The Long Run Demand for Money in South Africa (1918-60): Some PreliminaryFindings s

by THOMAS MAXWELL"Men are motivated by three basic desires-food, love and money-and of these, the least understood is money".*(1)

1. IntroductionTHIS RESEARCH WAS motivated amongst other things by Heller's assertion that "there is a stable demand for money function inthe long run".*(2) It was felt that the existence of a high degree of forced savings during the second World War and thesubsequent rapid evolution of the financial sector made this assertion a priori questionable and worthy of further empiricalinvestigation. This paper is an attempt to shed some empirical light on the following questions:(i) The feasibility of distinguishing idle from active balances, and if this proves possible, the determination of the wealth andinterest elasticities of these balances.(ii) Dropping the explicit distinction between idle and active balances to:(a) determine the role of interest rates(b) determine the appropriate constraint on the demand function(c) determine the effect of changing the definition of the variables.(iii) To examine the stability of the demand function over time.

2. Description of ProceduresAs this paper is essentially concerned with empirical investigation, no attempt has been made to add to the existing literaturecovering the theoretical side of the problem.*(3) It was initially hoped to build a simultaneous equation model of the bankingsector, but paucity of data made this impossible and consequently a reduced form estimation was adopted. The model adopted isof the form:

1971 SAJE v39(1) p14

Where: is the real stock of money demanded at time t.Zt is predetermined nominal stock of money at time t.Pt is the price level at time t.Mt is the observed real money stock at time t.Equation (iii) thus represents the equilibrium condition in the market. Unless we can be certain that is dependent on some variableexogeneous to eqn. (i), a devil in the guise of the identification problem raises its cloven hoof. However, in view of the mechanisminvolved in the sale of gold whereby the central bank purchases all the newly mined gold, so injecting reserves into the bankingsystem, we have identified at least one variable endogeneous to equation (ii) but exogeneous to equation (i), and this it is hoped issufficient to obviate the identification problem.The major problem to be determined is the identification of the appropriate variables that comprise the right hand side of thedemand equation. The data described in the appendix was fitted to the various functional forms of the demand equation describedbelow by means of ordinary least squares regressions. At once we have to decide whether to estimate the function in logarithmic orarithmetic form. The logarithmic form has certain advantages, principally ease of interpretation of coefficients and in view of thefact that logarithmic functions gave consistently better estimates than arithmetic functions, they were adopted as the basicfunctional form.

3. Idle Balance RelationsAll methods of estimating idle balances imply a disaggregation of the demand function of the form:

where the first term on the right hand side represents transactions balances (assumed to depend principally on income) and thesecond term represents idle balances (assumed to depend principally on the rate of interest and possibly on wealth W). Mostempirical determinations of idle balances follow the method first mooted by A. J. Brown.*(4)This method consists in assuming that idle balances are zero in a period of maximum velocity (note this assumes that transactionsand income velocities are the same during this period), and then assuming that this estimate is the actual

8

1971 SAJE v39(1) p15

transactions velocity during the whole period under consideration, to calculate idle balances as the residual from the actual moneystock and the calculated stock required to finance the transactions.Thus idle balances are computed by means of the formula:Lt = Mt - Min (Mt/Yt). YtDIAGRAM I

1971 SAJE v39(1) p16

The results of plotting idle balances as calculated by the above formula against the rate of interest are shown in diagram 1. In viewof the fact that the results did not depend critically on the interest rate adopted and in view of the remarks at the end of this sectionon the interpretation of these results, it was felt that a single diagram would be sufficient to illustrate the results.An examination of the diagram reveals two distinctive features. Firstly there is a tendency for idle balances to be small duringperiods of high interest rates and large during periods of low rates. This is in accordance with Keynesian theory. The secondfeature is that the schedule underwent a significant and non-reversible shift during the war period.It could be argued that it is unrealistic to assume idle balances to be zero during the period of maximum velocity, and consequentlyan alternative definition was tried, viz.Lt = Lt + Stwhere St are savings deposits i.e. M2 - M1. This relation yielded essentially the same graphical respresentation with the exceptionthat the shift in the function was even more pronounced.Idle balances were than regressed against the interest rate and wealth (over the entire period and over the pre-war and post-warperiods separately) in an attempt to discover whether the shift was due to a misspecification of the function. The wealth variableproved significant in the great majority of cases, though often having a negative coefficient in the post-war period, and to have acoefficient of unity, working at a 1% level of confidence. The fact that the idle balance relations were homogeneous of degree 1 inwealth enabled a graphical representation of the function to be easily obtained.In order to keep the scale on the vertical axis the same, the assumption that the function was homogeneous of degree 1 in wealthwas changed to the assumption that it was homogeneous of degree 1 in the ratio of wealth in any year to a particular reference yearwhich for convenience was taken to be 1930, the year in which velocity was a maximum.Comparison of wealth corrected idle balances with the previous results revealed essentially the same pattern of results with theshift of the function being less marked though still discernable.All the above calculations of idle balances depended critically on the assumption that once the transaction velocity was calculatedit remained constant over the entire period. This assumption can justifiably be criticized as unrealistic. Once we relax theassumption, there are essentially three alternatives open to us.(i) Assume a secularly falling Vt,(ii) Assume a secularly rising Vt,(iii) Assume a Vt that changes over the business cycle.

1971 SAJE v39(1) p17

For ease of comparison with the other results, it was assumed that Vt = 7•13 in 1930 in accordance with the previous results, andwas changing at 4% per annum, the average rate of growth of G.D.P. during the whole period. In the third case Vt was assumed tohave the same base value and the same rate of change, except that it was assumed to be increasing during the upswing of the cycleand decreasing during the downswing.*(5)The same procedure concerning adjustment for wealth was adopted for these definitions as for the previous ones. The resultsyielded by these alternative definitions did not differ in any substantial fashion from the previous ones.A substantially different method of calculating idle balances has recently been suggested by Konstas and Khonja.*(6) Theirmethod when applied to the data yielded a significant number of negative idle balances regardless of the interest rate adopted andof the time period considered. This unfortunately precludes any comparison with results obtained by a different method.One further question remains to be considered, viz the liquidity trap. An investigator trying to obtain empirical evidence about theexistence or non-existence of the liquidity trap has essentially two methods open to him.First he can fit a constant elasticity demand function to the data during a period of high interest rates and again during a period oflow interest rates and determine by a test on the F-ratio devised by G. C. Chow*(7) whether the interest elasticity is higher duringthe period of low rates than during the period of high rates. Working at a 1% confidence level, the results did not give anytrustworthy evidence in favour of the liquidity trap hypothesis.

9

The second alternative is to fit a function with a variable interest elasticity and to see whether it provided "better" results than aconstant elasticity function fitted over the same period. The two variable elasticity functions tried were:(i) lnlt = a + Br(ii) In view of the lack of any satisfactory definition of the criterion for judging betterness, any evaluation of the results must besubjective. Adoption of the standard error of the estimate as the criterion failed to reveal any significant preference for the variableelasticity function over the constant elasticity function.Even though the evidence does not provide any clear-cut decision, the greater part of the evidence indicates that the liquidity trap,if it existed at all in the 1930's, was not a significant phenomenon in South Africa. Further evidence, though indirect, in favour ofthis conclusion was provided by examination of the residuals.The validity of the above section is critically dependent on the soundness of the

1971 SAJE v39(1) p18

methods used to calculate idle balances. In the author's opinion these are too mechanistic for any great reliance to be placed onthem, and although they do conform in a broad fashion to economic theory, the nagging doubt still remains that this relationshipmight be a by-product of the method of calculation wherein idle balances appear as a residual and not a genuine economicrelationship.In view of this fact it was felt that any further investigation into this realm would bring us into the region of if not negative, at leastdiminishing returns. However, one fact, which will prove of vital importance in the latter sections, has emerged with startling clarity,viz. the shift in the function between the pre- and post-war periods.

4. Demand FunctionsThe first type of function to be fitted to the data was of the form:1nM = a0 + a11nr + an21nA

where r is the interest rate and A the appropriate constraint. The results of this set of regressions are given in table (i) of theappendix. The results are presented using one interest rate only viz. the 12 month deposit rate, the reason underlying this choicebeing that the results were not critically dependent on the interest rate adopted and the 12 month deposit rate has the advantage ofbeing obtainable in the form of a consistent series over the whole period.*(8)When viewed over the whole period, the fit is reasonably good with the permanent income model proving superior. However, theDurbin-Watson statistic is distressingly low indicating a possible serious misspecification of the model. The Chow-test whenapplied to pre-war and post-war periods indicated at a 1% confidence level that the function had undergone a sizeable parametricshift during that period.Consequently the next step was to estimate the function over the two sub-periods separately. In the pre-war period, all thecoefficients had the correct signs, the fit was reasonably good but the Durbin-Watson still indicated a possible misspecification.The results for the post-war period, however, were substantially different. The fits were reasonable and the Durbin-Watsonstatistic still indicated a possible misspecification. The major difference lay in the signs of the coefficients. In the great majority ofcases the constraint coefficient for M1 was negative, and sometimes significantly negative (this depends on the interest rateadopted) whereas the constraint coefficient for M2 though usually having the correct sign was insignificant.This dramatic change in the function from one sub-period to another provides a second verification of the high F-values (often ashigh as 120) obtained in the Chow-test. The reason for the negative signs on the constraint is obvious once we take

1971 SAJE v39(1) p19

into account that M1 was declining both in nominal and in real terms during the post-war period and further the insignificance ofthe constraints in the M2 equations is explained by the fact that remained nearly constant over the sub-period.There are essentially three ways of explaining this phenomenon:(i) We can assume that the institutional structure has remained unchanged and a change in tastes has been responsible for thechange in the function.(ii) We can assume that individual tastes have remained unchanged and that the change in the function can be explained by achange in the institutional framework.(iii) We can assume that it is some combination of the above.It is not possible to decide which of the above possible explanations is correct without some further empirical evidence and so thisquestion will be left in abeyance until further results have been discussed.Before going on to discuss alternative forms of demand functions, there is one further possibility that should be explored, viz. the

10

possibility that the function works better when fitted in nominal terms, for it can be seen from equations (i), (ii) and (iii) that we haveassumed the function to be homogeneous of degree 1 in price. Repetition of the results with values expressed in nominal terms andthe price variable appearing explicitly on the R.H.S. yielded results not differing significantly from the above with the price indexappearing significantly in the equation with a coefficient of approximately unity. This would indicate that the above results are nota consequence of a misspecification of the real variables.The next functional form to be attempted was a lagged stock adjustment mechanism of the form:1nMt = a0 + a11nMt-1 + a21nrt + a31nAtThe results of this set of regressions are presented in table (ii) of the appendix. When viewed over the period as a whole thisfunction yields substantially better results. The S.E.E. has decreased markedly and the Durbin-Watson statistic nearly alwaysindicates freedom from auto-correlation at 1%. However, the F-test still indicates that a parametric shift in the function hasoccurred, though the F-values themselves are not as large as previously. Once again, when fitted over the separate sub-periods thefunctions performed differently.When fitted to the pre-war period, the lagged adjustment model gave good results for both M1 and M2, the standard error ofestimate being small, the Durbin-Watson high and the coefficients being significant and having the expected sign. However, whenfitted to the post-war period, the results were not significantly different from those obtained previously. The Durbin-Watson stillindicated autocorrelation, the constraints in the M1 equations still tended to have a negative sign (once again this was largelyindependent of the particular interest rate adopted) and to be insignificant. In the M2 equations there was tendency for theintroduction of a lag to increase the fit but often it made the constraint take on a perverse sign.

1971 SAJE v39(1) p20

Attempts at introducing a lagged interest rate*(9) both with and without the lagged money stock yielded poorer results than thoseobtained above. As a test to determine whether the estimation procedure introduced any bias into the coefficients, the regressionswere re-run using the 3-Pass Least Squares method.*(10) The results obtained by this method often differed only in the thirddecimal place from the results presented above.At this state it was felt that it was going to prove impossible to find a function which would serve equally well over both periods.As it turns out, the lagged stock adjustment model described above yielded the best, judging by the size of the standard error ofestimate, results for the pre-war period and was consequently adopted as the function best suited to describe the demand formoney in the pre-war period.In order to construct a better fitting function for the post-war period we shall have to take a closer look at the development of theeconomy during that period.The South African economy during the post-war period can be characterised as having a high rate of economic growth and rapidlyexpanding secondary and tertiary sectors. Concomitant on these would be a growing financial awareness and an increasingdemand for the services of financial intermediaries. Indeed, the latter part of the 1950's was characterised by the rapid growth of"near-banks", and other financial intermediaries whose liabilities provided an ever-widening spectrum of alternative liquid assetswhich would prove superior to M1 as a temporary store of value.*(11) Also these institutions provided to some extent substitutesfor M1 - M2. Thus the latter part of the period can be characterised by a change in the institutional structure generating an increase

in the range of substitutes.The immediate post-war period can be characterised by the running down of idle balances as shown by diagram 1.The mid-period, for convenience we shall take it to be about 1950-55, provides us with no clue as to the reason for the negativesign on the constraint. One possible explanation could be that before an actual change in the institutional structure occurs, theremust be a change in tastes to provide the motive for the change and it was just this change in tastes which accounted for thenegative sign.The absence of quarterly estimates of G.D.P. makes it extremely difficult to adduce any empirical evidence in support of the abovehypothesis, though one piece of indirect evidence is available. It is reasonable to assume that, in the absence of any changes intaste or in institutional structure, idle balances would have returned to their desired levels within a few years after the war andconsequently

1971 SAJE v39(1) p21

if it were the running down of idle balances accumulated during the war that was swamping the entire period, estimation of thefunction during the period 1950-60 should yield the correct sign. However, we still obtain negative constraint elasticities during thisperiod. While this is not conclusive, it does lend credence to the hypothesis that both tastes and the institutional structure havechanged in such a way as to make M1 a relatively inferior store of value and consequently to increase the importance of thetransactions motive in determining the holdings of M1. In addition it is extremely plausible that economies of scale have been

11

operational in determining cash holdings and this is a further factor tending to decrease the size of the constraint coefficient.In the light of the above discussion, it was felt that the most important single variable omitted from the functional forms specifiedabove was an index of the change in tastes and/or the change in institutional structure. Attempts at constructing an index of thefinancial structure by considering both the number of financial intermediaries and the value of their liabilities outstanding at theend of the year were doomed to failure on account of the high degree of multicollinearity between the index and the constraint. Themost successful index is a simple linear time trend giving rise to a function of the form below:1nMt = a0 + a11nrt + a21nrt + a21nAt + a31nt

This reflects the hypothesis that the change in tastes and/or in the institutional structure can be captured in arithmetic form by alinear time trend. Attempts to introduce an exponential growth trend yielded consistently inferior results. In every case laggedmoney stock and the lagged value of the interest rate were insignificant (even at 5%) and consequently were dropped from the finalform. The results of fitting this function are shown in table (iii) of the appendix. As these were by far the best results obtained forthis period, the above function was taken as representing the demand function for the post-war period.*(12)

5. ConclusionThe one factor which emerges with startling clarity from this study is that the demand function has undergone a parametric shift ofa significant magnitude from the pre-war period to the post-war period. And further this shift cannot be simply ascribed to a mererunning down of idle balances accumulated during the war period. Further, when viewing the post-war period in isolation we aredrawn to the conclusion that it will be impossible to define a demand function in isolation from the institutional environment, apoint in regard to which all but the most ardent quantity theorist would tend to agree.Examination of all results, over the whole period and both sub-periods, revealed that an interest elastic Permanent Income modelgave the best results, followed by a current income model and lastly the wealth model. The relative failure of the

1971 SAJE v39(1) p22

wealth model does not necessarily imply that it is not the appropriate model, for its failure could be the result of the wealth measureadopted. Examination of the significance of the interest rate in the various equations tested indicated that whenever a reasonable fitwas obtained (say greater than 0.3) the interest coefficient had the predicted sign and was significant. This may be taken as fairlyconclusive evidence that the demand for money is interest elastic, contrary to Friedman's assertion.While the lack of comparable data has forced this study to terminate in 1960 and the absence of quarterly figures has precluded anyanalysis of the short-run function, which judging from the above results should be an extremely rewarding field of study, the aboveresults nevertheless give one possible explanation of the difficulties encountered in the application of monetary policy during thepost-war years. For the results for the post-war period indicate that any model for under-standing the workings of monetary policythat is cast in a static framework is of necessity incompletely specified for it fails to take account of the interaction of dynamicfactors on the demand for money function.University of British Columbia.

APPENDIX I AND II

1971 SAJE v39(1) p23

Appendix I(The figure in parenthesis immediately underneath a coefficient is its t-value.)TABLE I

Dept. Variable Const. 12D Y Yp W D.W. S.E.E. NOBS.

M1 (18-60) -2.972(-2.544)

-0.626(-8.940)

1.100(20.951)

0.294 0.171 0.942 43

M1 (18-39) 5.588(1.848)

-0.461(-4.337)

0.681(4.834)

0.373 0.138 0.797 22

M1 (45-60) 21.137(7.241)

-0.189(-2.633)

-0.013(-0.092)

0.938 0.045 0.736 16

M1 (18-60) -4.201(-3.826)

-0.647(-10.155)

1.161(23.089)

0.426 0.155 0.952 41

12

M1 (18-39) 1.763(0.515)

-0.450(-4.378)

0.863(5.399)

0.645 0.132 0.832 20

M1 (45-60) 21.186(7.130)

-0.188(-2.595)

-0.015(-0.107)

0.935 0.045 0.763 16

M1 (18-60) -4.282(-2.191)

-0.796(-7.728)

1.127(13.022)

0.237 0.258 0.868 43

M1 (18-39) 9.480(2.758)

-0.530(4.165)

0.479(3.127)

0.416 0.168 0.701 22

M1 (45-60) 21.117(9.230)

-0.188(-2.690)

-0.011(-0.109)

0.936 0.045 0.763 16

M2 (18-60) -5.274(-5.366)

-0.591(-9.894)

1.221(27.235)

0.375 0.146 0.963 43

M2 (18-39) 0.391(0.144)

-0.458(-4.802)

0.941(7.455)

0.242 0.124 0.878 22

M2 (45-60) 18.146(4.700)

-0.125(-1.322)

0.136(0.759)

0.439 0.060 0.074 16

M2 (18-60) -6.389(-6.729)

-0.609(-11.048)

1.275(29.326)

0.517 0.134 0.968 41

M2 (18-39) -3.966(-1.274)

-0.439(-4.692)

1.148(7.894)

0.518 0.120 0.894 20

M2 (45-60) 17.996(4.585)

-0.128(-1.342)

0.143(0.785)

0.454 0.060 0.077 16

M2 (18-60) -7.177(-3.950)

-0.777(-8.110)

1.269(15.774)

0.279 0.240 0.900 43

M2 (18-39) 4.285(1.276)

-0.527(-4.239)

0.727(4.863)

0.298 0.164 0.787 22

M2 (45-60) 19.021(6.257)

-0.117(-1.256)

0.093(0.676)

0.451 0.060 0.066 16

1971 SAJE v39(1) p24

TABLE II

Dept.Variable Const. Mt-l 12D Y Yp W D.W.

S.E.E.

NOBS.

M1 (18-60) -0.797(-1.081)

0.613(8.570)

-0.317(-5.788)

0.415(4.740)

1.805

0.099

0.981

42

M1 (18-39) 2.279(0.860)

0.411(3.028)

-0.360(3.891)

0.455(3.062)

1.697

0.112

0.871

21

M1 (45-60) 18.638(3.230)

0.134(0.507)

-0.517(-1.624)

-0.027(-0.188)

1.057

0.046

0.749

16

M1 (18-60) -1.269(1.570)

0.581(7.425)

-0.342(-5.901)

0.468(4.739)

1.920

0.099

0.980

41

M1 (18-39) 1.030(0.345)

0.375(2.547)

-0.372(-3.939)

0.549(2.953)

1.937

0.115

0.837

20

M1 (45-60) 18.678(3.231)

0.136(0.511)

-0.156(-1.595)

-0.030(-0.205)

1.053

0.046

0.749

16

13

M1 (18-60) -0.706(-0.797)

0.759(13.531)

-0.278(-4.766)

0.262(3.491)

2.052

0.108

0.977

42

M1 (18-39) 3.202(1.088)

0.541(4.115)

-0.356(-3.465)

0.279(2.184)

2.059

0.124

0.844

21

M1 (45-60) 18.449(3.383)

0.148(0.542)

-0.149(-1.456)

-0.031(-0.273)

1.066

0.046

0.750

16

M2 (18-60) -1.954(-2.638)

0.588(8.227)

-0.300(-5.895)

0.497(5.310)

1.641

0.087

0.987

42

M2 (18-39) -1.200(0.559)

0.426(3.558)

-0.344(-4.159)

0.613(4.284)

1.579

0.095

0.931

21

M2 (45-60) 8.431(1.588)

0.636(2.437)

0.004(0.043)

-0.036(-0.208)

1.338

0.051

0.312

16

M2 (18-60) -2.409(-2.736)

0.561(6.679)

-0.321(-5.601)

0.545(4.816)

1.835

0.091

0.985

42

M2 (18-39) -2.879(-1.062)

0.380(2.640)

-0.346(-3.950)

0.737(3.688)

1.906

0.103

0.922

20

M2 (45-60) 8.458(1.596)

0.641(2.340)

0.008(0.075)

-0.042(-0.238)

1.344

0.051

0.313

16

M2 (18-60) -1.496(-1.726)

0.764(14.071)

-0.250(-4.586)

0.295(3.796)

1.997

0.979

0.983

42

M2 (18-39) 0.151(0.063)

0.584(4.959)

-0.316(-3.382)

0.384(3.045)

2.075

0.011

0.907

21

M2 (45-60) 8.175(1.600)

0.690(2.459)

0.037(0.370)

-0.075(-0.553)

1.466

0.051

0.327

16

1971 SAJE v39(1) p25

TABLE III

Dept.Variable Const. 12D Y Yp W Trend D.W.

S.E.E. NOBS.

M1 -3.501(-0.548)

-0.192(-3.952)

1.515(3.911)

-2.516(-4.058)

1.926

0.030

0.892

16

M1 -1.858(-0.275)

-0.196(-3.749)

1.409(3.447)

-2.304(-3.592)

1.822

0.032

0.876

16

M1 5.138(1.077)

-0.169(-3.311)

1.050(3.429)

-2.299(-2.573)

2.346

0.033

0.876

16

M2 -19.727(-3.243)

-0.130(-2.804)

2.485(6.729)

-3.867(-6.546)

1.838

0.029

0.781

16

M2 -19.303(-3.182)

-0.142(-3.024)

2.447(6.678)

-3.729(-6.484)

1.575

0.029

0.778

16

M2 -3.534(-0.600)

-0.089(-1.420)

1.591(4.207)

-3.245(-4.085)

1.942

-0.041

0.577

16

Explanation of Symbols:12D - the 12 month deposit rate at Commercial banks.Y - Gross Domestic Product.Yp - Permanent Income.

14

W - Wealth.D.W. - Durbin-Watson Statistic.S.E.E. - Standard Error of Estimate. - Correlation coefficient, corrected for the number of degrees of freedom.NOBS - Number of observations used in the regression.

[APPENDIX II

1971 SAJE v39(1) p26

Appendix IIUnless otherwise stated, all figures are expressed in millions of Rands and are for the end of the calendar year.*(13) Real valueswere obtained from nominal values by deflating with an implicit G.D.P. deflator.One problem which must be settled before finalising the definitions of money and income is how to deal with the governmentsector. Van Staden*(14) has given some convincing reasons in the South African institutional framework as to why governmentdeposits at the Reserve Bank should not be regarded as part of the money supply. Consequently, this convention has beenadopted. Gordon*(15) has recommended using private spending rather than National Income as the macro-measure of income, butdata for private spending is not available over the period under consideration and hence for pragmatic reasons we are forced toinclude the government sector in the macro-measure of income.*(16)Money. All data was obtained from issues of the South African Reserve Bank Quarterly Bulletin of Statistics.1. M1 consists of the sum of notes and coins outside the banking sector and demand deposits at commercial banks. For the period

1918-1958 the data is available directly. For the period Jan. 1959 to Dec. 1960 the following procedure was adopted:(a) Coin holdings were estimated by subtracting holdings of coin by commercial banks (in South Africa and South West Africa)and the Reserve Bank from the total amount of coin issued. This latter figure includes coin in circulation in South West Africa andthe High Commission Territories and thus is not strictly comparable with earlier figures.(b) Notes in circulation were estimated by subtracting holdings of notes by commercial banks (in S.A. and S.W.A.) from notesissued by the Reserve Bank, including notes of other banks for which the Reserve Bank has assumed liability. This series is notstrictly comparable with the previous one on account of the volume of notes in circulation in South West Africa.(c) Figures for demand deposits for commercial banks in South Africa alone are available.2. M2 is defined as consisting of the sum of M1 and the following components:

(i) Savings deposits at commercial banks.(ii) Savings deposits at Permanent Building Societies.

1971 SAJE v39(1) p27

(iii) Savings deposits at the Post Office.(a) Figures for savings deposits at commercial banks are available as at 31st December for the period under consideration.(b) Up to and including 1944, figures for Post Office savings were only available as at 31st March. From 1945 onwards they areavailable for 31st December.(c) Up to and including 1944, figures for Building Societies savings were only available for the end of the financial year and therewas no common financial year. For convenience the end of the financial year was taken to be the 31st March.The figures up to 1944 were adjusted from 31st March to 31st December of the previous year by means of a linear interpolation.Constraints. All data was obtained directly from officials of the research division of the South African Reserve Bank.Gross Domestic Product measured at market prices was used as the macro-measure of income.Permanent Income as originally conceived by Friedman is essentially a weighted average of past current incomes. In constructingsuch a series there are essentially two problems to be faced, viz., the determination of the duration of the weighting period and theweighting pattern.*(17) Although the two choices are not conceptually independent, it will be convenient for expositional reasonsto regard them as if they were.There are two a priori reasons for preferring a short (of the order of 5 years) weighting pattern to a longer one.In a rapidly evolving economy, it was felt that on psychological grounds, income of more than half a decade ago would not have asignificant effect on money holdings in the current period. This assumption may not be valid if the monetary system hasundergone a violent upheaval during the life of an individual since there is some evidence for example that German memories of thehyper-inflation of the early 1920s still exert a limited influence on patterns of monetary behaviour. However, South Africa did notundergo a disruption of similar magnitude during the period under consideration, and consequently the above objection has onlylimited import. There is in addition a further reason for choosing a short weighting period over a long one. If, for any reason an

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exogeneous parametric shift of the function occurred, a long weighting period might swamp the shift and consequently give amerely statistical illusion of stability.The major objection to the adoption of too short a weighting period, apart from a fall in predictive ability, is the introduction of asubstantial degree of auto-correlation. Tests using the various weighting patterns described below indicated

1971 SAJE v39(1) p28

that the extension of the weighting period beyond 3 years produced insignificant improvements in the correlation coefficient andthe Durbin-Watson statistic. This implies that providing the lag exceeds a certain minimum duration, extension of the weightingperiod has no effect. A period of 4 years was adopted because of the above reasons and on account of the availability of data.In estimating the weighting pattern a simple adaptive expectations model of the form:

where is the constructed measure of permanent income and Yt is current income was chosen as the naïve comparison model.Repeated application of the Koyk transform gives rise to an exponentially declining weighting pattern. However, it can be arguedthat the above measure is deficient in that it ignores the effect of secular growth.Comparison of the results of the simple exponential pattern and the secularly adjusted exponential pattern with both weightsnormalised to sum to unity, showed that the latter was marginally superior and consequently was adopted as the naive model.Two other more sophisticated methods were used to compute permanent income. The first of these was that used by ShirleyAlmon.*(18) It consists of constraining the weights to lie on a polynomial of specified degree which is itself constrained to be zeroat the end of the weighting period. The other method consisted of estimating a rational polynomial lag function of specified degreeand duration.*(19) Comparison of the results obtained utilizing the above two methods with the results from the naive modelyielded the surprising result that the naive model proved superior on all counts.Consequently, the naive model was adopted as the measure of permanent income. It has the additional advantage of having asimple economic interpretation. Real permanent income was thus constructed from real values of current income by the followingformula: The weights are derived from the following formula:

where a = 0•044 is the average growth rate over the period.Recomputation of the results over the two subperiods under consideration yielded the same conclusions, even though a washigher in the post-war period than in the pre-war period. Consequently the same weighting pattern was used when calculatingpermanent income over sub-periods.

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It would thus appear, bearing our criteria in mind, that once a certain minimum weighting period has been exceeded, neither theduration of the lag nor the weighting pattern is critical.In common with most countries, South Africa has no economically significant wealth figures, and consequentially any discussionof the empirical measure of wealth must be constrained to the mundane level of method of compilation and coverage. The onlyconsistent wealth figures for the period under consideration consist of the consolidated value of private and governmentalholdings of:(i) Buildings and Constructions.(ii) Machinery, Plant and Equipment.(iii) Inventories.The divergence between these figures and the economist's concept of wealth is sufficiently great to cast a shadow of doubt overthe economic significance of any empirical results obtained from the above data. However, in view of the lack of any alternativemeasure of wealth with a greater degree of economic content, it was decided to utilize the above series to determine to what extentmoney holdings were influenced by such a measure of wealth. It is also possible that the above measure of wealth would act as anindex for the more general measure of wealth, in which case the statistical results would not be entirely void of any economicmeaning.Interest RatesUnless otherwise stated, all data was obtained from the South African Reserve Bank Quarterly Bulletin of Statistics.A. Short-term rates. Three alternative measures of the short-term rate of interest were used.(i) The 6 month Treasury Bill rate. Figures are available for this up to December 1958 when issue was discontinued with thefollowing exception. South Africa went off the gold standard on 28th December 1932 and this caused a substantial increase inliquidity. As a consequence the Treasury found that it had no need to borrow money and consequently stopped issuing both 6

16

month and 12 month bills on 13th February 1933. Both types of bills were first re-issued on 2nd June 1936, except that the ratequoted was the discount rate and not the rate of interest as previously.*(20)(ii) The 12 month Treasury Bill rate. Figures are available up to the end of 1954 when they were discontinued. The same caveatapplies for the period 1933-36.As a consequence of this excess of liquidity in the thirties it was felt that, at least for a few years after the re-issue of Treasury bills,the rate quoted would riot accurately reflect the true cost of short-term borrowing. To counter this objection a third measure of theshort-term rate of interest will be used.

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(iii) The return on 12 month deposits at commercial banks. These figures are available in the form of a consistent series for thewhole period under consideration.B. Long-term rates. Three alternative measures of a long-term interest rate are available for the period under consideration, none ofwhich are entirely satisfactory.(i) The minimum overdraft rate at commercial banks. Figures for this are available in consistent form for the period underconsideration. However, there are two objections to using this as an index of the long-term market rate of interest. Firstly, theduration of the overdraft is not specified and secondly it would be rather sluggish in changing in response to market figures.(ii) The rate of return on the debt held by the Public Debt Commissioners.*(21) This measure has three major shortcomings. Firstly,part of the assets held by the commissioners do not earn interest and part is held in the form of short-term paper. Thus the figurequoted will have some elements of a short-term rate embodied in it. However, the ratio of short-term debt is of the order of 6% oftotal debt. Secondly, for policy reasons, the commissioners will tend to hold the short end of long-term government stock and thefigure would thus represent a medium rather than a long-term rate of interest. Finally, the rate quoted will not represent the rate ofinterest reigning in that particular year, but rather a weighted average of past rates. This arises on account of the fact that thecurrent market rate will affect the quoted rate only to the extent that funds are available to purchase existing securities at the marketrate quoted that year. A further problem that arises is that the figures are quoted for the end of the financial year, viz. 31st March,and not for the end of the calendar year. It was assumed that error involved in taking this figure to correspond with the end of theprevious year was small enough to be ignored.(iii) The average rate of return on the Public Debt.*(22) This figure suffers from some of the objections voiced above in that itcontains significant amounts of short-term and non-interest bearing debt. The major objections to this figure arise from the methodof calculation adopted in compiling it. To derive it, the face value of the total debt has been divided into the value of the fixedannual contractual interest payments, and thus the figure obtained is to a large extent independent of the market rate of interest. Inaddition there are two other definitional problems. The first of these, the fact that the figures are quoted for the end of the financialyear was dealt with in the same way as previously. The second is that up to and including 1950 a figure was quoted for the averagerate of return on the debt held internally, whereas from 1951 onwards the figure was quoted for all the debt. As of 31st March 1951,95.66% of the total debt was held internally and so the error involved is likely to be small.

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Endnotes1Time, (Jan., 15, 1968), p. 30.

2H. R. Heller, "The Demand for Money in South Africa", South African Journal of Economics, Vol. 34, (Dec., 1966), pp. 335-40.

3For an excellent survey of the theoretical literature, see D. E. W. Laidler, The Demand for Money: Theories and Evidence,(Scranton, Penn.) 1969.

4 A. J. Brown: "Interest, Prices and the Demand Schedule for Idle Money", Oxford Economic Papers, Vol. 2, May, 1939), pp. 46-69.

5 Unpublished data on the business cycle in South Africa was very kindly made available to me by Dr. J. C. du Plessis.

6 P. Konstas and M. W. Khonja, "The Keynesian Demand for Money Function: Another Look and Some Additional Evidence".Journal of Money, Credit and Banking, Vol. 1, (Nov., 1969), pp. 765-77.

7 G. C. Chow, "Tests of Equality between Sets of Coefficients in Two Linear Regressions", Econometrica, Vol. 28, (July, 1960), pp.591-605.

8 The use of this rate, however, entails one objection in that it is the rate of return on a component of M2 and consequently does notreflect the rate of return on alternative assets. However, savings deposits at commercial banks comprise only a small proportion ofM2 and the fact that the results do not depend critically on the particular rate adopted indicate that this objection is not serious.

9 E. L. Feige, "Expectations and Adjustments in the Monetary Sector", American Economic Review, Vol. 57 (Papers and Proceedings,May 1967), pp. 462-73.

10L. D. Taylor and T. A. Wilson, "Three-Pass Least Squares: A Method for Estimating Models with a lagged Dependent Variable",Review of Economics & Statistics, (Vol. 46), (Nov. 1964), pp. 329-46.

11For an excellent survey of the South African financial sector see: G. F. D. Palmer, "The Development of a South African MoneyMarket", South African Journal of Economics, Vol. 26, (Dec., 1958), p. 239-52; A. B. Dickman and G. F. D. Palmer, The South AfricanMoney Market-Some Further Developments, South African Journal of Economics, Vol. 28, (Dec., 1960), pp. 354-69; D. W.Goedhuys, "Money on the Wing, or the Rise of Non-Bank Lenders". South African Journal of Economics, Vol. 32, (Sept., 1964) pp.211-18; and A. B. Dickman, "The South African Money Market-Progress and Problems since 1960", South African Journal ofEconomics, Vol. 35, (Sept., 1965), pp. 213-36.

12 Attempts at fitting this type of function to the pre-war period yielded inferior results when compared with the lagged stockadjustment model.

13 The regressions were also run using average figures for the year with no noticeable change in the results.

14B. van Staden: "A Monetary Analysis for South Africa", South African Reserve Bank Quarterly Bulletin, No. 67, (March, 1963), pp.XIV-XXVIII.

15R. A. Gordon: "The Treatment of Government Spending in Income-Velocity Estimates", American Economic Review, Vol. 40,(March, 1950), pp. 152-59.

16 The use of this convention lays the author open to a justifiable change of inconsistency. However, he pleads in mitigation thatsimilar inconsistencies have been made by most other researchers in this field.

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17For an excellent survey of the problems encountered see, Z. Griliches: "Distributed Lags: A Survey", Econometrica, Vol. 35, (Jan.,1967), pp. 16-49.

18Shirley Almon, "The Distributed Lag between Capital Appropriations and Expenditures", Econometrica, Vol. 33 (Jan., 1965), pp.178-196.

19The program to perform this calculation was kindly made available to me by Derek Ford of U.B.C. For the theory underlying thecalculation see P. Dhrymes, J. Phoebus, L. R. Klein, K. Stiglitz, "Estimation of Distributed Lags"; Discussion Paper No. 77. Dept. ofEconomics, University of Pennsylvania.

20G. de Kock, A History of the South African Reserve Bank (1920-52), (Pretoria, 1954).

21Figures for this were obtained from the appropriate issues of the Report of the Public Debt Commissioners as published by theGovernment printer.

22Figures for this were obtained from the appropriate issues of the Report of the Controller and Auditor General as published by theGovernment printer.

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