# Economic reforms and long-run money demand in China: implications for monetary policy.

I. Introduction

Although money demand equations have been estimated for many western countries, only recently have researchers investigated the demand for money in centrally planned economies like China. Chow |7~, who helped pioneer the analysis of Chinese macro data, estimates a simple money demand function derived from the quantity theory. Using annual data from 1952 through 1983, he concludes that the quantity theory "provides a reasonable first approximation in explaining the demand for money in China." |7, 325~ Portes and Santorum |27~ use real and nominal adjustment specifications and test for the homogeneity of money demand with respect to the price level and real income.(1) Feltenstein and Farhadian |11~ estimate a money demand function based on Cagan's |3~ work, and Blejer et al. |1~ estimate an error correction model using data for only the 1980s. Both studies find that the demand for real balances is explained by real income and an opportunity cost measure.

A common feature of such studies is the use of a standard lagged-adjustment specification to capture the short-run dynamics of money demand. Such dynamic specifications have been the subject of much recent work, the bulk of which suggests that they fail on theoretical and econometric grounds.(2) Another feature is the presumption that a long-run equilibrium relationship underlies the short-run dynamic models being estimated.(3) If such an equilibrium relationship does not exist, attempts to measure the short-run dynamics of a given specification are misdirected.

The purpose of this study is to determine if there exists a long-run, equilibrium relationship between nominal money balances, real income, prices and interest rates using data for China. We do so by applying the tests for cointegration due to Johansen and Juselius |20~. While most previous applications of such tests to money demand have focused on advanced market economies |15; 18; 20~, this study represents an exploratory attempt to determine if such basic economic forces also hold in centrally planned economies like China. While the limited sample (1952-88) affects the power of our test statistics, the results are informative and provide a basis to which future studies can be compared.

Our analysis also allows us to consider which monetary measure is preferable in determining the long-run effect of monetary policy actions. Previous work by Portes and Santorum |27~ and Chen |5~, for example, indicates that currency in circulation is preferable to a broader measure. Such conclusions, based on estimates of short-run money demand functions, may not hold when considering the long-term equilibrium relationship. Moreover, the issue of which aggregate to use has become increasingly important in light of continuing economic reforms in China.

The format of the paper is as follows. Section II provides an overview of economic and financial reforms in China. Section III provides a brief discussion of the cointegration test procedures. A description of the data is in section IV followed by our empirical results in section V. Concluding remarks close the paper in section VI.

II. Reforms

Economic and financial reforms since the late 1970s in China have brought about major changes in the conduct of Chinese monetary policy.(4) Before the reforms, currency in circulation was considered the nation's money supply since cash was used mainly for transactions between the state and household sectors of the economy. Macroeconomic policy was determined solely by the State Council: Independent monetary policies conducted by a central bank did not exist, and ". . . the role of monetary policy was essentially to support the implementation of the physical output targets contained in the |central~ plan . . ." |1, 12~ The economic reforms emphasized the use of market forces for the allocation of resources.

The banking system was reformed in order to separate banking functions and create new policy instruments to achieve better control over the economy. In particular, the People's Bank of China (PBC) was created in 1984 with its own monetary policy instruments. The PBC controls the total volume of credit in the economy and works closely with the State Council in making important macroeconomic policy decisions. The commercial aspects of banking are controlled by the Industrial and Commercial Bank of China. Although this bank competes with specialized banks and others established at the province level, the government credit plan continues to influence monetary policy decisions.(5)

Financial reforms gave state enterprises more freedom in decision-making and permission to retain some of their profits. These earnings were allowed to be put in special time deposit accounts (in the form of trust deposits) and used to finance investment expenditures. Most state enterprises also were allowed for the first time to use checking accounts for many financial transactions |28~. Financial reforms promoted household savings by introducing new financial instruments and services. New institutions were created for this purpose, including credit cooperatives and special savings banks. The role of the specialized savings banks is to raise sufficient funds consistent with the desired investment level set by the State Council. Naughton |23~ observes that these institutional developments brought about a substantial increase in the volume of bank deposits, the greatest growth being in enterprise deposits and urban savings deposits, followed by rural deposits.(6)

A potential implication of these financial reforms is the increased importance of monetary aggregates in policy decisions. De Wulf and Goldsborough note that ". . . together with the need for greater emphasis on developments in household bank deposits, which are a fairly close substitute for cash, the greater autonomy of enterprises and local governments implies that broader monetary aggregates than household currency holdings should become increasingly important in setting targets for monetary policy . . ." |8, 233~ Thus, China's policy makers must address the choice of currency in circulation (M0) or the broader monetary aggregate that includes savings deposits (M2) in setting policy. In this vein, others have compared the relationship between economic activity and M0 or M2 using a variety of models. Portes and Santorum |27~ use Granger-type causality tests, and Chen |5~ a vector autoregressive (VAR) model to study the empirical link between the monetary aggregates and economic activity. Both studies conclude that currency (M0) is better related to economic activity and, hence, the preferable policy measure. In contrast, Hafer and Kutan |16~ provide support for both M0 and M2 in setting monetary policy. By establishing whether there exists a long-run relationship between either monetary aggregate and income, prices and interest rates, this paper contributes to this literature. If such a relationship is rejected, the feasibility of an aggregate in formulating policy must be questioned.

III. Methodological Issues(7)

Even though economic time series may be nonstationary in their level, there may exist some linear combination of these variables that converge to a long run relationship over time. If the series individually are stationary after differencing but a linear combination of their levels is stationary, then the series are said to be cointegrated. Engle and Granger's |10~ test for cointegration is cast in terms of bivariate relationships. Johansen and Juselius |20~ extend these tests to a multivariate setting.

The question is whether a cointegrating vector between money balances, income and interest rates exists for China. To test for cointegration among these variables, consider the equation

|X.sub.t~ = ||Pi~.sub.1~ |X.sub.t-1~ + . . . + ||Pi~.sub.k~ |X.sub.t-k~ + ||Epsilon~.sub.t~ (t = 1, . . . , T) (1)

where |X.sub.t~ is a sequence of random vectors with components (|X.sub.1t~, . . . , |X.sub.pt~) and the innovations to this process (the |Epsilon~'s) are drawn from a p-dimensional i.i.d. Gaussian distribution with co-variance |Lambda~ and |X.sub.-k+1~, . . . , |X.sub.0~ fixed. Equation (1) is simple a VAR model, usually estimated in first-difference form since most macroeconomic time series are nonstationary in their levels. This approach necessarily leads to a loss of information about the variables' long-term relationship and, if they are cointegrated, results in a misspecification of the model.

Letting |Delta~ represent the first difference operator, equation (1) can be written in the form

|Delta~|X.sub.t~ = ||Gamma~.sub.1~ |Delta~|X.sub.t-1~ + . . . + ||Gamma~.sub.k-1~ |Delta~|X.sub.t-1+k~ - |Pi~|X.sub.t-k~ + ||Epsilon~.sub.t~ (2)

where

||Gamma~.sub.i~ = -I + ||Pi~.sub.1~ + . . . + ||Pi~.sub.i~ (i = 1, . . . , k - 1)

and

|Pi~ = I - ||Pi~.sub.1~ - . . . - ||Pi~.sub.k~.(8)

The difference between the standard first-difference version of the VAR model and equation (1) is the term |Pi~|X.sub.t-k~. It is this part of the equation that conveys the information about the long-run relationship between the X variables of the model. If |X.sub.t~ is nonstationary in levels but its first difference is stationary, then it is said to be integrated of order one. Because there are several elements of the vector which may be cointegrated individually, it may be that one or more linear combinations of these nonstationary vectors are stationary. In other words, there may exist more than one linear combination of the variables that converges to some long-run relationship over time.

The test procedure examines the p x p |Pi~ matrix. If this matrix has rank 0 then all elements of ||Pi~.sub.t~ have unit roots and first-differencing is suggested. If the matrix is of full rank p, then all elements of |X.sub.t~ are stationary in their levels. When 0 |is less than~ rank (|Pi~) = r |is less than~ p, there are r cointegrating relations among the elements of |X.sub.t~ and p - r common stochastic trends. If |Pi~ has rank r |is less than~ p, this implies that |Pi~ = |Alpha~|Beta~ where |Alpha~ and |Beta~ are p x r matrices, the former being interpreted as a matrix of error correction terms and the latter as a matrix of cointegration vectors. Johansen and Juselius |20~ provide a likelihood ratio test statistic for the rank of |Pi~, called the maximum eigenvalue test. In the maximum eigenvalue test the null hypothesis of r cointegrating vectors is compared to the alternative of r + 1 cointegrating vectors.

IV. Data

The period of study is 1952 through 1988, a sample dictated by data availability. Our analysis uses two monetary aggregates, currency (M0) and a broader monetary measure comprised of currency plus savings deposits (M2). Currency accounts for a decreasing proportion of M2 across the sample period reflecting the advance of financial reforms in China. For example, currency accounted for 80 percent of M2 in 1952, falling to 60 percent by 1970. Following the reforms which began in the late 1970s, the proportion of currency in M2 has decreased further to about 35 percent by the late 1980s. The growing importance of savings deposits reflects the evolution of China's financial structure and raises the question of whether M0 or M2 yields the most reliable money demand relationship. The annual money supply data are taken from Chen |5~ and updated using the International Financial Statistics (IFS) data tape.

Two price measures are used. One is official index of retail prices, and the other is an implicit national income deflator measured by the ratio of nominal to real national income. The usefulness of China's official price measure, especially before the reforms of the late-1970s, has been questioned in previous work. The goal of a number of studies |4; 5; 11; 27~ is to estimate a price level measure for China that reflects underlying economic forces. Blejer et al. |1~ argue that, based on their money demand estimates using the official measure, repressed inflation in China may be less than commonly believed. Chow |7~ also suggests that his results are not inconsistent with those expected using a "correct" price index for China. While it is beyond the scope of this study to determine the "correct" price measure, the results from our analysis offer additional, albeit indirect, evidence on this issue. The retail price index is taken from the Statistical Yearbook of China (various issues). The implicit deflator is generated using real and nominal national income taken from the IFS.

Real national income is used as the scale measure. Since two price measures are used, for consistency we define real income in two ways: one measure deflates nominal income by the retail price index, the other uses the national income deflator. Nominal income measures gross output from agriculture, industry, construction, transportation and commerce.

The only interest rate series available on a consistent basis is the 1-year saving deposit rate. This measure, also used by Portes and Santorum |27~ is not ideal. For M0 it may represent an opportunity cost measure, but for M2 it really is an own rate of return. Since the types of market interest rates (e.g., government rates) used in money demand studies of more advanced economies do not exist for China, the savings deposit rate is the best interest rate measure available. Data for the interest rate are taken from Hsiao |19~ and Byrd |2~ and updated using the IFS tape.(9)

V. Empirical Results

Unit Root Tests

It is necessary to first determine the degree of integration for each series, since cointegration tests cannot be carried out if some of the time series are stationary in their levels while others are difference stationary. We test for unit roots using the familiar Dickey-Fuller |9~ test, based on estimating the regression

|Delta~|X.sub.t~ = |Alpha~ + |Beta~|X.sub.t-1~ + |Eta~, (3)

where |Delta~ is the first-difference operator, |Alpha~ is the constant term, X is the log of the variable being tested and |Eta~ is a stationary random error term. The null hypothesis of a unit root is rejected when |Beta~ is significantly negative. Equation (3) is estimated for each of the variables used in our study.(10) The results, reported in Table I, indicate that the data do not reject the hypothesis of a unit root in the log-levels of each series. When the first-difference version of equation (3) is estimated, the unit root hypothesis is rejected in every instance. Note that the hypothesis is rejected only at the 10 percent level for the retail price index series. The results in Table I do not reject the hypothesis that all of the series are integrated of order one.

Cointegration Tests

Before turning to a discussion of the cointegration test results, we should note that we do not impose a priori constraints on the money demand model. Because we are interested in the long-run equilibrium relationship, no lagged adjustment mechanism is used. Second, we do not constrain the price elasticity of money demand to unity but directly estimate it. This allows us to test whether the demand function is homogeneous of degree one in prices. Third, since it is not clear which measure of prices is "correct," both the retail price index (RPI) and the national income deflator (DEF) are used. Using both measures and testing the hypothesis that the function is homogeneous of degree one in prices provides indirect evidence about the usefulness of each price series as a meaningful economic measure. Finally, we attempt to capture the effects of economic and financial reform by including a shift term in the test equation. This is done by using a dummy variable that takes a value of one for the 1979-1988 period and zero elsewhere. This use of a shift term is similar in spirit to the analysis of Hoffman and Rasche |18~.

The cointegration test results are found in Table II.(11) The maximum eigenvalue test results in the upper tier of Table II use the retail price index. The results indicate that, for both M0 and M2, TABULAR DATA OMITTED the hypothesis that there is not a unique long-run equilibrium relationship among the variables cannot be rejected.(12) One interpretation is that nominal money balances wander arbitrarily from real income, the interest rate and the retail price index. The test results in the lower tier of Table II use the national income deflator. In sharp contrast to the evidence using the retail price index, the hypothesis of a single cointegrating vector among the variables is not rejected for M0 and M2. This indicates that we cannot reject the hypothesis that there exists a long run money demand function for both measures of money only when the price level measure is the national income deflator.

To facilitate an economic interpretation of these results, we normalize the cointegrating vector on nominal money balances. The resulting values are the long-run elasticities. Using these elasticities, we consider three standard hypotheses: Is the long-run income elasticity unity? Is the long-run interest elasticity zero? Is the money demand function homogeneous of degree one with respect to the price level? Since there is no evidence of cointegration for the money demand functions using the retail price index, these hypotheses are tested only for the equations using the national income deflator. The estimated long-run elasticities and hypothesis test results are reported in Table III.(13)

The results for M0 indicate that the unitary income elasticity hypothesis is not rejected, a finding similar to Portes and Santorum |27~ who used a different estimation procedure and a shorter sample period. The evidence in Table III also does not reject the hypothesis that the long-run interest elasticity is zero. The results do reject the hypothesis of price homogeneity: The estimated long-run coefficient on the price level is 2.48, significantly larger than unity at the five TABULAR DATA OMITTED percent level. In contrast to evidence from studies of U.S. money demand, the demand for nominal currency balances in China is not proportional to the price level. In other words, a one percent increase in the price level leads to about a 2.5 percent increase in the demand for nominal M0. One explanation might be that the real cost of transactions rises with the price level. This is opposite the explanation suggested by Goldfeld |12~ to explain the finding that adding a price level term to his standard equation for the U.S. resulted in an estimated price elasticity that was significantly less than unity. If the demand for money is a demand for real money balances, rejecting the price homogeneity hypothesis for nominal M0 raises the question of whether the empirical relationship identified in Table III is in fact a money demand function.

The results for M2 fare much better from a theoretical standpoint. The estimated income elasticity of 1.42 is significantly greater than unity at the five percent level. The finding of a large income elasticity is not uncommon in studies of money demand for economies like China. Using a different specification and shorter sample (1954-83), Feltenstein and Farhadian |11~ estimate that the income elasticity for real M2 balances in China to be 1.37. Blejer et al. |1~ also find the long-ran income elasticity for the broad money and currency to be 1.53 and 1.66, respectively. They argue that ". . . this could reflect the monetization of the economy under the reforms as the coordination of economic activity has increasingly taken place through markets . . ." |1, 35~. Like the results for M0, the interest elasticity of M2 is not significantly different from zero.

Unlike the results for M0, however, the demand for nominal M2 is proportional to changes in the price level. The hypothesis that the M2 function is homogenous of degree one with respect to prices is not rejected at any reasonable level. This suggests that using M2 may provide a more reliable money demand function in that the variables in the function have the expected signs and elasticities. It also means that M2 is a measure with which the long-run economic effects of monetary policy actions on major macroeconomic variables, such as prices and real income, could be gauged.

VI. Conclusion

We have investigated the fundamental issue of whether there exists a long-run, equilibrium money demand relation for China. The results are linked directly to concerns about choosing the monetary aggregate that best determines the long-run economic effects of monetary policy actions. Our empirical tests indicate that when the retail price index is used, the hypothesis of an equilibrium money demand relation, for currency (M0) or currency plus savings deposits (M2), is rejected by the data. When the national income deflator series is used, however, we cannot reject the hypothesis that there is a long-run equilibrium relationship between the demand for money balances and its economic arguments.

The evidence points to the broader M2 measure as the preferred aggregate. The results reveal that the demand for M0 is not proportional to the price level. In contrast, M2 demand is proportional to changes in the price level, an important result if one places confidence on the empirical results being a money demand function. The suggestion that M2 provides a better long-run guide to monetary policy is consistent with recent results using U.S. data |15; 17~.(14) The interesting aspect of this result is that their economic and financial systems are so vastly different. Whether this finding is coincidence or not suggests a clear avenue for future research.

1. The real adjustment specification uses a lagged value of the dependent variable. The nominal adjustment version uses a lagged "dependent" variable of the form (|M.sub.t-1~/|P.sub.t~). This version is posited on the notion that individuals take the price level as given and adjust their nominal money balances to some desired level |12~.

2. Theoretical problems with these models are discussed in Laidler |21~. Empirical implications and difficulties are examined by Goodfriend |13~.

3. Blejer et al. |1~ estimate a long-run model to measure deviations of actual real balances from equilibrium. Unfortunately, they report no tests of the long-run model. Moreover, their short sample (1983/I-1988/III) leads one to question the existence of such a long-run equilibrium relationship.

4. A more complete discussion is provided by Blejer et al. |1~.

5. In addition to the PBC, the following specialized banks have been established, since 1984: the Agricultural Bank of China; the People's Construction Bank of China; the Industrial and Commercial Bank of China; the Bank of Communications; and the China International Trust and Investment Company Bank.

6. Naughton |23~ notes that available data are not disaggregated enough to separate deposits held among different sectors. Still, broad-brush evidence reveals the extent of financial reform. For example, from 1970 to 1987, the proportion of total savings deposits held by rural households increased from 19 percent to 33 percent with the remainder held by urban dwellers. Moreover, while enterprise deposits are not separable into demand and time deposit components, household demand deposits in 1987 remained a relatively minor component of the broad money measure, about 8 percent of the total. The latter figure implies that while financial reform created new deposits, the bulk of deposits was and is primarily in time deposits. This suggests that the preferable money measure on which to focus monetary policy may be a store of purchasing power measure.

7. This section draws on Hafer and Jansen |15~.

8. To get this equation, first subtract |X.sub.t-1~ from both sides of equation (1) and collect terms on |X.sub.t-1~. Then add -(||Pi~.sub.1~ - 1) |X.sub.t-1~ + (||Pi~.sub.1~ - 1) |X.sub.t - 1~). Repetition of this and collecting of terms yields equation (2).

9. We also experimented with expected inflation as an alternative opportunity cost measure. But how does one properly measure inflation expectations? Blejer et al. |1~ use lagged values of inflation with mixed results, finding the coefficient positive in some instances and in others negative. While one can tell a credible story for each, the question remains as to what is being measured. Also, Hafer |14~ demonstrates that empirical models of the expectations formation process using Chinese data may not be robust to minor specification changes.

10. Following Perron |25~ we initially included lags of the dependent variable. If the lag is not significant at least the 10 percent level, it is then excluded. This process quickly revealed that the standard Dickey-Fuller specification is appropriate for our annual data series. We also conducted the Phillips-Perron tests. Since these results are not qualitatively different from the Dickey-Fuller tests, they are not reported.

11. For cointegration tests, we set k equal to 2 in equation (2). This choice of lag is determined by two criteria: (1) Each equation in the system has white-noise errors. This is tested by using the Ljung-Box statistics. (2) Additional lags in the VECM system are not statistically significant. This is done by estimating equation (2) for different lag structures and then testing the significance of additional lags using likelihood-ratio statistics.

12. The results for M2 do not reject (10% level) the existence of 2 or fewer vectors. Since we do reject r = 0, however, little weight is given to this outcome.

13. Although not reported, the 1979 shift term is positive and statistically significant at the 1 percent level in both M0 and M2 cointegration equations. As one would expect from the reforms, the positive coefficient suggests that the reforms brought about a level increase in the demand for money. It also is interesting to note that the cointegration test results actually are little affected by omitting this term. This suggests that even though the level of the empirical relationship may have shifted in 1979 with the economic and financial reforms, the underlying economic relationship among money balances, real income and the price level remained unchanged. Indeed, this argument is similar to that used by Hoffman and Rasche |18~.

14. Hafer and Kutan |16~ provide corroborating evidence. Portes and Winter |26~ also show that standard models used to analyze household behavior in Western economies perform equally well in modeling household behavior in centrally planned economies.

References

1. Blejer, Mario, David Burton, Steven Dunaway and Gyorgy Szapary. "China: Economic Reform and Macroeconomic Management." IMF Occasional Paper No. 76, Washington, D.C., January 1991

2. Byrd, William. China's Financial System: The Changing Role of Banks. Boulder, Colorado: Westview Press, 1983.

3. Cagan, Phillip. "The Monetary Dynamics of Hyperinflation," in Studies in the Quantity Theory of Money, edited by Milton Friedman. Chicago: University of Chicago Press, 1956.

4. Chen, Nai-Ruenn and Chi-ming Hou, "China's Inflation, 1979-83: Measurement and Analysis." Economic Development and Cultural Change, July 1986, 811-39.

5. Chen, Chien-Hsun, "Monetary Aggregates and Macroeconomic Performance in Mainland China." Journal of Comparative Economics, June 1989, 314-24.

6. Cheng, Hang-Sheng. "Monetary Policy and Inflation in China," in Monetary Policy in Pacific Basin Countries, edited by Hang-Sheng Cheng. Boston: Kluwer Academic Publishers, 1988, 401-29.

7. Chow, Gregory C., "Money and Price Level Determination in China." Journal of Comparative Economics, September 1987, 319-33.

8. De Wulf, Luc and David Goldsborough. "The Evolving Role of Monetary Policy in China." IMF Staff Papers June 1986, 209-42.

9. Dickey, David A. and Wayne A. Fuller, "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, June 1979, 427-31.

10. Engle, Robert F. and Clive W. J. Granger, "Co-integration and Error Correction: Representation, Estimation, and Testing." Econometrica, March 1987, 251-76.

11. Feltenstein, Andrew and Ziba Farhadian, "Fiscal Policy, Monetary Targets, and the Price Level in a Centrally Planned Economy: An Application to the Case of China." Journal of Money, Credit and Banking, May 1987, 137-56.

12. Goldfeld, Stephen M., "The Case of the Missing Money." Brookings Papers on Economic Activity, 3:1976, 683-730.

13. Goodfriend, Marvin. "Reinterpreting Money Demand Regressions," in Carnegie-Rochester Conference Series, edited by Karl Brunner and Allan Meltzer. Spring 1985, 207-42.

14. Hafer, R. W., "Inflation and Price Instability in China: A Comment." China Economic Review, Fall 1992, 213-18.

15. ----- and Dennis W. Jansen, "The Demand for Money in the United States: Evidence from Cointegration Tests." Journal of Money, Credit and Banking, May 1991, 155-68.

16. ----- and A. M. Kutan, "Further Evidence on Money, Output and Prices in China." Journal of Comparative Economics, September 1993, 701-09.

17. Hallman, Jeffrey, Richard Porter and David Small, "Is the Price Level Tied to the M2 Monetary Aggregate in the Long-Run?" American Economic Review, September 1991, 841-58.

18. Hoffman, Dennis and Robert H. Rasche, "Long-Run Income and Interest Elasticities of Money Demand in the United States." Review of Economics and Statistics, November 1991, 665-74.

19. Hsiao, Katharine Huang. Money and Monetary Policy in Communist China. New York: Columbia University Press, 1971.

20. Johansen, Soren and Katarina Juselius, "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money." Oxford Bulletin of Economics and Statistics, May 1990, 169-210.

21. Laidler, David E. W. The Demand for Money: Theories and Evidence, 4th ed. New York: Dun-Donnelley Publishing, 1992.

22. MacKinnon, James G., "Critical Values for Cointegration Tests." Working Paper, University of California, San Diego, January 1990.

23. Naughton, Barry, "Macroeconomic Policy and Response in the Chinese Economy: The Impact of the Reform Process." Journal of Comparative Economics, September 1987, 334-53.

24. Osterwald-Lunum, M. G., "A Note with Quantiles of the Asymptatic Distribution of the Maximum Likelihood Cointegration Ranks Test Statistics: Four Cases." Oxford Bulletin of Economics and Statistics, August 1992, 461-72.

25. Perron, Pierre, "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis." Econometrica, November 1989, 1361-401.

26. Portes, Richard and D. Winter, "The Demand for Money and for Consumption Goods in Centrally Planned Economies." Review of Economics and Statistics, February 1978, 8-18.

27. Portes, Richard and Anita Santorum, "Money and the Consumption Goods Market in China." Journal of Comparative Economics, September 1987, 354-71.

28. Wolken, Lawrence C., "The Restructuring of China's Banking System Under the Economic Reforms 1979-1989." Columbia Journal of Business, Spring/Summer 1990, 53-63.

Although money demand equations have been estimated for many western countries, only recently have researchers investigated the demand for money in centrally planned economies like China. Chow |7~, who helped pioneer the analysis of Chinese macro data, estimates a simple money demand function derived from the quantity theory. Using annual data from 1952 through 1983, he concludes that the quantity theory "provides a reasonable first approximation in explaining the demand for money in China." |7, 325~ Portes and Santorum |27~ use real and nominal adjustment specifications and test for the homogeneity of money demand with respect to the price level and real income.(1) Feltenstein and Farhadian |11~ estimate a money demand function based on Cagan's |3~ work, and Blejer et al. |1~ estimate an error correction model using data for only the 1980s. Both studies find that the demand for real balances is explained by real income and an opportunity cost measure.

A common feature of such studies is the use of a standard lagged-adjustment specification to capture the short-run dynamics of money demand. Such dynamic specifications have been the subject of much recent work, the bulk of which suggests that they fail on theoretical and econometric grounds.(2) Another feature is the presumption that a long-run equilibrium relationship underlies the short-run dynamic models being estimated.(3) If such an equilibrium relationship does not exist, attempts to measure the short-run dynamics of a given specification are misdirected.

The purpose of this study is to determine if there exists a long-run, equilibrium relationship between nominal money balances, real income, prices and interest rates using data for China. We do so by applying the tests for cointegration due to Johansen and Juselius |20~. While most previous applications of such tests to money demand have focused on advanced market economies |15; 18; 20~, this study represents an exploratory attempt to determine if such basic economic forces also hold in centrally planned economies like China. While the limited sample (1952-88) affects the power of our test statistics, the results are informative and provide a basis to which future studies can be compared.

Our analysis also allows us to consider which monetary measure is preferable in determining the long-run effect of monetary policy actions. Previous work by Portes and Santorum |27~ and Chen |5~, for example, indicates that currency in circulation is preferable to a broader measure. Such conclusions, based on estimates of short-run money demand functions, may not hold when considering the long-term equilibrium relationship. Moreover, the issue of which aggregate to use has become increasingly important in light of continuing economic reforms in China.

The format of the paper is as follows. Section II provides an overview of economic and financial reforms in China. Section III provides a brief discussion of the cointegration test procedures. A description of the data is in section IV followed by our empirical results in section V. Concluding remarks close the paper in section VI.

II. Reforms

Economic and financial reforms since the late 1970s in China have brought about major changes in the conduct of Chinese monetary policy.(4) Before the reforms, currency in circulation was considered the nation's money supply since cash was used mainly for transactions between the state and household sectors of the economy. Macroeconomic policy was determined solely by the State Council: Independent monetary policies conducted by a central bank did not exist, and ". . . the role of monetary policy was essentially to support the implementation of the physical output targets contained in the |central~ plan . . ." |1, 12~ The economic reforms emphasized the use of market forces for the allocation of resources.

The banking system was reformed in order to separate banking functions and create new policy instruments to achieve better control over the economy. In particular, the People's Bank of China (PBC) was created in 1984 with its own monetary policy instruments. The PBC controls the total volume of credit in the economy and works closely with the State Council in making important macroeconomic policy decisions. The commercial aspects of banking are controlled by the Industrial and Commercial Bank of China. Although this bank competes with specialized banks and others established at the province level, the government credit plan continues to influence monetary policy decisions.(5)

Financial reforms gave state enterprises more freedom in decision-making and permission to retain some of their profits. These earnings were allowed to be put in special time deposit accounts (in the form of trust deposits) and used to finance investment expenditures. Most state enterprises also were allowed for the first time to use checking accounts for many financial transactions |28~. Financial reforms promoted household savings by introducing new financial instruments and services. New institutions were created for this purpose, including credit cooperatives and special savings banks. The role of the specialized savings banks is to raise sufficient funds consistent with the desired investment level set by the State Council. Naughton |23~ observes that these institutional developments brought about a substantial increase in the volume of bank deposits, the greatest growth being in enterprise deposits and urban savings deposits, followed by rural deposits.(6)

A potential implication of these financial reforms is the increased importance of monetary aggregates in policy decisions. De Wulf and Goldsborough note that ". . . together with the need for greater emphasis on developments in household bank deposits, which are a fairly close substitute for cash, the greater autonomy of enterprises and local governments implies that broader monetary aggregates than household currency holdings should become increasingly important in setting targets for monetary policy . . ." |8, 233~ Thus, China's policy makers must address the choice of currency in circulation (M0) or the broader monetary aggregate that includes savings deposits (M2) in setting policy. In this vein, others have compared the relationship between economic activity and M0 or M2 using a variety of models. Portes and Santorum |27~ use Granger-type causality tests, and Chen |5~ a vector autoregressive (VAR) model to study the empirical link between the monetary aggregates and economic activity. Both studies conclude that currency (M0) is better related to economic activity and, hence, the preferable policy measure. In contrast, Hafer and Kutan |16~ provide support for both M0 and M2 in setting monetary policy. By establishing whether there exists a long-run relationship between either monetary aggregate and income, prices and interest rates, this paper contributes to this literature. If such a relationship is rejected, the feasibility of an aggregate in formulating policy must be questioned.

III. Methodological Issues(7)

Even though economic time series may be nonstationary in their level, there may exist some linear combination of these variables that converge to a long run relationship over time. If the series individually are stationary after differencing but a linear combination of their levels is stationary, then the series are said to be cointegrated. Engle and Granger's |10~ test for cointegration is cast in terms of bivariate relationships. Johansen and Juselius |20~ extend these tests to a multivariate setting.

The question is whether a cointegrating vector between money balances, income and interest rates exists for China. To test for cointegration among these variables, consider the equation

|X.sub.t~ = ||Pi~.sub.1~ |X.sub.t-1~ + . . . + ||Pi~.sub.k~ |X.sub.t-k~ + ||Epsilon~.sub.t~ (t = 1, . . . , T) (1)

where |X.sub.t~ is a sequence of random vectors with components (|X.sub.1t~, . . . , |X.sub.pt~) and the innovations to this process (the |Epsilon~'s) are drawn from a p-dimensional i.i.d. Gaussian distribution with co-variance |Lambda~ and |X.sub.-k+1~, . . . , |X.sub.0~ fixed. Equation (1) is simple a VAR model, usually estimated in first-difference form since most macroeconomic time series are nonstationary in their levels. This approach necessarily leads to a loss of information about the variables' long-term relationship and, if they are cointegrated, results in a misspecification of the model.

Letting |Delta~ represent the first difference operator, equation (1) can be written in the form

|Delta~|X.sub.t~ = ||Gamma~.sub.1~ |Delta~|X.sub.t-1~ + . . . + ||Gamma~.sub.k-1~ |Delta~|X.sub.t-1+k~ - |Pi~|X.sub.t-k~ + ||Epsilon~.sub.t~ (2)

where

||Gamma~.sub.i~ = -I + ||Pi~.sub.1~ + . . . + ||Pi~.sub.i~ (i = 1, . . . , k - 1)

and

|Pi~ = I - ||Pi~.sub.1~ - . . . - ||Pi~.sub.k~.(8)

The difference between the standard first-difference version of the VAR model and equation (1) is the term |Pi~|X.sub.t-k~. It is this part of the equation that conveys the information about the long-run relationship between the X variables of the model. If |X.sub.t~ is nonstationary in levels but its first difference is stationary, then it is said to be integrated of order one. Because there are several elements of the vector which may be cointegrated individually, it may be that one or more linear combinations of these nonstationary vectors are stationary. In other words, there may exist more than one linear combination of the variables that converges to some long-run relationship over time.

The test procedure examines the p x p |Pi~ matrix. If this matrix has rank 0 then all elements of ||Pi~.sub.t~ have unit roots and first-differencing is suggested. If the matrix is of full rank p, then all elements of |X.sub.t~ are stationary in their levels. When 0 |is less than~ rank (|Pi~) = r |is less than~ p, there are r cointegrating relations among the elements of |X.sub.t~ and p - r common stochastic trends. If |Pi~ has rank r |is less than~ p, this implies that |Pi~ = |Alpha~|Beta~ where |Alpha~ and |Beta~ are p x r matrices, the former being interpreted as a matrix of error correction terms and the latter as a matrix of cointegration vectors. Johansen and Juselius |20~ provide a likelihood ratio test statistic for the rank of |Pi~, called the maximum eigenvalue test. In the maximum eigenvalue test the null hypothesis of r cointegrating vectors is compared to the alternative of r + 1 cointegrating vectors.

IV. Data

The period of study is 1952 through 1988, a sample dictated by data availability. Our analysis uses two monetary aggregates, currency (M0) and a broader monetary measure comprised of currency plus savings deposits (M2). Currency accounts for a decreasing proportion of M2 across the sample period reflecting the advance of financial reforms in China. For example, currency accounted for 80 percent of M2 in 1952, falling to 60 percent by 1970. Following the reforms which began in the late 1970s, the proportion of currency in M2 has decreased further to about 35 percent by the late 1980s. The growing importance of savings deposits reflects the evolution of China's financial structure and raises the question of whether M0 or M2 yields the most reliable money demand relationship. The annual money supply data are taken from Chen |5~ and updated using the International Financial Statistics (IFS) data tape.

Two price measures are used. One is official index of retail prices, and the other is an implicit national income deflator measured by the ratio of nominal to real national income. The usefulness of China's official price measure, especially before the reforms of the late-1970s, has been questioned in previous work. The goal of a number of studies |4; 5; 11; 27~ is to estimate a price level measure for China that reflects underlying economic forces. Blejer et al. |1~ argue that, based on their money demand estimates using the official measure, repressed inflation in China may be less than commonly believed. Chow |7~ also suggests that his results are not inconsistent with those expected using a "correct" price index for China. While it is beyond the scope of this study to determine the "correct" price measure, the results from our analysis offer additional, albeit indirect, evidence on this issue. The retail price index is taken from the Statistical Yearbook of China (various issues). The implicit deflator is generated using real and nominal national income taken from the IFS.

Real national income is used as the scale measure. Since two price measures are used, for consistency we define real income in two ways: one measure deflates nominal income by the retail price index, the other uses the national income deflator. Nominal income measures gross output from agriculture, industry, construction, transportation and commerce.

The only interest rate series available on a consistent basis is the 1-year saving deposit rate. This measure, also used by Portes and Santorum |27~ is not ideal. For M0 it may represent an opportunity cost measure, but for M2 it really is an own rate of return. Since the types of market interest rates (e.g., government rates) used in money demand studies of more advanced economies do not exist for China, the savings deposit rate is the best interest rate measure available. Data for the interest rate are taken from Hsiao |19~ and Byrd |2~ and updated using the IFS tape.(9)

V. Empirical Results

Unit Root Tests

It is necessary to first determine the degree of integration for each series, since cointegration tests cannot be carried out if some of the time series are stationary in their levels while others are difference stationary. We test for unit roots using the familiar Dickey-Fuller |9~ test, based on estimating the regression

|Delta~|X.sub.t~ = |Alpha~ + |Beta~|X.sub.t-1~ + |Eta~, (3)

where |Delta~ is the first-difference operator, |Alpha~ is the constant term, X is the log of the variable being tested and |Eta~ is a stationary random error term. The null hypothesis of a unit root is rejected when |Beta~ is significantly negative. Equation (3) is estimated for each of the variables used in our study.(10) The results, reported in Table I, indicate that the data do not reject the hypothesis of a unit root in the log-levels of each series. When the first-difference version of equation (3) is estimated, the unit root hypothesis is rejected in every instance. Note that the hypothesis is rejected only at the 10 percent level for the retail price index series. The results in Table I do not reject the hypothesis that all of the series are integrated of order one.

Table I. Unit Root Test Results Test Statistic (a) Variable(b) Level First-Difference M0 -0.10 -4.65(*) M2 0.50 -3.92(**) Rate -1.98 -7.59(*) RPI 0.13 -3.39(***) DEF 0.05 -4.38(*) RY(RPI) -1.92 -3.70(**) RY(DEF) -1.78 -3.99(**) a. Critical values for the test statistics are -4.25 at 1%(*), -3.55 at 5%(**) and -3.21 at 10%(***). They are taken from MacKinnon |22~. b. Logarithms of variables are used. M0 is currency and M2 is currency plus savings deposits. Rate refers to the 1-year savings rate. RPI is the retail price index, and DEF represents the national income deflator. RY(RPI) is real income measured using the retail price index, and RY(DEF) is real income using the national income deflator.

Cointegration Tests

Before turning to a discussion of the cointegration test results, we should note that we do not impose a priori constraints on the money demand model. Because we are interested in the long-run equilibrium relationship, no lagged adjustment mechanism is used. Second, we do not constrain the price elasticity of money demand to unity but directly estimate it. This allows us to test whether the demand function is homogeneous of degree one in prices. Third, since it is not clear which measure of prices is "correct," both the retail price index (RPI) and the national income deflator (DEF) are used. Using both measures and testing the hypothesis that the function is homogeneous of degree one in prices provides indirect evidence about the usefulness of each price series as a meaningful economic measure. Finally, we attempt to capture the effects of economic and financial reform by including a shift term in the test equation. This is done by using a dummy variable that takes a value of one for the 1979-1988 period and zero elsewhere. This use of a shift term is similar in spirit to the analysis of Hoffman and Rasche |18~.

The cointegration test results are found in Table II.(11) The maximum eigenvalue test results in the upper tier of Table II use the retail price index. The results indicate that, for both M0 and M2, TABULAR DATA OMITTED the hypothesis that there is not a unique long-run equilibrium relationship among the variables cannot be rejected.(12) One interpretation is that nominal money balances wander arbitrarily from real income, the interest rate and the retail price index. The test results in the lower tier of Table II use the national income deflator. In sharp contrast to the evidence using the retail price index, the hypothesis of a single cointegrating vector among the variables is not rejected for M0 and M2. This indicates that we cannot reject the hypothesis that there exists a long run money demand function for both measures of money only when the price level measure is the national income deflator.

To facilitate an economic interpretation of these results, we normalize the cointegrating vector on nominal money balances. The resulting values are the long-run elasticities. Using these elasticities, we consider three standard hypotheses: Is the long-run income elasticity unity? Is the long-run interest elasticity zero? Is the money demand function homogeneous of degree one with respect to the price level? Since there is no evidence of cointegration for the money demand functions using the retail price index, these hypotheses are tested only for the equations using the national income deflator. The estimated long-run elasticities and hypothesis test results are reported in Table III.(13)

The results for M0 indicate that the unitary income elasticity hypothesis is not rejected, a finding similar to Portes and Santorum |27~ who used a different estimation procedure and a shorter sample period. The evidence in Table III also does not reject the hypothesis that the long-run interest elasticity is zero. The results do reject the hypothesis of price homogeneity: The estimated long-run coefficient on the price level is 2.48, significantly larger than unity at the five TABULAR DATA OMITTED percent level. In contrast to evidence from studies of U.S. money demand, the demand for nominal currency balances in China is not proportional to the price level. In other words, a one percent increase in the price level leads to about a 2.5 percent increase in the demand for nominal M0. One explanation might be that the real cost of transactions rises with the price level. This is opposite the explanation suggested by Goldfeld |12~ to explain the finding that adding a price level term to his standard equation for the U.S. resulted in an estimated price elasticity that was significantly less than unity. If the demand for money is a demand for real money balances, rejecting the price homogeneity hypothesis for nominal M0 raises the question of whether the empirical relationship identified in Table III is in fact a money demand function.

The results for M2 fare much better from a theoretical standpoint. The estimated income elasticity of 1.42 is significantly greater than unity at the five percent level. The finding of a large income elasticity is not uncommon in studies of money demand for economies like China. Using a different specification and shorter sample (1954-83), Feltenstein and Farhadian |11~ estimate that the income elasticity for real M2 balances in China to be 1.37. Blejer et al. |1~ also find the long-ran income elasticity for the broad money and currency to be 1.53 and 1.66, respectively. They argue that ". . . this could reflect the monetization of the economy under the reforms as the coordination of economic activity has increasingly taken place through markets . . ." |1, 35~. Like the results for M0, the interest elasticity of M2 is not significantly different from zero.

Unlike the results for M0, however, the demand for nominal M2 is proportional to changes in the price level. The hypothesis that the M2 function is homogenous of degree one with respect to prices is not rejected at any reasonable level. This suggests that using M2 may provide a more reliable money demand function in that the variables in the function have the expected signs and elasticities. It also means that M2 is a measure with which the long-run economic effects of monetary policy actions on major macroeconomic variables, such as prices and real income, could be gauged.

VI. Conclusion

We have investigated the fundamental issue of whether there exists a long-run, equilibrium money demand relation for China. The results are linked directly to concerns about choosing the monetary aggregate that best determines the long-run economic effects of monetary policy actions. Our empirical tests indicate that when the retail price index is used, the hypothesis of an equilibrium money demand relation, for currency (M0) or currency plus savings deposits (M2), is rejected by the data. When the national income deflator series is used, however, we cannot reject the hypothesis that there is a long-run equilibrium relationship between the demand for money balances and its economic arguments.

The evidence points to the broader M2 measure as the preferred aggregate. The results reveal that the demand for M0 is not proportional to the price level. In contrast, M2 demand is proportional to changes in the price level, an important result if one places confidence on the empirical results being a money demand function. The suggestion that M2 provides a better long-run guide to monetary policy is consistent with recent results using U.S. data |15; 17~.(14) The interesting aspect of this result is that their economic and financial systems are so vastly different. Whether this finding is coincidence or not suggests a clear avenue for future research.

1. The real adjustment specification uses a lagged value of the dependent variable. The nominal adjustment version uses a lagged "dependent" variable of the form (|M.sub.t-1~/|P.sub.t~). This version is posited on the notion that individuals take the price level as given and adjust their nominal money balances to some desired level |12~.

2. Theoretical problems with these models are discussed in Laidler |21~. Empirical implications and difficulties are examined by Goodfriend |13~.

3. Blejer et al. |1~ estimate a long-run model to measure deviations of actual real balances from equilibrium. Unfortunately, they report no tests of the long-run model. Moreover, their short sample (1983/I-1988/III) leads one to question the existence of such a long-run equilibrium relationship.

4. A more complete discussion is provided by Blejer et al. |1~.

5. In addition to the PBC, the following specialized banks have been established, since 1984: the Agricultural Bank of China; the People's Construction Bank of China; the Industrial and Commercial Bank of China; the Bank of Communications; and the China International Trust and Investment Company Bank.

6. Naughton |23~ notes that available data are not disaggregated enough to separate deposits held among different sectors. Still, broad-brush evidence reveals the extent of financial reform. For example, from 1970 to 1987, the proportion of total savings deposits held by rural households increased from 19 percent to 33 percent with the remainder held by urban dwellers. Moreover, while enterprise deposits are not separable into demand and time deposit components, household demand deposits in 1987 remained a relatively minor component of the broad money measure, about 8 percent of the total. The latter figure implies that while financial reform created new deposits, the bulk of deposits was and is primarily in time deposits. This suggests that the preferable money measure on which to focus monetary policy may be a store of purchasing power measure.

7. This section draws on Hafer and Jansen |15~.

8. To get this equation, first subtract |X.sub.t-1~ from both sides of equation (1) and collect terms on |X.sub.t-1~. Then add -(||Pi~.sub.1~ - 1) |X.sub.t-1~ + (||Pi~.sub.1~ - 1) |X.sub.t - 1~). Repetition of this and collecting of terms yields equation (2).

9. We also experimented with expected inflation as an alternative opportunity cost measure. But how does one properly measure inflation expectations? Blejer et al. |1~ use lagged values of inflation with mixed results, finding the coefficient positive in some instances and in others negative. While one can tell a credible story for each, the question remains as to what is being measured. Also, Hafer |14~ demonstrates that empirical models of the expectations formation process using Chinese data may not be robust to minor specification changes.

10. Following Perron |25~ we initially included lags of the dependent variable. If the lag is not significant at least the 10 percent level, it is then excluded. This process quickly revealed that the standard Dickey-Fuller specification is appropriate for our annual data series. We also conducted the Phillips-Perron tests. Since these results are not qualitatively different from the Dickey-Fuller tests, they are not reported.

11. For cointegration tests, we set k equal to 2 in equation (2). This choice of lag is determined by two criteria: (1) Each equation in the system has white-noise errors. This is tested by using the Ljung-Box statistics. (2) Additional lags in the VECM system are not statistically significant. This is done by estimating equation (2) for different lag structures and then testing the significance of additional lags using likelihood-ratio statistics.

12. The results for M2 do not reject (10% level) the existence of 2 or fewer vectors. Since we do reject r = 0, however, little weight is given to this outcome.

13. Although not reported, the 1979 shift term is positive and statistically significant at the 1 percent level in both M0 and M2 cointegration equations. As one would expect from the reforms, the positive coefficient suggests that the reforms brought about a level increase in the demand for money. It also is interesting to note that the cointegration test results actually are little affected by omitting this term. This suggests that even though the level of the empirical relationship may have shifted in 1979 with the economic and financial reforms, the underlying economic relationship among money balances, real income and the price level remained unchanged. Indeed, this argument is similar to that used by Hoffman and Rasche |18~.

14. Hafer and Kutan |16~ provide corroborating evidence. Portes and Winter |26~ also show that standard models used to analyze household behavior in Western economies perform equally well in modeling household behavior in centrally planned economies.

References

1. Blejer, Mario, David Burton, Steven Dunaway and Gyorgy Szapary. "China: Economic Reform and Macroeconomic Management." IMF Occasional Paper No. 76, Washington, D.C., January 1991

2. Byrd, William. China's Financial System: The Changing Role of Banks. Boulder, Colorado: Westview Press, 1983.

3. Cagan, Phillip. "The Monetary Dynamics of Hyperinflation," in Studies in the Quantity Theory of Money, edited by Milton Friedman. Chicago: University of Chicago Press, 1956.

4. Chen, Nai-Ruenn and Chi-ming Hou, "China's Inflation, 1979-83: Measurement and Analysis." Economic Development and Cultural Change, July 1986, 811-39.

5. Chen, Chien-Hsun, "Monetary Aggregates and Macroeconomic Performance in Mainland China." Journal of Comparative Economics, June 1989, 314-24.

6. Cheng, Hang-Sheng. "Monetary Policy and Inflation in China," in Monetary Policy in Pacific Basin Countries, edited by Hang-Sheng Cheng. Boston: Kluwer Academic Publishers, 1988, 401-29.

7. Chow, Gregory C., "Money and Price Level Determination in China." Journal of Comparative Economics, September 1987, 319-33.

8. De Wulf, Luc and David Goldsborough. "The Evolving Role of Monetary Policy in China." IMF Staff Papers June 1986, 209-42.

9. Dickey, David A. and Wayne A. Fuller, "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, June 1979, 427-31.

10. Engle, Robert F. and Clive W. J. Granger, "Co-integration and Error Correction: Representation, Estimation, and Testing." Econometrica, March 1987, 251-76.

11. Feltenstein, Andrew and Ziba Farhadian, "Fiscal Policy, Monetary Targets, and the Price Level in a Centrally Planned Economy: An Application to the Case of China." Journal of Money, Credit and Banking, May 1987, 137-56.

12. Goldfeld, Stephen M., "The Case of the Missing Money." Brookings Papers on Economic Activity, 3:1976, 683-730.

13. Goodfriend, Marvin. "Reinterpreting Money Demand Regressions," in Carnegie-Rochester Conference Series, edited by Karl Brunner and Allan Meltzer. Spring 1985, 207-42.

14. Hafer, R. W., "Inflation and Price Instability in China: A Comment." China Economic Review, Fall 1992, 213-18.

15. ----- and Dennis W. Jansen, "The Demand for Money in the United States: Evidence from Cointegration Tests." Journal of Money, Credit and Banking, May 1991, 155-68.

16. ----- and A. M. Kutan, "Further Evidence on Money, Output and Prices in China." Journal of Comparative Economics, September 1993, 701-09.

17. Hallman, Jeffrey, Richard Porter and David Small, "Is the Price Level Tied to the M2 Monetary Aggregate in the Long-Run?" American Economic Review, September 1991, 841-58.

18. Hoffman, Dennis and Robert H. Rasche, "Long-Run Income and Interest Elasticities of Money Demand in the United States." Review of Economics and Statistics, November 1991, 665-74.

19. Hsiao, Katharine Huang. Money and Monetary Policy in Communist China. New York: Columbia University Press, 1971.

20. Johansen, Soren and Katarina Juselius, "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money." Oxford Bulletin of Economics and Statistics, May 1990, 169-210.

21. Laidler, David E. W. The Demand for Money: Theories and Evidence, 4th ed. New York: Dun-Donnelley Publishing, 1992.

22. MacKinnon, James G., "Critical Values for Cointegration Tests." Working Paper, University of California, San Diego, January 1990.

23. Naughton, Barry, "Macroeconomic Policy and Response in the Chinese Economy: The Impact of the Reform Process." Journal of Comparative Economics, September 1987, 334-53.

24. Osterwald-Lunum, M. G., "A Note with Quantiles of the Asymptatic Distribution of the Maximum Likelihood Cointegration Ranks Test Statistics: Four Cases." Oxford Bulletin of Economics and Statistics, August 1992, 461-72.

25. Perron, Pierre, "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis." Econometrica, November 1989, 1361-401.

26. Portes, Richard and D. Winter, "The Demand for Money and for Consumption Goods in Centrally Planned Economies." Review of Economics and Statistics, February 1978, 8-18.

27. Portes, Richard and Anita Santorum, "Money and the Consumption Goods Market in China." Journal of Comparative Economics, September 1987, 354-71.

28. Wolken, Lawrence C., "The Restructuring of China's Banking System Under the Economic Reforms 1979-1989." Columbia Journal of Business, Spring/Summer 1990, 53-63.

Printer friendly Cite/link Email Feedback | |

Author: | Kutan, A.M. |
---|---|

Publication: | Southern Economic Journal |

Date: | Apr 1, 1994 |

Words: | 5033 |

Previous Article: | On the optimal rate structure of an individual income tax. |

Next Article: | Output, capital, and labor in the short and long run. |

Topics: |