ABSTRACT
A flow of funds account takes the form of a matrix: each column indicates disaggregated sectors and each row implies financial instruments. Entries in each cell indicate purchases or sales of assets during a discrete period of time. They can be positive, negative or zero depending on the position of a sector; for example, if the sector accumulates obligations in the asset in question, then it is a negative entry. The flow of funds matrix contains the interlocking nature of the accounting system as a whole. In its column, though each sector is free to choose the composition of assets, total net acquisitions of financial assets (NAFA) in any time period are constrained by the sector’s overall surplus or deficit on income and capital accounts. When stock data, rather than flow data, enter in the matrix, each column implies a given sector’s balance sheet, since this is the presentation of assets and liabilities of the sector in question, at a point time. Since purchases of an asset by one sector are to be accomplished by sales of the asset by another sector, each row sums zero. Each entry in the matrix is determined either exogenously or endogenously. The latter accounts for portfolio choices of the disaggregated sectors, usually based on portfolio demand functions relating financial assets to interest rates. The market clearing conditions are normally met by equating the asset demand and supply, and each market is solved for either the asset yield (or the asset price) or the total supply. This constitutes a system-wide flow of funds model. This survey has concentrated on demand functions for a single-sector study,
because sector studies are the essential building blocks of a flow of funds model (Green and Murinde 1999), and also the empirical work of a complete flow of funds model is rare; exceptions are those of such as Green (1984) for the United Kingdom, Hendershott (1977) for the United States. To qualify in a system-wide model, we consider the following properties of a systemof demand functions. First, the theoretical foundation is some form of utility-maximising behaviour by agents: it implies restrictions on the coefficients, then gives potentially highly collinear explanatory variables; the estimation of asset demands is much facilitated by such restrictions (Perraudin 1987: 741). Second, there is the need to incorporate the adding-up restrictions implied by the accounting framework of the balance sheet, thereby it maintains the internal consistency of any solution: in each sector a
its fixed of asset holdings, but not the total, thus the interest rate coefficients must sum to zero across equations. Third, the demand and supply equations are properly specified, such that a market clearing condition determines the yields or quantities within the system, and the total impact of policy changes on the financial sector can be analysed (e.g. the impact of an increase in deposit rates on the increases in total deposits and the subsequent portfolio switches). In this survey, the aim is to address the main features of the various asset
demand functions from both theoretical and empirical aspects, so that it may contribute to the construction of a flow of funds model for developing economies. This is a selective survey; demand functions are chosen, which are theoretically designed or empirically applied to financial asset choice with a view to modelling a flow of funds. The asset demand model is then largely classified into three types; the pitfalls model approach, the mean-variance approach and the consumer demand theory approach. All three approaches hold the common assumption of separability: the portfolio balance decision is separated from the consumption-saving decision (Tobin 1969 and Buckle and Thompson 1992), though we will investigate some attempts at integrating both decisions in due course. For many years portfolio modelling generated disappointing empirical results:
it is said that modelling a portfolio behaviour is the ‘graveyard of applied economics’ (Buckle and Thompson 1992). The main problem lies in the heavily parameterised specification leading to statistical inefficiency. The particular attention is therefore placed on recent developments in portfolio modelling, which pave the way to mitigating the problem. The outline of each section is as follows: In Section 2.2, discussion centres
around the pitfalls model. The basic accounting framework for portfolio modelling of n assets is set out in a simple stylised model as a system of linear equations. One of the model’s main features is that it advocates the ‘general disequilibrium’ framework for the dynamics of stock adjustment to a ‘general equilibrium’. The dynamics of cross-adjustment are incorporated in that the adjustment of any one asset holding depends not only on its own deviation of the previous actual level from desired level of asset holdings, but also on the deviations from equilibrium of other assets.1 The pitfalls model is probably the most influential statement of wealth allocation from the viewpoint of empirical implementation for a flow of funds. At the same time it is known to have several limitations. First, there is no theoretical foundation in the pitfalls model: the explanatory variables are chosen in an ad hoc manner, not explicitly derived from the utility maximising behaviour (Buckle and Thompson 1992). Second, the cross-adjustment mechanism makes the size of a flow of funds model very large, hence the model suffers from heavy parametrisation leading to anomalies in parameter. Third, it is argued that the pitfalls dynamic model is a stock adjustment model and hence fails to distinguish between new cash flows and previously held wealth. Markowitz (1952) and Tobin (1958) laid the foundation of portfolio selection
theory based on the mean-variance (M-V) hypothesis. M-V is an attractive way to
functions. it the asset demands of an investor who maximises a function of the mean-variance of his or her end-of-period real wealth. The early stage of the work is limited to the explanation of the quantities of the various assets that are specified as functions of the expected returns and the expected risks, treating the structure of interest rates as exogenous. The model specification is therefore similar to the pitfalls model (e.g. Parkin et al. 1970, White 1975, Bewley 1981 and Spencer 1984). Consequently, in general these studies tend to share the same problem ofmulticollinearity as experienced in the pitfalls model. On these grounds, these models are consolidated in the pitfalls type model in their discussion. Frankel and Dickens (1983), Frankel and Engel (1984) and Frankel (1985) have
brought the theory of mean-variance optimisation to the asset demand functions by inverting the model: the properly specified interest rate equations based on the CapitalAsset PricingModel (CAPM) ofM-V are linked with the portfolio demand functions and the estimation is to regress interest rates on asset shares. The CAPM itself is, however, subject to some methodological criticisms. Roll (1977) argued that the results were sensitive to a failure to include all relevant assets in the portfolio. The CAPM also requires stringent assumptions that expected returns and the ‘betas’ (the covariance with the market return) are constant over time, but this is inconsistent with the changes in asset supplies and the consequent changes in expected returns. Besides, many empirical studies are embarrassed by the presence of statistically insignificant and wrongly signed coefficients. In Section 2.3, discussion is focused on the CAPM-based inverted (demand) model, titled the M-V approach. This is a direct study of a determinant of interest rates using a flow of funds, and also a way of mitigating the theoretical problems of CAPM. Barr and Cuthbertson (1989) advocated the demand for assets in the context of
neoclassical demand theory. In demand theory the utility functional forms implicitly impose theoretical constraints of the basic axioms of rational choice, hence it does not need to assume homogeneity or symmetry, yet it is possible to test these properties. This is contrasted with the pitfalls model, which satisfies the minimum requirement of adding-up, but is not consistent with the theoretical constraints of homogeneity and symmetry. In consumer theory there is, however, no fixed functional form of utility func-
tion. A specific functional form is applied such as in the linear expenditure system (LES) and the Rotterdam model. These are the most popular demand models. However, the underlying specified utility function is an additive one, so that the system suffers from the limitations of additive systems (Thomas 1985). There is therefore a trade-off between flexibility and the degree of freedom (Theil 1980 and Prasad 2000). A flexible functional form circumvents this problem without the cost of a reduced efficiency of estimates, including the Cobb-Douglas, the constant elasticity of substitution (CES), Translog (Transcendent Logarithm) and AIDS functions. In Section 2.4, the focus is on the particular flexible functional forms of Translog and AIDS models. The Translog model developed by Christensen et al. (1973) approximates the direct (indirect) utility function by functions that are quadratic in the logarithms of the quantities consumed (the
The function’ has frequently been used in assessing the substitutability between financial assets with some fruitful results. TheAIDS model, put forward by Deaton and Muellbauer (1980a), approximates the cost function by functions that are quadratic in the logarithms of prices. The AIDS model has a number of attractions in terms of empirical application as compared with other demand system and is empirically well supported. In Section 2.5, some empirical evidence and limitations on a flow of funds
model for developing economies are reviewed, although there are limited sources of information. The concluding remarks are found in Section 2.6.
