"The Existence of a World Demand for Money Function". A Reply

Frowen, S. F.; Kouris, G. Article "The Existence of a World Demand for Money Function". A Reply Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Frowen, S. F.; Kouris, G. (1979) : "The Existence of a World Demand for Money Function". A Reply, Kredit und Kapital, ISSN 0023-4591, Duncker & Humblot, Berlin, Vol. 12, Iss. 1, pp. 73-82, https://doi.org/10.3790/ccm.12.1.73 This Version is available at: https://hdl.handle.net/10419/292836 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ The Existence of a World Demand for Money Function A Reply By S. F. Frowen, Guildford and G. Kouris, London In his comments Zis (1978) maintains, in short, that there is neither theoretical nor empirical foundation in the claim that our findings of a significant interest elasticity and instability of the world demand for money support Keynesian propositions. This would imply that the Parkin (1976) conclusions that world inflation can be controlled by controlling the world money supply is correct. In his comments Zis erroneously assumes that in our view demand for money functions are identical in all countries. In fact, we entirely agree with him that the individual country functions might well differ. As explained in the Frowen and Kouris paper (1977, page 3), our results refer to the sample of the ten pooled countries and inevitably our estimated elasticities would represent an average behaviour identical to the world behaviour reflected in the results obtained by Gray, Ward and Zis (1976) when grouping the ten countries together and estimating a function on the aggregate variables. In both cases the hypothesis tested is the same. Zis is no doubt aware that traditionally in macro economics many issues such as consumption or production behaviour have been approached both by using time series and cross-section analysis. Our methodology is simply a combination of the two approaches which has the distinct advantage firstly of being able to operate with a sample large enough to take account of differences between each cross-section unit and secondly of virtually eliminating the distributed lag bias. Our starting point was that because of differences in the demandfor-money behaviour across regions, a simple aggregation of the relevant data of countries to be considered in a study at world level totally neglects these differences. There is no need to remind Zis that Friedman (1963), in his study on money holdings expressed in terms OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 74 S. F. Frowen and G. Kouris of weekly incomes across countries, such as the U. S., Israel, India, Yugoslavia etc., showed that the ratios are somewhat different between countries. It is precisely these kinds of heterogeneities that we wished to screen out in an attempt to estimate a world demand for money. Although under a fixed exchange rate regime the money supplies of individual countries could legitimately be viewed as one entity, it is quite logical to assume that spending patterns (and thus the desired demand to hold money balances) diverges between countries. Thus these differences when not allowed for in a world aggregate would impair the validity of the exercise. For this reason we allowed for such differences and upon statistical testing found them significant. As to the criticism that the interpretation of our results lacks theoretical foundation in so far as the claim supporting the Keynesian case is concerned, the point Zis makes does not seem to be at all profound. When one sets out to estimate a world demand for money function under the assumption that during a fixed exchange rate period the entire world can be viewed as one economy ... etc., it follows by definition that both the monetarist and the Keynesian theories can be applied as if we were dealing with an individual country. For example, in the same way as we regard England, Wales and Scotland as integral parts of one closed economy, the United Kingdom, we can also regard the individual countries included in our study as integral parts of a fixed exchange rate world, a world which for all practical purposes is just another closed economy. We are grateful to Zis for raising the question of the conversion to dollars of the national money supply and national income series. This provides us with the opportunity of commenting on what appears to us as an inconsistency in the Gray, Ward and Zis paper, an inconsistency we neglected to point out earlier. When aggregation over a number of countries with dissimilar currencies takes place, both the money stock and income must be converted to a common unit of measurement, say the U. S. dollar. There are basically three alternatives to this approach. Firstly, to convert both magnitudes by using current exchange rates, i. e. the exchange rate prevailing at each quarter (option chosen by G. W. Z.). Secondly, to use constant exchange rates for a given year throughout. Thirdly, to convert the money supply by ussing current exchange rates and income by using constant exchange rates (alternative chosen by us). A fourth option, to convert money by using constant exchange rates and income by current exchange rates, is OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 The Existence of a World Demand for Money Function 75 logically precluded as will be made evident in the arguments that follow. There are strong arguments for using constant exchange rates in converting real national GNPs to a common denominator. This is because we want the variation of GNP over time to reflect changes in living standards and thus explain the transactions demand for money. When GNP is converted at current exchange rates we artificially impart an extra variation on the series which has nothing to do with actual changes in income. For example, in the 1967/68 period real GNP in the U. K. rose by about 2.3 °/o while at the same time the external value of the pound against the dollar declined by 14 <Vo. This means that if the U. K. GNP is converted into U. S. dollars it would depict a sharp fall of 11.7 Vo from 1967 to 1968! This would clearly be absurd and such an anomaly can only be avoided if GNP is converted at constant exchange rates. In reality what we actually need is purchasing power parities so that a proper weighting could be given to national GNPs before aggregation takes place. Purchasing power parities for the years and the number of countries covered in our study unfortunately do not exist. Thus the second best method is to use as weights the exchange rates prevailing at a given point in time which for conversion purposes would be kept constant during the whole period. At least in this way the true variation of GNPs is not distorted. Likewise one may argue that national money stocks should also be converted at constant exchange rates so that changes in the money supply would reflect only the rise in money that actually circulates within countries. If instead we express national money supplies in dollar terms by using current exchange rates, the money supplies across countries would appear at times to rise or slow down in response to exchange rate changes rather than to changes in the real growth rate of the money supply that takes place within the domestic economy. Thus whenever there has been an appreciation of the DM, the money supply in Germany, viewed in terms of dollars, would seem to have increased even if at the given year of appreciation the actual stock of money had not risen by one extra DM. Hence following the G. W. Z. theory that under fixed exchange rates the entire world can be viewed as one economy where every country constitutes a mere region in it, there are powerful arguments for wishing to explain in this world the true movements of the money supply, incomes and inflation rates and not the distorted ones that arise OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 76 S. F. Frowen and G. Kouris when we take into account fluctuations in the external values of domestic currencies. In these circumstances it is proper to use constant exchange rates for converting both incomes and money stocks. Nevertheless, G. W. Z. chose to convert GNPs and money stocks using current exchange rates. Thus the variables used for their empirical work are subject to a distortion. Furthermore, there is an even more serious argument against the use of current exchange rates. Take, for example, a hypothetical case where during a period of three years both real income and the money supply within a country have remained constant while externally the national currency has depreciated against the dollar. The mere conversion of income and money into dollars at current exchange rates will create an artificial positive correlation between the two variables while in reality there was none. This procedure would lead to a world demand for money which is more stable than would otherwise be the case. This is due, of course, to the conversion into dollars which quite falsely made the correlation between variations in the money supply and variations in income stronger than it really is. We would not be surprised if at times the use of current exchange rates produced a stable world demand for money even under floating exchange rates. In fact, by following this method the more frequent the fluctuations in exchange rates the stronger the association between money and income and thus the better defined the demand for money would appear on estimation. The reasoning outlined so far points to the fact that for world aggregates the best procedure is to use constant exchange rates. We have followed a middle course, however, in that we used constant exchange rates for converting GNPs but current exchange rates for converting money stocks. The justification for doing so is as follows: there are three possible types of exchange rate regimes, namely rigidly fixed exchange rates, freely floating exchange rates and an adjustable peg system with periodic changes in parities. In the first case, estimating a world demand for money is a legitimate exercise. In the second case there is no fixed link between national currencies and thus the exercise is a void one. In the third case, however, which is the one that characterised the period under investigation, a world demand for money may be identified but it must be recognised that every time an exchange rate change has taken place, the validity of the whole exercise is impaired. If one is to be honest in empirical estimation, some allowance for the "shocks" that the world demand for money has OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 The Existence of a World Demand for Money Function 77 sustained, must be made. To our mind, one way of allowing for these shocks is to convert the money supply at the current exchange rate so that whenever there has been a realignment of exchange rates, the distortion is taken care of in the world demand for money function. This method appears to be preferable to disregarding the fact that some fluctuation in exchange rates has occurred during the period under review and to using constant exchange rates as if this period had been one of rigid exchange rates. Instead, we maintain that the use of current exchange rates for converting the money supply and constant exchange rates for converting income is probably the best procedure to follow. In this way even when there are fluctuations in the money stock caused by exchange rate changes, which of course are not accounted for in the explanatory side of the equation, this will be primarily absorbed by the error term. According to the G. W. Z. approach, however, this extra source of variability will be absorbed directly by the income variable thus producing an income elasticity which would be biased upward. We now come to what appears to be the crux of the matter, namely the statistical and economic differences between the G. W. Z. study and ours. To start with we restate what G. W. Z. regard as their best model, which in fact is the specification we have chosen ourselves. Using the aggregate data of the ten countries for the period 1957 (2) - 1971 (2) we estimate the function: Mt = a + bYt + crt + dMt_t where all variables are in natural logarithms and Mt-i is the result of a partial adjustment hypothesis on the dependent variable. The interest rate used is the Eurodollar rate. The results obtained are as follows: Mt = - 1.1887 + 0.1794 Yt - 0.02269 rt + 0.7911 Mt_1 (4.57) (7.49) (6.68) (17.24) R2 = 0.997 DW = 1.30 These results came as a surprise to us since they are not identical to those quoted by G. W. Z. for the same time period and identical specification*. In fact, the results quoted by G. W. Z. were as follows: * The basic diference is that the GNPs series that we used were actual quarterly figures while the series used by G. W. Z. were obtained by interpolation from annual figures. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 78 S. F. Frowen and G. Kouris Mt = 0.663 + 0.234 Yt - 0.0125 Rt + 0.610 Mt_t R2 = 0.99 Our use of the G. W. Z. data reveal a much higher lagged money stock coeffizient which implies a slower speed of adjustment. Concentrating on the empirical results, as one would expect, the lagged money sstock variable is explaining too much, thus reducing the income effect to explaining very little, the classical case of the distributed lag bias. In most cases where lagged endogenous variables are used as regressors they tend to dominate the explanatory side of the equation, so that the rest of the coefficients are biased downwards. In this sense the distributed lag bias appears to be similar to the type of bias encountered in the presence of multi-collinearity which is detrimental to the correct estimation of any of the coefficients. As is well known this bias vanishes only as the sample increases (i. e. asymptotically) something we claim to have accomplished in our study. A measure of the bias could be obtained from comparing the simple correlation coefficient between Yt and Mt (which is 0.985) and the overall multiple correlation coefficient (which is 0.998). Apparently these are quite close. One can proceed by using first differences of logs instead of levels so that the association between Yt and Mt (and hence the bias) becomes weaker. The results are as follows: span 1957 (3) - 1971 (2) DM = 0.3083DYt - 0.0225Drt + 0.5805DMt_t (4.69) (3.69) (5.81) = 0.554 DW = 1.94 where the operator D signifies first differences. The results look plausible with the lagged money stock becoming less significant and the partial adjustment coefficient taking a rasonable value of 0.42. The simple correlation coefficient between DYt and DMt-1 is 0.35 while the multiple correlation coefficient is 0.75. The size of the former is less than half the size of the latter, revealing that the distributed lag bias has been considerably reduced. We can now test, by splitting the period, whether the world demand for money is stable or not. We will follow the G. W. Z. procedure of estimating the same function to the first forty and the last forty observations. We are aware, of course, that by so doing the overlap between the two sub-samples is quite considerable (twenty-three observations), and hence there is an in-built OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 The Existence of a World Demand for Money Function 79 stability already in the function. By again using first differences we obtained the following results: span = 1957 (3) - 1967 (2) DMt = 0.3352 DYt - 0.0275 Drt + 0.5608 DMt_t (4.81) (3.56) (4.95) R2 = 0.588 DW = 1.70 simple correlation between DYt and DMt. i = 0.396, R = 0.767. span = 1961 (3) - 1971 (2) DMt = 0.2950 DYt - 0.0177 Drt + 0.5283 DMt_t (3.36) (2.61) (4.24) R2 = 0.411 DW = 1.83 simple correlation between DYt and DMt-1 = 0.151, R = 0.641. Long Run Elasticities SPAN Y R Adjustment parameter 1957 (3) - 1971 (2) 0.735 - 0.054 0.420 1957 (3) - 1967 (2) 0.763 - 0.063 0.439 1961 (3) - 1971 (2) 0.625 - 0.038 0.472 The interest elasticity is very significant in both periods in contrast to the G. W. Z. results who found it insignificant. In bath periods the function is well defined (especially for an equation expressed in differences) although in the second period the explanatory power deteriorates. Our simple indicator of the distributed lag bias shows that it has been to a considerable extent weakened by the use of first differences. In conclusion, the aggregate data reveal that an interest rate effect is very significant in the world demand for money. The function seems to be quite unstable if fitted in different time periods as the interest elasticity is almost half in value, while the income elasticity is reduced by about 20%. Adjustments towards the desired money holding, however, tend to be more stable over time. In general, these results agree quite closely with our own findings, where the pooling method was used, and we see no grounds for any criticism of our study by Zis. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02 80 S. F. Frowen and G. Kouris In fact, quite the opposite: our empirical investigation demonstrates that if some allowance for the distributed lag bias is made and better quality data are used, the G. W. Z. results tend to be reversed completely. References Friedman, M.: Inflation: Causes and Consequences (New York: Asia Publishing House, 1963). — Frowen, S.F. and Kouris, G.: "The Existence of a World Demand for Money Function: Preliminary Results". Kredit und Kapital, vol. 10, No. 1, 1977, pp. 1 -17. — Gray, M.R., Ward, R. and Zis, G.: "The World Demand for Money Function: Some Preliminary Results", in Parkin, M. and Zis, G. (eds.) Inflation in the World Economy (Manchester University Press, 1976) — Parkin, M.: "Inflation in the World Economy: 19581975, Surrey Papers in Economics, No. 11, November 1976. — Zis, G.: "A Note on 'The Existence of a World Demand for Money Function: Preliminary Results'", Kredit und Kapital, vol.11, No. 3, 1978, pp. 340 - 347. Zusammenfassung Die Existenz einer internationalen Geldnachfragefunktion Eine Replik Mit diesem Beitrag wollen wir der Behauptung von Zis entgegentreten, daß unsere Arbeit über die Existenz einer internationalen Geldnachfragefunktion sowohl der theoretischen als auch der empirischen Gültigkeit entbehrt. Die Behauptungen von Zis können sowohl durch die entwickelten theoretischen Behauptungen als auch durch die durchgeführten ökonometrischen Tests völlig widerlegt werden. Wir halten die Behauptung aufrecht, daß die zu testende Hypothese gültig ist, ob man nun das Verhalten der internationalen Geldnachfragefunktion testet, indem man Ländergruppen zusammenfaßt, oder diese Länder in einer zusammengefaßten Zeitreihen-Kreuzstichprobe behandelt. Darüber hinaus ist unsere Technik der Aggregation ökonometrisch höherwertig, weil sie das Problem der Multikollinearität und die Verzerrungen der Lag-Verteilung vermindert. Wenn man tatsächlich den Versuch unternimmt, einen Teil der Verzerrungen der Lag-Verteilung aus den Daten von G.W. Zis zu eliminieren, dann ändern sich ihre Resultate vollständig und stimmen in der Tendenz mit unseren übereiin. Was die Frage anbelangt, welches der geeignetste Weg sei, nationale Geldvariablen auf einen gemeinsamen Nenner zu bringen, so haben wir darüber hinreichend diskutiert und kamen zu dem Schluß, daß der Ansatz von G. W. Zist die laufenden Wechselkurse zu benutzen, eine positive Verzerrung auf OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.12.1.73 | Generated on 2023-01-16 12:44:02