are used as input into the equation to predict the values of the endogenous variables in the following period.

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