The Role of Money in Economic Activity: Some Results for 17 Developed Countries

Victor E. Argy

doi:10.5089/9781451969238.024.A003

Author:

Mr. Victor E. Argy

Mr. Victor E. Argy https://isni.org/isni/0000000404811396 International Monetary Fund

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Publication Date:: 01 Jan 1970

eISBN:: 9781451969238

Language:: English

Keywords:: SP; exchange rate; currency; money supply; broad money; rate of change in income; quantity theory model; expenditure variable; Monetary base; Consumption

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IT IS WIDELY RECOGNIZED that the most efficient method of evaluating the role of money in economic activity is by estimating a complete econometric model in which the financial sector is represented in some detail.1 Because estimation of these models is time consuming and difficult, however, a number of simple, “short-cut” methods have been proposed and used in recent years. Three of these methods in particular have achieved considerable prominence. One method involves relating income to money in the current and earlier periods (years or quarters). These regressions are usually run in level or first difference form.2 A second method is to run regressions of consumption against money and autonomous expenditures.3 This approach has several variants: alternative definitions of money and autonomous expenditures may be used; money and autonomous expenditures may be used together or separately; and, finally, one may experiment with a range of lag patterns for the two variables. Essentially, this particular test is intended to compare the relative efficiency of money (representative of a version of the Quantity Theory) and autonomous expenditures (representative of Keynesianism) in predicting consumption. A third method is to run regressions of income against an indicator of monetary policy and an indicator of fiscal policy.4 This method is not too dissimilar to the second one, in that it also represents a test of some variant of the Quantity Theory against Keynesianism. The difference is that Keynesianism here is represented by budgetary policy rather than expenditure in general.5 The paper presents the results for 17 developed countries of the first two approaches mentioned above.6 Section I deals with the first approach, Section II deals with the second approach, and Section III summarizes the main results of the paper.

Abstract

IT IS WIDELY RECOGNIZED that the most efficient method of evaluating the role of money in economic activity is by estimating a complete econometric model in which the financial sector is represented in some detail.¹ Because estimation of these models is time consuming and difficult, however, a number of simple, “short-cut” methods have been proposed and used in recent years. Three of these methods in particular have achieved considerable prominence. One method involves relating income to money in the current and earlier periods (years or quarters). These regressions are usually run in level or first difference form.² A second method is to run regressions of consumption against money and autonomous expenditures.³ This approach has several variants: alternative definitions of money and autonomous expenditures may be used; money and autonomous expenditures may be used together or separately; and, finally, one may experiment with a range of lag patterns for the two variables. Essentially, this particular test is intended to compare the relative efficiency of money (representative of a version of the Quantity Theory) and autonomous expenditures (representative of Keynesianism) in predicting consumption. A third method is to run regressions of income against an indicator of monetary policy and an indicator of fiscal policy.⁴ This method is not too dissimilar to the second one, in that it also represents a test of some variant of the Quantity Theory against Keynesianism. The difference is that Keynesianism here is represented by budgetary policy rather than expenditure in general.⁵ The paper presents the results for 17 developed countries of the first two approaches mentioned above.⁶ Section I deals with the first approach, Section II deals with the second approach, and Section III summarizes the main results of the paper.

I. A First Approach

As indicated above, the simplest possible test of the impact of money on income is to run regressions of income and money.⁷ If level data is used, the common trends in the series will ensure that there is a close relationship between the two variables. This may in fact truly reflect long-term causation from money to income. If, however, one is more interested in the short-run relationship between income and money, trends will need to be removed. As first difference data, especially for periods of 14–17 years, generally retain something of a trend in the series, percentage changes in the series were used in this study. In effect, then, we ran regressions of percentage changes in income against percentage changes in money (narrowly and broadly defined) for given time periods. Before we examine the results, however, we should ask ourselves, What are the weaknesses of this type of approach? It is worth distinguishing four types of criticism that may be leveled against this approach.

First, it represents a reduced form equation that excludes other influences on income. This consideration presumably would not be serious if these “other” influences were uncorrelated with money and were randomly distributed over time.⁸

Second, if we assume that money is controlled by the authorities and if variations in rates of change in money reflect policy decisions to stabilize the economy, it is possible to show that the coefficient for money under these conditions need not correspond to the “true” coefficient, which represents the impact of money on income. A few examples will illustrate this point.

Consider a simple model where the rate of change in income (Ȳ) may be explained by the rate of change in money ( $\bar{M} o$ ) in the same period as well as a number of other unspecified variables, including perhaps lagged values of rates of change in income. Suppose, too, that the objective of the authorities is to moderate fluctuations in the rate of growth of income—in other words, to bring about a reasonably steady growth in income. We begin by defining a neutral monetary policy as one that involves a steady growth in the money supply. Since the rate of change in income is also explained by variables other than the rate of change in money, the rate of change in income in these conditions will fluctuate in line with fluctuations in these other variables. If monetary policy, in the form of variations in the rate of change in money, is now introduced, what will happen to the rate of change in income? It is useful to distinguish three possibilities.⁹

Case A

Monetary policy is completely successful in stabilizing the rate of change in income, so that the rate of change in income is constant. This is perfect stabilization.

Case B

Monetary policy is partially successful in stabilizing the rate of change in income. The rate of change in income continues to fluctuate, but fluctuations are now dampened.

Case C

Monetary policy destabilizes the rate of change in income. Here fluctuations in the rate of change in income are more severe.

Suppose now that one ran regressions of the rate of change in income, as the dependent variable, against the rate of change in money. In the light of the above possibilities, what coefficients for the rate of change in money would one expect?

Case A

The coefficient would tend to be zero, and there would be no significant relationship between the two variables. This situation is obviously unrealistic, but it is interesting as an extreme possibility.¹⁰

Case B

Here one would expect a negative coefficient, its size depending on the extent to which fluctuations in the rate of change in income were dampened.

Case C

Where monetary policy tends to be destabilizing, a positive coefficient should result, implying that variations in the rate of monetary change have accentuated the fluctuations in the rate of change in income.¹¹

A third difficulty with the approach is that the coefficient may reflect the possibility of reverse causation from income to money.¹² It is difficult on a priori considerations to say what the sign of the coefficient for income would be. This will depend on the institutional conditions in particular economies. On the one hand, there are a number of factors making for a negative relationship with money; a rise in income will raise currency demands, taxes, and imports. The rise in income may also raise market interest rates; in a number of countries, this may result in a switch to current deposits with contractionary effects on the money supply because of the higher reserve requirements on current deposits. On the other hand, the rise in market rates may stimulate more central bank borrowing, lower desired reserves, and encourage capital inflows, all of which may have an expansionary effect on the money supply.¹³

A fourth difficulty is that if lags from money to income are variable the relationship between money supply and income will tend to be rather weak.¹⁴

Notwithstanding these difficulties, regressions of income against money have become popular. Indeed, much of the literature on the merits (or otherwise) of the Friedman position has come to revolve around the closeness in the relationship between money and income; in other words, How good is money as a predictor of income?¹⁵ For this reason it is at least worthwhile to look at the evidence not only for one or two countries but for a large number of countries to see what light it throws on the meaningfulness of this approach.

Table 1 sets out the results of the regressions for the 17 developed countries. Six regressions for each country are shown. Equation (1) relates percentage changes in income (Ȳ) to percentage changes in narrowly defined money ( $\bar{M} o$ ) in the same period. Equation (2) relates percentage changes in income to percentage changes in narrowly defined money in the same year as well as the previous year. Equations (3) and (4) duplicate these regressions for broadly defined money ( $\bar{Q} o$ ). Equation (5) regresses percentage changes in income against percentage changes in narrowly defined money in the previous year only, while equation (6) duplicates this for broadly defined money. Money is lagged only one year in these regressions. As lagging money more than one year gave poor results for almost every country, these additional regressions are not shown. A few general observations on the results are in order.

Table 1.

Seventeen Developed Countries: Results of Regressions of Percentage Changes in Gross Domestic Product (Ȳ) Against Percentage Changes in Money ( $\bar{M} o$ and $\bar{Q} o$ )

(Mo=notes and coins in hands of public and current deposits; Qo = Mo plus time and, sometimes, savings deposits; in annual data, money is estimated as the mean for the year; t-ratios are shown below coefficients.)

Sources: United Kingdom—Central Statistical Office, Annual Abstract of Statistics and Financial Statistics; all other countries—International Monetary Fund, International Financial Statistics.

The most striking impression is that the results tend on the whole to be very poor. Taking account of sign (with positive coefficients considered to be right), plausibility in the sizes of the coefficients (sums of coefficients should not be much above 1), and over-all ${\bar{R}}^{2}$ , there are few countries where the results give any indication of a good, close relationship between the variables. The only countries where the relationship is quite close are Belgium, Finland, and Italy. At the other extreme are the countries where the relationship is poor indeed—Austria, France, Germany, Japan, Sweden, Switzerland, Australia, New Zealand, and the United Kingdom. In the remaining countries (Canada, Denmark, the Netherlands, Norway, the United States) the relationship is rather weak.

Another interesting feature of the results is that many of the coefficients for the same period money have the wrong (negative) signs. There are as many as 13 “wrong” signs in 34 cases.¹⁶ The explanation may lie in stabilizing policy and/or reverse causation, as discussed above. There are fewer (5) wrong signs for the previous period. In nearly every country the lagged money supply appears to be better than the same year’s money supply. This suggests that at least some impact is felt on income about a year later.

The results also may throw light on the question of the appropriate definition of money. It is frequently said that the most appropriate concept of money is the one that yields the most stable function, frequently interpreted in terms of the closeness of the relationship with income. Comparing regressions (2) and (4), we find that in ten countries the narrower definition has a closer relationship with income,¹⁷ in two countries there is no difference between the definitions, and in five countries (Canada, Denmark, Italy, Japan, and Norway) the broader definition does better.

We may summarize then by saying that percentage changes in money appear on the whole for most countries to be a rather poor predictor of percentage changes in income.

It is useful to compare the results of these regressions with regressions of first differences in income and money. These comparisons are made in Table 2. They show that the results are substantially improved in nearly every case where first differences are used. As noted earlier, the fact that first differences retain something of a trend is not in itself a sufficient argument for dismissing the first difference results.

Table 2.

Seventeen Developed Countries: Comparison of ${\bar{R}}^{2}$ for Percentage Changes and for First Differences

Table 2.

Seventeen Developed Countries: Comparison of ${\bar{R}}^{2}$ for Percentage Changes and for First Differences

	${\bar{R}}^{2}$ Percentage Changes				${\bar{R}}^{2}$ First Differences
	Mo_t	Mo _t-1	Qo_t	Qo _t-1	Mo_t	Mo _t-1	Qo_t	Qo _t-1
Australia	0.043		0.000		0.272		0.471
Austria	0.256		0.129		0.539		0.453
Belgium	0.681		0.676		0.848		0.787
Canada	0.238		0.384		0.655		0.659
Denmark	0.278		0.301		0.727		0.752
Finland	0.512		0.000		0.405		0.454
France	0.000		0.000		0.497		0.558
Germany	0.289		0.112		0.184		0.000
Italy	0.648		0.709		0.787		0.725
Japan	0.088		0.187		0.696		0.754
Netherlands	0.337		0.136		0.653		0.600
New Zealand	0.051		0.009		0.000		0.000
Norway	0.221		0.324		0.755		0.768
Sweden	0.184		0.000		0.792		0.612
Switzerland	0.000		0.000		0.000		0.000
United Kingdom	0.137		0.000		0.557		0.161
United States	0.292		0.204		0.681		0.649

Table 2.

Seventeen Developed Countries: Comparison of ${\bar{R}}^{2}$ for Percentage Changes and for First Differences

	${\bar{R}}^{2}$ Percentage Changes				${\bar{R}}^{2}$ First Differences
	Mo_t	Mo _t-1	Qo_t	Qo _t-1	Mo_t	Mo _t-1	Qo_t	Qo _t-1
Australia	0.043		0.000		0.272		0.471
Austria	0.256		0.129		0.539		0.453
Belgium	0.681		0.676		0.848		0.787
Canada	0.238		0.384		0.655		0.659
Denmark	0.278		0.301		0.727		0.752
Finland	0.512		0.000		0.405		0.454
France	0.000		0.000		0.497		0.558
Germany	0.289		0.112		0.184		0.000
Italy	0.648		0.709		0.787		0.725
Japan	0.088		0.187		0.696		0.754
Netherlands	0.337		0.136		0.653		0.600
New Zealand	0.051		0.009		0.000		0.000
Norway	0.221		0.324		0.755		0.768
Sweden	0.184		0.000		0.792		0.612
Switzerland	0.000		0.000		0.000		0.000
United Kingdom	0.137		0.000		0.557		0.161
United States	0.292		0.204		0.681		0.649

II. A Second Approach

In this section we examine the results of applying the Friedman-Meiselman type of approach to the question of appraising the significance of money. We begin by making some critical comments on the approach and later look in detail at the results of using the approach.

Table 3 sets out four macromodels (models A, B, C, and D), which, in the main, are self-explanatory and familiar. Two of the models are labeled Keynesian and the other two, Quantity Theory. There is a simple and a sophisticated Keynesian model and corresponding simple and sophisticated Quantity Theory models.¹⁸

Table 3.

Monetary and Expenditure Analysis of Consumption—A Framework¹

^¹To simplify the derivations, constants are omitted from the behavioral equations.

^²This technique is adapted from Barrett and Walters, op. cit.

The Keynesian models have two behavioral equations: a consumption function and an import function. In the simple version, both consumption and imports are a function of income alone; in the sophisticated version, consumption and imports are a function of current income as well as of the lagged values of consumption and imports. This is tantamount to a distributed lag function, i.e., making consumption and imports a function of current and all past values of income, with progressively declining weights attaching to the earlier levels of income. Each model is solved for consumption in terms of the exogenous variables.¹⁹

The Quantity Theory models also have two behavioral equations: a money demand function and an import function. The import functions are the same as in the Keynesian models, with a simple version and a distributed lag version. The money demand function has a simple version, where the demand for money is a function of income, and a sophisticated version, where money demand is a function of current income and the money supply in the previous year (the distributed lag version). Both Quantity Theory models assume that money demand is equilibrated to the money supply. Again, each model is solved for consumption in terms of the exogenous variables.

Several points are worth noting about the models. They represent in the main purist cases in that the Keynesian models exclude the influence of monetary variables and the Quantity Theory models exclude the influence of nonmonetary variables. This is not too unfair to the quantity theorists who tend to play down the role of nonmonetary influences; but it is unfair to the Keynesians not only because they concede some role to money but also because models that are well within the spirit of Keynesian thinking tend to be much more elaborate than even our sophisticated version. It is possible to argue that in the interest of simplicity in testing for a large number of countries no further sophistication is feasible, but there remain two problems with the Keynesian model. The first has to do with the treatment of money, and the second has to do with the definition of autonomous expenditures. On the first question, if money is incorporated in the model in a Keynesian fashion, by making the demand for money a function of interest rates and investment a function of interest rates, the autonomous component of expenditures would have to exclude the part that is due to interest rate changes. This, in other words, would be defining autonomous expenditures as the part of expenditure that is independent of money. However, this extension would require estimation of the individual functions that make up the model and again would be inconsistent with the objective of these tests, which is to retain some simplicity. The second question concerns the definition of autonomous expenditures. To resolve this difficulty we experimented with two alternative definitions of autonomous expenditures, one including investment in stocks (A in Table 3 and A₁ in the regressions in Table 4) and the other excluding investment in stocks (A₂ in Table 4), which may be endogenous, in the sense of responding to income in the same period. No attempt was made to exclude private fixed investment, but further experimenting is possible along these lines. If investment in stocks is treated as endogenous, the Keynesian and Quantity Theory equations would of course need to be modified correspondingly. (This adjustment is not shown in Table 3.)

Table 4.

Seventeen Developed Countries: Regressions of Consumption Against Money and Autonomous Expenditures

(t-ratios shown below all coefficients)

Sources: International Monetary Fund, International Financial Statistics; Organization for Economic Cooperation and Development, National Accounts Statistics.

An interesting by-product of these models is that autonomous expenditures should enter into the Quantity Theory equations but with a negative coefficient approaching 1.²⁰ The rationale for this is that since autonomous expenditures cannot influence income an increase in autonomous expenditures, as defined, will be exactly neutralized by a decrease in consumption. Hence, one test of the two extreme versions lies in the signs of the coefficient for autonomous expenditures.

In the end what we are really trying to find out is the relative importance of the Keynesian and monetary variables. A large number of regressions were run, combining the variables in various ways and using the two definitions of money (narrow and broad) and the two definitions of autonomous expenditures. Consider now the following equations:

\begin{matrix} Δ C_{t} = f (Δ {Mo}_{t}, Δ {Mo}_{t - 1}) & (1) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ {Qo}_{t}, Δ {Qo}_{t - 1}) & (2) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ A 1_{t}, Δ A 1_{t - 1}) & (3) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ A 2_{t}, Δ A 2_{t - 1}) & (4) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ {Mo}_{t}, Δ {Mo}_{t - 1}, Δ A 1_{t}, Δ A 1_{t - 1}) & (5) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ {Qo}_{t}, Δ {Qo}_{t - 1}, Δ A 1_{t}, Δ A 1_{t - 1}) & (6) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ {Mo}_{t}, Δ {Mo}_{t - 1}, Δ A 2_{t}, Δ A 2_{t - 1}) & (7) \end{matrix}

\begin{matrix} Δ C_{t} = f (Δ {Qo}_{t}, Δ {Qo}_{t - 1}, Δ A 2_{t}, Δ A 2_{t - 1}) & (8) \end{matrix}

where C=consumption. Two tests may be applied to this set of equations:

Test 1:

${\bar{R}}_{5}^{2} - {\bar{R}}_{3}^{2}$ contribution by the addition of narrow money to A1
where ${\bar{R}}_{5}^{2} - {\bar{R}}^{2}$ for equation (5) and ${\bar{R}}_{3}^{2} - {\bar{R}}^{2}$ for equation (3)
${\bar{R}}_{6}^{2} - {\bar{R}}_{3}^{2}$ contribution by the addition of broad money to A1
${\bar{R}}_{7}^{2} - {\bar{R}}_{4}^{2}$ contribution by the addition of narrow money to A2
${\bar{R}}_{8}^{2} - {\bar{R}}_{4}^{2}$ contribution by the addition of broad money to A2

Test 2:

${\bar{R}}_{5}^{2} - {\bar{R}}_{1}^{2}$ contribution by the addition of A1 to narrow money
${\bar{R}}_{6}^{2} - {\bar{R}}_{2}^{2}$ contribution by the addition of A1 to broad money
${\bar{R}}_{7}^{2} - {\bar{R}}_{1}^{2}$ contribution by the addition of A2 to narrow money
${\bar{R}}_{8}^{2} - {\bar{R}}_{2}^{2}$ contribution by the addition of A2 to broad money

where tests 1 and 2 are crude tests of the relative significance of the two variables.

Before we look at the results, a brief comment on equations 1-8 is in order. Equations 5-8 are difficult to derive as reduced forms of complete macromodels. As indicated earlier, if money influences a component of autonomous expenditures, the proper indicator of autonomous expenditures would need to be the residual, which is independent of money. For A₂ this may be serious for private fixed capital formation, much less serious for exports, and hardly relevant to government expenditures. This raises difficult questions about the interpretation of equations 5-8. While, for example, it is meaningful to interpret the coefficients of autonomous expenditures as the effects on consumption when money is held constant, it hardly makes sense to treat the coefficient for money as the impact on consumption when autonomous expenditures are held constant, since money will directly influence some part of autonomous expenditures, and possibly consumption. This is a difficulty that cannot be overcome as long as simplicity must be maintained. Equations 5-8 may also be interpreted as “combinations” of the purist models 1-4. This device, suggested by Barrett and Walters,²¹ is illustrated in the combined models E and F in Table 3.

Another question concerns the fact that equations 1-4 do not correspond to specific macromodels in Table 3.²² While equations (3) and (4) have their counterparts in the sophisticated Keynesian version of Model B, equations (1) and (2) do not have exact counterparts in the Quantity Theory models. The answer to this is that while regressions were run for all the models set out in Table 3 the particular tests that were applied could not have used the models in their original form. For example, it would hardly have been appropriate to move from equation (16) to equation (8) in Table 3 to determine the explanatory significance of autonomous expenditures, since autonomous expenditures already appear in the Quantity Theory equation. (However, comment will be made later on the signs of the coefficients for autonomous expenditures.) It was thought, therefore, that autonomous expenditures should be dropped from the Quantity Theory equations for the regressions.

The results of the regressions for equations 1-8 are given in Table 4 and the results of tests 1-2, based on these regressions, are shown in Table 5. Consider first the results of test 1. A large positive result would suggest that the addition of monetary variables improves the results substantially. The results are not so easy to generalize because we are dealing with two definitions of money and two definitions of autonomous expenditures. For example, while in some countries one measure of money is more reliable, in other countries it is the other measure that is more reliable. No pattern appears here. With respect to autonomous expenditures, for any given definition of money, there appears to be a small tendency for the improvement to be greater when expenditures are defined to include inventories. (This is so in 12 of the 17 countries.) The more interesting results of this test, however, are the over-all ones.

Table 5.

Explanatory Power of Monetary and Expenditure Variables

Table 5.

Explanatory Power of Monetary and Expenditure Variables

	Test 1				Test 2
	Addition of monetary variables to autonomous expenditures				Addition of autonomous expenditures to monetary variables
	A ₁		A ₂		A ₁		A ₂
	Mo	Qo	Mo	Qo	Mo	Qo	Mo	Qo
Countries ${\bar{R}}^{2}$	5-3	6-3	7-4	8-4	5-1	6-2	7-1	8-2
Australia	9.3	9.4	11.8	9.0	15.4	2.2	12.5	-3.6
Austria	43.1	23.1	25.5	10.7	11.2	7.0	21.3	8.3
Belgium	14.3	9.3	12.6	6.7	-4.8	-4.5	-4.6	-5.2
Canada	24.2	25.0	16.3	17.6	4.9	7.7	5.6	8.9
Denmark	6.8	8.7	-2.4	-1.3	1.5	0.4	5.5	3.6
Finland	12.5	11.0	16.6	11.1	7.0	26.9	-2.0	13.9
France	-4.0	6.4	-4.3	10.3	3.8	0.0	-1.8	-1.4
Germany	-3.3	-2.1	-4.9	-3.3	48.8	70.9	42.7	65.2
Italy	-0.1	0.5	3.4	4.2	5.4	11.1	9.5	15.4
Japan	37.9	37.5	18.6	17.5	1.4	2.9	1.7	2.5
Netherlands	18.5	12.8	10.1	6.0	7.4	9.4	10.1	13.7
New Zealand	41.0	34.9	43.5	37.6	12.7	12.3	13.1	12.9
Norway	15.3	13.0	12.3	10.0	-1.8	0.5	-1.1	0.2
Sweden	-0.7	5.9	-3.6	-3.6	8.4	35.8	15.5	36.3
Switzerland	3.7	21.1	-2.4	2.3	9.3	3.7	22.1	3.8
United Kingdom	16.2	-9.0	17.1	-11.6	-10.6	7.9	28.5	18.3
United States	-4.8	12.2	0.5	21.1	-10.1	-9.6	-12.6	-8.5

Table 5.

Explanatory Power of Monetary and Expenditure Variables

	Test 1				Test 2
	Addition of monetary variables to autonomous expenditures				Addition of autonomous expenditures to monetary variables
	A ₁		A ₂		A ₁		A ₂
	Mo	Qo	Mo	Qo	Mo	Qo	Mo	Qo
Countries ${\bar{R}}^{2}$	5-3	6-3	7-4	8-4	5-1	6-2	7-1	8-2
Australia	9.3	9.4	11.8	9.0	15.4	2.2	12.5	-3.6
Austria	43.1	23.1	25.5	10.7	11.2	7.0	21.3	8.3
Belgium	14.3	9.3	12.6	6.7	-4.8	-4.5	-4.6	-5.2
Canada	24.2	25.0	16.3	17.6	4.9	7.7	5.6	8.9
Denmark	6.8	8.7	-2.4	-1.3	1.5	0.4	5.5	3.6
Finland	12.5	11.0	16.6	11.1	7.0	26.9	-2.0	13.9
France	-4.0	6.4	-4.3	10.3	3.8	0.0	-1.8	-1.4
Germany	-3.3	-2.1	-4.9	-3.3	48.8	70.9	42.7	65.2
Italy	-0.1	0.5	3.4	4.2	5.4	11.1	9.5	15.4
Japan	37.9	37.5	18.6	17.5	1.4	2.9	1.7	2.5
Netherlands	18.5	12.8	10.1	6.0	7.4	9.4	10.1	13.7
New Zealand	41.0	34.9	43.5	37.6	12.7	12.3	13.1	12.9
Norway	15.3	13.0	12.3	10.0	-1.8	0.5	-1.1	0.2
Sweden	-0.7	5.9	-3.6	-3.6	8.4	35.8	15.5	36.3
Switzerland	3.7	21.1	-2.4	2.3	9.3	3.7	22.1	3.8
United Kingdom	16.2	-9.0	17.1	-11.6	-10.6	7.9	28.5	18.3
United States	-4.8	12.2	0.5	21.1	-10.1	-9.6	-12.6	-8.5

On the whole, some countries show consistently large improvements and other countries consistently poor improvements (or even deterioration, as shown by negative results). The countries where money appears to be quite important are Austria, Canada, Japan, and New Zealand. Money is less important but nevertheless continues to make a significant contribution in Australia, Belgium, Finland, the Netherlands, and Norway. In Germany, Italy, and Sweden money appears to add little to the explanation of consumption. The results for France, Denmark, Switzerland, the United Kingdom, and the United States are more difficult to interpret. For example, in the United Kingdom money is moderately significant if defined narrowly but the contribution is negative if money is defined more broadly. For the United States and France the result is almost the exact opposite, in that money is significant only if defined broadly. In Switzerland broad money makes a very large contribution when autonomous expenditures include inventories. In Denmark there is a moderate contribution when autonomous expenditures include inventories. We may conclude then that in a large majority of the countries in the study (14 out of 17) the addition of monetary variables makes a contribution to the explanation of consumption.

We may deal with test 2 rather briefly. In countries where monetary variables were extremely weak, expenditure variables appear to be strong. This is particularly striking in Germany, Sweden, and, to a lesser extent, Italy. In nearly all countries autonomous expenditures also make a contribution. The only countries where the contribution is consistently negative are Belgium and the United States.

The conclusion, then, that for most countries both monetary and expenditure variables make some contribution to the explanation of consumption is not surprising and is, of course, consistent with Keynesian thinking. In particular the results appear to give support to the view, denied by the monetarists, that autonomous expenditures may make an independent contribution to income.

We saw earlier that monetary models should yield coefficients for autonomous expenditures that are negative and approaching 1. This is seen by reference to equations (12) and (16) in Table 3. Regressions of these equations do not confirm this hypothesis. The coefficient is positive in almost every single case, confirming the earlier conclusion that both monetary and expenditure variables are important.

For a majority of the countries both monetary and expenditure variables are significant (or just miss significance) in at least one of the equations combining the variables. In Belgium and the United States only the monetary variables show up as significant, whereas in Germany and Italy only expenditure variables are significant. In France and Norway neither variable is significant.²³

The coefficients ${\bar{R}}^{2}$ on the whole are fairly high, with the two variables explaining in most countries at least 60 per cent of the first difference in consumption. Three excellent fits are obtained for Canada, Japan, and the Netherlands. In these three countries the coefficients are in line with theoretical expectation and the explanatory power of the equations is quite high.

The multipliers for money and expenditures are nearly always reduced when the variables are combined in the equations. For example, in Canada the monetary multiplier drops from 2.031 (Σ(Mo_t, Mo_t-1)) in equation (1) to 1.377 (Σ(Mo_t, Mo_t-1)) in equation (5). The multiplier for autonomous expenditures drops from 0.445 to 0.190.

The multipliers derivable directly from the equations are consumption multipliers. To convert the consumption into an income multiplier, corrections are needed. For example, the expenditure multiplier needs to be raised, since the coefficient for A_t is substantially larger when income is the dependent variable. On the other hand, an adjustment downward needs to be made to the coefficient for money in the same period (compare equation (14) with equation (16) in Table 3). Consider, for example, equation (7) for Canada. The coefficient for Mo_t would need to be adjusted to approximately 0.52, whereas the Mo_t-1 coefficient can be left unadjusted (on the plausible assumption that f=k). This yields a monetary multiplier for income of about 1.2. A rough expenditure multiplier for income of about 0.3 may be obtained after making some correction to the expenditure coefficients. This expenditure multiplier is very low compared with theoretical expectation of its “true” value.²⁴ On the whole, the expenditure multipliers for most countries are on the low side (i.e., below 1). The only exceptions would appear to be Germany, Denmark, and Italy, where the multipliers might exceed unity.

It is not surprising that the regressions throw little light on the relative lags for the monetary and expenditure variables. There is certainly no evidence on the basis of these results for a longer monetary lag. Indeed, in two countries (Japan and the United Kingdom) the lag appears to be longer for expenditure.

III. Conclusions

We have discussed two approaches to evaluating the role of money in economic activity. Neither is rigorous nor free of serious criticism. One question we might ask is whether the two approaches give consistent results in the sense that countries with strong monetary effects on one approach are also countries with strong monetary effects on the other approach, and vice versa. As we saw, the results for the first approach were extremely poor, but we did conclude that in Belgium, Finland, and Italy monetary variables appeared to be quite significant; in Canada, Denmark, Norway, and the United States the monetary variables were somewhat less significant; and in Austria, France, Germany, Japan, Sweden, Switzerland, Australia, New Zealand, and the United Kingdom monetary variables showed up poorly indeed. In the main these results are not in line with the results obtained by our second approach. Italy, for example, had poor monetary effects; Japan and Austria, on the other hand, had strong monetary effects. For the United States money defined broadly does better on the second approach but worse on the first approach. In France broad money does well on the second approach. The most consistent results are obtained for Germany and Sweden, where on both approaches monetary variables appear to be very weak. The result for the United Kingdom is not inconsistent in that on both approaches narrow money appears to perform better than broad money. For the rest of the countries the best that can be said is that there is moderate consistency in the results.

Perhaps more reliance should be placed on the results of the second approach, as it is slightly more sophisticated than the first. If we were to take these results seriously, an intriguing question is, Why should we find such differences in the role of money for different developed countries? Why, in other words, should money appear so strong in Japan and, at the other extreme, so weak in Germany and Sweden?²⁵ One can only speculate about the answer to these questions. The differences could be due to different interest elasticities in the money demand function. For example, other things being equal, the economy with the lower interest elasticity of money demand will tend to have stronger monetary effects.²⁶ Again, changes in the cost of finance may have different effects on expenditures in different countries, depending on institutional conditions, e.g., the extent of self-finance. Finally, credit rationing effects could be different, depending on facilities available for nonbank finance.²⁷

APPENDICES

I. Monetary Policy and Income

It may be useful to formalize the points made about the coefficient for money when money is used as an instrument of policy. Consider the following simple model:

\begin{matrix} (1) & \bar{Y} = \bar{M} o + E \end{matrix}

where

Suppose for simplicity that the coefficient for money is 1. In the absence of any monetary policy, $\bar{M} o$ will be constant and fluctuations in income will be due only to the error term. Now introduce monetary policy. This gives rise to the three possibilities discussed in the text.

1. Perfect stability (Case A)

Then

\begin{matrix} (2) & \bar{M} o_{t} = K - E \end{matrix}

where K is the constant percentage change in money. Substituting for E in (1) yields a coefficient for $\bar{M} o_{t}$ , which is zero.

2. A stabilizing monetary policy (Case B)

Here

\begin{matrix} (3) & \bar{M} o_{t} = K - aE \end{matrix}

where a < 1. Substituting again in (1) yields a coefficient $(\frac{a - 1}{a})$ , which is negative.

3. A destabilizing monetary policy (Case C)

Here

\begin{matrix} (4) & \bar{M} o_{t} = K + aE . \end{matrix}

The coefficient here, after substitution, is $\frac{1 + a}{a}$ , which is positive.

II. Effects on Income of Source of Change in Money Supply

It is interesting to inquire whether the results of the first approach might be improved by explicitly taking account of the possibility that a change in the money supply may have a different effect on income, depending on the source of change in the money supply. It is frequently argued that a decrease in the money supply brought about by a reduction in bank advances generates a stronger effect on income than an equivalent decrease from a liquidation of government securities in the open market. The assumption is that the first has direct effects on the availability of funds for expenditure (implying that expenditure simply could not be financed from other sources) while the second has only indirect interest rate effects. There are several interesting implications in this. First, the coefficient of money with respect to income may itself be a function of the composition of bank assets. Second, whether or not the ultimate effect on income is different, the lags in the operation of monetary policy may be affected significantly by the composition of bank assets. It is conceivable, for example, that a change in the composition of bank assets, leaving the money supply unchanged, has no lasting impact on income, but nevertheless there may be some early change that is in due course neutralized.²⁸ Third, explicit allowance for the composition of bank assets may be an interesting way to give new life to a monetarist model. Taking account of different sources of changes in the money supply is consistent with a monetarist explanation and may be one way of improving the empirical relation between income and money, e.g., by explaining not only the possible change in the size of the money coefficient but also the variability in the lag.

The problem is to test these propositions empirically. The simplest way is to explain income in terms not only of money but also of bank asset composition, in current and some past periods. An alternative is to run regressions of velocity against both interest rates and asset composition.²⁹ The major difficulty with this approach has to do with the likelihood of reverse causation from income or velocity to asset composition. For example, it is known that during cyclical upswings there tend to be progressive increases in the ratio of advances to total bank assets; hence, a positive and significant coefficient for asset composition may simply be due to the familiar cyclical relation between income, velocity, and asset composition and not necessarily to causation from asset composition to income and velocity. This problem is serious; nevertheless, quarterly and annual regressions of the form indicated above were run for a number of the industrial countries. On the whole, the results were disappointing. No clear pattern emerged, with the size, significance, and signs of the coefficients very much dependent on the number of variables in the equation and the form of the regression (level or first difference data). The results of a single equation from annual data for the six countries to which the test was applied are the following:³⁰ Y = gross national product, Mo = money including time deposits, and L = ratio of advances to total bank assets; t-ratios are shown below coefficients.

United Kingdom (1951-65)

\begin{matrix} Y = - \underset{(2.075)}{18.19} + \underset{(2.505)}{4.069} {Mo}_{t} + \underset{(0.425)}{6.409} L_{t} & {\bar{\begin{matrix} R \end{matrix}}}^{2} = 0.965 \end{matrix}

Canada (1950-68)

\begin{matrix} Y = - \underset{(2.846)}{13.49} + \underset{(19.976)}{2.549} {Mo}_{t} + \underset{(2.649)}{27.69} L_{t} & {\bar{\begin{matrix} R \end{matrix}}}^{2} = 0.991 \end{matrix}

Norway (1950-68)

\begin{matrix} Y = - \underset{(2.820)}{20.89} + \underset{(24.455)}{1.945} {Mo}_{t} + \underset{(2.011)}{22.90} L_{t} & {\bar{\begin{matrix} R \end{matrix}}}^{2} = 0.996 \end{matrix}

Netherlands (1950-68)

\begin{matrix} Y = - \underset{(2.043)}{4.735} + \underset{(18.196)}{2.854} {Mo}_{t} + \underset{(1.164)}{8.983} L_{t} & {\bar{\begin{matrix} R \end{matrix}}}^{2} = 0.993 \end{matrix}

France (1950-68)

\begin{matrix} Y = - \underset{(2.344)}{0.332} + \underset{(10.726)}{1.837} {Mo}_{t} + \underset{(2.731)}{529.6} L_{t} & {\bar{\begin{matrix} R \end{matrix}}}^{2} = 0.996 \end{matrix}

Germany (1956-67)

\begin{matrix} Y = - \underset{(1.985)}{800.0} + \underset{(4.021)}{1.129} {Mo}_{t} + \underset{(2.295)}{1412.0} L_{t} & {\bar{\begin{matrix} R \end{matrix}}}^{2} = 0.967 \end{matrix}

Le rôle de la monnaie dans l’activité économique: quelques résultats obtenus pour dix-sept pays développés

Résumé

Dans cette étude, l’auteur évalue deux méthodes assez simples utilisées pour évaluer le rôle de la monnaie dans l’activité économique et les applique ensuite à dix-sept pays développés. La première consiste à effectuer une régression des variations du revenu exprimées en pourcentage par rapport aux variations de la monnaie également exprimées en pourcentage (définition étroite et large). Cette approche soulève un certain nombre de difficultés, y compris la possibilité d’une relation causale inverse (allant du revenu à la monnaie), l’omission des autres influences sur le revenu et la variabilité possible dans le décalage de la relation entre la monnaie et le revenu. Les résultats obtenus avec cette méthode ont été en général peu satisfaisants pour la plupart des pays. Les seuls pays pour lesquels la monnaie s’est révélée être une assez bonne variable explicative sont la Belgique, la Finlande et l’Italie. Dans une annexe, l’auteur essaye de déterminer s’il serait possible d’améliorer les résultats obtenus avec la première méthode en tenant explicitement compte de la possibilité qu’une variation de la masse monétaire peut avoir un effet différent selon l’origine de la variation de la monnaie. Il a donc effectué des régressions du revenu par rapport à la monnaie et par rapport aux différents actifs bancaires. Les résultats ont été décevants et il n’a pas été possible de tirer des conclusions positives.

La seconde méthode, vulgarisée par les travaux de Milton Friedman et de David Meiselman, consiste à effectuer des régressions des différences premières de la consommation par rapport aux différences premières de la monnaie et des dépenses autonomes pour la période courante et les périodes antérieures. Deux définitions de la monnaie (étroite et large) et deux définitions des dépenses autonomes (avec et sans les stocks) sont utilisées dans cette étude. L’objectif est de déterminer, d’une part, si l’adjonction des variables monétaires aux variables des dépenses améliore le résultat et, d’autre part, si l’adjonction des variables des dépenses aux variables monétaires contribue à expliquer la consommation. Les résultats ont tendance à étayer le point de vue que, pour une majorité de pays, les variables monétaires comme les variables des dépenses contribuent dans une certaine mesure à expliquer la consommation.

La función que desempeña el dinero en la actividad económica: Resultados hallados para 17 países desarrollados

Resumen

En este trabajo se analizan dos métodos sencillos para evaluar la función que le corresponde al dinero en la actividad económica. Luego, se aplican esos dos métodos a 17 países desarrollados. El primer método entraña hallar la regresión entre las variaciones porcentuales del ingreso y las variaciones porcentuales del dinero (dándole tanto una estrecha como una amplia definición). Este método está abierto a una serie de dificultades, incluida la posibilidad de causalidad a la inversa (o sea, del ingreso al dinero), el olvido de las otras influencias sobre el ingreso, y la posible variabilidad en el desfase que va del dinero al ingreso. La aplicación de este enfoque dio resultados en general muy pobres para la mayoría de los países. Los únicos países en que el dinero resultó ser un preconizador bastante bueno del ingreso fueron Bélgica, Finlandia, e Italia. En un apéndice, se intenta averiguar si se podrían mejorar los resultados del primer enfoque si se tiene en cuenta específicamente la posibilidad de que una variación en la oferta monetaria puede tener distintos efectos sobre el ingreso según cual sea la fuente de esa variación en el dinero. Se halla la regresión del ingreso con respecto al dinero, así como también con respecto a la composición de los activos bancarios. Los resultados fueron desilusionantes, y no se pudo llegar a ninguna conclusión firme.

El segundo método, popularizado por la obra de Milton Friedman y David Meiselman, entraña regresiones entre diferencias del primer grado en el consumo, y diferencias del primer grado en el dinero y en el gasto autónomo, tanto para el período actual como para los anteriores. En este estudio se usan dos definiciones del dinero (una estrecha y una amplia) y dos definiciones del gasto autónomo (según se incluyan o se excluyan las existencias). El objetivo es llegar a averiguar, por una parte, si mejora el resultado al añadir variables monetarias a las variables del gasto y, por otra parte, si se obtiene una mejor explicación del consumo al añadir variables del gasto a las variables monetarias. Los resultados tienden a apoyar la opinión de que tanto las variables monetarias como las del gasto, en la mayoría de los países, aportan una cierta contribución a la explicación del consumo.

Mr. Argy, Chief of the Financial 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.

In these models a number of monetary variables appear in the expenditure functions: sometimes money appears directly; usually the “cost of finance” is represented; sometimes an index of credit rationing appears; and occasional use is made of an indicator of wealth or capital values.

For illustrations of this, see A. A. Walters, “Money Multipliers in the U.K. 1880-1962,” Oxford Economic Papers, New Series, Vol. 18 (1966), pp. 270-83; Richard G. Davis, “How Much Does Money Matter? A Look at Some Recent Evidence,” Federal Reserve Bank of New York, Monthly Review, Vol. 51 (1969), pp. 119-31; Anna Jacobson Schwartz, “Why Money Matters,” Lloyds Bank Review, New Series, No. 94 (1969), pp. 1-16; Milton Friedman, “Interest Rates and the Demand for Money,” Journal of Law and Economics, Vol. 9 (1966), pp. 71-85; Michael W. Keran, “Monetary and Fiscal Influences on Economic Activity: The Foreign Experience,” Federal Reserve Bank of St. Louis, Review, Vol. 52 (1970), pp. 16-28.

Milton Friedman and David Meiselman, “The Relative Stability of Monetary Velocity and the Investment Multiplier in the United States, 1897-1958,” in Stabilization Policies (Commission on Money and Credit, Englewood Cliffs, N.J., 1963), pp. 165-268; Albert Ando and Franco Modigliani, “The Relative Stability of Monetary Velocity and the Investment Multiplier,” pp. 693-728, and Michael De Prano and Thomas Mayer, “Tests of the Relative Importance of Autonomous Expenditures and Money,” pp. 729-52, The American Economic Review, Vol. LV (September 1965); C. R. Barrett and A. A. Walters, “The Stability of Keynesian and Monetary Multipliers in the United Kingdom,” The Review of Economics and Statistics, Vol. XLVIII (1966), pp. 395-405.

Leonall C. Anderson and Jerry L. Jordan, “Monetary and Fiscal Actions: A Test of Their Relative Importance in Economic Stabilization,” Federal Reserve Bank of St. Louis, Review, Vol. 50 (1968), pp. 11-24. See also the subsequent criticisms and rejoinders in the same journal, April 1969 (pp. 6-16) and August 1969 (pp. 19-23).

This approach represents a test of the monetarist claim that fiscal policy has no lasting impact on income.

The major difficulty in applying the third approach lies in obtaining data on indicators of fiscal policy for a sufficient number of countries. See, for example, Keran, op. cit.

Ideally, quarterly data should be used for this exercise, but there are few countries for which such data are available for a reasonable number of years.

The approach leaves open the transmission mechanism for money. Conceivably, it is consistent with a Keynesian-type transmission mechanism.

See Appendix I for a more rigorous demonstration of these points.

This case is noted by John Kareken and Robert M. Solow, “Lags in Fiscal and Monetary Policy: Part I, Lags in Monetary Policy,” in Stabilization Policies (cited in footnote 3), pp. 14-96. See also Walters, op. cit.

An illustration of this would occur where the monetary authorities tend to accommodate the money supply to changes in income, e.g., to avoid sharp changes in interest rates.

An unpublished paper by the author, “The Determinants of the Money Supply,” deals more rigorously with these issues.

Even if the money supply series led the income series it would not follow that causation necessarily ran from money to income. First, the lead in the money series may simply be a policy response at particular phases in the cycle. Second, prospective changes in expenditure may provoke accommodating changes in cash balances with the result that changes in the money supply might be observed to precede changes in income. Third, as Tobin has recently shown, a model may be constructed where money has no impact on income, yet, if it responds to changes in expenditure, the observed money series may well lead the observed income series. See James Tobin, “Money and Income: Post Hoc Ergo Propter Hoc?” The Quarterly Journal of Economics, Vol. LXXXIV (1970), pp. 301-17. See also C. A. E. Goodhart, “The Importance of Money,” Bank of England, Quarterly Bulletin, Vol. 10 (1970), pp. 159-98.

The lag may be variable for a number of reasons. The source of change in the money supply may be relevant, e.g., whether there is a direct wealth effect, how much of the change is due to the availability of advances (see the discussion later). Also, open market operations at the long end may generate a shorter lag on income than operations at the short end. Again, the degree of capacity utilization may play a part, e.g., in an expansion the greater the slack in capacity, the quicker will be the effect.

See Milton Friedman and Walter W. Heller, Monetary vs. Fiscal Policy (New York, 1969). Although Friedman would appear to accept this interpretation, his views on the variability of the lags should lead him to expect a rather weak relationship (see point four above).

From equations (2) and (4) in Table 1.

One reason for this may be that a rise in income may raise market interest rates. If the time deposit rate tends to be inflexible, it will encourage a switch into current deposits—hence, a closer relation between current deposits and income than between total deposits and income.

This approach is adapted from the work of Barrett and Walters, op. cit. These authors do not treat imports as endogenous.

Consumption instead of income is chosen as the dependent variable because autonomous expenditures are an important part of income.

See Barrett and Walters, op. cit.

Op. cit.

They are, however, similar to the many equations run in this area in recent years.

Nevertheless, the ${\bar{R}}^{2}$ , especially for Norway, is high.

Edward Gramlich reviews fiscal multipliers derived from empirical studies in the United States in an unpublished paper, “The Usefulness of Monetary and Fiscal Policy as Discretionary Stabilization Tools.”

One reason could be the following. Suppose that in countries A and B money is “equally” powerful but the variance of percentage changes in money is larger in A than in B. Then money in A would explain more of the variance in consumption than in B.

A weak monetary effect may be due to the existence of a wide range of money substitutes and the operations of nonbank financial intermediaries.

This may well be a reason for the strong monetarist effects found for Japan. It is well known that banks (at least until quite recently) were a major source of finance and that businesses were heavily indebted to the banking system.

Consider, for example, a switch from government securities to advances. The reduction in securities raises interest rates, which has a delayed effect on income; but the increase in advances may affect income at an earlier stage.

For an example along these lines for the United States, see William L. Silber, “Velocity and Bank Portfolio Composition,” The Southern Economic Journal, Vol. XXXVI (October 1969), pp. 147-52.

Of course, these results are quite selective.

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IMF Staff papers: Volume 17 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1970: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969238

ISSN:: 1020-7635

Pages:: 193

DOI:: https://doi.org/10.5089/9781451969238.024

Keywords
I. A First Approach
II. A Second Approach
III. Conclusions
- APPENDICES
Le rôle de la monnaie dans l’activité économique: quelques résultats obtenus pour dix-sept pays développés
- Résumé
La función que desempeña el dinero en la actividad económica: Resultados hallados para 17 países desarrollados
- Resumen

Symbols
Y	= Gross domestic product
c	= Consumption
If, Is	= Investment in fixed capital and investment inventories, respectively
G	= Government expenditure
X	= Exports
M	= Imports
Mo	= $Mean money supply = \frac{{Mo}_{t} + {Mo}_{t - 1}}{2} (t = one year)$
A	= If+Is+G+X
A. Simple Keynesian Model
$\begin{matrix} (1) & Y = C + A - M \end{matrix}$
$\begin{matrix} (2) & C = cY \end{matrix}$
$\begin{matrix} (3) & M = mY \end{matrix}$
$\begin{matrix} (4) & C_{t} = \frac{c}{1 - c + m} A_{t} \end{matrix}$
B. Sophisticated Keynesian Model
$\begin{matrix} (5) & Y = C + A - M \end{matrix}$
${\begin{matrix} (6) & C_{t} = c_{1} Y_{t} + aC \end{matrix}}_{t - 1}$
${\begin{matrix} (7) & M_{t} = m_{1} Y_{t} + kM \end{matrix}}_{t - 1}$
$\begin{matrix} (8) & C_{t} = \frac{c_{1}}{1 + m_{1} - c_{1}} A_{t} + \frac{c_{1} (m_{1} a + a - {km}_{1})}{{(1 + m_{1} - c_{1})}^{2}} A_{t - 1} \dots \end{matrix}$
C. Simple Quantity Theory Model
$\begin{matrix} (9) & {Mo}_{t} = \frac{1}{v} Y_{t} \end{matrix}$
$\begin{matrix} (10) & M_{t} = {mY}_{t} \end{matrix}$
$\begin{matrix} (11) & Y_{t} = C_{t} + A_{t} - Y_{t} \end{matrix}$
$\begin{matrix} (12) & C_{t} = v (1 + m) {Mo}_{t} - A_{t} \end{matrix}$
D. Sophisticated Quantity Theory Model
$\begin{matrix} (13) & {Mo}_{t} = {bY}_{t} + {fMo}_{t - 1} \end{matrix}$
$\begin{matrix} (14) & Y_{t} = \frac{1}{b} {Mo}_{t} - \frac{f}{b} {Mo}_{t - 1} \end{matrix}$
$\begin{matrix} (7) & M_{t} = m_{1} Y_{1} + {kM}_{t - 1} \end{matrix}$
$\begin{matrix} (15) & Y_{t} = C_{t} + A_{t} - m_{1} Y_{1} - {kM}_{t - 1} \end{matrix}$
$\begin{matrix} (16) & C_{t} = \frac{1 + m_{1}}{b} {Mo}_{t} - [\frac{f (1 + m_{1}) - {km}_{1}}{b}] {Mo}_{t - 1} - A_{t} \dots \end{matrix}$
Combining the Keynes and Quantity Theory Models²
E. Simple Model
(Multiply equation (4) by x and equation (12) by (1—x); then add equations.)
$\begin{matrix} (17) & {xC}_{t} = \frac{cx}{1 - c + m} A_{t} \end{matrix}$
$\begin{matrix} (18) & (1 - x) C_{t} = v (1 - x) (1 + m) {Mo}_{t} - (1 - x) A_{t} \end{matrix}$
$\begin{matrix} (19) & C_{t} = v (1 - x) (1 + m) {Mo}_{t} + [\frac{cx}{1 - c + m} - (1 - x)] A_{t} \end{matrix}$
F. Sophisticated Model
(Use the same procedure as in E for equations (8) and (16).)
$\begin{matrix} (20) & C_{t} = \frac{(1 - x) (1 + m_{1})}{b} {Mo}_{t} - [\frac{(1 - x) [f (1 + m_{1}) - {km}_{1}]}{b}] {Mo}_{t - 1} + \frac{{xc}_{1}}{1 + m_{1} - c} - (1 - x) A_{t} + \frac{{xc}_{1} (m_{1} a + a - {km}_{1})}{{(1 + m_{1} - c_{1})}^{2}} A_{t - 1} \dots \end{matrix}$

Symbols
Y	= Gross domestic product
c	= Consumption
If, Is	= Investment in fixed capital and investment inventories, respectively
G	= Government expenditure
X	= Exports
M	= Imports
Mo	= $Mean money supply = \frac{{Mo}_{t} + {Mo}_{t - 1}}{2} (t = one year)$
A	= If+Is+G+X
A. Simple Keynesian Model
$\begin{matrix} (1) & Y = C + A - M \end{matrix}$
$\begin{matrix} (2) & C = cY \end{matrix}$
$\begin{matrix} (3) & M = mY \end{matrix}$
$\begin{matrix} (4) & C_{t} = \frac{c}{1 - c + m} A_{t} \end{matrix}$
B. Sophisticated Keynesian Model
$\begin{matrix} (5) & Y = C + A - M \end{matrix}$
${\begin{matrix} (6) & C_{t} = c_{1} Y_{t} + aC \end{matrix}}_{t - 1}$
${\begin{matrix} (7) & M_{t} = m_{1} Y_{t} + kM \end{matrix}}_{t - 1}$
$\begin{matrix} (8) & C_{t} = \frac{c_{1}}{1 + m_{1} - c_{1}} A_{t} + \frac{c_{1} (m_{1} a + a - {km}_{1})}{{(1 + m_{1} - c_{1})}^{2}} A_{t - 1} \dots \end{matrix}$
C. Simple Quantity Theory Model
$\begin{matrix} (9) & {Mo}_{t} = \frac{1}{v} Y_{t} \end{matrix}$
$\begin{matrix} (10) & M_{t} = {mY}_{t} \end{matrix}$
$\begin{matrix} (11) & Y_{t} = C_{t} + A_{t} - Y_{t} \end{matrix}$
$\begin{matrix} (12) & C_{t} = v (1 + m) {Mo}_{t} - A_{t} \end{matrix}$
D. Sophisticated Quantity Theory Model
$\begin{matrix} (13) & {Mo}_{t} = {bY}_{t} + {fMo}_{t - 1} \end{matrix}$
$\begin{matrix} (14) & Y_{t} = \frac{1}{b} {Mo}_{t} - \frac{f}{b} {Mo}_{t - 1} \end{matrix}$
$\begin{matrix} (7) & M_{t} = m_{1} Y_{1} + {kM}_{t - 1} \end{matrix}$
$\begin{matrix} (15) & Y_{t} = C_{t} + A_{t} - m_{1} Y_{1} - {kM}_{t - 1} \end{matrix}$
$\begin{matrix} (16) & C_{t} = \frac{1 + m_{1}}{b} {Mo}_{t} - [\frac{f (1 + m_{1}) - {km}_{1}}{b}] {Mo}_{t - 1} - A_{t} \dots \end{matrix}$
Combining the Keynes and Quantity Theory Models²
E. Simple Model
(Multiply equation (4) by x and equation (12) by (1—x); then add equations.)
$\begin{matrix} (17) & {xC}_{t} = \frac{cx}{1 - c + m} A_{t} \end{matrix}$
$\begin{matrix} (18) & (1 - x) C_{t} = v (1 - x) (1 + m) {Mo}_{t} - (1 - x) A_{t} \end{matrix}$
$\begin{matrix} (19) & C_{t} = v (1 - x) (1 + m) {Mo}_{t} + [\frac{cx}{1 - c + m} - (1 - x)] A_{t} \end{matrix}$
F. Sophisticated Model
(Use the same procedure as in E for equations (8) and (16).)
$\begin{matrix} (20) & C_{t} = \frac{(1 - x) (1 + m_{1})}{b} {Mo}_{t} - [\frac{(1 - x) [f (1 + m_{1}) - {km}_{1}]}{b}] {Mo}_{t - 1} + \frac{{xc}_{1}}{1 + m_{1} - c} - (1 - x) A_{t} + \frac{{xc}_{1} (m_{1} a + a - {km}_{1})}{{(1 + m_{1} - c_{1})}^{2}} A_{t - 1} \dots \end{matrix}$

Ȳ	=	percentage changes in income
$\bar{M} o$	=	percentage changes in money
E	=	all “other” influences on money (error term).

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I. A First Approach

II. A Second Approach

III. Conclusions

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I. Monetary Policy and Income

II. Effects on Income of Source of Change in Money Supply

Le rôle de la monnaie dans l’activité économique: quelques résultats obtenus pour dix-sept pays développés

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La función que desempeña el dinero en la actividad económica: Resultados hallados para 17 países desarrollados

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