APPENDICES: I. Estimation of Coefficients
In estimating the coefficients, the United Kingdom was used as an illustration. The methodology used will be illustrated by taking the coefficient for ΔM in equation (9)
To begin with, it is easy to assign plausible values for some coefficients: c, the marginal propensity to consume, was given a single value of 0.6, and d, the marginal propensity to import, was given two values—a lower limit of 0.2 and an upper limit of 0.4. The figure for the upper limit was derived from Ball and Drake,14 who estimated the following import equation:
where M represents imports of goods and services; GDP, gross domestic product; and K8, the stock of inventories. The coefficient for GDP is the marginal propensity to import. This coefficient is almost certainly too high; however, it is used in the text for illustrative purposes.
Suppose now that the coefficients b, f, e, and g were available in “elasticity” form (be, fe, ee, ge), where be for example, represented the percentage change in investment divided by the percentage change in the interest rate, fe represented the percentage change in interest rate divided by the percentage change in the money supply, and so on. Then
where I, R, M, K, and Y represent “mean” values of these variables. Our coefficient for ΔM would then be
We would need to know not only the size of the relevant elasticities but also the relative mean values of I, M, Y, and K (with R eliminated by substitution). The only problem with this procedure is in the estimation of the g. First, it is difficult to get a meaningful figure for K (net short-term capital flows); second, ge would appear to have little meaning in an equation where the dependent variable was net short-term capital imports, whose value could approach zero. As a result, arbitrary figures of 100 and 20 were used for g. A figure of 100, for example, implies that a 1 per cent change in the interest will normally result in a change of £100 million in short-term capital flows. Elasticities were used for be, fe, and ee, but a slope value was used for g. On the basis of U.K. data, the ratio I/Y was assumed to be 0.2 and the ratio I/M was assumed to be 0.5. The mean interest rate was assumed to be 6, the mean gross national product was assumed to be £37,000 million, and the mean money supply was assumed to be £13,000 million. Two values were used for be: 0.4 and 0.8. There is no empirical work on this for the United Kingdom, but these values are consistent with econometric studies in the United States.15 In the estimation of fe and ee, the U.K. study that is most useful is one by Kavanagh and Walters.16 They estimated the following interest rate equation (for the period 1926–60):
where R is the long rate, M is the money supply, and Y is aggregate income. Both coefficients were significant, and both approximated 1. Elasticities for both variables of 0.5 and 1 were used in the computations.
Mr. Argy, Assistant Chief of the Special Studies Division of the Research Department, is a graduate of the University of Sydney, Australia. He has been a lecturer at the University of Auckland, New Zealand, and a lecturer and senior lecturer at the University of Sydney. He has contributed several articles to economic journals.
There is some question as to whether the level of activity has a significant effect on export performance. For a U.K. study, see R. J. Ball, J. R. Eaton, and M. D. Steuer, “The Relationship Between United Kingdom Export Performance in Manufactures and the Internal Pressure of Demand,” The Economic Journal, Vol. LXXVI (1966), pp. 501–18.
In equation (9) if g is sufficiently large (i.e., short-term capital flows are strongly influenced by the interest rate) d — ge may be negative. In this case, an increase in autonomous expenditures will improve the balance of payments. This is true where, with fixed money supply, the rise in the interest rate will improve capital flows by more than the increment in imports owing to the rise in income. This example is excluded from the “plausible” range of solutions used in the text.
The effect of allowing for these financial and import constraints on income expansion is to lower the multiplier from
This disregards complications arising from the fact that different components of expenditure may have different import contents.
The model, of course, also assumes that the current and capital accounts are independent. There is also some question as to whether the interest rate in the capital account determines “stocks” or “flows.” The model uses a flow variable. A stock relationship complicates the mechanism of adjustment suggested above. If short-term flows are a function of the change in the interest rate (the stock version), then in order to maintain an improved given flow the interest rate would need to be raised continuously.
There are difficulties arising from the fact that the money in the model should strictly refer to “mean” money in the period. When money is defined in this way, the terms for domestic credit and net overseas assets should also correspond to this definition in order to satisfy the identity. This was disregarded in the interest of simplicity; also, the results would be changed only mildly by effecting this transformation.
The coefficient for ΔD for the other solutions is (b) 0.09; (c) 0.16; (d) 0.05; (e) 0.19; (f) 0.03.
This conclusion need not follow if we allow for foreign repercussions. Where the foreign impact is allowed for, the domestic expansion will generate some increase in exports; hence, some increase in the money supply in long-run equilibrium will be sustainable. This point was suggested to the author by an unpublished paper by D. Roper, “Some Dynamic Implications of a Keynesian Model of the Open Economy Under Fixed Exchange Rates.”
In our model, this must also mean that the rate of interest reverts to its original level, since the rate of interest is determined by income and the money supply, both of which are ultimately unchanged. Of course, in the progression to equilibrium, the rate of interest will change, and this will result in a temporary movement in short-term capital flows. Movements in capital flows were disregarded in the text.
If the increase in credit is constant in each period, the solution will be different. As equilibrium is approached, the money supply increases at a declining rate. In equilibrium the level of income will be higher, and the periodic increase in credit will leak overseas. This is one case dealt with by J. J. Polak in “Monetary Analysis of Income Formation and Payments Problems,” Staff Papers, Vol. VI (1957), pp. 1–50.
The total drop over time in the money supply will be the cumulative deficits. In this example they sum to roughly 310 units. In equilibrium the level of income will be some 54 units above the original level, the rate of interest will be higher (since income is higher and the money supply is lower), and the balance of payments will be zero with additional imports exactly offset by increased capital flows. Note that in this model if g = 0 (i.e., capital flows do not respond to the interest rate), the long-term coefficient for ΔZ is zero, implying in this instance that an increase in autonomous investment cannot ultimately produce a rise in income.
There are two differences worth noting between this model and the total domestic credit one. The first is the feasibility of controlling total credit instead of central bank claims; the discussion in the text suggests that the latter is easier to control. The second is the fact that where central bank claims are controlled an unanticipated change in net overseas assets will have a multiple effect on money. For total domestic credit, the multiplier was unity.
If the marginal propensity to import were 0.2, the net income multiplier would be 1.7 and the balance of payments coefficient would drop from 0.5 to 0.33.
R.J. Ball and Pamela S. Drake, “Export Growth and the Balance of Payments,” The Manchester School of Economic and Social Studies. Vol, XXX (1962), pp. 105–19.
See Thomas Mayer, “Multiplier and Velocity Analysis—An Evaluation,” The Journal of Political Economy, Vol. LXXII (December 1964), pp. 563–74.
N.J. Kavanagh and A.A. Walters, “Demand for Money in the UK, 1877–1961: Some Preliminary Findings,” Oxford University Institute of Economics and Statistics, Bulletin, Vol. 28 (1966), pp. 93–116.
This model is very similar to the model developed by Polak, op. cit. The major difference is that Polak defines his time period in such a way that an increase in money will generate an equal increase in income. This means defining the time period for any country as the fraction of the year represented by the inverse of velocity.