Monday, March 30, 2015

Central Banking: The Basics

1. Credit Fluctuations and Financial Crisis

Last post, we discussed the role of fluctuations in total credit extended to the value of production and also to the total money stock. When credit is expanded, this is typically indicative of an increase in the value of production. This can occur either through an increase in production itself, an increase in prices, or an increase in demand for cash balances which may lead to an increase in demand for credit assuming that prices do not immediately adjust to accommodate the change in demand for money. The relation between credit and money implies a relationship between aggregate demand and credit. When the volume of credit extended increases on net, this is equivalent to an increase in the money stock, and therefore an increase in aggregate demand (MV). Thus, changes in the credit stock, absent a change in demand for money, shifts the aggregate demand curve in the same direction. After a period where credit has been misallocated, something only discovered ex post, there must follow a contraction as the value of collateral adjusts to reflect underlying demands of the economy. While this process works to reallocated resources to their most highly value use, the fall in credit also precipitates a fall in income. Falling incomes encourages agents and firms to take a more conservative stance financially until they expect that the crisis is nearing an end. This tendency creates aggregate oscillations known as the business cycle. We will discuss the business cycle in later posts. For now it is sufficient that we recognize that the phenomenon exists.

When these oscillations in the volume of available money and credit grow extreme, banks that might otherwise be economically sustainable risk default. The same holds true for other businesses. In the worst case, these fluctuations may create a wave of insolvencies that turn a minor crisis into a financial pandemic. Nominal fluctuations begin to affect the structure of the real economy. This is what occurred in the recent crisis. Many large financial firms were holding bundles of AAA rated mortgage backed securities. The AAA rating hid from non-critical observers the risk contained in these securities. Before the crisis in 2007 and 2008, banks held these securities were able to acquire very high levels of leverage. The ratio of debt to cash on hand grew to dangerously high levels. When the value of these assets collapsed, leverage levels increased as many of these firms were on the brink of collapse. Assets that had served as money – mortgage backed securities – fell in price. This was equivalent to a drop in the broader money stock as it necessitated a contraction of credit in order for the system to stay solvent. In order to avoid collapse, the Federal Reserve provided the market with liquidity by buying up “toxic” assets, i.e., the overvalued mortgage backed securities. Ignoring the politics that were at issue, we observe that the Federal Reserve was, in an unorthodox manner, serving the role of lender of last resort.

2. The Central Bank and the Money Stock

The central bank’s primary means of policy implementation depends on its control of the money stock. This control provides it the ability to intervene within a market. There are 3 means by which a central bank typically intervenes.
a. Discount Rate 
The central bank lends money directly to other banks through the discount window. In the early days, this was the central bank’s primary means of intervention. It has come to play a smaller role in the modern environment. 
b. Open Market Operations 
This is a favorite tool of central banks. Open market operations is the general process in which central banks engage when they buy and sell debt on the open market. If the central bank purchases debt, it has increased the monetary base, usually with the expectation that this increase will promote credit creation. If the central bank sells, bonds, it diminishes the base money stock and, by so doing, discourages the creation of new credit. Most central bank policies imply an inflationary bias, so this latter case is less common. 
c. Reserve Requirements 
The central bank can influence the broader money stock by changing the proportion of commercial bank liabilities that are required to be held with the central bank. By increasing reserve requirements, the central bank contracts the total money stock. By decreasing reserve requirements, the central bank enables the expansion of the total money stock.
3. The Central Bank as the Lender of Last Resort

The lender of last resort role is probably the strongest justification for central bank management of the money stock. During a crisis, banks need liquidity. Under some banking regimes, private banks collectively established institutions that stabilized the banking system during crises (as we will see next post). The norm has been for governments to establish a central bank.

The central bank is responsible, not only for providing liquidity during a crisis, but also to manage the base money stock. This is of particular significance for the functioning of credit markets. If a bank or banks risks collapse, cannot acquire credit, and appears to be solvent, the central bank’s role is to provide temporary liquidity to the institution. This function provides stability to the system during periods of credit collapse.

a. Moral Hazard 
The lender of last resort role creates a problem of second-order: moral hazard. In a system where stability is provided privately, provision of liquidity is constrained by expectation of repayment. This expectation is formed by the creditor’s local knowledge of the bank receiving emergency funds. In the private system, this role is decentralized as major players within different banking systems (networks) play the role of lender of last resort. The implementation of a central bank degrades this local knowledge and distorts incentives. Banks with relatively high levels of risky assets might not receive credit under the private system. They are more likely to receive credit under a system of central banking as 1) politics plays a greater role in allocating credit and 2) private bankers and investors may form the expectation that the central bank will always provide them liquidity. This encourages private banks to extend more credit than they would otherwise.
4. Relative Prices and the Flow of Goods and Currency
a. Fixed Exchange Rates (Gold Flows) 
During the years of the gold standard, this role was fulfilled by adjusting the base money stock according to business conditions. This might lead to fluctuations in the reserve ratio as well as gold flows. Under this system, exchange rates could not adjust to bring international prices to parity. Instead, prices denominated in gold were brought into parity by arbitrageurs.

One part of this process is the price-specie-flow mechanism. Let us assume that the economy is in equilibrium. If the central bank increases the portion of the base money stock comprised of paper money absent a change in the gold stock, this will tend (though not always) to promote credit creation and increase prices within the nation. This leads to discrepancies between the prices of domestic goods and goods from abroad. The discrepancy in prices encourages gold to flow out of the country to other nations where prices are lower and goods are therefore cheaper. Domestic interest rates are also depressed, thus encouraging gold to leave the country. Likewise, a contraction of the paper money by the central bank will lead to a domestic deflation which encourages the flow of gold from foreign countries into the domestic economy.

In the long run, the price of any like goods tend to equalize. This gives rise to purchasing power parity. Traders can earn a profit by purchasing goods or claims to goods in a country where prices are relatively lower and selling them in countries where prices are relatively lower. This shifts demand away from the more expensive goods and toward the cheaper goods which diminishes the discrepancy in prices. This long-run tendency is the process on which the law of one price depends. Anywhere where there is a discrepancy in the price of goods represents a profit opportunity. Consequently, in a gold standard world, gold has only one international price, deviations from which are constrained (Samuelson 1980).
b. Floating Exchange Rates 
For the most part, central banks no longer hold gold. They hold currency and debt, both foreign and domestic, as the large share of their assets. The effects that operated under the gold standard still effect prices, but these changes tend to be swamped by swift changes in exchange rates. If a central bank increases the money stock, ceteris paribus, then we can expect that prices will tend to rise on average. The currency loses value. If the exchange rate of the currency adjusts before domestic prices, then there exists an arbitrage opportunity for investors who purchase these domestic goods and sell them abroad. Under the gold standard, fixed exchange rates led goods to flow into the country as prices rose. Relatively cheaper foreign goods would flow into the country engaged in inflation. With no fixed exchange rate, however, the flow of goods out of the country whose currency has devalued relative to other currencies is the consequence of inflation.

5. The Federal Funds Rate

In the United States, the Federal Reserve sets a target for the Federal Funds Rate. This is the rate at which banks lend to one another, often overnight. Since new money first comes into possession by banks that sell assets to the Fed, this rate is relatively responsive to changes in the money stock.

6. Types of U.S. Government Debt

The Federal Reserve usually expands money by buying government debt. This debt is divided into 3 categories
a. Treasury Bills 
This is comprised of debt that matures within one year. These represent the bulk of debt purchases by the Federal Reserve. 
b. Treasury Notes 
Treasury notes include debt that matures in 1 to 10 years. 
c. Treasury Bonds 
Treasury bonds mature in greater than 10 years.

Wednesday, March 25, 2015

Money and Credit: Origins, Instruments, and Dynamics

Banking

When money first arises, agents must find a way to economize on cash balances. Agents can hold on to commodities, but this is a risky practice. Commodity money may deteriorate or be lost or stolen. Theft was especially a problem for those making long trips through the countryside. Holding on to cash balances is costly. Early on, agents realize this. Those with enough wealth begin to keep their money with a trusted third party. Historically, when gold came into use as money, agents left their gold at a warehouse in exchange for a deposit slip. These deposit slips served a role as a medium of exchange. If the warehouse has multiple branches, the deposit slips might be exchanged at another branch, thus increasing the marketability of the slips by diminishing agents’ incentive to discount the them. These slips are part of a more general class of money known as fiduciary currency (the root of the word fiduciary comes from the Latin word for “faith”). These are promises to repay.
                
Eventually, the keepers of the warehouses realize that they can lend the money entrusted to them so long as depositors do not rush all at once to retrieve their commodity money. This is fractional reserve banking. Banks hold some portion of their reserves (the money lent to them) while lending the remainder. This allows cash to be employed when it would otherwise sit in reserve. For depositors, this diminishes the cost of holding cash balances. In a gold standard world, for example, instead of holding and exchanging in actual gold, agents can exchange deposit slips. Meanwhile, they earn interest on the money that they have temporarily relinquished to the bank. This creates a tendency for the total money stock, which in our example is the total gold plus the total amount of deposit slips to fluctuate due to changes in demand to hold currency. We measure the relative size of the total money supply by comparing the base money stock to the total amount of money in circulation.

MT= MB / r
               
Where:
MT = Total Money Stock (MB + Liquid Credit Instruments)
MB = Base Money
r = Reserve Ratio (Aggregate)

The logic here is straightforward. Collectively, banks collectively form an aggregate reserve ratio. It is defined by the amount of currency they have on hand divided by their total liabilities. Monetary dynamics fall out of this identity. When banks extend credit on net, the reserve ratio drops. When banks contract credit on net, the ratio increases. When agents deposit currency on net, the ratio increases. When agents withdraw currency on net, the ratio falls (Hawtrey 1919).

We might also think of the reserve ratio as its inverse: the money multiplier. This represents the ratio of total currency to base currency. The ratio of currency to deposits plays an important role in this identity as it allows us to observe the effect of a change in currency or deposits on the money multiplier.
Mt = C + D
Mb = C + R
Mt/Mb = (C + D) / (C + R)
Mt/Mb = (C/D + 1) / (C/D + r)
Where:
Mt / Mb = Money Multiplier
C = Currency
D = Deposit 
*Other variables defined as above

Notice that the numerator is larger than the denominator as long as r < 1. This means that as C increases, the denominator grows at a faster rate than the numerator. The money multiplier falls under this scenario. Likewise, as the total stock of currency shrinks, the money multiplier grows. Similarly, as the amount of deposits decreases, the denominator, C/D + r, grows at a faster rate than the numerator. The money multiplier falls. As deposits increase, the money multiplier also increases.

Unspent Margin: Cash Balances, Money on Account, and Substituting for Available Credit Lines

Agents respond to the incentives of this relatively flexible system. We assume that agents economize on cash balances. That is, they decide to hold cash for several reasons. Agents receive income in discrete units, so they must build up reserves in preparation for periods where income has yet to be received. Agents also hold currency or deposit balances in order to hedge for risk. Last, agents deposit their currency in discrete quantities. (This was more important before the development of direct deposit and electronic quasi-monies.) Agents may economize on cash balances by leaving their money on deposit to collect interest. They may also choose to allot some wealth to long-term investments where it collects more interest than an ordinary demand deposit account. They may also choose to substitute an available credit line for balances of cash or deposits. By doing this, an agent may collect a higher yield from long-term investments while still having ample liquidity to deal with fluctuations in their own demand for money.

The unspent margin serves as analytical proxy for demand for money. First we must identify the unspent margin. “The unspent margin is equal to all the cash, whether in circulation or in the banks, plus the net interest bearing assets of the banks (Hawtrey 1919).” The unspent margin represents portfolio demand for money. In a world where credit influences the money stock, a net increase in loans by the banks will first have the effect of increasing the unspent margin. When credit is expanded without being exchanged for goods, the credit represents an increase in the money stock with an offsetting expenditure. Demand for money increases (velocity falls) as a result. A contraction of credit represent a fall in demand for money. Demand for money falls as agents relinquish cash to the bank and the bank fails to offset the decrease in liabilities. In either case, prices must adjust to in order to facilitate the exchange despite a change in the money stock.

It is from this pattern that Hawtrey made an observation concerning the relation between incomes and changes in credit.

Apart from this shuffling of debts, all the credit created is created for the purposes of being paid away in the form of profits, wages, salaries, interest, rents – in fact, to provide the incomes of all who contribute, by their services or their property, to the process of production, production being taken in the widest sense to include whatever produces value. It is for the expenses of production, in this wide sense, that people borrow, and it is of these payments that the expenses of production consist. So we reach the conclusion that an acceleration or retardation of the creation of credit means an equal increase or decrease in people’s incomes.


In the world that we have constructed thus far, exchange only occurs when both agents expect to profit. This implies an expectation of the lender that the borrower has or will earn the means to repay the loan at a later date. The borrower will typically produce goods or provide services in order to raise the income required for repayment. In a world of voluntary exchange, then, incomes rise and fall with increases and decreases of the credit stock as this reflects changes in the expected value of production.

Monday, March 23, 2015

The Nature and Role of the Interest Rate

What is Interest?

When an agent owns wealth, whether in the form of a commodity or currency, he or she may decide to temporarily relinquish control of his or her asset in exchange for a return whose value is dependent upon the length of time for which the asset is relinquished. The value of the return divided by the original investment – the value of that which was lent – represents the rate of return. The rate of return implies a time period over which investment occurs. Typically this period is one year. If the rate of return is 10%, an agent who invests $100 or an asset worth $100 in year one receives a value of $110 in year two. The rate of return in this sense is a rate of return for an individual investment. We might weight the returns from an agent’s investments to calculate an average rate of return for an individual agent or we might attempt to calculate the rate of return for the market as a whole. The latter of these is known as the market rate of return.
                
When working with the rate of return, either for analysis of the past or estimations of the future, we use the equation for present-value. In its simplest form, we compound over one year (period):

PV = FV/(1 + r)

Where:
PV = Present Value
FV = Future Value
r = Interest Rate

We can use this equation to estimate the rate of return for any investment, monetary or otherwise. Alchian and Allen (1983, 108) show us that we might calculate the rate of return using physical assets. This is known as an own rate of interest. (For a discussion of own rates see this post from David Glasner). Imagine that we have 3 pound of grapes. That one pound of grapes might be sold immediately or they might be processed for a year and sold as a bottle of wine. Let us assume that, aside from time, this process is costless. In this case, the present value of the grapes is equal to the price they would sell for on the market. The future value is equal to the price that a bottle of wine is expected to fetch one year from the present. If the bottle of wine is expected to sell for $1.10 and the three pounds of grapes is expected to sell for $1.00, then we again have a case where the expected rate of return is 10%:

1 + re = $1.10/$1.00
1 + re = 1.1
re = .1

This calculation can also be performed ex post in order to compare the actual return to the return on another investment.

Recall that agents achieve profit by transforming the present state of the world into one that they prefer more greatly. Interest helps to expand this definition of profit. We can now imagine not only a transformation of the present state, but so also the exchange of expected states in the future. If an agent comes to realize a return that is less the market rate of return, she may choose to invest in assets whose returns she expects to at least match the market rate of return. This exercise in arbitrage is what drives the market toward an equilibrium state so long as expectations are convergent; that is, so long as agents’ expectations about the present state of reality and its future unfolding tend to cohere with one another. This is not an unreasonable assumption as those who fail to predict the future state of the market will tend to be out-competed by those who do. In the short run, extreme, even systematically destabilizing outcomes may occur. We should beware against ignoring context and process by turning belief in market efficiency into a tautology. (For more on expectations, see Koppl 2002; Koppl and Butos 1993)

The rate of interest emerges as a result of agents’ time-preferences. Given one’s context, an agent reflects time preference in his or her decisions to refrain from consumption or not. If an agent refrains from consumption and invests his or her wealth for a period of time, that agent increases the availability of loanable funds. Assuming normal conditions – i.e., the future is expected to look mostly like today – a typical agent demonstrates positive time preference. He prefers having goods in the present to having the same goods in the future. Absent other influences, this results in a positive rate of interest. It is possible that markets might arrive at a negative rate of interest, but this categorically cannot be the result of an inversion of time-preference where agents prefer a state in the future to an otherwise identical state in the present. This positive time preference leads agents to invest so long as they receive a positive rate of interest.

The other, secondary determinate of the interest rate is the productive sector. If agents are lending their wealth to other agents with expectation of a certain rate of return, then agents who are borrowing expect either to earn higher rate of return. If this expectation is incorrect, the borrower will incur a loss, and in the worst case, default. For now we deal with the first case. Time preference is reflected by the supply of loanable funds, investment opportunities determine the demand for loanable funds. If an increasing number of agents expect that rate of return in the market will be greater than the interest rate, the demand for loanable funds will increase (See Figure 1). The rate will tend to rise until agents, in aggregate, no longer expect a rate of return higher than the interest rate. Likewise, the interest rate will fall if agents, in aggregate, expect that the rate of return will be less than the market rate of interest. (This analysis may be further complicated by differing expectations for a variety of time horizons. For simplicity, I leave this case out.)

























Figure 1

Natural Rate of Interest

The interest rate plays a significant role in coordinating investment across time. Of particular concern in the natural rate. Wicksell explains,

There is a certain rate of interest on loans which is neutral in respect to commodity prices, and tends neither to raise nor to lower them. This is necessarily the same as the rate of interest which would be determined by supply and demand if no use were made of money and all lending were effected in the form of real capital goods. It comes to much the same thing to describe it as the current value of the natural rate of interest on capital. ([1898] 1936, 102)

The natural rate of interest is the rate of interest that would exist absent nominal factor such as fluctuations in the money stock or fluctuations in demand for money. The nominal rate of interest is thought to fluctuate within proximity of the natural rate and is ultimately bounded by the natural rate. In the long run, the natural rate constrains the viability of particular investments, although in the short-run profits might be made from investments that are unsustainable. If a tendency arises for unsustainable investment projects to receive funds, this will eventually be checked by liquidity constraints. A rising interest rate thus reveals this problem and forces funds to be allocated away from those projects.

Real and Nominal Rates

Interest rates are observed in nominal form. This means that the observed rate of interest can, and typically does, deviate from the natural rate, defined in terms of a real rate. In equilibrium, meaning all exchanges have been made and under conditions where perception and expectations cohere with objective reality, the observed rate is equal to the sum of the real rate and the inflation rate. This is known as the Fisher Equation

i = r + π

                Where:
                                i = Nominal (Observed) Interest Rate
                                r = Real Interest Rate
                                π = Inflation Rate


Through a process of trial and error, agent action factors the average rate of inflation into the money rate of interest. Within this construct, the money rate of interest converges with the natural rate of interest.

To sum, the interest rate is emerges as the result of positive time preference. Individuals value present goods over future goods. The interest rate tells us by how much agents, on average, these agents prefer the future to the present. A secondary factor of influence over the interest rate is the rate of return on investments in the market. If opportunities for profitable investment, in terms of dollar value, are expected to exceed the rate of return, this pushes the rate of interest upward. Likewise, if there is a general expectation that the value of investment opportunities are shrinking, this will push down the rate of interest. In the long run, the interest rate will tend to reflect the real return on capital. Nominal factors such as changes in demand for money and changes in the available money stock tend to produce short-run deviations away from the natural rate. These fluctuations tend to be limited by liquidity restraints and are mitigated by a short-run rise in the interest rate. In the long run, inflation will be factored into the observed rate such that observed rate of interest is equal to the sum real rate and the nominal rate of interest. Finally, the reader should be aware that this analysis occurs within a static framework and ignores complications that arise due to destabilizing events such as herding, distortions from Big Players, political, economic, and/or natural disasters, etc... These additional sorts of details require a careful study of history and the use of simulation to further our understanding.

Tuesday, March 3, 2015

Say's Principle and Macroeconomic Analysis

In his 1936 treatise, Keynes formulated Say’s Law as proposing that “supply creates its own demand.” It is not clear exactly what Keynes meant by this. The statement implies an assumption of equilibrium where all excess demands are zero. That is, if supply creates its own demand, than quantity demand of a good and the quantity supplied must be equal. This is at worst a misrepresentation of Say’s Identity and at best an incoherent statement that appeared in one of the most popular economics treatises in history.

What is Say’s Law and why does it matter? In A Treatise on Political Economy, Say argues
A man who applies his labour to the investing of objects with value by the creation of utility of some sort, can not expect such a value to be appreciated and paid for, unless where other men have the means of purchasing it. Now, of what means do these consist? Of other values of other products, likewise the fruits of industry, capital, and land. Which leads us to a conclusion that may at first sight appear paradoxical, namely, that it is production which opens a demand for products.
Ultimately, goods must pay for goods. If an agent wishes to purchase a product, he or she must either exchange another good directly for the desired good or else acquire by exchange money to purchase the item. Confusion arises when money must be integrated into the framework. Unfortunately, Say does not do a good job of explaining the significance of money within this schema.

Thus, to say that sales are dull owing to the scarcity of money, is to mistake the means for the cause; an error that proceeds from the circumstance, that almost all produce is in the first instance exchanged for money, before it is ultimately converted into other produce: and the commodity, which recurs so repeatedly in use, appears to vulgar apprehensions the most important of commodities, and the end object of all transactions, whereas it is only the medium. Sales cannot be said to be dull because money is scarce, but because other products are so. Should the increase of traffic require more money to facilitate it, the want is easily supplied, and is a strong indication of prosperity – a proof that a great abundance off values has been created, which it is wished to exchange for other values.

Say’s description implies that he understands that there can be an excess demand for money that raises money price. That increase in price will encourage an increase in the available money stock. Having brushed off the problem of insufficient demand by relying on an invisible-hand process, Say give a less than satisfactory supply-side argument for explaining general gluts.

It is because the production of some commodities has declined, that other commodities are superabundant. To use a more hackneyed phrase, people have bought less, because they have made less profit; and they made less profit for one or two causes; either they have found difficulties in the employment of their productive means, or these means have themselves been deficient.

Say describes here a misallocation of resources that only adjustment of price, and subsequently, of the capital structure can fix. It is possible however, that the processes that coordinate market activity might be interrupted by extreme swings in demand for money. It is this problem for which Leijonhufvud and Clower’s extension of Say’s Law as “Say’s Principle” (they refer to it as SP) provides a clear explanation.

Leijonhufvud and Clower describe Say’s Principle first in terms of individual agents. The core of their claim goes that “the net value of an individual’s planned trades is identically zero.” Individual agents make decisions concerning the allocation of their money. An agent may decide to spend all available money on goods and hold no cash on hand or he may decide to withhold some amount of money for safe-keeping. In the latter case, the agent has a positive portfolio demand for money. Algebraically, the authors represent this budget constraint in a system of exchange where such a constraint is implied by secure property rights:

               Pxdx + pydy + dm– sm,0 = 0

They explain further in terms of common interpretations,

‘No one plans to supply anything of value without also planning some use for the proceeds from the sale, which may include simply planning to hold money until a later decision is made to purchase other commodities.’ This statement is correct and sensible.”

‘Confronted with given prices, each transactor must plan to supply commodities of sufficient value to finance all his planned net demands.’ This statement is also correct.

If you have not intuited this by now, understand that Say’s Principle is simply an observation of agent action given a budget constraint.

When money is not included as the “mth commodity”, it is possible that excess supplies of goods can exist. However, when money is included we find that all excess supplies are equally offset by excess demands for goods. This is of special significance if one is to understand macroeconomic fluctuations. Distortionary representations of Say’s Principle connect the identity to an equilibrium assumption. This seems to be what Keynes was implying. Say’s Principle, however, is in no way dependent on an assumption of equilibrium. Rather, it is an observation. Movement toward equilibrium requires some minimum threshold of convergent expectations amongst the population of agents as well as some combination of flexible prices and an endogenous money stock.

Money is different from all other goods in that it comprises one side of every monetary exchange. For this reason, we may separate economic goods into two categories for the sake of analysis. There is 1) money and then there are 2) all other goods. The value of goods in the second category are enumerated in a given currency unit. An excess supply of any good occurs when agents plan, in aggregate, to purchase less of the commodity than is available at a given price. This leads, by definition, to an excess demand for the “mth” good, money, meaning that at given the current constellation of prices, agents demand more money than is available. This will tend to push the price of money – the amount of goods that money exchanges for – upward and, conversely, the prices of commodities downward. This does not mean that the price of all commodities will necessarily fall, but that there will be deflationary pressure as the real stock of money (M/P) is others unable to facilitate exchange of goods until either prices have fallen or the nominal money stock (just M) rises. Until the problem is corrected, there will be a fall in output and employment of both labor.

We can illustrate Say’s principle with graphs of the money stock and of aggregate supply and demand. Those of you reading last week should recognize these graphs.



This represents an economy where agents have elected to increase the nominal value of their dollar holdings. Before prices adjust to reflect this change, there will be 1) and excess demand for money and 2) an excess supply of goods. Not enough money exists to facilitate exchange until prices drop. Eventually, prices must drop in order to clear available inventories. If the general fall in prices takes an extended period of time to occur, then there will be a depression: an extended fall in real output. This comes with an increase in unemployment and a fall in living standards for those agents not prepared for the depression.
   
Two solutions to this problem have been discussed. Either prices can fall to alleviate growing inventories or the money stock can increase. This has policy implications. 1) A central bank can attempt to alleviate, either in whole or in part, fluctuations in demand for money. The most popular formulation of this proposal is that the central bank should attempt to stabilize MV by adjusting M to offset changes in V. Leijonhufvud and Clower note some historical skepticism about this approach:

. . . Its use raises other issues. To whom is ‘the engine of inflation’ to be entrusted? What limits to that party’s discretionary use of the throttle would it be advisable to impose? . . . Reliance on the automatic solution, in this [classical] view, is argued to be the lesser of two evils.

Perhaps a better solution to this problem is to enact policies that enable the money stock to automatically fluctuate according to changes in demand for it. This might include the removal, or at least minimization, of barriers to liquidity that discourage asset owners from converting those assets into cash (i.e., the capital gains tax and legal restrictions applied to particular classes of assets). Another significant element in promoting a robust economy is the facilitation of expectation formation in regard to public policy. Government agencies are “Big Players” whose plans and actions are considered by agents in the formation of their own expectations (Koppl 2002). If “Big Players” act unpredictably, agents will be less able to coordinate. If these “Big Players” are unable to accommodate this need due to the nature of the political process, then there may be a case for a shrinking of the scope of influence for these government agencies. Of course, this is not to deny that it is possible that changes in government structure might also accommodate this need, but this is even more difficult of a task to accomplish.

I leave you with Say’s perspective concerning this problem.


. . . Wherever , by reason of the blunders of the nation or its government, production is stationary, or does not keep pace with consumption, the demand gradually declines, the value of the product is less than the charges of its production; no productive exertion is properly rewarded; profits and wages decrease; the employment of capital becomes less advantageous and more hazardous; it is consumed piecemeal, not through extravagance, but through necessity, and because the sources of profit are dried up. The laboring classes experience a want of work; families before in tolerable circumstances, are more cramped and confined; and those before in difficulties are left altogether destitute. Depopulation, misery, and returning barbarism, occupy the place of abundance and happiness.

Wednesday, February 25, 2015

Upward-Sloping Short-run Aggregate Supply

Today we add short-run aggregate supply (SRAS) to the analysis. The short-run aggregate supply curve is tricky to justify theoretically. Given an increase in the money supply, the SRAS convey that total output increases as a result of increase in aggregate demand and a delay in price adjustments. It is convenient to think of this in terms of nominal income and then consider the behavior of the individual variables.

Imagine that there is an increase in the money stock of 5%. Given the log-derivative of the equation of exchange, this looks like
%∆M + %∆V = %∆P + %∆y
Rewrite as:
%∆M + %∆V = %∆(Py)
For now, let’s assume that portfolio demand for money is constant. Now,
%5 + %0 = %∆(Py)
%∆(Py) = %5
Within a static model, we know that in the long-run, the price level will absorb the entirety of the change, and that y remains unchanged. This is known as the classical dichotomy. Often rendered, “Reals affect reals, and nominal affect nominal.” In the real world, however, we see that nominal changes have real effects. A more realistic rendition states, when the economic activity is in something close to an equilibrium condition, changes in nominal aggregates do not lead to long-lasting changes in a given measure of aggregate output. It is possible that at first a change in y comprises some portion of the change in the nominal income. In the long run, y returns to its original level as prices come to fully reflect the increase in the money stock.

A thought experiment is enough to convey the nature of short-run effects. Imagine that, over night, Hume’s money fairy has increased everyone’s money balances by exactly double. If, at the moment this occurred, not before, all agents became aware of this doubling, there would be no effect on the allocation and employment of resources. Now, let’s imagine that our agents only become aware of this slowly. Some agents are able to spend the money before prices rise. Of course some suppliers have become aware of this change, but certainly all of them have not. At least some of those who recognize their increase in cash balances will make purchasers from those suppliers who have not changed the price. These suppliers may even believe that there has been an increase in demand and will sell more than they would have if that had realized that they suffer from “money illusion.” This leads to a temporary increase in output that will last as long as suppliers do not increase their prices. Eventually, competition and a need for solvency forces them to act in accordance with economic reality. Prices rise and output falls back to its long-run level.

As prices rise, there is no reason to expect that all prices move in the same direction at the same time. It is possible that a substantial portion of the increase in money is used to purchase only one or a few types of goods. These markets receiving the new money will increase prices more quickly than those that do not. For example, the doubling of the money stock might increase the price of luxury goods by 3 or 4 times since those who discover the new money early on feel richer. Relative prices shift as money enters the economy through the purchase of specific goods.

As prices rise, not only are relative prices distorted, but so also is the function of profit. Profits appear to be augmented by the price increases, but again, this is only due to "money illusion." Irving Fisher’s observation is of help to us:

“I remember particularly a long talk with one very intelligent German woman who kept a shop in the outskirts of Berlin. She gave all kinds of trivial reasons for the high prices. . . When I talked with her the inflation had gone on until the mark had depreciated by more than ninety-eight per cent, so that it was only a fiftieth of its original value (that is, the price level had risen about fifty fold), and yet she had not been aware of what had really happened. Fearing to be though a profiteer, she said: ‘That shirt I sold you will cost me just as much to replace as I am charging you.” Before I could ask her why, then, she sold it at so low a price, she continued: “But I have made a profit on that shirt because I bought it for less.

 She had made no profit; she had made a [economic] loss. She thought she had made a profit only because she was deceived by the ‘Money Illusion’. . She had kept her accounts in what was in reality a fluctuating unit, the market. In terms of this changing unit her accounts did indeed show a profit; but if she had translated her accounts into dollars, they would have shown a large loss. . . ” (392)

I am an economist by training. I don’t think in terms of price levels in my day to day life. I notice that the prices of goods change from time to time. Some of the change may be due to an increase in the money stock. Some may be from changes in demand due to preferences or to supply shocks. A change in price tells us nothing about why a price has changed. Uneven adjustment of prices changes the nature of monetary exchange. Humans think in terms of observed nominal prices. Losses are easier to stomach when they are written on a balance sheet as a nominal gain, as Fisher’s story shows. Even if all agents came to know of the increase in the money stock beforehand, their preparations cannot prevent the realization of errors in prediction of prices of specific goods that are inevitable for the vast majority of agents. Agents with expectations of an increase in the money stock cannot necessarily prevent a temporary increase in AD. Distortion of the profit and loss mechanism promotes this outcome.

Now that we've worked through this thought experiment, we are ready to consider what happens by considering a graph of aggregate demand, short-run aggregate supply, and long-run aggregate supply. We consider an increase in aggregate demand.




Two effects are working here. The short run effect, which temporarily elevates y, and the long-run effect, which dominates the short-run effect having P absorb the total change in the money stock. It is important that we do not interpret long-run and short-run as representing specific time span. These are categories that describe types of change. The long-run is the state to which the model eventually converges. Long-run changes always swamp short-run changes. It is possible that long-run effects set in very quickly so that short-run changes are hardly observed. Or short-run changes may last for an exceptionally long period of time. There is no measurement of time that can consistently define the long-run and short-run. 

Tuesday, February 24, 2015

Dynamics of Aggregate Demand

Money may be thought of as the life blood of any economy. Possession of money by an agent empowers that agent to coordinate resources and even other agents. It is a mistake to look at money only as one good among money. This perspective may aid analysis of changes in the value of money and its allocation, but they only partly capture money’s influence. Money is the universal numeraire. It is the measuring rod that aids economic calculation. In every exchange that occurs in a monetary economy, money is one side of transaction – the other side being the good or service offered in exchange for money. Given this feature, a dichotomy arises between the demand side and the supply side of the economy. The demand side is represented by the money that is available to be used for the purchase of goods and services. The supply side is comprised of the flow of existing goods over some time period and the stocks already on hand. To avoid shortages or surpluses, sellers of goods must adjust prices to accommodate changes in demand for goods. Markets also experience fluctuations in aggregate demand as 1) the money stock fluctuates and 2) general demand to hold money changes. That is, the tendency of agents to collectively decrease or increase consumption over a period is reflected by fluctuations in total expenditures of all agents.

Those of you who are familiar with macroeconomics or have been engaging the previous posts in thorough dialectic will, I hope, see what this implies for macroeconomic analysis. The equation of exchange helps us to identify the aggregate demand and aggregate supply. Recall that MV = Py. Total expenditures on final goods and services is equal to the nominal value total income. For the exercise, let us assume that the economy is static so as to avoid analytical problems that arise from innovation. For now, we will assume that prices adjust to accommodate changes in the supply of and demand for money. Of course, the store owner would likely never imagine that he is accommodating these changes. She instead adjusts price of the good based on changes in available stocks of the good itself as well as changes in the price inputs. She also accounts for expected changes in demand for the good at the given price. Remember, as Hayek (1945) argues, that suppliers need not know the source of a price change. They only need to correctly interpret an appropriate cue or cues that helps them adjust prices to prevailing conditions. In this early analysis, we shall make the grandiose assumption that prices adjust instantaneously. In the future, we shall consider situations where the given array of prices produce excess supplies of goods. For now, we will consider the nature of changes in the aggregate demand curve both at the instance of the change and the equilibrium outcome results.
               
Now we have appropriately identified our objects of analysis and the objects that comprise them, we may move forward in employing the aggregate variable M, V, P, and y. Aggregate demand and aggregate supply are both described in P-y space. As mentioned above, the aggregate demand curve is defined by total outlays, MV. The curve intersects the long-run aggregate supply (LRAS) curve at some price level comprising the equilibrium state. The value y* at this point is the value of real income in the long-run. At this level, the economy is said to be at full employment.
                




Figure 1
The aggregate demand curve falls as a result of an decrease in either the money stock, M, or an increase in demand for money (equivalently a fall in velocity). In Figure 1, the AD curve falls, but the reason is not indicated. For the sake of analysis, let us assume that this change was either entirely the result of a fall in the money stock or an increase in demand, but not a combination of both. Possible changes in the composition of total expenditures, MV, that yield this result are shown below in Figures 2 and 3.
Figure 2

                    
Figure 3
The effect of changes in total expenditures is dependent upon the nature of subsequent price changes. If adjustment of prices is instantaneous, than there will be no change in y. Iif agents perfectly predict changes in prices given a change in the money stock or a change in demand for money, there will be no temporary change in output. This is the long run effect of changes in these variables, given that complications do not arise within the capital structure. (Say a wave of bankruptcies results from an increased rate of insolvency. Contracts are typically set in nominal, not real terms. In that case, nominal changes can, therefore have real effects.)

If prices do not instantly adjust, then we are left with an excess demand for money and an excess supply of goods. The excesses perfectly offset one another. The value of the excess demand for money [Figure 4] is equivalent to the value of the excess supply of goods [Figure 5]. This can only be alleviated by an adjustment in the price level – i.e., adjustment of all prices to cohere with the new allocation of money. The process of the opposite adjustment works in reverse. An increase in AD brought about by a fall in demand for money or an increase in the money stock will create excess demand for goods and an excess supply of money. As with the previous example, this will eventually be offset by changes in prices. (You  may want to refer back to this paragraph in the coming discussion of Say’s Principle.)
 Figure 4
Figure 5

A final warning. The process of adjustment in a real economy is not as smooth as aggregate analysis might suggest. Remember that this is a tool for conceptualizing aggregate changes in a monetary economy. A change in the price level tells us little about changes in relative prices (price ratios). These will be considered in the section on monetary policy under the heading of the non-neutrality of money.

Thursday, February 19, 2015

Intuitive Sums: Making the Equation of Exchange Easy to Interpret

Today I’m going to work some fast math magic. Yesterday I reviewed the equation of exchange. Working with the products can be somewhat confusing. So, briefly, I will show the reader how to transform the equation of exchange into (approximate) sums of percent changes. The process is straight forward.

1. Begin with the equation in its basic form
MV = Py
2. Log both sides
ln(MV) = ln(Py)
3. Convert into sums of logs
ln(M) + ln(V) = ln(P) + ln(y)
4. Take the first derivative of both sides
(dM/M) + (dV/V) = (dP/P) + (dy/y)
5. The result is approximately the sum of percent changes
%∆M + %∆V = %∆P + %∆y
6. Rearrange so that desired variable is on the left hand side of the equation. I’ll leave this last step to you.
Notice that this is useful for setting up a regression. If you have data for the 3 variables, you can estimate the fourth. It should be kept it mind that measures of velocity tend to be measures of this sort. If I were to attempt to measure changes in velocity, the form of the equation would be,
%∆V = %∆P + %∆y - %∆M.
Notice that this is similar to the log version
ln(V) = ln(P) + ln(y) – ln(M).
A regression with the log measures will estimate the log of velocity while the equation using the derivative of the logs will estimate percent changes.

One last trick: P and y can be merged, and rightly so. P is a variable that is estimated. Better sometimes to use the aggregate, Y instead.
MV = Py 
MV = Y 
V = Y/M 
ln(V) = ln(Y) – ln(M) 
(dV/V) = (dY/Y) - (dm/M) 
%∆V = %∆Y - %∆M
Enjoy!