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Determinants of money multipliers.

In the present day world of fairly well-developed banking systems where money stock in an economy is jointly determined by the policies of the Central Bank, the scheduled banks and the non-bank public, the determination of money stock is an important variable in the formulation formulation /for·mu·la·tion/ (for?mu-la´shun) the act or product of formulating.

American Law Institute Formulation
 of an appropriate monetary policy. In Pakistan however very frequent and significant changes in money supply during the fiscal year suggest strong arbitrariness in the formulation and implementation of the monetary policy.

There are various approaches to the process of money stock determination, one approach is through money multipliers. Changes in money multipliers reflect the portfolio decisions of the commercial banks, non-bank public and the monetary authority. Extensive developments in the theory and applied research in the formulation of money multipliers by Friedman and Schwartz (1960); Brunner and Meltzer (1964); Hosek (1970); Bomhoff (1977) and others have estimated money multipliers for the industrialised Adj. 1. industrialised - made industrial; converted to industrialism; "industrialized areas"

industrial - having highly developed industries; "the industrial revolution"; "an industrial nation"
 economies but with the exception of Hosek they treat the determinants of the money multipliers as exogenous Exogenous

Describes facts outside the control of the firm. Converse of endogenous.
 and are taken as given. However the determinants of money multipliers depend on various interest rates and measures of economic activity which are not constant.

In this study we estimate the determinants of the money multipliers firstly because they are not constant, rather they reflect the behavioural Adj. 1. behavioural - of or relating to behavior; "behavioral sciences"
 response of commercial banks and non-bank public to variations in interest rates. Secondly, they are important because the financial sector in Pakistan over the period of study has been controlled which, may affect the determinants of money multipliers contrary to theoretical and empirical expectations as established in the literature, particularly for the advanced industrialised economies.

This study differs from the earlier studies on money stock determination and money multipliers in Pakistan. See Mangla and Ladenson (1978); Hamadani (1976) and Khalid (1980) in that it uses post-1974 data which pertains to present Pakistan only.


This study adopts Hosek's model of the determinants of money multipliers which comprises of four ratios:

K = f(y, rTD) ... ... ... ... (1)

where K is defined as ratio of currency in circulation (CC) to demand deposits (DD) CC/DD. Y is the GNP GNP

See: Gross National Product
 at current prices and is used as a proxy for permanent income. Alternatively we also use YNA YNA Yellow Naped Amazon (bird species; Amazona ochrocephala auropalliata)
YNA You're Not Alone
YNA Young Numismatists of America
YNA Young Naturalists Awards
YNA York Neurosurgical Associates, PC
, the non-agricultural GNP. rTD is the commercial bank deposit rate used as a proxy for opportunity cost.

Y is postulated pos·tu·late  
tr.v. pos·tu·lat·ed, pos·tu·lat·ing, pos·tu·lates
1. To make claim for; demand.

2. To assume or assert the truth, reality, or necessity of, especially as a basis of an argument.

 to be positively related to K. rTD is postulated to bear a negative sign.

T = f(YNA, rg) ... ... ... ... (2)

where T is defined as the ratio of time deposits (TD) to demand deposits (DD) TD/DD.

rg is the government bond rate.

Alternatively we use rTD also.

rg is postulated to bear a negative sign because as the bond rate rises above the commercial bank rate it may shift time deposits to other assets other assets

Assets of relatively small value. For financial reporting purposes, firms frequently combine small assets into a single category rather than listing each item separately.
 like government banks thus lowering the ratio.

R = f(Ms, CR/DT, YNA, rg) ... ... ... ... (3)

where R is defined as the ratio of total reserves (TR) of the banks to total deposits (DT).

Ms is changes in money supply and is postulated to bear a positive sign. CR/DT is the ratio of credit to total deposits and is postulated to bear a positive sign.

B = f(CR/DT, GS, rb) ... ... ... ... (4)

where B is the ratio of borrowing from the State Bank of Pakistan The State Bank of Pakistan (SBP) is the central bank of Pakistan. While its constitution, as originally laid down in the State Bank of Pakistan Order 1948, remained basically unchanged until January 1, 1974, when the bank was nationalised, the scope of its functions was  to total deposits (B/DT).

Gs is the government securities held by the commercial banks.

rb is the difference between the commercial banks loan rate and the bank rate.

Alternatively we use Rc, the call money rate also. Gs will bear a positive sign as securities can be used as collateral for borrowing from the State Bank of Pakistan.

rb is expected to be positive, the higher the difference between the two rates, the greater the demand for borrowing from the Central Bank.

All data for this study is taken from the Monthly Bulletins of the State Bank of Pakistan, Data for GNP are taken from the Economic Surveys of Pakistan.


The results of the determinants of money multipliers or the ratios reported in Tables 1-4 are evaluated with respect to the postulated signs of their coefficients and the structural constraints CONSTRAINTS - A language for solving constraints using value inference.

["CONSTRAINTS: A Language for Expressing Almost-Hierarchical Descriptions", G.J. Sussman et al, Artif Intell 14(1):1-39 (Aug 1980)].
 on the financial sector.

1. Currency Ratio

Among the determinants of the currency ratio while rTD bears the correct negative sign and is highly significant the coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

 of YNA is also negative. It implies that the demand for currency increases less than the increase in demand deposits.

2. Time Deposit Ratio

For this ratio the signs of Y and YNA are contrary to theoretical expectations. Their coefficients are highly significant but negative. This implies that time deposits increase by less than demand deposits. However this outcome is confirmed by the financial statistics of Pakistan over the period of study that the demand deposits increased by more than time deposits.

Secondly rg bears the correct sing but is insignificant. This is again a structural problem of the financial sector of Pakistan. This insignificance in·sig·nif·i·cance  
The quality or state of being insignificant.

Noun 1. insignificance - the quality of having little or no significance
unimportance - the quality of not being important or worthy of note
 is not surprising because of the lack of a developed bond market in Pakistan.

3. Excess Reserve Ratio

Among the determinants of the excess reserve ratio YNA and rg bear the correct signs and are highly significant. The outcome for YNA implies that increases in non-agricultural income leads to increases in demand deposits so the excess reserve ratio is affected. The significance of rg confirms the use of this variable as a proxy for the interest rate in this ratio. It implies that in the long-run portfolio holders may consider the substitution Substitution

put her own son in place of Orestes; her son was killed and Orestes was saved. [Gk. Myth.: Zimmerman, 32]


robber freed in Christ’s stead. [N.T.: Matthew 27:15–18; Swed. Lit.
 between time deposits and government securities.

TR/DT and Ms bear incorrect signs and are insignificant. This is explained by the credit restrictions in the financial structure of Pakistan over the period of study. Due to credit restrictions the banks were not interested in increasing time or demand deposits and were neither compelled to maintain reserves strictly in proportion as implied by TR/DT.

4. The Borrowing Ratio

The very insignificant coefficients of the borrowing ratio do not imply that this ratio is not regulated by purely economic factors. These results are due to the problem of excess liquidity with the commercial banks and restrictions on credit expansion.

These results confirm that the determinants of money multipliers are responsive to interest rates and economic activity variables as much as the financial structure of Pakistan permits. They reflect the behavioural response of commercial banks and non-bank public to variations in interest rates and Central Bank's monetary policy. Therefore the relationships between the determinants of money multipliers and interest rates can be used to study the effect of multipliers on the monetary policy in the past and also predict money multipliers to help develop a rational monetary policy in the future. Therefore, we estimate the money multipliers for the post-1974 period using Hosek's formulation:

M = . 1 + K + T/(r + TR - B) (1 + T) + K ... ... ... ... (5)

where r is the ratio of required reserves Required reserves

The dollar amounts, based on reserve ratios, that banks are required to keep on deposit at a Federal Reserve Bank.

required reserves 
 to total deposits., It is 5 percent for both demand and time liabilities throughout the period 1974-1991.

The actual and estimated values for money multipliers based on the values of the determinants of the money multipliers are reported in Table 5.

It will be seen from Table 5 that even with considerable structural constraints on the financial sector of Pakistan the money multipliers estimated from actual and estimated values move very close.

We estimate the predictive power The predictive power of a scientific theory refers to its ability to generate testable predictions. Theories with strong predictive power are highly valued, because the predictions can often encourage the falsification of the theory.  of the money multipliers by estimating the percentage variation from the Root Mean Square Error (RMSE) as follows:

RMSE = [square root of 1/T ([??] - m).sup.2]]

where T is the total number of observations and m and m are the estimated and actual values of the multipliers estimated by the four ratios.

The RMSE is divided by the mean of the series of the actual multiplier i.e. 9.953/1.7 x 100 = 5.8.

Now given that Ms = m.H. (Money supply = the multiplier multiplied by the high-powered money stock) the percent variation implies that given the values of multipliers and high-powered money which is controlled by the government, we can predict the stock of money at any point with the error margin of 5 to 6 percent.


The results of the study show that although some results on the determinants of money multipliers are not compatible with theoretical expectations which are based on the highly developed financial structures of the advanced economies they are compatible with the structural developments in the financial sector of the Pakistani economy. Furthermore, the results show, quite clearly, that the size of the money stock can be predicted with the monetary base as the control variable, if the multiplier is predicted after taking into account the determinants on the various components of multipliers which are not constant and hence should be used effectively in the formulation of the monetary policy in Pakistan of which money stock is the major component.

Comments on "Determinants of Money Multipliers"

In discussing the role of money in Pakistan we are, in the first place, implicitly assuming that the State Bank of Pakistan can determine the growth of the money supply. The debate between the monetarists and the non-monetarists indicates that this assumption needs careful understanding. The monetarists argue that monetary authorities can control money supply whereas the others argue that the stock of money is simultaneously determined along with the variables of the financial and the real sectors of the economy.

If that is so it then seems that the stock of money is not only controlled by the monetary authorities but also depends on the behaviour of the public in the real and financial sectors, which cannot be controlled by the monetary authorities.

The monetarists agree to the above statement but their argument is that the behaviour of the public and the banking system is stable and can be predicted. It is this belief underlying the argument that the monetarists suggest that the stock of money can be controlled by the authorities concerned. Consequently it is made clear to us that the issue between the monetarists and the non-monetarists needs empirical investigation.

Given the model M = mH and the debate between the monetarists and non-monetarists, three questions need clarification:

(a) Whether all the variables (ratios) determining the size of the m multiplier are controllable or not?

(b) Whether the functions 1-4 explaining these variables (ratios) are fairly stable and can be predicted?

(c) Whether the source of H can be controlled by the monetary authorities?

It is suggested that Equations 1 and 3 regarding the currency deposit ratio and excess reserves Excess reserves

Amount of reserves held by an institution in excess of its reserve requirement and required clearing balance. Also see reserves.

Excess reserves

Actual reserves that exceed required reserves.
 may be estimated with the following specification:

1. K = f (interest rates, average consumption, income distribution and seasonal changes).

2. E = f(market interest rates, discount rates, required reserves uncertainty of deposits and withdrawals and government regulations).

Furthermore, empirical evidence suggests that these ratios are unstable unstable,
adj 1. not firm or fixed in one place; likely to move.
2. capable of undergoing spontaneous change. A nuclide in an unstable state is called
radioactive. An atom in an unstable state is called
 in the short run. So far as the source of the monetary base or high-powered money is concerned, it includes the Central Bank's credit to the government, the commercial banks and its net foreign assets. It is known that the Central Bank's credit to the government, is largely determined by the budget deficit, which the Central Bank cannot control fully. Credit provided to the commercial banks is mainly controlled through monetary policy. Finally, foreign asset holding of the central bank is determined by the trade and payments balance, over which the central bank has limited direct control.

Thus far, it is clear from the above discussion that if we suggest that the monetary authorities can control the stock of money it simply implies that the authorities can influence the variables determining the money multiplier, budget deficits and trade balances etc. In less developed countries the story is far from what is implied above. Underdeveloped un·der·de·vel·oped
Not adequately or normally developed; immature.
 economies have little control over the stock of money because the monetary authorities can exercise their power in a limited manner.

So far as the econometric e·con·o·met·rics  
n. (used with a sing. verb)
Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models.
 problems are concerned, it is noted that with lagged dependent variables in the regression regression, in psychology: see defense mechanism.

In statistics, a process for determining a line or curve that best represents the general trend of a data set.
 equations, two difficulties may arise:

1. With no autocorrelation Autocorrelation

The correlation of a variable with itself over successive time intervals. Sometimes called serial correlation.
 problem, results are biased particularly with the small sample size.

2. With the presence of autocorrelation the results are biased and inconsistent. Variances are large so the results reported cannot be taken seriously.

Shahnaz Rauf

F. G. College for Women, F-7/2, Islamabad.


Bomhoff, Edward J. (1977) Predicting the Money-Multiplier: A Case Study for the U.S. and the Netherlands. Journal of Monetary Economics.

Brunner, Karl, and A. H. Meltzer (1964) Some Further Investigations of Demand and Supply Functions for Money. Journal of Finance. May.

Friedman, M., and Anna Schawrtz (1960) Monetary History of the United States “American history” redirects here. For the history of the continents, see History of the Americas.
The United States of America is located in the middle of the North American continent, with Canada to the north and the United Mexican States to the south.
: 1957-1960. NBER NBER National Bureau of Economic Research (Cambridge, MA)
NBER Nittany and Bald Eagle Railroad Company
 Princeton University Princeton University, at Princeton, N.J.; coeducational; chartered 1746, opened 1747, rechartered 1748, called the College of New Jersey until 1896. Schools and Research Facilities

Hamadani, Mazahar H. (1976) Money-Multiplier as a Determinant determinant, a polynomial expression that is inherent in the entries of a square matrix. The size n of the square matrix, as determined from the number of entries in any row or column, is called the order of the determinant.  of Money Supply: The Case of Pakistan. The Pakistan Development Review 15: 2.

Hosek, William R. (1970) Determinants of Money Multiplier. Quarterly Review of Economics and Business. Summary.

Khalid, Masood A. (1980) Determinants of Money-Multiplier: A Case Study of Pakistan. M.Sc. Thesis Quaid-i-Azam University Quaid-i-Azam University, (more correctly Qaid-i A'zam University) is located in Islamabad, Pakistan, and is one of largest public universities in Pakistan. Founded as the University of Islamabad in 1965, it was later renamed in 1976 as Quaid-i-Azam University , Islamabad.

Mangla, I. U., and Ladenson (1978) Short-run Forecast of Money Stock in Pakistan. The Pakistan Development Review 17: 2.

Faiz Bilquees is Senior Research Economist at the Pakistan Institute of Development Economics Pakistan Institute of Development Economics (PIDE) is a think tank in Islamabad, Pakistan.

Pakistan Institute of Development Economics was established at Karachi in 1957 and in 1964 accorded the status of an autonomous research organisation by the Government of Pakistan.
, Islamabad.
Table 1
Results of the Currency Ratio

   C        [K.sub.-1]        Y         [Y.sub.NA]      rTD

 0.999          --        -0.0000007        --        -0.041
(4.015)                    (1.259)                    (2.607)

 0.916          --            --        -0.000005     -0.027
(13.528)                                 (2.228)      (1.908)

 1.055        -0.029      -0.0000007        --         0.045
(3.469)      (0.094)       (1.181)                    (2.393)

   t        [R.sup.2]     [R.sup.-2]        DW           F

 0.020        0.580         0.490         1.784        6.443

 0.032        0.655         0.581         2.208        8.851

 0.021        0.569         0.426         1.871        3.968

Table 2
Results of the Time-Deposit Ratio

   C       [T.sub.-1]       Y        [Y.sub.NA]     rg        rTD

  0.245         --           --        -0.00002    -0.137      --
 (1.8004)                              (3.197)     (1.124)

  0.479       0.658       -0.00003        --       -0.010      --
 (0.562)     (3.321)      (2.159)                  (0.144)

 -0.696        --         -0.00002        --       -0.166    -0.013
 (0.714)                  (2.231)                  (1.689)   (0.454)

  0.382       0.695       -0.000001       --         --      -0.004
 (1.853)     (3.906)      (2.137)                            (0.224)

   t       [R.sup.2]    [R.sup.-2]       DW          F

 0.098       0.477        0.365        0.910       4.268

 0.005       0.705        0.607        1.513       7.188

   --        0.385        0.254        0.984       4.913

   --        0.693        0.623        1.605       9.818

Table 3
Results of the Excess-Reserve Ratio

   C      [E.sub.-1]    [DELTA]      CR/DT         Y        YNA

3.244     -0.898       -0.00002    -0.0004      0.00004      --
(8.704)   (6.065)      (3.311)     (0.923)      (1.218)

3.166     -0.879       -0.00003    -0.0005        --      0.000009
(6.465)   (5.322)      (2.425)     (0.989)                (0.329)

2.575     -0.750       -0.00004    -0.0006        --      0.000005
(6.930)   (4.731)      (3.435)     (1.259)                (6.118)

0.797     -0.400       -0.00002    -0.000008      --      0.000005
(4.768)   (1.638)      (1.455)     (0.009)                (2.788)

  IG         rTD       [R.sup.2]   [R.sup.-2]     DW         F

-0.226        --       0.889       0.823        1.721     13.372

-0.219        --       0.874       0.799        1.546     11.591

-0.163        --       0.838       0.764        1.926     11.392

  --      0.630        0.630       0.511        0.988     2.229

Table 4
Determinants of the Borrowing Ratio

C         [B.sub.-1]   CR/DT        GS            rb        RC

 0.216    --            0.0007      -0.0000007    --        -0.006
(2.969)                (0.954)      (0.919)                 (0.862)

 0.281    --            0.0002      -0.00000003   --        -0.008
(3.486)                (0.299)      (0.327)                 (1.143)

 0.195    --            0.0005      -0.0000004    -0.021    --
(3.009)                (0.727)      (0.5803)      (0.629)

 0.183     0.273        0.0002       0.00005       --       -0.004
(1.154)   (0.904)      (0.256)      (0.046)                 (0.468)

   t      [R.sup.2]    [R.sup.-2]       DW           F

--        0.150        0.031        1.576         0.826

 0.005    0.278        0.055        1.904         1.250

--        0.129        0.056        1.433         0.696

-0.003    0.237        0.109        1.635         0.683

Table 5
Estimates of the Actual and
Predicted Money Multipliers

Period   Actual (m)   Predicted (m)

1975       1.8053        1.5838
1976       1.9870        1.8540
1977       1.8730        1.8301
1978       1.7180        1.8177
1979       1.7639        1.7941
1980       1.8396        1.8732
1981       1.7822        1.6814
1982       1.7079        1.7583
1983       1.6055        1.6771
1984       1.7167        1.6805
1985       1.6891        1.6668
1986       1.7249        1.6769
1987       1.5257        1.6100
1988       1.5486        1.6213
1989       1.5380        1.6297
1990       1.5989        1.6465
1991       1.5235        1.5464
COPYRIGHT 1993 Reproduced with permission of the Publications Division, Pakistan Institute of Development Economies, Islamabad, Pakistan.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1993 Gale, Cengage Learning. All rights reserved.

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Author:Bilquees, Faiz
Publication:Pakistan Development Review
Article Type:Report
Geographic Code:9PAKI
Date:Dec 22, 1993
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