Abstract
This paper examines economic developments in Trinidad and Tobago during 1990–94. Economic activity in 1992–93 was severely affected by a fall in output in the oil/gas sector, a sharp drop in the average oil export price, and persisting weakness in the nonpetroleum sector. As a result, real GDP declined further by a cumulative 3½ percent in the two-year period, and unemployment rose to more than 20 percent. Real domestic expenditure fell by 3½ percent a year, with declines in both consumption and investment.
VIII. The Demand for Currency and Broad Money
This section analyzes the demand for currency and broad money in Trinidad and Tobago through econometric models that incorporate cointegration and error correction mechanisms. Cointegration requires finding long-term relationships between currency and broad money and other economic variables such as income and the interest rate. 1/ Once found, these long-run relationships describe in effect the steady state. Moreover, if cointegration exists, general dynamic models may be specified with error correction mechanisms that show the process of adjustment of the economic variables from their short-run position to the steady state. 2/
Generally, it is expected that an increase in real income would lead to an increase in the demand for currency and broad money, and vice versa. An increase in the real interest rate would result in a decline in the demand for currency, but would have an ambiguous effect on the demand for broad money. The effect of an increase in the real interest rate on the demand for broad money would depend on the weight of currency and demand deposits and interest-earning deposits instruments in broad money. An increase in inflation--holding everything else constant--would result in a decline in the demand for currency and broad money. However, an increase in inflation that brings about an increase in nominal interest rates would not necessarily have an effect on broad money as the increase in the demand for interest earning assets could offset the decline in the demand for currency and demand deposits.
In general dynamic models, the sign of the coefficient corresponding to the error correction mechanism must be negative to ensure that an adjustment indeed takes place from the short-run position to the steady state. In other words, the difference between the desired and actual demand for currency and broad money becomes smaller over time in order to eventually reach the steady state, or desired long-run relationships. The presence of the error correction term reflects in effect efforts to correct for errors from past decisions.
The long-run relationships (or solutions) can be derived from fifth-order autoregressive-distributed lag representations for real currency and real broad money. For Trinidad and Tobago, the estimations of long-run relationships using quarterly data yielded 3/
and
where ct* represents real currency, rt denotes the real interest rate, yt stands for real income as measured by the real GDP, and m2t* is real broad money. 1/ With the exception of the real interest rate, all other variables are in natural log terms.
The signs of the coefficients for the long-run relationship for real currency are consistent with what is expected by economic theory. 2/ An increase in real income would result in an increase in the demand for real currency. The long-run elasticity of real income with respect to real currency is statistically not different from one, which implies that a 1 percent increase in real income would result in almost a 1 percent increase in real currency holdings. In other words, a long-run real income elasticity of one implies a constant income velocity. An increase in the real interest rate would bring about a decline in real currency holdings. This result is consistent with the notion that the real interest rate represents the opportunity cost of holding money.
The results of the long-run relationship for real broad money are partly in line with what is predicted by economic theory. An increase in real income would lead to an increase in the demand for real broad money in the long-run. The long-run elasticity of real income with respect to real broad money is statistically greater than one (i.e., an increase of 1 percent in real income would bring about a larger increase in real broad money), indicating a process of financial deepening in Trinidad and Tobago. An increase in the real interest rate would result in a decline in real broad money in the long-run. However, the opposite would be expected because currency plus demand deposits represent only 26 percent of broad money. The result then could reflect the effects of the financial repression characterized in part by interest rate controls over the period of the estimation. 1/
An ordinary least squares estimation (OLS) estimation of a general dynamic demand function for real currency yielded the following results:
where Δ represents change, pt is the level of prices, and dct denotes a dummy variable that accounts for the seasonal increase in currency demand in the fourth quarter of every year, and ecmct-1 stands for the error correction mechanism (or the error disturbance term of the long-run relationship in equation (1)). Lagged variables are indicated by the suffix t-i, where The numbers in parenthesis represent t-statistics, with an asterisk implying significance at the 10 percent level, two asterisks at 5 percent level, and three asterisks at the 1 percent level. 2/ The diagnostic tests are followed in parenthesis by their 5 percent critical values. The residuals in this general dynamic demand function for real currency are not subject to serial autocorrelation nor heteroscedasticity, and are normally distributed because the values of the diagnostic tests do not exceed their critical values The acceptable parameter consistency test demonstrates the stability of the demand for real currency.
The results in equation (3) show that the demand for real currency in Trinidad and Tobago is consistent with some of the expected results, and indicate the importance of a persistence effect as well as the existence of cointegration. A 10 percent increase in prices--holding everything else constant--would result in a decline of 9.9 percent of a percentage point in the change of real currency in Trinidad and Tobago. 1/ A 10 percent increase in real currency--holding the change in prices constant--would lead to nearly a 2 percent of one percentage point increase in the change of real currency in three quarters. The coefficient of the error correction term has the expected sign, and is significant at the 1 percent level. However, the small size of the coefficient associated with this term indicates a very slow adjustment from the short-run position to the steady state. The coefficient of the dummy variable is also significant at the 1 percent level. Changes in real income and the real interest rate are not significant in determining real currency demand in the short-run, and thus were excluded from the estimation of this general dynamic demand for real currency.
An OLS estimation of a general dynamic demand for real broad money gave the following results:
where ecm2t-1 denotes the error correction term obtained from the static long-run solution for real broad money demand in equation (2). As with the estimated general dynamic demand for real currency, all the diagnostic tests are acceptable in this estimation of real broad money. Moreover, the acceptable parameter consistency test indicates the stability of the demand for real broad money.
The results in equation (4) show that the demand for real broad money in Trinidad and Tobago in general reflects what is predicted by economic theory, and demonstrate the importance of a persistence effect, and the existence of cointegration. A 10 percent increase in prices--holding everything else constant--would result in a decline of almost 7 percent of a percentage point of the change in real broad money. A 10 percent increase in real income would bring about an increase of 4 percent of a percentage point in the change in real broad money demand. A 10 percent increase in real broad money--holding everything else constant--would lead to an increase of somewhat more than 2 percent of a percentage point in the change in real broad money in two quarters.
The coefficient of the error correction mechanism has the expected sign and is significant at the 1 percent level, indicating that agents in Trinidad and Tobago adjust their holdings of real broad money in the short- run with the objective of eventually attaining their desired holdings of real broad money. However, the coefficient related to this term is small, suggesting a slow adjustment process towards the steady state. Changes in the real interest rate do not have any effects on changes in the demand for real broad money, and thus were excluded from this estimation of changes in the demand for real broad money.
References
Barro, Robert J., “Unanticipated Money Growth and Unemployment in the United States,” in Robert E. Lucas Jr. and Thomas J. Sargent (eds.), Rational Expectations and Econometric Practice, (Minneapolis: The University of Minnesota Press, 1981).
Hendry, David F., “PC-GIVE: An Interactive Econometric Modeling System” (Oxford: Institute of Economics and Statistics and Nuffield College of University of Oxford, January 1989).
International Monetary Fund, International Financial Statistics, various issues, (Washington: International Monetary Fund).
APPENDIX I Cointegration, Error Correction Mechanisms and Money Demand Functions
The presence of error correction mechanisms in money demand functions implies the existence of cointegration, which describes the steady state or long-run relationships between economic variables. In other words, cointegration assures that economic variables do not drift far apart. Cointegration, however, requires that economic variables be stationary, or have a unit root, to ensure that these variables have convergent trends in order to avoid estimating spurious statistical models. In summary, if yt and zt are nonstationary time series integrated to order one, or I(1), requiring a differencing of one time to make them stationary, cointegration exists if there is a δ in a simple log-linear model described as yt + δ zt = μt such that μt is I(0). In that case, yt and zt are said to be cointegrated. 1/
For determining if time series are stationary, an Augmented Dickey-Fuller test (ADF) can be used. Under this test, the null hypothesis is that time series have a unit root, or are integrated to order one, I(1), with the alternative hypothesis that the time series does not have a unit root, or are I(0). The ADF test consists in running the following model using OLS for each of the variables
where Δyt represents the first difference of each of the variables being tested for stationarity, Φi a constant, t a time variable, yt-1 the lagged level of the variable, Δyt-i (i = 1, … n) lagged changes of each of the variables being tested, and μt an error term. The number of lags in the equation, n, is selected such that pt is white noise. The null hypothesis specifies that ρi = 1.
Table 16 shows the results of the ADF tests using quarterly data for real currency in circulation (c), real broad money (m2), real GDP (y), real interest rates (r), and the price level (p). 2/ Other than real interest rates, all the variables are in natural log terms. The tests show that all the variables have a unit root. Moreover, because the tests indicate that the price level has a unit root, inflation also is a stationary variable.
Trinidad and Tobago: Unit Root Test (1967.Q2-1994.Q1)
Augmented Dickey-Fuller 1/
The numbers in parenthesis indicate the number of lags sufficient for the error-term to be white noie.
Obtained from Banerjee, et al. (1993).
Trinidad and Tobago: Unit Root Test (1967.Q2-1994.Q1)
Augmented Dickey-Fuller 1/
| Currency (c) | -0.97 | (4) |
| Real broad money (M-2) | -0.40 | (2) |
| Real GDP (y) | -1.18 | (1) |
| Real interest rate (r) | -1.05 | (3) |
| Prices (p) | -2.36 | (4) |
| Critical value at 5 percent level 2/ | -3.45 |
The numbers in parenthesis indicate the number of lags sufficient for the error-term to be white noie.
Obtained from Banerjee, et al. (1993).
Trinidad and Tobago: Unit Root Test (1967.Q2-1994.Q1)
Augmented Dickey-Fuller 1/
| Currency (c) | -0.97 | (4) |
| Real broad money (M-2) | -0.40 | (2) |
| Real GDP (y) | -1.18 | (1) |
| Real interest rate (r) | -1.05 | (3) |
| Prices (p) | -2.36 | (4) |
| Critical value at 5 percent level 2/ | -3.45 |
The numbers in parenthesis indicate the number of lags sufficient for the error-term to be white noie.
Obtained from Banerjee, et al. (1993).
The economic framework for the demand functions for real currency and real broad money can be represented by an autoregressive-distributed lag relationship expressed as
where mt represents the natural log of either currency in circulation or broad money in real terms, pt the natural log of the price level, yt the natural log of real income (real GDP), rt the real interest rate, ot other independent variables, μt an error term distributed as (0, σ2), αo a constant term, and αi, βi, γi and σi parameters. Lagged variables are indicated by the suffix t-i. This autoregressive distributed lag relationship can be reduced to a more parsimonious relation by eliminating the most insignificant lagged elements and imposing certain assumption. 1/ From equation (2) or a simpler relationship, a long-run relation (or solution) can be derived. 2/
Following Hendry, et al. (1991), the autoregressive-distributed lag model can be reparameterized to take into account short-run dynamics as
where Ψ is a constant, λi(L) (i = 0, …,5) represents a finite polynomial in the lag operator L, ecmt-1 = mt-1* - mt-1, the error correction mechanism defined as the lagged difference between desired currency or broad money holdings, mt-1*, and actual currency or broad money holdings, mt-1, derived from the long-run solution obtained from estimating an autoregressive-distributed lag model, and ϵt an error term. This equation represents in effect a partial adjustment model that allows for the attainment of desired long-run real currency and real broad money holdings through an error correction mechanism. The parameterization (first- or higher-order differences) is arbitrary within lag polynomials, and sign restrictions need not be imposed a priori. Moreover, insignificant terms can be excluded in the estimation of this equation.
Cointegration exists when the error term of the long-run solution does not have a unit root, or is I(0). To test for cointegration, equation (1) also can be used, although, the distribution of the critical values for this test differs from that to determine the validity of unit root tests. 1/ Table 17 shows the cointegration tests of the error term of the long-run solutions for real currency and real broad money presented in Section VIII. Both tests show that the t-statistic corresponding to the coefficient of the lagged error term in running equation (1) exceed the 5 percent MacKinnon critical value, 2/ and thus would seem to imply that there is no cointegration between real currency or real broad money and real income and real interest rates. However, cointegration also can be tested within the framework of a model that includes an error correction mechanism, since cointegration is implied by the existence of an error correction representation of the relevant variables by the Granger Representation Theorem. 3/ Since equations (3) and (4) in Section VIII show a significant error correction representation, it can be concluded that cointegration is present in both equations.
Trinidad and Tobago: Tests of Cointegration
Obtained from Banerjee, et al. (1993).
Trinidad and Tobago: Tests of Cointegration
| Real currency (ecmc) | -2.17 |
| Real broad money (ecm2) | -2.55 |
| MacKinnon critical value of 5 percent 1/ | -5.18 |
Obtained from Banerjee, et al. (1993).
Trinidad and Tobago: Tests of Cointegration
| Real currency (ecmc) | -2.17 |
| Real broad money (ecm2) | -2.55 |
| MacKinnon critical value of 5 percent 1/ | -5.18 |
Obtained from Banerjee, et al. (1993).
References
Banerjee, Anindya, Juan Doledo, John W. Galbraith and David F. Hendry. Cointegration, Error-Correction, and the Econometric Analysis of Non-Stationary Data (Oxford: Oxford University Press, 1993).
Boughton, James, “Long-Run Money Demand in Large Industrial Countries,” IMF Staff Papers, Vol. 38, No. 1 (Washington), March 1991.
Campbell, John Y. and Pierre Perron, “Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots,” in Olivier Jean Blanchard and Stanley Fisher (eds.), NBER Macroeconomics Annual 1991 (Cambridge, MA: MIT Press, 1991).
Cuthbertson, Keith, Stephen G. Hall and Mark P. Taylor. Applied Econometric Techniques (Ann Arbor: The University of Michigan Press, 1992).
Hendry, David F. Econometrics: Alchemy or Science, (Oxford: Blackwell Publishers, 1993).
Hendry, David F. and Neil R. Ericcson, “An Econometric Analysis of U.K. Money Demand in Monetary Trends in the United States and the United Kingdom,” American Economic Review, Vol. 81, No. 1 (Nashville), March 1991.
Kremers, Jeroen J.M., Neil R. Ericsson and Juan J. Dolado, “The Power of Cointegration Tests,” Oxford Bulletin of Economics and Statistics, Vol. 54, No. 3 (Oxford), August 1992.
APPENDIX II Time Series Properties and Diagnostic Tests
In addition to well known time series properties, PC-GIVE provides diagnostic tests, including for homoscedastic serial uncorrelated errors (or white noise) and the distribution of residuals. 1/ The time series properties are defined as follows:
| R2 | = | Squared coefficient of the multiple correlation |
| F | = | F-statistic |
| σ | = | Standard error of the regression |
| RSS | = | Residual sum of squares |
| The diagnostic tests are defined as follows: | ||
| LM1 | = | Lagrange multiplier for first order residual autocorrelation distributed as F-form |
| IM2 | = | Lagrange multiplier for first through fourth order residual autocorrelation distributed as F-form |
| ARCH | = | Test for first through fourth order autoregressive conditional heteroscedasticity distributed as F-form |
| NORM | = | CHI square distributed test of the normality of the error term based on the estimation of skewness and kurtosis of the residuals compared to their counterparts under a normal distribution |
| HET | = | F-form test for heteroscedastic errors |
| CHI (N/N) | = | Index of numerical parameter constancy for N forecasts. It is calculated as CHI (N/N), which yields an approximate F- test; values greater than 2 imply poor ex-ante forecasts |
| R2 | = | Squared coefficient of the multiple correlation |
| F | = | F-statistic |
| σ | = | Standard error of the regression |
| RSS | = | Residual sum of squares |
| The diagnostic tests are defined as follows: | ||
| LM1 | = | Lagrange multiplier for first order residual autocorrelation distributed as F-form |
| IM2 | = | Lagrange multiplier for first through fourth order residual autocorrelation distributed as F-form |
| ARCH | = | Test for first through fourth order autoregressive conditional heteroscedasticity distributed as F-form |
| NORM | = | CHI square distributed test of the normality of the error term based on the estimation of skewness and kurtosis of the residuals compared to their counterparts under a normal distribution |
| HET | = | F-form test for heteroscedastic errors |
| CHI (N/N) | = | Index of numerical parameter constancy for N forecasts. It is calculated as CHI (N/N), which yields an approximate F- test; values greater than 2 imply poor ex-ante forecasts |
Reference
Hendry, David F., “PC-GIVE: An Interactive Econometric Modeling System” (Oxford: Institute of Economics and Statistics and Nuffield College of University of Oxford, January 1989).
Currency refers to currency in circulation, and broad money stands for the broadest monetary aggregate or M2.
Appendix I describes the economic framework that incorporates cointegration and error correction mechanisms in demand functions for currency and broad money. It also provides a test to analyze the stationary of the time series used in this chapter. The test shows that all the variables included in the demand functions for real currency and real broad money are stationary as required by cointegration.
The econometric work was done in the statistical package PC-GIVE. See Hendry (1989) for details about this package.
Data on currency, broad money, prices, and nominal interest rates were obtained from the International Financial Statistics. Currency and broad money were deflated by the consumer price index to obtain real currency and real broad money. Real interest rates were calculated as nominal interest rates minus inflation. The quarterly real GDP was derived from the annual real GDP by a linear interpolation model.
Appendix I presents a test for cointegration for both equations (1) and (2). The test would suggest that real currency and real broad money are not cointegrated with real income and the real interest rate. However, cointegration also can be tested in general dynamic models that include error correction mechanisms. The significance of error correction mechanism in general dynamic models indicates the existence of cointegration.
Section VII presents a description of the financial repression in Trinidad and Tobago.
See Appendix II for a description of time series properties and diagnostic tests.
In other words, a 1 percent increase in prices would bring about a decline of 1 percent in real currency holdings in Trinidad and Tobago. See Barro (1981) for an interpretation of coefficients in equations estimated with first- and higher-order differences of variables in natural log terms.
For additional details, see Campbell, et al. (1991), Cuthbertson, et. al. (1991) and Hendry, et el. (1991).
Data used to estimate equations (1) and (2) in Section VIII.
See Boughton (1991) for a discussion on autoregressive-distributed lag relationships and their reduction to parsimonious equations and derived static long-run solutions.
For the coefficients obtained from estimating equation (2) or a simpler relationship, all the diagnostic tests (as described in Appendix II) must be acceptable. See Cuthbertson, et al. (1992).
See Banerjee, et al. (1993) for a discussion on cointegration tests and the distribution of critical values for these tests.
See Kremers, et al. (1992) for a description of the cointegration test using MacKinnon critical values.
See Campbell, et al. (1991) and Hendry, et al. (1991) for a detailed description and the implications of the Granger Representation Theorem.
See Hendry (1989) for details on these tests.