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Theoretical and Empirical Approaches
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Partial equilibrium models are still influential today because of its power on explaining empirical data. It is often assumed that real money balances are positively related to income and inversely related to the opportunity cost of holding money.

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These influences can be referred to the two most important motives of money demand, i. These provide the original ideas for money demand function. Based on the Transactions Motive , money demand focuses on the liquidity provided by money. A typical partial equilibrium money demand function usually has a form:.

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M is money demand, P is the price level, R is the nominal interest rate, and y is the real output. The function L R,y is called liquidity function.

These 1 models provide significant empirical insights into money demand. Based on the Speculative Motive , money demand focuses on the potential return on various assets including money as an additional motive. Keynes [ 1 ] stressed that the choice between money and bonds also depends on both the current nominal interest rate and the expected future interest rate.

Tobin [ 2 ] argued that money could be regarded as a risk free asset with zero return and money demand can then be determined according to the portfolio management approach. This was an evolutionary tradition with several distinct approaches to the role of money, e. Fisher, Pigou and Wicksell.

Demand for Money: Keynesian Theory compared with Classical Theory

Despite different representations, they share a common feature, i. Take logs on both hand sides, and then take derivative with respect to time:. Fisher assumed that the velocity v t is constant and output level is in full employment i. Pigou claimed that the velocity v t is a function of interest rate R and.

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Wicksell, as a Swedish monetary economist within the Classical tradition, has a very distinctive and different treatment of the quantity theory. He focuses on the transmission mechanism relating changes in the money supply to changes in the price level for a pure credit economy in the short run. Keynesian money demand theory: Classical quantity theory was criticized by Keynes [ 1 ], who asserted the usual absence of fully employment in the economy, and argued that output and velocity depend on the money supply. Keynes summarized three motives of holding money:. The transactions-motive , i.

The transactions motive is further separated into an "income motive" to bridge the interval between the receipt of income and its disbursement by households, and a "business motive" to bridge the interval between payments by firms and their receipts from the sale of their products.

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Hence, the transactions money demand rises as the nominal income, P t y t , increases. The transactions motive is essentially consistent with Classical quantity theory. To provide for contingencies requiring sudden expenditure and for unforeseen opportunities of advantageous purchases, and also to hold an asset of which the value is fixed in terms of money [ 1 ]. The speculative-motive, i. The individual has to make a decision between holding bonds and holding money, with a speculative motive to maximize the maturity value equal to principal plus interest.

As a result, the speculative money demand increases as the bond price rises, or conversely, as the interest rate falls. The main role of quantity theory is limited to a money demand theory. On the supply side, Friedman asserted that the determinants of the money supply are independent of those of the money demand. Friedman also argued that money demand and velocity function are highly stable, so monetary policy has a strong and reliable impact on the economy.

This is different from the early Keynesian viewpoints that these functions are volatile and that the monetary policy could not be a reliable stabilization policy, so fiscal policy is strongly preferred. Constant semi-interest elasticity of money demand: In the light of the original ideas developed by Classical, Keynesian and Monetarist, some popular partial equilibrium models are developed. His specification of the money demand function can be rewritten as:. Here, b is the "semi-interest elasticity" of money demand, because the magnitude of the interest elasticity rises as the nominal interest rate R goes up.

Rising price elasticity from a rising tax rate is a standard result in public finance literature. Therefore, the success of the Cagan model is that it treats inflation as a tax in a way that is consistent with fiscal tax theory. An example for this money demand function is shown below Graph 1.

The Demand for Money

Constant interest elasticity of money demand: These models, based on Baumol-Tobin framework, are more suitable for the scenarios when inflation is not significantly high, as opposed to Cagan model. Baumol [ 4 ] assumes that people have a steady flow of income over the period partial equilibrium , which can be either deposited in bank to earn nominal interest rate R or held as cash without any interest. The second conclusion is that the real money demand m takes a square root form.

It is positively correlated with real income and cost of banking while negatively correlated with the cost of interest. There are mainly two drawbacks on this model.

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  6. Secondly, the income elasticity is usually considered to be around 1 rather then 0. Should that not be the case, the velocity of money would go to zero or infinity. On the other hand, however, some argue that this is exactly how money demand should be analysed because of technological evolution. Woodford argues this as why the economy is moving to a moneyless world and that the velocity of money continues to rise for ever.

    There is little empirical support for these arguments and most studies still find income elasticity around 1. Tobin money demand: Money can be treated as a risk free asset when people allocate their wealth. It is a so-called asset approach to money demand. Money is desirable for its zero risk but undesirable for its zero return.

    Hence, the optimal portfolio between money and bond considers the trade-off between risk and expected return.

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    Money in the utility function MIUF model: The central idea is that there is a marginal condition along which the consumer makes the decision of how much money to hold, i. The marginal cost of money is the foregone interest from having to carry around money for use in exchange during the period. This opportunity cost is equal to the higher one between the bank savings account interest rate and the government bond interest rate. The marginal benefit of money is the key way in which the monetary economies differ.

    The benefit could be that money facilitates the exchange or reduces the shopping time. However, abstracting from the precise nature of the benefit, the MIUF simply states that money gives utility. The first order conditions give the marginal rate of substitution MRS between money and consumption is equal to the nominal interest rate:.

    However, this does not hold in general. A more fundamental problem is that the money demand is not well defined at the Friedman optimum, i. We can equivalently rewrite all the period budget constraints by one "intertemporal budget constraint" using no-Ponzi game condition, i. On the one hand, we can derive the Intertemporal Condition , which implies that the market discount rate is equal to the subjective discount rate in steady state:.

    This condition is the same as that in Samuelson, i. This is because the condensed budget constraint in this dynamic problem is exactly the same as that in the static problem, i. The money demand and elasticities can be derived once specific utility function form is given. Substitute this utility function into the general conclusions above to obtain the money demand and elasticities with a constant interest elasticity feature:.

    Lucas discusses how this specification is not realistic at low nominal interest rates in the sense that Friedman optimum does not hold. To deal with this problem, he considers an example in which government consumes a fraction of resources and the resulting optimal nominal interest rate is above 0.


    Substitute this utility function into the general conclusion to obtain the money demand and elasticities with a constant semi-interest elasticity feature:. This gives an interest elasticity of money demand, which will rise in magnitude with R as in Cagan. Cash-in-advance model: Transactions motive is the main purpose of holding money when money is the only means of exchange.

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    Cash- In-Advance CIA model assumes that good can only be bought by money and the balance of money is determined in previous period.