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Weighted Monetary Aggregate

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swayam sarangi

on 11 November 2014

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Transcript of Weighted Monetary Aggregate

Monetary Aggregates
Broad categories measuring the total supply of the money supply within an economy.
M1 M2 M3 M4
Monetary aggregates are watched closely by economists and investors
They give a clear picture of the true size of the "working" money supply
Allows investors to measure the rate of change in the monetary aggregates and overall monetary velocity.
Key in determining overall central-banking policy.
Simple Sum Aggregates
Conventional aggregation procedure
Been in practice for a long period of time and is still being used by almost all the central banks around the world
Easy to use
Fair enough indicator of key metrics like GDP and inflation when aggregated over highly liquid assets.
Weighted Monetary Aggregates
In contrast to the conventional measure of aggregation, the Weighted Monetary Aggregates assign weights to the component assets based on their monetary service flow or user cost.
(Index of Money Supply)
This approach to monetary aggregation was derived and advocated by William A. Barnett (1980) and has led to the construction of monetary aggregates based on Diewert's (1976) class of superlative quantity index numbers. The new aggregates are called the Divisia aggregates or Monetary Services Indexes.
Measures Of Money
Official Statistics on monetary aggregates are constructed using the simple sum aggregation procedure.
It assumes perfect substitutability between the component assets.

Rationale Behind WMAs
Distinction between transaction
and savings deposit blurred.
Aggregating by a homogeneous measure of "moneyness"
As the dollar amount of components change through time, they may represent different degrees of moneyness.
Constructing indexes that reflect the total utility based on the monetary service flow from each asset.
"user cost"
- rate of return on a pure store of wealth asset and the own rate of return on each asset.


substitution effect
arising out of financial innovation.
No scope for
aggregation bias

Global Experience
Conditional applicability of WMAs

Volatile Currency Value
Unstable Demand Functions
Relevance for Economic Unions
Gulf Cooperation Council
European Monetary Union
Volatile Currency Value
- From studies conducted in Turkey, it has been observed that during episodes of high inflation, the relationship of money and price gets more direct.
Hence, this enhances the explanatory power of WMAs on inflation.

- With higher currency substitutability and a flexible exchange rate regime, the currency value fluctuates more and is consistent to what is displayed by the WMAs.

- In countries with stable currency value, the relation between money and price loosens up. Yet, WMAs can still give a satisfactory account of GDP.

Oscillating inflation rate in Turkey from early 70s till late 90s
Countries such as Canada have stable money demand functions, thus, stable velocity of circulation; Simple Sum Aggregates, therefore, prevail in explaining macro-economic variables.
David Longworth and Joseph Atta-Mensah report that broad monetary aggregates generally the
best in predicting inflation, M1 works well in predicting nominal spending, and real M1 is the
best predictor of real output.
When the money demand function in unstable, the velocity of circulation of money is shaken, making Simple Sum Aggregates misleading.
How could we
M1 and M2?
The key factor lying behind this such anomaly is shifting money demand for monetary assets resulting from exogenous shocks, consequently affecting the velocity of circulation in the economy. For instance, in the case of the missing M2, there was a shift away from time deposits to mutual funds, specially bonds and stocks mutual fund, in an environment of low interest rates.
Gulf Cooperation Council
- Used an approach devoid of utility function specifications, econometric
inferences and parameter estimation.

- Treats residents as heterogeneous agents.

- Divisia growth rates display business cycle patterns that are consistent with monetary policy.

European Monetary Union
- Aggregation theoretic framework is applied to money holdings of a representative European resident, here treated as homogenous rational agent (utility function is weakly separable in consumption and monetary assets).

- Two findings unfolded:
1. WMAs accounted for financial innovation spreading at different rates across the European land.
2. displays the impact of enhanced exchange rate stability as the European economy steadily transits to a monetary union.

- Yet, since SSAs were as explanatory as Divisia indices, and the latter being uncontrollable due to fluctuating interest rates, economists have advised the European Union to cling to M3 as the main target variable.

Alternative approaches to the construction of WMAs
Substitution Approach
User-cost Approach
Policy-oriented statistical Approach
When the transition into a monetary union is complete and financial integration thorough throughout, the European Divisia is of no use since it can no longer give any nuances between different countries about their pace of financial integration and innovation.
Substitution Approach
Based on the work of V K Chetty
Degree of moneyness of an asset associated with the elasticity of substitution between that asset and a highly liquid reference asset
Substitutability determines the money equivalent of other assets
Methods of estimating various elasticities of substitution and thereby the aggregation of liquid assets are devised
User-cost Approach
Popularized by FED economists like Barnett, Offenbacher and Spindt
Alternate monetary assets are viewed as durable goods, and therefore their 'prices' are represented by the corresponding user costs (one-period holding costs)
User cost of a durable good (in this case, of a monetary asset) is given by the current purchase price minus discounted expected resale value of the depreciated good in the next period
Unlike durable goods, however, monetary assets appreciate as they bear interest
Interest rates are based on an asset's ability of generate 'monetary services'; one unit of monetary services is the amount of monetary assets which buys one unit of commodity basket in the base period
Policy-oriented Statistical Approach
Defines, based on the quantitative relationships among money, output and prices, some a-priori criteria in deciding on a suitable aggregate of financial assets
Roper-Turnovsky method in this approach suggests that the optimal monetary aggregate is the one which minimizes the forecast variance in nominal income
Construction of Divisia Monetary Indices for WMAs and RBI's report on Construction & Evaluation of Divisia Monetary Indices in India

The Oversimplification Problem
Divisia Monetary Indices
Simple sum aggregates are just too simple
Countries currently using SSA's
Why equations matter.
Diewert & Barnett to the Rescue: Divisia Index
Ideation of the method
The String of equations
Applications of Divisia Index
Computational Difficulties
Removes the Aggregation Bias
Serve as better predictor of inflation and output

Determining appropriate weights for monetary components
requires a large pool of data
. There is, thus, a higher risk of
specification or omission errors
Merits and Demerits of using Divisia Index
Data obtained is very often
inaccurate or unavailable
and may thus lead to
redundant results


Before 1998
After 1998
Straight from the horse's mouth
What are we using now ?
Which department/departments is/are responsible for construction of WMA's?
Trends in Construction of Indicators
Fluctuating Variables
There are myriads of
factors affecting the weights

Also, there is often a
lag in the adjustment
process of weights with respect to the changing factors
Examples of effects of fluctuating variables
evolving and diversifying
Financial Assets.
Benchmark Rate of Return
Adds up assets with varying maturity dates
Finding a totally illiquid asset is unrealistic, or at best, an extremely difficult task
The underlying assumption that no frequent adjustment is made in the portfolio holdings is unrealistic and as a result the portfolio adjustment costs are ignored,
underestimating the actual user cost

Empirical Issues
The diverging opinions among economists do not promise any consensus in the near future
Which one to choose?
Simplicity > Complexity
The simplicity and ease with which Simple Sum Aggregates are computed, despite the unreasonable assumption of perfect substitutability of all the components, provides economic agents to obtain an overall picture of money supply in the economy.
What are Monetary Aggregates?
Why they Matter?
What are Simple Sum Aggregates
What are Weighted Monetary Aggregates
Advantages of WMAs over SSAs
Leads to Aggregation bias and distorts monetary aggregates
Assumption of
perfect substitability
between component assets irreconcilable with empirical evidence and economic intuition.
Assignment of
equal weights
to all components, which is inconsistent with economic theory.
Bias and Freakishness
Forbes, September 26 1983
We conclude this section knowing that Weighted Monetary Aggregates are superior to Simple Sum Aggregates on Conceptual Grounds.
Vivek Soni
Limitations Of SSAs
Makes use of broader measure of money feasible (M3 and higher).
We have identified the drawbacks of the conventional monetary aggregation procedure and the growing need to formulate a new method that can forecast key metrics like GNP, Inflation and Unemployment better.
1) Introduction
2) SSAs and WMAs
3) Advantages of WMAs over SSAs
Index numbers can be used to aggregate assets by a homogeneous characteristic
Financial Developments have altered the relationship between M1 growth and the growth of GNP, rendering it less useful as an intermediate target for monetary policy
Weighted Monetary

The Model
Complexities regarding calculation of Divisia Index
Acts as a better aggregate measure only under repressive economic conditions
Studies before 1998 primarily aimed at testing the importance of Simple Sum Aggregates using both parametric separability tests and non parametric separability tests without any comparison based analysis. A few of them include :
Ramachandran & Kamaiah(1994)
Subrahmanyam & Swami (1994)
Kannan (1989)
After 1998 with more information about the future movement of prices and income and stability regarding data on demand functions, studies focussed on evaluation performance of WMAs vs SSAs. A few of the studies include:
Subrahmanyam and Swami (1991)
Acharya and Kamaiah(1994)
DEAP Report (2005)
We are currently using the Multiple Indicator Approach, which takes into consideration the impact of a number of macroeconomic variables which affect liquidity.
The Department of Economic Policy And Research along with the Monetary Policy Department are behind the construction of of monetary aggregates
The multiple indicator approach was further revised by Bimal Jena's Committee(1996) to the augmented multiple indicator approach.
However, under the Raghuram Rajan era, inflation targeting approach is to be followed from 2015-16 (the Urjit Patel committe).
Divisia Index Equation
Limitations of SSAs
Need to eliminate the
aggregation bias
present in Simple sum aggregates by use of index numbers.
The need to assign weights to the financial components based on their
degree of 'moneyness'.
Interest rates
Fails to internalize financial innovation.
Obscure relationship between elasticity of substitution and moneyness
Yielded unduly large elasticity of substitution when applied to Indian data
Parameter sensitivity
Differences in monetary services not considered
Parameter free
Readily adaptable to changing financial landscape
Provides better indicators for framing monetary policies
Disagreement regarding choosing benchmark assets etc.

Assigns weights to different components thus captures impact of changes in components accurately
Lack of a sound theoretical underpinning of money
No generally agreed criterion as a standard for an "ideal" monetary aggregate
Exclusivity to a particular target
Better forecasting ability of the resultant monetary aggregates
The Model
"Despite their theoretical appeal, the superlative indexes have a number of shortcomings"
-Fischer, Hudson and Pradhan (1993)
WMAs become significant when:
1. Computational Difficulties
2. Effects of fluctuating Variable on weights
3. Problems of Benchmark Rate of Return
4. Empirical Issues
Construction of WMA is
It is
Major instabilities discredit the weights

Unpredictable changes in the price level

inflationary path Real rate of return

These changes distorts the degree of 'moneyness' associated with the components

Changes in the interest rates

Rate of User cost Weight of
interest of currency currency
"The alleged superiority of the superlative monetary aggregates over their simple-sum counterparts could not be established convincingly"
- Subrahmanyam and Swami (1989)
A new empirical weighted monetary aggregate for the UK

"The properties of this new aggregate are contrasted with those of the corresponding simple sum and Divisia aggregates. The new weighted monetary aggregate is found to be
highly stable and conforms well with standard money demand properties
. The aggregate also displays sensible impulse response and persistence profiles to monetary shocks."
Leigh Drake andTerence C. Mills
Francisco Alonso et al show how the weighted monetary aggregates can give a good account of GDP.
In many cases, the difference between the results of SSAs and WMas are statistically insignificant.
E.g. Canada and Spain
Currency has the highest user (opportunity) cost.
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