# The substitutability of monetary assets in Taiwan.

I. Introduction

The financial sector of the Taiwan economy has experienced major structural changes in the past decade. The banking system has been liberalized, a regulated money market has developed, and the foreign exchange market has been deregulated. Nevertheless, Taiwan's financial sector is still characterized by dualism, with the coexistence of both regulated and unregulated (curb) markets. The ratio of financial loans from the unregulated market to those from the regulated market for the total private enterprise has been consistently large, averaging 27.5% for the period 1971-88.(1) Interest rates in the unregulated markets of Taiwan are generally much higher than those in the regulated markets. Figure 1 shows the disparity in interest rates between these two markets. The difference in interest rates grew during the 1970s, reaching an annual rate of 23 percent in the second quarter of 1979. Since then, the differential has declined steadily to about 17 percent in 1988.

Because the financial loans from the unregulated market constitute a major portion of all private borrowing in Taiwan, we believe that studies of characteristics of financial markets in Taiwan should include the unregulated market as well as the regulated market. It is the purpose of this paper to extend the study of asset substitutability in Taiwan to include the unregulated financial market.

Accurate empirical measurement of the degree of substitutability among various liquid assets is important for two distinct but related reasons. The first is the well-known Gurley-Shaw thesis [14] which relates the role of nonbank financial intermediaries to the monetary process. According to this view, any government monetary policy will be substantially offset if the liabilities of financial intermediaries are close substitutes for money. The second reason has to do with the appropriate definition of "money" and asks if a simple-sum aggregate such as M2 is a good measure of the money stock and is an appropriate monetary target [2; 3; 6; 10; 15].

The most common procedure to measure the degree of substitutability is the estimation of interest cross-elasticity from a demand function for currency and demand deposits [12; 13; 18]. The demand function typically includes the rates of return on one of more near-money assets, plus an income or wealth measure as an explanatory variable. Theory and empirical estimates, however, provide little guidance about the magnitude of cross-elasticity that constitutes a "close" substitutability.(2) The interest cross-elasticity approach therefore fails to bridge the gap between empirical estimates and policy issues.

This paper follows the approach, first proposed by Chetty and later extended by Barnett, of estimating the degree of asset substitutability by direct estimation of the parameters of a utility function. Following Barnett, our model specifically recognizes the consumer's inter-temporal choice implicit in the choice between consumption and holding assets. We consider an infinitely lived consumer who derives utility from consumer goods and the services provided by real money holdings. Including the equity holdings in the unregulated financial market in the consumer budget constraint, we account explicitly for the existence of dual markets. Moreover, the model allows for the possibility that a consumer's liquidity service may vary with economic growth. We assume that the shares of assets in the consumer's portfolio are time-dependent and are functions of income. Estimates of the parameters of this model are used to construct a measure of a monetary aggregate which is consistent with the individual's utility maximization. The remainder of this paper is divided into three sections. In section II, a general theoretical model is presented. Section III describes data and presents the empirical results. Section IV presents a comparison of various measures of monetary aggregates. A brief conclusion is given in section V.

II. The Model

Consider the decision problem of an infinitely lived consumer who derives utility from both consumption and the liquidity service provided by holding various assets. Denote the consumption and liquidity service at time t by [C.sub.t] and [L.sub.t].

The consumer is assumed to maximize the discounted utility.(3) (1) [Mathematical Expression Omitted] where [Rho] is the subjective discount rate and U(.) is the concave utility function, and U(.) is monotonically increasing in both [C.sub.t] and [L.sub.t].

Since our interest is in the estimation of liquidity service [L.sub.t], it is necessary to specify how liquidity service is related to asset holding. The measure of liquidity service is assumed to be a constant elasticity of substitution (CES) function of real money holing, [M.sub.t]/[P.sub.t] and real savings and time deposits, [S.sub.t]/[P.sub.t], where [P.sub.t] is a price index, (2) [Mathematical Expression Omitted] The coefficient [Lambda] determines the elasticity of substitution between real money holding and real savings and time deposits, and is given by 1/(1 - [Lambda]). The distribution coefficient [[Delta].sub.t] is assumed to be time-dependent. When [[Delta].sub.t] = 1/2 and [Lambda] = 1, the real money holding and real savings and time deposits are identical with respect to liquidity service. In this case, money and interest bearing deposits are perfect substitutes, and the liquidity measure L is equivalent to the simple-sum monetary aggregate, (M + S)/P.

The consumer budget constraint at time i is (3) [Mathematical Expression Omitted] where [N.sub.i] is the equity holdings in the unregulated market and serves as the numeraire asset.(4) [Y.sub.i] is real income from non-asset service, [r.sub.i] is the nominal rate of return on holding equity, and [d.sub.i] is the nominal rate of return on savings and time deposits.

Following Barnett [2], the budget constraints (3) can be solved for the equity holding for the period i = t + T. By repeatedly backward substituting the equity holding [N.sub.j] for the period j [is less than or equal to] t + T down to period t, the multi-period constraints can be expressed as a single constraints, (4) [Mathematical Expression Omitted] where [[Eta].sub.i] = 1, for i = t

The budget constraint (4) shows that the Jorgensonian user cost (or rental price) of holding money [M.sub.i] at the ith period is [Mathematical Expression Omitted] and the user cost of holding savings and time deposits [S.sub.i] is [Mathematical Expression Omitted] At current period i = t, the user costs for [M.sub.t] and [S.sub.t] are, respectively, (5) [Mathematical Expression Omitted]

The consumer's portfolio choice then is to maximize the utility function (1) subject to the single constraint (4). Alternatively, the multiperiod budget constraints (3) can be solved for [C.sub.t], [C.sub.t+1], . . . , and then can be substituted into the utility function (1) directly. Differentiating the resulting equation with respect to [N.sub.t], [M.sub.t], and [S.sub.t] yields the following first-order conditions for maximization.(5) (6) [Mathematical Expression Omitted] (7) [Mathematical Expression Omitted] (8) [Mathematical Expression Omitted]

Equation (6) states that the optimal allocation of inter-temporal consumption requires that the utility cost of giving up a unit of consumption in period t, i.e., [Delta] U/[Deltal] [C.sub.t] is to be exactly compensated in period (t + 1), i.e., [Rho] (1 + [r.sub.t]) [P.sub.t] ([Delta] U/ [Delta] [C.sub.t + 1])/[P.sub.t + 1]. Equation (7) equates the utility cost of foregoing one unit of consumption in period t and the utility gain from allocating that unit to money holding [Mathematical Expression Omitted] and then to consumption in the next period, [Rho] [P.sub.t] ([Delta] U/[Delta] [C.sub.t + 1)/[P.sub.t + 1]. Similarly, equates (8) equates the utility cost of reducing current consumption and the utility gain of increasing liquidity and of consumption in the next period.

Solving equation (6) for [Delta] U/[Delta] [C.sub.t + 1] and substituting it into equations (7) and (8), the first-order conditions can be combined to yield an equation that determines the ratio of money to savings and time deposits, (9) 1n([M.sub.t]/[S.sub.t] = 1n [[Delta].sub.t]/(1 - [Delta].sub.t])/(1 - [Lambda]) + 1n[([r.sub.t] - [d.sub.t])/[r.sub.t]]/(1 - [Lambda]).

Equation (9) states that the ratio of user cost of the savings and time deposits, ([r.sub.t] - [d.sub.t])/(1 + [r.sub.t]), to the user cost of money holding, [r.sub.t]/(1 + [r.sub.t]), determines the variation in the ratio of liquidity assets. Since the return [r.sub.t] on the equity holding [N.sub.t] is a determinant of user costs, we explicitly recognize the importance of the unregulated financial market in the consumer portfolio choice. The asset ratio in equation (9) also varies with the time-dependent distribution coefficient [[Delta].sub.t] of the liquidity service CES function (2). Given a time period t, the marginal rate of substitution (MRS) between the real money holding and the real savings and time deposits is defined as the ratio of the marginal utilities of their liquidity services. [MRS.sub.t] = [[[Delta].sub.t]/(1 - [[Delta].sub.t]) ([M.sub.t]/[S.sub.t]).sup.[Lambda] - 1]

The MRS varies with the ratio of asset stocks ([M.sub.t]/[S.sub.t]) and [[Delta].sub.t]. We propose that [[Delta].sub.t] be specified to be a function of the non-asset income [Y.sub.t] and seasonal variation in a logistic form, (10) [Mathematical Expression Omitted] where [Q.sub.t] is a seasonal dummy variable. This specification allows the liquidity services of money and savings and time deposits to depend on economic growth. The seasonal variation accounts for a temporary shift in the marginal utility of liquidity service in short-run.

Substituting equation (10) into (9), a regression equation of the logarithm of the asset stock ratio (M/S) can then be estimated, (11) 1n([M.sub.t]/[S.sub.t] = [a.sub.o]/(1 - [Lambda]) + [a.sub.1] [Q.sub.t]/(1 - [Lambda]) +

where [U.sub.t] is an added random error term.

III. Data and Estimation

The quarterly time series data used in the analysis are obtained from Financial Statistics Monthly published by the Central Bank of China, and Quarterly National Income Statistics in Taiwan Area published by the Directorate-General of Budget, Accounting and Statistics. The sample periods cover from the first quarter of 1971 to the fourth quarter of 1987 for a total of 68 quarters.

The liquid asset holdings consist of the household holdings of MIB and S = M2 - M1B. The money holding M1B includes net currency and demand deposits, passbook and passbook savings deposits. The measure of S includes time deposits with various maturities of one, three, nine months, and one year, and savings deposits with maturities of one, two, and three years. The household holdings portions of M1B and M2 are calculated directly from the annual flow of fund accounts in the Flow of Funds in Taiwan District, published by the Central Bank of China. These household holdings of monetary assets are deflated by the consumer price index P. However, the GNP deflator is used for calculating the real GNP figures. All measures are in millions of NT dollars.

Since the equity holdings is to serve as the numeraire asset and is defined as the assets held by individuals outside the regulated money market, we measure its return r with the interest rate in the unregulated money market. Since Taipei is the largest and most active unregulated market in Taiwan, we use the average interest rate of loans against post-dated checks in Taipei city in our estimation. The other asset return, d, represents the interest rate paid to the time and saving deposits in the regulated money market, and is a weighted geometric mean of the deposits with various maturities. The weights are the shares of these deposits.

A diagnostic test on the correlograms of the regression error in equation (11) reveals characteristics of a mixed autoregressive moving average stochastic process in the terms [U.sub.t]. In estimating the equation, an autoregressive moving average of first-order is therefore employed. The ARMA (1, 1) assumes the stochastic process, [U.sub.t] = [Phi] [U.sub.t-1] + [Theta] [[Epsilon].sub.1] + [[Epsilon].sub.t]. The ARMA (1, 1) model requires ~[Phi]~ < 1 for stationarity and ~[Theta]~ < 1 for invertibility.

In estimating the asset substitution equation (11), the ratio of user costs in money holding [M.sub.t] and time deposits [S.sub.t] is lagged by 4 quarters. That is, the lagged regressor [[(r - d)/r].sub.t-4] is used in the regression. This is due to the fact that the interest on the deposits with maturities over 12 months are generally received annually. Furthermore, over 81% of savings and time deposits [S.sub.t] had maturity over 12 months during the sample period.

The quarter dummy variable [Q.sub.t] is defined as [Q.sub.t] = 1 if it is in the quarter, and [Q.sub.t] = 0 otherwise. The coefficient is expected to be positive to reflect the short-term seasonal demand for liquid assets during the Chinese New York holiday.

The asset substitution is estimated by Fair's instrumental variable method [11] with an ARMA (1, 1) process. The instruments used in the estimation are the fuel price index, exports, and government expenditures since these instruments were largely determined by the external factors that are not under the influence of monetary shock.(6) (12) [Mathematical Expression Omitted] where the standard errors are given in parentheses.

All coefficients are statistically significant and have the expected signs. The elasticity of substitution 1/(1 - [Lambda]) is estimated to be 0.8525 which is considerably smaller than the elasticity of substitution in the U.S. estimated by Chetty [6] and by Poterba and Rotemberg [19].(7) The inelastic substitution estimate, however, is larger than Barnett's [2] estimate of 0.28 between the supernumerary transaction balance and the supernumerary passbook saving aggregate. The low elasticity of substitution in Taiwan nevertheless rejects the infinite elasticity of substitution implied in the simple-sum monetary aggregate. This result does not provide strong support for the Gurley and Shaw hypothesis that savings and time deposits are good substitutes for money in Taiwan. In fact, our finding of low substitution between these two assets is consistent with, and reinforces the importance of the existence of dual financial markets in Taiwan. Given the presence of a large unregulated money market that offers high nominal rates of return, an individual must make his portfolio choice between high yield and high risk in the unregulated market, and the low yield and low risk in the regulated market. The portfolio choice between the two markets is not relevant if the size of the equity holding in the unregulated market is minimal or the marginal utility of future consumption from the equity holding is zero. Neither of these cases is consistent with the Taiwan financial market.

Given the estimated coefficients in equation (11) the implied liquidity services or aggregate is given by (13) [Mathematical Expressions Omitted] where [Mathematical Expression Omitted]. in order to compare the estimates of the liquidity services given in equation (13) with the simple-sum real monetary aggregate (M + S)/P, it is necessary to make certain adjustments to this measure. Since the liquidity services defined in [L.sub.t] are an ordinal measure, no monotonic transformation of [L.sub.t] alters the estimates of the coefficients. To compare the two series, we therefore normalize the estimated series [L.sub.t] so that the geometric means of the two series within the sample period are identical. This implies that the quarterly series of [L.sub.t] calculated from equation (13) is multiplied by 2.0187. The new liquidity series [Mathematical Expressions Omitted] is then (14) [Mathematical Expressions Omitted]

Table AII in Appendix shows the simple-sum real M2 aggregate and the adjusted liquidity series [L.sup.a] along with two other quarterly aggregates. The real M2 and [L.sup.a] series are remarkably close and have identical turning points during these periods. The upper part of Figure 2 depicts the quarterly rates of change. The average quarterly rate of change for real M2 aggregate is 4.1%, and the average for the liquidity series [L.sub.a] is 4.5%. The lower part of Figure 2 displays the inflation rate in the consumer price index. The inflation rate over time moves inversely to the demand for liquidity series [L.sup.a] and real M2. The simple correlation between the inflation rate and change in real M2 is -0.78, while it is -0.72 between the inflation rate and changes in [L.sup.a].

The rejection of an infinite elasticity of substitution implied in the simple-sum monetary assets is based on consumer utility maximization. An alternative test of the simple-sum aggregation based on an ad hoc demand for money equation was illustrated by Clements and Nguyen [9]. Their approach is to estimate the regression (15) [Mathematical Expression Omitted] where [Delta] 1n([X.sub.t]) = 1n ([X.sub.t]) -- 1n([X.sub.t-1]) denotes the difference. The liquidity or "moneyness" of each monetary asset is identified by its elasticity [Alpha.sub.i]. The shares of each asset are defined as [s.sub.1] = M / (M + S) and [s.sub.2] = S / (M + S). Under the simple-sum aggregate, the elasticity shall be equal to the share, [Alpha.sub.i] = [s.sub.i]. The long-run version of the simple-sum aggregate requires the equality of the long-run elasticity, [Alpha.sub.i] / (1 - [Beta.sub.3]) and the share of the asset [s.sub.i].

The estimated regression of equation (15) yields [Mathematical Expression Omitted] where the standard errors are given in parentheses. All coefficients are statistically significant and have expected signs. The short-run elasticities for money, and for time and savings deposits are 0.1114 and 0.1551 respectively. The corresponding long-run elasticities are 0.1716 and 0.2388 for M1B and S. These elasticities are far from the sample mean shares of 0.2913 for the holding in M1B and 0.7088 for the holding in S. Reestimating the regression with the restriction of constant returns to scale in the long-sum elasticity, the likelihood ratio test rejects the hypothesis of the simple-sum aggregate. Similar rejection is also obtained with the restriction of setting the long-run elasticities of M1B and S to the sample mean of the corresponding shares [s.sub.i].

These empirical findings based on an ad hoc demand equation are consistent with and comfirm the rejection of the simple-sum aggregate based on consumer utility maximization.

IV. Comparison of Various Liquidity Measures

The CES liquidity measure defined in (2) is a functional quantity aggregate of the real monetary assets. The simple-sum real monetary aggregate is a linear aggregate, which is a special case of functional aggregates. As defined in Barnett [2], the functional quantity aggregate depends only upon the quantities of the real monetary assets and unknown coefficients such as [Delta.sub.t] and [Lambda] in the CES function. It does not depend upon the user costs of assets. Two other index numbers, the Fisher Ideal quantity index and the Tornquist-Theil Divisia quantity index are also frequently used as liquidity measures [20]. These indices do not depend upon unknown coefficients. The Fisher Ideal liquidity measure is defined as [Mathematical Expression Omitted] and the Tornquist-Theil Divisia liquidity measure is [Mathematical Expression Omitted] where [Mathematical Expressions Omitted] is the user cost of the ith monetary asset [Mathematical Expressions Ommitted] at period t, and [Mathematical Expressions Omitted] if the share of the total user cost, i.e., [Mathematical Expression Omitted].

The series of liquidity measures, real M2, [L.sub.a], F and T are shown in Table AII in the Appendix. On average, the liquidity series [L.sub.a] is 3.2% higher than the real M2 series, while both the Fisher F and the Tornquist-Theil T measures are 1.4% larger than real M2. However, the variations in these four series are very close with the simple correlation coefficient between any two series being 0.999. The sample means and standard deviations are given in Table I.

To test the usefulness of the various aggregates, we follow the suggestion of Belongia and Chalfant [4] to compare these four monetary aggregates in the context of a St. Louis equation [1; 5]. This equation involves estimation of the impact of monetary and fiscal action on nominal GNP.

The updated version of a St. Louis equation is applied here by using an Almon distributed lag. The St. Louis equation to be estimated with AR(1) is written as [Mathematical Expression Omitted] where the dots over variables indicate quarterly rates of change. The variable Y is nominal GNP, L is the various nominal monetary aggregates (M2, [L.sup.a], F or T), G is government expenditures, and X is exports. A second degree polynomial with no endpoint restriction is employed in the Almon lag estimation.

Table II reports the results of estimating the equation across four monetary aggregates. In each case, government expenditures and exports show significant explanatory power in the determination of GNP. In contrast, Table II does not support the simple-sum M2 as a measure of the monetary aggregate. All three other measures, the liquidity measure [L.sup.a], the Fisher Ideal F, and the Tornquist-Theil Divisia T, have significant coefficients at the 5% level at least. [Tabular Data II Omitted]

V. Conclusion

In this paper, we have derived and estimated a model of monetary asset substitutability in Taiwan during the seventies and eighties when the financial sector experienced some major structural changes. The empirical results suggest that the high elasticities of substitution among financial assets in many developed countries may not necessarily be applicable to developing economies such as Taiwan with a dual financial system. An adequate model for the analysis

of asset substitution should take into account asset flows between the regulated and unregulated markets. [Tabular Data AI Omitted] (1)Table AI in the Appendix tabulates the estimated sizes of these markets. The regulated financial sector consists of financial intermediaries, the money market, and the capital market. The principal regulatory agencies are the central bank and the treasury department. The unregulated financial sector includes those financial loans among individuals, families, public and private business, and installment and leasing companies outside the regulated financial sector. These transactions are not organized are not subject to government regulations. The principle types of transactions are unsecured loans, deposits with firms, loan against post-dated checks, and loans from private financial cooperations (Pio-Hui). (2)Previous estimates [7; 8; 16; 17] of the interest cross-elasticity in Taiwan range from -0.00083 to -0.3449. (3)Unlike the model of Poterba and Rotemberg [19], the consumer's utility maximization presented in this paper is assumed to be nonstochastic. (4)Poterba and Rotemberg [19] argue that if numeraire asset [N.sub.t] gives utility explicitly and directly in (1), the utility function can be redefined, according to the budget constraint, to exclude the numeraire asset from the function. The direct utility of the assets is then attributed to the future consumption in (1). (5)These first-order conditions are the nonstochastic version of the Euler equations i.e., the perfect certainty case. See Poterba and Rotemberg [19]. (6)We are grateful to the referee for the suggestion of the instruments and the methods of estimation. (7)Chetty's estimate of elasticity of substitution between money and time deposit is 34.69; between money and the liabilities of saving and loan associations is 101.85; between money and deposits in mutual savings banks is 27.637. Poterba and Rotemberg's estimates are 1.308 and 1.230, respectively, for returns without and with tax adjustment.

References

[1]Andersen, L. C. and J. L. Jordan, "Monetary and Fiscal Actions: A Test of their Relative Importance in Economic Stabilization." Review, Federal Reserve of St. Louis, November 1968, 11-24. [2]Barnett, William A., "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory." Journal of Econometrics, September 1980, 11-48. [3]--, "The Optimal Level of Monetary Aggregation." Journal of Money, Credit, and Banking, Part 2, November 1982, 687-710. [4]Belongia, Michael T. and James A. Chalfant, "The Changing Empirical Definition of Money: Some Estimates from a Model of the Demand for Money Substitutes." Journal of Political Economy, April 1989, 387-97. [5]Carlson, Keith M., "A Monetary Analysis of the Administration's Budget and Economic Projections." Review, Federal Reserve Bank of St. Louis, May 1982, 3-14. [6]Chetty, V. Karuppan, "On Measuring the Nearness of Near-Moneys." American Economic Review, June 1969, 270-81. [7]Chen, Chau-Nan, and Jih-Her Hsu. "Demand for Money in Taiwan," in Essays on Money and Finance in Taiwan, edited by Cheng-Hsiung Chou. Taipei: Lien-Ching Publishing Company, 1975, pp. 299-304. [8]Chiang, Shuo-Chieh. "Strategies on Solving Financial Crisis due to Foreign Asset Accumulation," in Essay on Money and Finance in Taiwan, edited by Cheng-Hsiung Chou, Taipei: Lien-Ching Publishing Company, 1975, 437-57. [9]Clements, Kenneth W. and Phuong Nguyen, "Economic Aggregates--Comment." Journal of Econometrics, September 1980, 49-53. [10]Edwards, Franklin R., "More on Substitutability Between Money and Near-Monies." Journal of Money, Credit, and Banking, August 1972, 551-71. [11]Fair, Ray C., "The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables with First Order Serially Correlated Errors." Econometrica, May 1970, 507-16. [12]Feige, Edgar L. The Demand for Liquid Assets: A Temporal Cross-Section Analysis, Engelwood Cliffs., N. J.: Prentice-Hall, 1964. [13]--and Douglas K. Pierce, "The Substitutability of Money and Near Monies: A Survey of the Time Series Evidence." Journal of Economic Literature, June 1977, 439-69. [14]Gurley, John G. and Edward S. Shaw. Money in a Theory of Finance, Washington, D.C.: The Brookings Institute, 1960. [15]Hamburger, Morris J., "The Demand for Money by Households, Money Substitutes, and Monetary Policy." Journal of Political Economy, December 1966, 600-623. [16]Hus, Jia-Ton, "Income Elasticity of Money Demand in Taiwan." Academia Economic Papers. Academia Sinica, Taipei, September 1983, 13-30. [17]Liang, Ming-E, Kung-Min Chen, and So-Hsiang Liu. Further Study on the Demand for Money in Taiwan. Taipei: Chung-Huq Economic Institute, 1982. [18]Moroney, John T. and Barry J. Wilbratte, "Money and Money Substitutes: A Time Series Analysis of Household Portfolios." Journal of Money, Credit, and Banking, May 181-98. [19]Poterba, James M. and Julio J. Rotemberg. "Money in the Utility Function: An Empirical Implementation," in New Approaches to Monetary Economics, edited by William A. Barnett and Kenneth J. Singleton. Cambridge: Cambridge University Press, 1987, pp. 219-40. [20]Serletis, Apostolos and A. Leslie Robb, "Divisia Aggregation and Substitutability Among Monetary Assets." Journal of Money, Credit, and Banking, November 1986, 430-46.

The financial sector of the Taiwan economy has experienced major structural changes in the past decade. The banking system has been liberalized, a regulated money market has developed, and the foreign exchange market has been deregulated. Nevertheless, Taiwan's financial sector is still characterized by dualism, with the coexistence of both regulated and unregulated (curb) markets. The ratio of financial loans from the unregulated market to those from the regulated market for the total private enterprise has been consistently large, averaging 27.5% for the period 1971-88.(1) Interest rates in the unregulated markets of Taiwan are generally much higher than those in the regulated markets. Figure 1 shows the disparity in interest rates between these two markets. The difference in interest rates grew during the 1970s, reaching an annual rate of 23 percent in the second quarter of 1979. Since then, the differential has declined steadily to about 17 percent in 1988.

Because the financial loans from the unregulated market constitute a major portion of all private borrowing in Taiwan, we believe that studies of characteristics of financial markets in Taiwan should include the unregulated market as well as the regulated market. It is the purpose of this paper to extend the study of asset substitutability in Taiwan to include the unregulated financial market.

Accurate empirical measurement of the degree of substitutability among various liquid assets is important for two distinct but related reasons. The first is the well-known Gurley-Shaw thesis [14] which relates the role of nonbank financial intermediaries to the monetary process. According to this view, any government monetary policy will be substantially offset if the liabilities of financial intermediaries are close substitutes for money. The second reason has to do with the appropriate definition of "money" and asks if a simple-sum aggregate such as M2 is a good measure of the money stock and is an appropriate monetary target [2; 3; 6; 10; 15].

The most common procedure to measure the degree of substitutability is the estimation of interest cross-elasticity from a demand function for currency and demand deposits [12; 13; 18]. The demand function typically includes the rates of return on one of more near-money assets, plus an income or wealth measure as an explanatory variable. Theory and empirical estimates, however, provide little guidance about the magnitude of cross-elasticity that constitutes a "close" substitutability.(2) The interest cross-elasticity approach therefore fails to bridge the gap between empirical estimates and policy issues.

This paper follows the approach, first proposed by Chetty and later extended by Barnett, of estimating the degree of asset substitutability by direct estimation of the parameters of a utility function. Following Barnett, our model specifically recognizes the consumer's inter-temporal choice implicit in the choice between consumption and holding assets. We consider an infinitely lived consumer who derives utility from consumer goods and the services provided by real money holdings. Including the equity holdings in the unregulated financial market in the consumer budget constraint, we account explicitly for the existence of dual markets. Moreover, the model allows for the possibility that a consumer's liquidity service may vary with economic growth. We assume that the shares of assets in the consumer's portfolio are time-dependent and are functions of income. Estimates of the parameters of this model are used to construct a measure of a monetary aggregate which is consistent with the individual's utility maximization. The remainder of this paper is divided into three sections. In section II, a general theoretical model is presented. Section III describes data and presents the empirical results. Section IV presents a comparison of various measures of monetary aggregates. A brief conclusion is given in section V.

II. The Model

Consider the decision problem of an infinitely lived consumer who derives utility from both consumption and the liquidity service provided by holding various assets. Denote the consumption and liquidity service at time t by [C.sub.t] and [L.sub.t].

The consumer is assumed to maximize the discounted utility.(3) (1) [Mathematical Expression Omitted] where [Rho] is the subjective discount rate and U(.) is the concave utility function, and U(.) is monotonically increasing in both [C.sub.t] and [L.sub.t].

Since our interest is in the estimation of liquidity service [L.sub.t], it is necessary to specify how liquidity service is related to asset holding. The measure of liquidity service is assumed to be a constant elasticity of substitution (CES) function of real money holing, [M.sub.t]/[P.sub.t] and real savings and time deposits, [S.sub.t]/[P.sub.t], where [P.sub.t] is a price index, (2) [Mathematical Expression Omitted] The coefficient [Lambda] determines the elasticity of substitution between real money holding and real savings and time deposits, and is given by 1/(1 - [Lambda]). The distribution coefficient [[Delta].sub.t] is assumed to be time-dependent. When [[Delta].sub.t] = 1/2 and [Lambda] = 1, the real money holding and real savings and time deposits are identical with respect to liquidity service. In this case, money and interest bearing deposits are perfect substitutes, and the liquidity measure L is equivalent to the simple-sum monetary aggregate, (M + S)/P.

The consumer budget constraint at time i is (3) [Mathematical Expression Omitted] where [N.sub.i] is the equity holdings in the unregulated market and serves as the numeraire asset.(4) [Y.sub.i] is real income from non-asset service, [r.sub.i] is the nominal rate of return on holding equity, and [d.sub.i] is the nominal rate of return on savings and time deposits.

Following Barnett [2], the budget constraints (3) can be solved for the equity holding for the period i = t + T. By repeatedly backward substituting the equity holding [N.sub.j] for the period j [is less than or equal to] t + T down to period t, the multi-period constraints can be expressed as a single constraints, (4) [Mathematical Expression Omitted] where [[Eta].sub.i] = 1, for i = t

= (1 + [r.sub.t])(1 + [r.sub.t+1])...(1 + [r.sub.t-1]), for t + 1 [is less than or equal to] i [is less than or equal to] t + T.

The budget constraint (4) shows that the Jorgensonian user cost (or rental price) of holding money [M.sub.i] at the ith period is [Mathematical Expression Omitted] and the user cost of holding savings and time deposits [S.sub.i] is [Mathematical Expression Omitted] At current period i = t, the user costs for [M.sub.t] and [S.sub.t] are, respectively, (5) [Mathematical Expression Omitted]

The consumer's portfolio choice then is to maximize the utility function (1) subject to the single constraint (4). Alternatively, the multiperiod budget constraints (3) can be solved for [C.sub.t], [C.sub.t+1], . . . , and then can be substituted into the utility function (1) directly. Differentiating the resulting equation with respect to [N.sub.t], [M.sub.t], and [S.sub.t] yields the following first-order conditions for maximization.(5) (6) [Mathematical Expression Omitted] (7) [Mathematical Expression Omitted] (8) [Mathematical Expression Omitted]

Equation (6) states that the optimal allocation of inter-temporal consumption requires that the utility cost of giving up a unit of consumption in period t, i.e., [Delta] U/[Deltal] [C.sub.t] is to be exactly compensated in period (t + 1), i.e., [Rho] (1 + [r.sub.t]) [P.sub.t] ([Delta] U/ [Delta] [C.sub.t + 1])/[P.sub.t + 1]. Equation (7) equates the utility cost of foregoing one unit of consumption in period t and the utility gain from allocating that unit to money holding [Mathematical Expression Omitted] and then to consumption in the next period, [Rho] [P.sub.t] ([Delta] U/[Delta] [C.sub.t + 1)/[P.sub.t + 1]. Similarly, equates (8) equates the utility cost of reducing current consumption and the utility gain of increasing liquidity and of consumption in the next period.

Solving equation (6) for [Delta] U/[Delta] [C.sub.t + 1] and substituting it into equations (7) and (8), the first-order conditions can be combined to yield an equation that determines the ratio of money to savings and time deposits, (9) 1n([M.sub.t]/[S.sub.t] = 1n [[Delta].sub.t]/(1 - [Delta].sub.t])/(1 - [Lambda]) + 1n[([r.sub.t] - [d.sub.t])/[r.sub.t]]/(1 - [Lambda]).

Equation (9) states that the ratio of user cost of the savings and time deposits, ([r.sub.t] - [d.sub.t])/(1 + [r.sub.t]), to the user cost of money holding, [r.sub.t]/(1 + [r.sub.t]), determines the variation in the ratio of liquidity assets. Since the return [r.sub.t] on the equity holding [N.sub.t] is a determinant of user costs, we explicitly recognize the importance of the unregulated financial market in the consumer portfolio choice. The asset ratio in equation (9) also varies with the time-dependent distribution coefficient [[Delta].sub.t] of the liquidity service CES function (2). Given a time period t, the marginal rate of substitution (MRS) between the real money holding and the real savings and time deposits is defined as the ratio of the marginal utilities of their liquidity services. [MRS.sub.t] = [[[Delta].sub.t]/(1 - [[Delta].sub.t]) ([M.sub.t]/[S.sub.t]).sup.[Lambda] - 1]

The MRS varies with the ratio of asset stocks ([M.sub.t]/[S.sub.t]) and [[Delta].sub.t]. We propose that [[Delta].sub.t] be specified to be a function of the non-asset income [Y.sub.t] and seasonal variation in a logistic form, (10) [Mathematical Expression Omitted] where [Q.sub.t] is a seasonal dummy variable. This specification allows the liquidity services of money and savings and time deposits to depend on economic growth. The seasonal variation accounts for a temporary shift in the marginal utility of liquidity service in short-run.

Substituting equation (10) into (9), a regression equation of the logarithm of the asset stock ratio (M/S) can then be estimated, (11) 1n([M.sub.t]/[S.sub.t] = [a.sub.o]/(1 - [Lambda]) + [a.sub.1] [Q.sub.t]/(1 - [Lambda]) +

[a.sub.2] 1n([Y.sub.t])/(1-[Lambda]) + 1n[([r.sub.t] - [d.sub.t])/[r.sub.t]]/(1 - [Lambda ]) + [U.sub.t]

where [U.sub.t] is an added random error term.

III. Data and Estimation

The quarterly time series data used in the analysis are obtained from Financial Statistics Monthly published by the Central Bank of China, and Quarterly National Income Statistics in Taiwan Area published by the Directorate-General of Budget, Accounting and Statistics. The sample periods cover from the first quarter of 1971 to the fourth quarter of 1987 for a total of 68 quarters.

The liquid asset holdings consist of the household holdings of MIB and S = M2 - M1B. The money holding M1B includes net currency and demand deposits, passbook and passbook savings deposits. The measure of S includes time deposits with various maturities of one, three, nine months, and one year, and savings deposits with maturities of one, two, and three years. The household holdings portions of M1B and M2 are calculated directly from the annual flow of fund accounts in the Flow of Funds in Taiwan District, published by the Central Bank of China. These household holdings of monetary assets are deflated by the consumer price index P. However, the GNP deflator is used for calculating the real GNP figures. All measures are in millions of NT dollars.

Since the equity holdings is to serve as the numeraire asset and is defined as the assets held by individuals outside the regulated money market, we measure its return r with the interest rate in the unregulated money market. Since Taipei is the largest and most active unregulated market in Taiwan, we use the average interest rate of loans against post-dated checks in Taipei city in our estimation. The other asset return, d, represents the interest rate paid to the time and saving deposits in the regulated money market, and is a weighted geometric mean of the deposits with various maturities. The weights are the shares of these deposits.

A diagnostic test on the correlograms of the regression error in equation (11) reveals characteristics of a mixed autoregressive moving average stochastic process in the terms [U.sub.t]. In estimating the equation, an autoregressive moving average of first-order is therefore employed. The ARMA (1, 1) assumes the stochastic process, [U.sub.t] = [Phi] [U.sub.t-1] + [Theta] [[Epsilon].sub.1] + [[Epsilon].sub.t]. The ARMA (1, 1) model requires ~[Phi]~ < 1 for stationarity and ~[Theta]~ < 1 for invertibility.

In estimating the asset substitution equation (11), the ratio of user costs in money holding [M.sub.t] and time deposits [S.sub.t] is lagged by 4 quarters. That is, the lagged regressor [[(r - d)/r].sub.t-4] is used in the regression. This is due to the fact that the interest on the deposits with maturities over 12 months are generally received annually. Furthermore, over 81% of savings and time deposits [S.sub.t] had maturity over 12 months during the sample period.

The quarter dummy variable [Q.sub.t] is defined as [Q.sub.t] = 1 if it is in the quarter, and [Q.sub.t] = 0 otherwise. The coefficient is expected to be positive to reflect the short-term seasonal demand for liquid assets during the Chinese New York holiday.

The asset substitution is estimated by Fair's instrumental variable method [11] with an ARMA (1, 1) process. The instruments used in the estimation are the fuel price index, exports, and government expenditures since these instruments were largely determined by the external factors that are not under the influence of monetary shock.(6) (12) [Mathematical Expression Omitted] where the standard errors are given in parentheses.

All coefficients are statistically significant and have the expected signs. The elasticity of substitution 1/(1 - [Lambda]) is estimated to be 0.8525 which is considerably smaller than the elasticity of substitution in the U.S. estimated by Chetty [6] and by Poterba and Rotemberg [19].(7) The inelastic substitution estimate, however, is larger than Barnett's [2] estimate of 0.28 between the supernumerary transaction balance and the supernumerary passbook saving aggregate. The low elasticity of substitution in Taiwan nevertheless rejects the infinite elasticity of substitution implied in the simple-sum monetary aggregate. This result does not provide strong support for the Gurley and Shaw hypothesis that savings and time deposits are good substitutes for money in Taiwan. In fact, our finding of low substitution between these two assets is consistent with, and reinforces the importance of the existence of dual financial markets in Taiwan. Given the presence of a large unregulated money market that offers high nominal rates of return, an individual must make his portfolio choice between high yield and high risk in the unregulated market, and the low yield and low risk in the regulated market. The portfolio choice between the two markets is not relevant if the size of the equity holding in the unregulated market is minimal or the marginal utility of future consumption from the equity holding is zero. Neither of these cases is consistent with the Taiwan financial market.

Given the estimated coefficients in equation (11) the implied liquidity services or aggregate is given by (13) [Mathematical Expressions Omitted] where [Mathematical Expression Omitted]. in order to compare the estimates of the liquidity services given in equation (13) with the simple-sum real monetary aggregate (M + S)/P, it is necessary to make certain adjustments to this measure. Since the liquidity services defined in [L.sub.t] are an ordinal measure, no monotonic transformation of [L.sub.t] alters the estimates of the coefficients. To compare the two series, we therefore normalize the estimated series [L.sub.t] so that the geometric means of the two series within the sample period are identical. This implies that the quarterly series of [L.sub.t] calculated from equation (13) is multiplied by 2.0187. The new liquidity series [Mathematical Expressions Omitted] is then (14) [Mathematical Expressions Omitted]

Table AII in Appendix shows the simple-sum real M2 aggregate and the adjusted liquidity series [L.sup.a] along with two other quarterly aggregates. The real M2 and [L.sup.a] series are remarkably close and have identical turning points during these periods. The upper part of Figure 2 depicts the quarterly rates of change. The average quarterly rate of change for real M2 aggregate is 4.1%, and the average for the liquidity series [L.sub.a] is 4.5%. The lower part of Figure 2 displays the inflation rate in the consumer price index. The inflation rate over time moves inversely to the demand for liquidity series [L.sup.a] and real M2. The simple correlation between the inflation rate and change in real M2 is -0.78, while it is -0.72 between the inflation rate and changes in [L.sup.a].

The rejection of an infinite elasticity of substitution implied in the simple-sum monetary assets is based on consumer utility maximization. An alternative test of the simple-sum aggregation based on an ad hoc demand for money equation was illustrated by Clements and Nguyen [9]. Their approach is to estimate the regression (15) [Mathematical Expression Omitted] where [Delta] 1n([X.sub.t]) = 1n ([X.sub.t]) -- 1n([X.sub.t-1]) denotes the difference. The liquidity or "moneyness" of each monetary asset is identified by its elasticity [Alpha.sub.i]. The shares of each asset are defined as [s.sub.1] = M / (M + S) and [s.sub.2] = S / (M + S). Under the simple-sum aggregate, the elasticity shall be equal to the share, [Alpha.sub.i] = [s.sub.i]. The long-run version of the simple-sum aggregate requires the equality of the long-run elasticity, [Alpha.sub.i] / (1 - [Beta.sub.3]) and the share of the asset [s.sub.i].

The estimated regression of equation (15) yields [Mathematical Expression Omitted] where the standard errors are given in parentheses. All coefficients are statistically significant and have expected signs. The short-run elasticities for money, and for time and savings deposits are 0.1114 and 0.1551 respectively. The corresponding long-run elasticities are 0.1716 and 0.2388 for M1B and S. These elasticities are far from the sample mean shares of 0.2913 for the holding in M1B and 0.7088 for the holding in S. Reestimating the regression with the restriction of constant returns to scale in the long-sum elasticity, the likelihood ratio test rejects the hypothesis of the simple-sum aggregate. Similar rejection is also obtained with the restriction of setting the long-run elasticities of M1B and S to the sample mean of the corresponding shares [s.sub.i].

These empirical findings based on an ad hoc demand equation are consistent with and comfirm the rejection of the simple-sum aggregate based on consumer utility maximization.

IV. Comparison of Various Liquidity Measures

The CES liquidity measure defined in (2) is a functional quantity aggregate of the real monetary assets. The simple-sum real monetary aggregate is a linear aggregate, which is a special case of functional aggregates. As defined in Barnett [2], the functional quantity aggregate depends only upon the quantities of the real monetary assets and unknown coefficients such as [Delta.sub.t] and [Lambda] in the CES function. It does not depend upon the user costs of assets. Two other index numbers, the Fisher Ideal quantity index and the Tornquist-Theil Divisia quantity index are also frequently used as liquidity measures [20]. These indices do not depend upon unknown coefficients. The Fisher Ideal liquidity measure is defined as [Mathematical Expression Omitted] and the Tornquist-Theil Divisia liquidity measure is [Mathematical Expression Omitted] where [Mathematical Expressions Omitted] is the user cost of the ith monetary asset [Mathematical Expressions Ommitted] at period t, and [Mathematical Expressions Omitted] if the share of the total user cost, i.e., [Mathematical Expression Omitted].

The series of liquidity measures, real M2, [L.sub.a], F and T are shown in Table AII in the Appendix. On average, the liquidity series [L.sub.a] is 3.2% higher than the real M2 series, while both the Fisher F and the Tornquist-Theil T measures are 1.4% larger than real M2. However, the variations in these four series are very close with the simple correlation coefficient between any two series being 0.999. The sample means and standard deviations are given in Table I.

Table I. Means and Standard Deviations of Various Monetary Aggregates Mean(*) Standard deviation(*) Real M2 924,295 692,883 [L.sup.a] 953,384 751,693 F 937,410 688,572 T 937,622 688,751 (*)Millions of NT dollars Table AII. Various Liquidity Measures(*) Year Real M2 [L.sup.a] F T 1971.1 213,309 179,072 213,309 213,309 1971.2 228,166 192,820 227,134 227,134 1971.3 239,454 200,108 237,819 237,818 1971.4 246,629 209,920 245,400 245,400 1972.1 253,420 222,459 255,075 255,076 1972.2 268,736 238,749 269,839 269,840 1972.3 280,056 244,043 280,042 280,042 1972.4 302,303 269,507 302,977 302,977 1973.1 339,991 327,340 353,416 353,497 1973.2 354,662 346,478 370,258 370,344 1973.3 350,530 344,159 367,662 367,748 1973.4 324,924 323,541 343,538 343,619 1974.1 283,804 281,442 301,939 302,010 1974.2 285,523 279,247 298,438 298,508 1974.3 316,745 306,283 328,240 328,316 1974.4 335,998 323,316 345,822 345,903 1975.1 373,796 359,300 386,910 387,000 1975.2 389,442 379,445 404,219 404,312 1975.3 414,177 404,725 429,829 429,929 1975.4 430,316 424,991 447,696 447,799 1976.1 442,242 436,840 460,935 461,043 1976.2 453,397 449,459 470,025 470,134 1976.3 477,422 472,896 492,919 493,033 1976.4 508,573 507,926 525,628 525,750 1977.1 547,571 544,956 567,991 568,122 1977.2 576,934 579,050 597,327 597,465 1977.3 598,877 600,283 620,312 620,456 1977.4 642,415 653,253 667,756 667,911 1978.1 678,756 692,082 713,028 713,197 1978.2 705,622 726,182 742,155 742,331 1978.3 748,189 771,937 785,170 785,357 1978.4 777,574 805,578 818,923 819,117 1979.1 757,825 778,656 792,461 792,647 1979.2 721,658 745,624 752,055 752,231 1979.3 701,454 724,644 731,356 731,527 1979.4 714,940 739,902 744,931 745,107 1980.1 689,747 708,888 716,296 716,464 1980.2 692,497 715,375 717,749 717,918 1980.3 694,391 717,675 720,047 720,217 1980.4 711,980 738,518 737,855 738,028 1981.1 712,950 732,538 737,660 737,833 1981.2 729,576 754,190 749,495 749,670 1981.3 742,238 766,417 759,690 759,868 1981.4 787,743 816,306 806,333 806,521 1982.1 875,370 901,481 901,108 901,318 1982.2 915,477 945,794 934,002 934,216 1982.3 962,244 994,362 981,066 981,291 1982.4 1,035,587 1,072,014 1,053,535 1,053,776 1983.1 1,099,640 1,108,640 1,099,377 1,099,629 1983.2 1,158,243 1,197,765 1,172,812 1,173,081 1983.3 1,231,759 1,278,195 1,245,104 1,245,390 1983.4 1,314,360 1,364,648 1,326,173 1,326,479 1984.1 1,390,835 1,440,184 1,406,141 1,406,464 1984.2 1,449,256 1,510,048 1,457,152 1,457,484 1984.3 1,527,082 1,591,994 1,531,773 1,532,120 1984.4 1,612,612 1,673,378 1,613,871 1,614,237 1985.1 1,620,306 1,635,065 1,607,395 1,607,730 1985.2 1,723,439 1,736,334 1,699,999 1,700,340 1985.3 1,846,186 1,856,406 1,816,660 1,817,021 1985.4 1,958,986 1,976,169 1,927,963 1,928,346 1986.1 1,983,624 2,013,685 1,957,721 1,958,110 1986.2 2,038,165 2,112,113 2,015,584 2,015,984 1986.3 2,131,693 2,247,389 2,114,842 2,115,267 1986.4 2,275,514 2,441,422 2,267,462 2,267,926 1987.1 2,431,193 2,632,888 2,450,279 2,459,989 1987.2 2,615,167 2,863,663 2,637,505 2,638,269 1987.3 2,722,404 2,998,131 2,747,505 2,748,298 1987.4 2,904,136 3,202,234 2,941,182 2,942,034 (*)Million of NT dollars

To test the usefulness of the various aggregates, we follow the suggestion of Belongia and Chalfant [4] to compare these four monetary aggregates in the context of a St. Louis equation [1; 5]. This equation involves estimation of the impact of monetary and fiscal action on nominal GNP.

The updated version of a St. Louis equation is applied here by using an Almon distributed lag. The St. Louis equation to be estimated with AR(1) is written as [Mathematical Expression Omitted] where the dots over variables indicate quarterly rates of change. The variable Y is nominal GNP, L is the various nominal monetary aggregates (M2, [L.sup.a], F or T), G is government expenditures, and X is exports. A second degree polynomial with no endpoint restriction is employed in the Almon lag estimation.

Table II reports the results of estimating the equation across four monetary aggregates. In each case, government expenditures and exports show significant explanatory power in the determination of GNP. In contrast, Table II does not support the simple-sum M2 as a measure of the monetary aggregate. All three other measures, the liquidity measure [L.sup.a], the Fisher Ideal F, and the Tornquist-Theil Divisia T, have significant coefficients at the 5% level at least. [Tabular Data II Omitted]

V. Conclusion

In this paper, we have derived and estimated a model of monetary asset substitutability in Taiwan during the seventies and eighties when the financial sector experienced some major structural changes. The empirical results suggest that the high elasticities of substitution among financial assets in many developed countries may not necessarily be applicable to developing economies such as Taiwan with a dual financial system. An adequate model for the analysis

of asset substitution should take into account asset flows between the regulated and unregulated markets. [Tabular Data AI Omitted] (1)Table AI in the Appendix tabulates the estimated sizes of these markets. The regulated financial sector consists of financial intermediaries, the money market, and the capital market. The principal regulatory agencies are the central bank and the treasury department. The unregulated financial sector includes those financial loans among individuals, families, public and private business, and installment and leasing companies outside the regulated financial sector. These transactions are not organized are not subject to government regulations. The principle types of transactions are unsecured loans, deposits with firms, loan against post-dated checks, and loans from private financial cooperations (Pio-Hui). (2)Previous estimates [7; 8; 16; 17] of the interest cross-elasticity in Taiwan range from -0.00083 to -0.3449. (3)Unlike the model of Poterba and Rotemberg [19], the consumer's utility maximization presented in this paper is assumed to be nonstochastic. (4)Poterba and Rotemberg [19] argue that if numeraire asset [N.sub.t] gives utility explicitly and directly in (1), the utility function can be redefined, according to the budget constraint, to exclude the numeraire asset from the function. The direct utility of the assets is then attributed to the future consumption in (1). (5)These first-order conditions are the nonstochastic version of the Euler equations i.e., the perfect certainty case. See Poterba and Rotemberg [19]. (6)We are grateful to the referee for the suggestion of the instruments and the methods of estimation. (7)Chetty's estimate of elasticity of substitution between money and time deposit is 34.69; between money and the liabilities of saving and loan associations is 101.85; between money and deposits in mutual savings banks is 27.637. Poterba and Rotemberg's estimates are 1.308 and 1.230, respectively, for returns without and with tax adjustment.

References

[1]Andersen, L. C. and J. L. Jordan, "Monetary and Fiscal Actions: A Test of their Relative Importance in Economic Stabilization." Review, Federal Reserve of St. Louis, November 1968, 11-24. [2]Barnett, William A., "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory." Journal of Econometrics, September 1980, 11-48. [3]--, "The Optimal Level of Monetary Aggregation." Journal of Money, Credit, and Banking, Part 2, November 1982, 687-710. [4]Belongia, Michael T. and James A. Chalfant, "The Changing Empirical Definition of Money: Some Estimates from a Model of the Demand for Money Substitutes." Journal of Political Economy, April 1989, 387-97. [5]Carlson, Keith M., "A Monetary Analysis of the Administration's Budget and Economic Projections." Review, Federal Reserve Bank of St. Louis, May 1982, 3-14. [6]Chetty, V. Karuppan, "On Measuring the Nearness of Near-Moneys." American Economic Review, June 1969, 270-81. [7]Chen, Chau-Nan, and Jih-Her Hsu. "Demand for Money in Taiwan," in Essays on Money and Finance in Taiwan, edited by Cheng-Hsiung Chou. Taipei: Lien-Ching Publishing Company, 1975, pp. 299-304. [8]Chiang, Shuo-Chieh. "Strategies on Solving Financial Crisis due to Foreign Asset Accumulation," in Essay on Money and Finance in Taiwan, edited by Cheng-Hsiung Chou, Taipei: Lien-Ching Publishing Company, 1975, 437-57. [9]Clements, Kenneth W. and Phuong Nguyen, "Economic Aggregates--Comment." Journal of Econometrics, September 1980, 49-53. [10]Edwards, Franklin R., "More on Substitutability Between Money and Near-Monies." Journal of Money, Credit, and Banking, August 1972, 551-71. [11]Fair, Ray C., "The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables with First Order Serially Correlated Errors." Econometrica, May 1970, 507-16. [12]Feige, Edgar L. The Demand for Liquid Assets: A Temporal Cross-Section Analysis, Engelwood Cliffs., N. J.: Prentice-Hall, 1964. [13]--and Douglas K. Pierce, "The Substitutability of Money and Near Monies: A Survey of the Time Series Evidence." Journal of Economic Literature, June 1977, 439-69. [14]Gurley, John G. and Edward S. Shaw. Money in a Theory of Finance, Washington, D.C.: The Brookings Institute, 1960. [15]Hamburger, Morris J., "The Demand for Money by Households, Money Substitutes, and Monetary Policy." Journal of Political Economy, December 1966, 600-623. [16]Hus, Jia-Ton, "Income Elasticity of Money Demand in Taiwan." Academia Economic Papers. Academia Sinica, Taipei, September 1983, 13-30. [17]Liang, Ming-E, Kung-Min Chen, and So-Hsiang Liu. Further Study on the Demand for Money in Taiwan. Taipei: Chung-Huq Economic Institute, 1982. [18]Moroney, John T. and Barry J. Wilbratte, "Money and Money Substitutes: A Time Series Analysis of Household Portfolios." Journal of Money, Credit, and Banking, May 181-98. [19]Poterba, James M. and Julio J. Rotemberg. "Money in the Utility Function: An Empirical Implementation," in New Approaches to Monetary Economics, edited by William A. Barnett and Kenneth J. Singleton. Cambridge: Cambridge University Press, 1987, pp. 219-40. [20]Serletis, Apostolos and A. Leslie Robb, "Divisia Aggregation and Substitutability Among Monetary Assets." Journal of Money, Credit, and Banking, November 1986, 430-46.

Printer friendly Cite/link Email Feedback | |

Author: | Charles Lin Shun-Ying |
---|---|

Publication: | Southern Economic Journal |

Date: | Apr 1, 1992 |

Words: | 5285 |

Previous Article: | Rational ignorance: the strategic economics of military censorship. |

Next Article: | Brand-name investment of candidates and district homogeneity: an ordinal response model. |

Topics: |