What is money? Money is not itself the name of a particular asset and is best defined independently of the particular assets that may exist in the economy at any one time, since the assets which function as money tend to change over time in any given country and among countries. At a theoretical level, money is defined in terms of the functions that it performs. What does money do? The traditional specification of these functions is: (1) Medium of exchange/payments; (2) Store of value, sometimes specified as a temporary store of value or temporary abode of purchasing power; (3) standard of deferred payments; (4) unit of account. Among of them medium of exchange and store of value are more important. The rest of the essays are including two main parts. In the first part, the changes to the main UK monetary aggregates over the last 20 years and its' reasons will be discussed. I will look at the alternative monetary measures in the second part.
Historically, the definition of money have measured the quantity of money in the economy as the sum of those items that serve as media of exchange in the economy. However, at any time in a developed monetary economy, there may be other items that do not directly serve as a medium of exchange but are readily convertible into the medium of exchange at little cost and trouble and can simultaneously be a store of value. What is apparent for each country is that money can be defined 'narrowly' or 'broadly'. In the UK there are 14 alternative monetary aggregates which have been used as targets over the last 2 decades. Definitions of the various measures are given in Table 1  in the appendix.
MO (which was introduced as a target in March 1984) is the narrowest concept. The latest seasonally adjusted figure for MO is £32,960m on 28th March. Before that, the most common 'narrow measure' of money was Ml, which was regarded as a proxy for that component serving as a means of payment. As such it became subject to two major reservations: (i) some current accounts receive interest and hence might also be regarded as 'savings' balances awaiting more permanent investment; and (ii) many other types of non-bank deposit (e.g. at building societies) may also serve the transactions functions of current accounts. Both examples reflect the trend of financial innovation. For these reasons M2 was devised in 1982 and is now regarded as the most appropriate measure of retail and transactions 'money'.  M2 is believed to be more directly related to transactions in goods and services than £M3, and less sensitive to relative interest rates than Ml. The major weakness of NIMl is that it excludes transactions balances at, for instance, building societies. Both Ml aggregates are redundant, having been superseded by the conceptually superior M2. In brief, the two Ml aggregates are too narrow to serve as a liquidity aggregate but also exclude too much to serve as a measure of transactions balances.
On the broad money side, the M3 aggregate previously compiled covered only the deposit liabilities of banks; it was demoted and eventually discontinued in the 1980s as the difference narrowed between the characteristics of deposits at banks and of those at building societies - which had previously had more of a savings character. The longest standing of the target aggregates is £M3. It is an unfortunate compromise, being too wide for transactions balance but not sufficiently broad as a liquidity measure as it is entirely to notes and coin and bank deposits. It is an arbitrary definition of liquidity, which is difficult to defend conceptually. As a liquidity concept, £M3 is deficient. PSLl and PSL2 are more comprehensive, as they include £M3 but also encompass a wider range of liquid assets held by the private sector. Of the two PSL aggregates, PSL2 is regarded as the more significant, while PSL1 as it excludes building society deposits, seems a rather curious intermediate aggregate between 'money' and broad liquidity. In the UK, formal compilation of a broader measure, M5, comprising M4 plus other liquid assets such as Treasury bills, was discontinued in 1991. Its behaviour was not significantly different from that of M4, because the competitive character of the banks and building societies meant that they satisfied a very large part of the demand for liquidity. A table of 'liquid assets outside M4' is however still published, so that the behaviour of such assets can be monitored in case it deviates significantly from that of M4. Table 2 in appendix shows the figures for £M3, M4 and MS during 1982 and 1987. M4 supply was £798.3 billions in June 1999.  The stock and flows of UK M4 were 870.9 £bn and 4.0 £bn in October 2000. 
One reason for these aggregates to move in different ways in the longer period is the existence of technological change in banking and in payment methods. Moreover, there was a competition between banks and building societies. The distinction between the banks and the larger building societies has become progressively blurred, and will become more so as the new freedoms given to the building societies in the 1986 Building Societies Act are exploited. The provision by some societies of accounts with cheque book facilities, and the spread of cash dispensers have facilitated this change in usage, which may well proceed further with, for example, the introduction of cheque guarantee cards by some societies. 
Finally, financial innovation has been extremely rapid in the last few decades. It has included technical changes in the servicing of various kinds of deposits, such as the introduction of automatic teller machines, banking from home through the use of computers, etc. It has also including the creation of new assets such as the NOW (negotiable orders of deposit), money market mutual funds, etc. There has also been the spread first of credit cards, then of debt or bank cards, followed still more recently by the attempts to create and market electronic money cards-sometimes also known as electronic purses or smart cards. Further, competition among the different types of financial intermediaries in the provision of liabilities that are close to demand deposits or readily convertible into the latter, has increased considerably in recent decades. Many of these innovations served to further blur the distinction between demand and savings deposits to the point of its being only in name rather than in effect, and also blurred the distinction between banks and some of the other types of financial intermediaries as providers of liquid liabilities. This process of innovation and the evolution of financial institutions into an overlapping pattern in the provision of financial services are still continuing.
In the second part the essay, I would like to look at the alternative monetary measures. Aggregation theory requires weak separability among the assets to be included in the monetary aggregate, so that a test for weak separability provides a mechanism for judging the validity of the assets to be included in the monetary aggregate. Once the assets to be included in the definition of money have been selected, the relative weight to be attached to each of the component assets h as to be determined. These weights can be arbitrarily set at unity for each of the assets, as in the definitions of Ml, M2 and M3-which are examples of simple sum aggregates-or they can be determined from the data itself Among the procedures for the latter are the estimation of a variable or constant elasticity of substitution function and the Divisia aggregates.
In defining money, the most common functional form for the monetary aggregate is the simple sum aggregate given by: M=X1+SiaiXi, i=2, 3.....1 This is a weighted sum aggregate that allows the coefficients 'ai' to take on any positive weights between zero and one. Another approach to monetary aggregation is derived from statistical index number theory and focuses on the quantity and price data and emphasizes the desirable properties of index numbers. The simple sum does not meet several of these properties. One aggregate that meets more of these properties is the Divisia aggregate, first proposed by Francis Divisia in 1925. Among these properties is the statistically desired property that any changes in the prices of the components of the index only change the price index and any changes in the quantities of the components only change the quantity index, while the multiple of the price and the quantity indices thus computed equals the index of the expenditures on the services of the assets. The Divisia aggregate xt (x1t,..., xnt) for the n monetary assets for the period t is given by: xt (x1t,..., xnt)=Pxitsit (i from 1 to n).2 This equation has the appealing log-linear form given by: ln xt=Sisit ln xit i=1,...,n. In both of the equations, the expenditure shares sit could be constant at 'si', or change over time as a result of the various types of innovations in the financial sector. These equations allow for such changes and, therefore, allow the resulting values of the Divisia aggregate to incorporate, at least to some extent, the impact of such innovations. The last one I am going to look at is the variable elasticity of substitution (VES) function. It has form: M (X1,..., Xm)=SaiXi1+Vi/()1/1+v1, (i from 1 to m). This approach focus on production functions rather than quantity and price data or utility
Which one is better simple sum aggregates(SM) or Divisia ones (DM)? Among these is Barnett et al. (1984). They used quarterly USA data from 1959 to 1982 and it was reported that neither the SM nor the DM did uniformly better than the other for all the criteria considered. And also Chrystal and MacDonald (1994) compared the simple sum and Divisia aggregates for a number of countries, including the USA, the UK and Canada for various periods over the 1970s and 1980s. Their tests encompassed the St Louis equation and causality tests, and used cointegration. We first examine their findings using the St Louis equation. For the USA, while Ml and M1A tended to do better than their Divisia versions, the latter did better for broader definitions of money. But DM2-with D standing for 'Divisia'-did not sufficiently dominate SM2-with S standing for 'simple sum'- for it to be clearly preferable. For the UK, the authors considered financial innovation to have sufficiently distorted the data to only include MO and M4 in their estimations. While DM4 was clearly preferable to 5M4, there was inadequate basis for choosing DM4 over MO. For Canada, while SMl was slightly preferable to DM1, the broader Divisia aggregates were preferred to their simple sum versions. For the causality tests, Chrystal and MacDonald considered it important to include an interest rate in their cointegration and error correction models. For the UK and Canada, both the DM and SM showed little causal impact on real output. For the USA, the Divisia measures were significant but not the simple sum measures. The overall comparison based on both the St Louis equation and the causality tests did not strongly favour one of the aggregates. 
To conclude, as the innovation and evolution in the financial institutions is still continuing and more financial instruments will be created, the definition of mou4' will change over time. For now neither the DM nor the SW do better than the other for all levels of aggregation, all relevant tests and all periods. The Divisia measures are likely to perform better than the latter in a dynamic period of financial and technical innovation. However, they have not always done better than simple sum aggregates in different types of empirical tests; so that there is no convincing evidence that the former unambiguously dominate over the latter.
M: nominal value of the monetary aggregate;
Xl: M1(currency in the hands of the public plus demand deposits in commercial banks);
Xi: nominal value of the ith liquid asset;
2 xt: Divisia aggregate for period t; sit: share of the ith asset in the expenditure on liquidity services in period t; P: product from 1 to n,
|MO (wide monetary base||Notes and coin outside the Bank of England + banks' operational deposits||June 1981||1984i|
|NIBM1 (non-interest- bearing Ml)||Notes and coin in circulation + NBPSii holdings of non-interest bearing sight bank deposits||June 1975||May 1991|
|Ml||NIBMI + NBPS holds of interest-bearing sight bank deposits||Dec. 1970||July 1989||1982-4|
|M2||NIBMi + NBPS holdings of interest-bearing retail deposits with banks and building societies + NBPS holdings of National Savings ordinary accounts||Sept. 1982iii|
|M3 (PM3 until May 1987)||Ml + NBPS holdings of bank time deposits + NBPS holdings of CDs with banks||March 1977iv||July 1989||1976-86|
|M3c (M3 until May 1987)||M3 + NBPS holdings of foreign currency bank deposits||Dec. 1970v||July 1989|
|PSL1||M3 - NBPS bank time deposits with original maturity > 2 years + NBPS holdings of bank bills, treasury bills, local authority deposits and certificates of tax deposit||Sept. 1979||May 1987|
|PSL2||PSL1 + NBPS building society deposits(excluding term shares)+short-term National Savings instruments||Sept. 1979||May 1987||1982-4|
|M4||M3 + NBPS building society shares, deposits and CDs - building society holdings of bank deposits, CDs and notes and coin||May 1987|
|M4c||M4 + NBNBSPSV bank and building society foreign currency deposits||May 1987||May 1991|
|MS||M4 + NBNBSPS holdings of bank bills, treasury bills, local authority deposits and certificates of tax deposit + short-term National Savings instruments- building society holdings of bank deposits, CDs and notes and coin||May 1987||May 1991|
|'Liquid assets outside M4'||MS + NBNBSPS holdings of bank and building society foreign currency deposits + further liquid assets of NBNBSPS and overseas sector||May 1991|
|DCE (Domestic credit expansion)||Change in bank lending to the non-bank private and public sectors||Dec. 1972||March 1986||1967-9