ch_7_money_inflation_and_welfare.pdf

Chapter 7 Money, inflation and welfare 7.1 Introduction In Chapter 5, we saw that in classical theory money was neutral, not having any effects on real variables such as consumption or output. The welfare effects of money and inflation, however, were not considered. Even if a change in the money s...

Chapter 7 Money, inflation and welfare 7.1 Introduction In Chapter 5, we saw that in classical theory money was neutral, not having any effects on real variables such as consumption or output. The welfare effects of money and inflation, however, were not considered. Even if a change in the money supply does not cause output or consumption to change, does it cause the utility or welfare of individuals to be affected? This chapter will discuss such issues, noting the difference between the neutrality and superneutrality of money. Finally, issues in hyperinflation will be considered. 7.2 Aims This chapter aims to study money, inflation and welfare in a flexible price environment. It will introduce such concepts as the real and nominal interest rates, the superneutrality of money, inflation tax and hyperinflations. 7.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: describe the relationship between real and nominal interest rates and why the relationship holds explain what superneutrality means and give examples of when monetary policy can be neutral but not superneutral define a monetary policy which maximises welfare and quantify the welfare cost associated with a given level of inflation describe the concepts of seigniorage and inflation tax discuss the merits of using inflation as a source of government revenue rather than other forms of tax define hyperinflation, and explain why it is undesirable and how it forms. 85 7. Money, inflation and welfare 7.4 Reading advice Before embarking on this chapter and before looking at any of the recommended reading you should revise your understanding of inflation from your EC2065 Macroeconomics course. You should also have re-read Chapter 5 of the subject guide on classical theory and monetary neutrality and the references therein. The model of hyperinflation and that of high but stable inflation are based on the papers by Cagan (1956) and Dornbusch (1992), respectively, and should be read after completing this chapter. 7.5 Essential reading Cagan, P. ‘The monetary dynamics of hyperinflation’, in Friedman, M. (ed.) Studies in the Quantity Theory of Money. (Chicago: University of Chicago Press, 1956). Dornbusch, R. ‘Lessons from experience with high inflation’, The World Bank Economic Review (6) 1992, pp.13–31. Lewis, M.K. and P.D. Mizen Monetary Economics. (Oxford; New York: Oxford University Press, 2000) Chapter 7. McCallum, B. Monetary Economics. (New York; Macmillan; London: Collier Macmillan, 1989) Chapters 6 and 7. 7.6 Further reading Books Cagan, P. ‘Hyperinflation’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Danthine, J.P. ‘Superneutrality’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Friedman, M. ‘The quantity theory of money’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Harris, L. Monetary Theory. (New York; London: McGraw-Hill, 1985) Chapter 19. Mankiw, N.G. Macroeconomics. (New York: Worth Publishers, 2002). Journal articles Diamond, P.A. ‘Search, sticky prices and inflation’, Review of Economic Studies 59(4) 1993, pp.53–68. Sargent, T. and N.Wallace ‘Some unpleasant monetarist arithmetic’, Federal Reserve Bank of Minneapolis Quarterly Review 531 (1981), Fall. 86 7.6. Further reading Neutrality In the classical model, which we assume here, prices are perfectly flexible and the economy is then one in which output is always at (full employment) equilibrium. We will also not consider other sources of non-neutrality such as contracts or debts denominated in nominal terms. In such an economy, as established in Chapter 5, money is neutral in the sense that in static equilibrium all real variables in the economy are independent of the quantity of nominal money and the price level is proportional to the quantity of money. It might appear that an immediate implication of neutrality is that the rate of growth of the quantity of money would also be neutral in the sense of affecting the rate of growth of the price level (inflation) but no real variables. This is known as ‘superneutrality’. Then inflation would indeed be a monetary phenomenon and at the same time would have no real effects. However, it turns out that even in a flexible price economy this implication is not correct, the reason being that expectations of the future growth rate of the quantity of money create expectations of inflation and expectations of inflation are not neutral. The starting point is the distinction between real and nominal interest rates, and the relationship between them; the ‘Fisher equation’. Real and nominal interest rates If people expect there to be inflation over some period, quoted interest rates no longer represent the rate at which goods today can be traded for goods in the future. Imagine a deposit paying a fixed interest rate, Rt % per annum on balances at the beginning of period t, paid at the beginning of period t + 1. Then £100 today becomes £100(1 + Rt ) in a year’s time. However, if the price level at the beginning of the year were Pt , and prices were to rise during the year at a rate πt+1 (πt+1 being the inflation rate between periods t and t + 1), the quantity of goods that can actually be purchased at the end of the year is £100(1 + Rt )/Pt (1 + πt+1 ). Thus not consuming £100/Pt goods at the beginning of the year enables one to consume £100(1 + Rt )/Pt (1 + πt+1 ) more goods at the end of the year. For small values of Rt and pt+1 , this expression can be approximated by £100(1 + Rt − πt+1 )/Pt , and the term (Rt − πt+1 ) is known as the ‘real’ rate of interest, rt . The relationship between the real and nominal rate of interest, which is known as the Fisher equation, is therefore by definition: rt = Rt − πt+1 . (7.1) While a borrower or financial institution can commit to a particular nominal interest rate at the beginning of the period, it is evident that the actual rate of inflation over that same period, between t and t + 1, will not be known until date t + 1. Hence at the beginning of the period, borrowers and lenders can only form expectations of the real interest rate based on their expectations of inflation over the period. The ex-ante real interest rate, rtA , measures the quantity of goods at the end of the period which people expect to be able to buy as a proportion of the quantity they could buy today with the money they deposit or lend. Then: e rtA = Rt − πt+1 (7.2) 87 7. Money, inflation and welfare e where πt+1 is the expected rate of inflation between dates t and t + 1, formed at date t. In the same way the ex-post real interest rate, rtP , measures the actual real interest rate during some past period, which is the quantity of goods at the end of the period that a depositor was actually able to buy relative to what could have been bought at the beginning. Evidently, rtP = Rt − πt+1 . (7.3) In measuring ex-post real interest rates it should be noted that current quoted nominal interest rates relate to the future whereas quoted inflation rates refer to the past, hence the different time subscripts. If one wanted to know the ex-post real interest rate for 2002 it would be necessary to subtract the 2002 inflation rate (as recorded at the end of the year/beginning of 2003) from the nominal rate quoted for one-year money at the beginning of the year. If everyone correctly forecasts the rate at which prices will rise over some period and acts on the basis of these expectations, inflation is said to be fully anticipated. In this e = πt+1 , and the ex-ante and ex-post real interest rates are therefore case of course, πt+1 equal. Activity 7.1 How can borrowers commit to paying the real rate of return on any sums lent to them? Superneutrality Superneutrality may be defined as the proposition that, where inflation is fully anticipated, the real rate of interest (rt ), is independent of the fully anticipated inflation rate, πt+1 . The real rate of interest measures the relative price of goods in the future as against goods today so it is clearly a ‘real’ variable relevant to intertemporal decisions (saving and investment). If it were to change in response to a change in the inflation rate, then inflation would not be neutral in that it would affect savings and investment decisions. However, if the real interest rate does not change when the inflation rate changes, then from the Fisher equation, it follows that the nominal rate, Rt , must adjust one-for-one with changes in the inflation rate. In the standard macro model, the real interest rate affects the goods market through its effects on saving and investment decisions. From the resource constraint; output, Y , is split between consumption, C, investment, I, and government spending, G, we can write:     + + − − Y = C Y − τ, r + I Y , r + G. (7.4) τ are taxes so that consumption depends positively on disposable income and negatively on the real interest rate. A high real interest rate will encourage saving (decrease current consumption) as one unit of consumption goods today can yield a larger number of consumption goods tomorrow. There is then a negative relationship between the real rate and output.   − r=H Y 88 . (7.5) 7.6. Further reading From the Fisher equation:   − R = H Y + π. (7.6) Equation (7.6) represents an IS curve, showing the combinations of output, Y , and nominal interest rate, R, that clear the goods market.1 Therefore, in the standard IS–LM model with the nominal interest rate on the vertical axis, an increase in the inflation rate will shift the IS curve upwards but leave the position of the LM curve unchanged. There must therefore be a one-off increase in the price level to restore equilibrium in the money market at the given level of equilibrium output, see Figure 7.1. The increase in the nominal interest rate reduces the demand for real money balances and the jump in the price level reduces the supply. Figure 7.2 shows (by way of concrete example) the case of a static economy, where initially the stock of money and hence the price level are constant, and where at time t0 a new policy is introduced such that the money stock grows at g% per year. The growth in the money stock will cause prices to increase, also at g% per year, and the anticipation of this inflation at time t0 will cause the nominal interest rate to jump at t0 by g percentage points. This in turn will cause the price level to jump at time t0 by an amount equal to g multiplied by the interest elasticity of the demand for money. In this standard model, changes in the fully anticipated inflation rate leave the real interest rate unchanged but affect not only the nominal interest rate but also the stock of real money balances, and it is this which leads to the welfare costs of fully anticipated inflation (see below). Figure 7.1: Superneutrality of money. The standard model is somewhat simplified in that it has no wealth effects in the IS curve. A full and general model would include such effects, and in such a model a fall in real money balances would constitute a fall in wealth, which would tend to raise savings. A rise in savings would shift the IS curve inwards and thus lower the equilibrium real interest rate and increase investment. This is known as the Mundell–Tobin effect. It says that in inflationary times people wish to hold less wealth in the form of real money balances and therefore attempt to acquire other forms of wealth including real capital. 1 While IS–LM model used to analyse economies with short term price stickiness, remember that there are no such rigidities in this model. 89 7. Money, inflation and welfare Figure 7.2: Nominal money balances and the price level. In practice, however, in most advanced economies fiat money balances constitute so tiny a proportion of people’s wealth that this effect can be ignored. Figure 7.3: Non-superneutrality of money. The case of non-superneutrality, caused by wealth effects in the consumption function, is shown in Figure 7.3. The IS curve is derived from an amended version of (7.4).   +   + + − − M Y = C Y − τ, r,  + I Y , r + G. (7.7) P Alternatively, this can be written in the form:  − r = H Y , +  M . P For any given output level, a fall in real money balances necessitates a fall in real interest rates in order to offset the decrease in aggregate demand. In goods market 90 (7.8) 7.6. Further reading equilibrium there is then a positive relationship between M/P and r. Following the increase in inflation, caused by the positive growth rate of nominal money balances, the IS curve shifts out as in Figure 7.1 but is partially offset because of the fall in wealth (fall in M/P ) which reduces consumption. The nominal interest rate only increases to R10 (< R1 in Figure 7.1) and since inflation is the same in both Figure 7.1 and Figure 7.3, the real interest rate, r10 , will be less than r0 , (i.e. the real rate has fallen). The welfare costs of inflation and the optimal quantity of money The key insight, which follows from Friedman’s price-theoretic approach to modelling the demand for money, is that the area under the demand curve measures the utility derived by individuals from holding money balances. The opportunity cost to individuals of holding money balances is measured by the nominal rate of interest, R. The consumers’ surplus enjoyed by individuals from holding money balances, that is, the excess of the utility they derive over the opportunity cost they incur, is thus measured by the area A in Figure 7.4. Figure 7.4: Seigniorage and inflation tax. Figure 7.5: . . . with positive inflation. Suppose that, initially, there is no inflation, so that the nominal interest rate in Figure 7.4 is equal to the real interest rate (R0 = r). Given this interest rate, the total stock of 91 7. Money, inflation and welfare money balances, which individuals wish to hold, is denoted (M/P )0 . The area B measures the annual income stream the government as issuer of money is able to acquire by the once and for all purchase of productive assets with the money it issues. (In a static economy with no inflation, the stock of money outstanding is constant, but the government was able to acquire real assets with it at the time it was introduced.) But if the money is fiat money, the cost of production is approximately zero, so the government is essentially able to acquire real assets ‘for free’ by virtue of its monopoly position on the money issue. This is known as ‘seigniorage’, and it represents a transfer of resources from money holders (households and firms) to the government. Seigniorage is essentially a form of taxation, and the area C in Figure 7.4 is the excess burden or deadweight loss associated with this tax. Holdings by individuals of money balances in excess of (M/P )0 yield positive utility and the additional money costs nothing to produce. Therefore, there would be economic benefit from expanding the quantity of real money balances held from (M/P )0 up to the point of ‘full liquidity’, L. However, this cannot be done through an expansion of the nominal money stock, because with an interest rate of R0 the desired holding of money balances is (M/P )0 , and any additional nominal money will lead to an increase in the price level to restore the desired quantity of real balances. The social utility of money in Figure 7.4 is measured by the area A + B, the sum of consumers’ surplus and the revenues obtained by the government from seigniorage. Given the demand curve, the maximum possible social utility that could be achieved is when the holdings of money balances are at L (full liquidity), which is Friedman’s ‘optimal quantity of money’. To induce individuals to hold the optimal quantity of money it is necessary that the nominal interest rate be zero. Only in this case will the demand for money be equal to L. Given the Fisher equation, the nominal interest rate will be zero when the rate of price inflation is equal to minus the real interest rate (i.e. R = 0 when p = −r). The welfare cost of fully anticipated inflation arises because inflation raises the nominal interest rate, reducing the demand for real money balances and therefore reducing the utility obtained from the use of money. In Figure 7.5 we consider an economy with fully anticipated inflation at a rate of p1 . The nominal interest rate is now R1 (= r + p1 ), and the demand for money is (M/P )1 . The consumers’ surplus is again measured by the area under the demand curve and above the opportunity cost of holding money, and is therefore the area A. The area B + D represents the revenue the government now derives from money issue, of which B is generally known as the ‘inflation tax’, and as before, D is seigniorage, real interest rate times real money balances. The inflation tax refers to the resources obtained by the government by the continuing process of printing money during times of inflation. (If the inflation rate is p1 , and the volume of real money balances (M/P )1 , the amount of nominal money the government will need to print per period to maintain the real stock of money constant is p1 (M/P )1 .) Comparing Figure 7.4 with Figure 7.5, the welfare cost of inflation may be measured as the loss of consumers’ surplus, B + C, plus the loss of seigniorage, E, less the inflation tax revenue, B. Welfare cost = B + C + E − B = C + E. (7.9) This is equal to the reduction in the quantity of real money balances demanded multiplied by the nominal interest rate averaged over that range. The welfare cost of 92 7.7. Inflation as taxation fully anticipated inflation arises because individuals choose to incur the cost and inconvenience of economising on money balances in times of inflation. Inflation raises the private cost of holding money balances though the social cost of creating money remains negligible. 7.7 Inflation as taxation If inflation is like a tax it not only reduces demand and has welfare costs, but also raises revenue for the government. Even though inflation has welfare costs, these costs may be lower than those of other forms of taxation. Returning to Figure 7.5, the net increase in government revenue from inflation is the inflation tax, area B, less the reduced yield from seigniorage, area E. If one measures the efficiency of a tax as the ratio of the welfare cost to the revenue raised, then the efficiency of inflation as a form of taxation is given by: C+E . (7.10) Efficiency = B−E The most efficient tax scores zero on this scale (no welfare cost) and the least efficient scores infinity (welfare cost but no revenue yield), or negative if the tax actually lowers total revenue. The relationship between the welfare cost and the revenue raised by the inflation tax depends on the interest elasticity of demand for money. The more inelastic the demand for money, the more efficient is inflation as a form of taxation. Activity 7.2 What other factors, other than efficiency, should determine the extent to which the government uses inflation as a form of taxation? Hyperinflation The popular image of hyperinflation is of very rapid, and in particular very rapidly accelerating, inflation, leading to astronomical prices and to a collapse of the monetary system. The most famous hyperinflation of this type in a major industrial country was Germany in 1922–23. Prices increased by 500,000 times within the space of a few months in the autumn of 1923, the prices of staple commodities like a loaf of bread or a newspaper ran into hundreds of billions of marks. Notwithstanding this, money remained the medium of exchange, although the attempt to spend money as soon as it was received itself generated faster inflation. The greatest cost of the hyperinflation, however, was the impoverishment of households with monetary assets whose value was destroyed. Hyperinflations of this type result from political instability such that the government is unable to finance its expenditure except through money creation. The acceleration of inflation results in part from deteriorating public finances and in part from the ‘flight of money’ caused by expectations of faster inflation. In the twentieth century, there were hyperinflations after the First World War in Austria, Germany, Hungary, Poland and Russia, and after the Second World War in Bulgaria, Greece, Hungary, Poland and Romania. More recently, there have been hyperinflations associated with the collapse of the former Soviet Union and with the effects of war, in particular in parts of former Yugoslavia (e.g. Serbia). 93 7. Money, inflation and welfare Activity 7.3 What has been the highest rate of inflation in your country? These rapidly accelerating hyperinflations are unsustainable, and are usually terminated by a financial reconstruction involving a new government, a new currency whose value is sometimes secured by a fixed exchange rate or currency board, and a fiscal reconstruction that may involve a repudiation of government debt or other obligations. To demonstrate how hyperinflations can lead to a collapse in the demand for money, consider the model of money demand by Cagan (1956). Take a standard money demand equation of the form:   M = ayt − bRt . (7.11) ln P t Replacing Rt with rt + pet+1 from the Fisher equation, this can be written as: e ln Mt = ln Pt + ayt − brt − bπt+1 . (7.12) Differentiate this with respect to time and assume that output growth and real interest rate changes are small relative to changes in nominal quantities, as is likely in periods of hyperinflations, which is what the Cagan model tries to study. e ) d(πt+1 d(ln Mt ) d(ln Pt ) = −b . dt dt dt (7.13) d(ln Mt )/dt is the growth rate of the money supply, mt , and d(ln Pt )/dt is the growth rate of the price level, or inflation, πt . Rearranging gives: πt = mt + b e d(πt+1 ) . dt (7.14) e )/dt is positive), then these If inflation is expected to increase in the future (i.e. d(πt+1 expectations can cause inflation to increase to a level above mt . Increases in inflation will cause individuals to increase their expectations of inflation, which in turn causes pt to increase even further from (7.14). The collapse in the demand for money is then partly caused by expectations of faster inflation next to growth rate of the money supply (mt ), which are, ultimately, self-fulfilling. Very rapid, continuing and non-explosive inflation A more recent phenomenon has been a widespread experience of very rapid but none the less continuing and non-explosive inflation. For example, there have been inflation rates averaging over 100 per cent a year lasting for 10 years or more in many South American countries such as Argentina, Brazil or Peru during the 1980s. Such very rapid but stable inflations can be explained in terms of a continuing but non-deteriorating government deficit. This can be demonstrated in the form of a very simple model due to Dornbusch. Assume a government whose expenditure falls short of the money it can raise from taxation by some amount, which is a fixed proportion, g, of nominal income. The government has a poor credit rating and is unable to borrow from the capital markets so this deficit can be financed only through the creation of money. The deficit per unit time period is given by: Deficit = gP y (7.15) 94 7.7. Inflation as taxation where P is the price level and y is real GDP. This deficit is financed by an increase in the money stock, so that: dM = gP y. (7.16) dt In the simplest version of the model the monetary sector is described by the quantity theory equation: M V = Py . (7.17) Dividing (7.16) by (7.17) gives: 1 dM · = gV. M dt (7.18) But (1/M ) · (dM/dt) is equal to the growth rate of the money supply, which is equal to the rate of inflation, p. This leads to the very simple expression for the inflation rate under these assumptions of: π = gV. (7.19) For large values of g and/or V the inflation rate can be quite rapid, but in the simplest versions of this model there is no reason why it should accelerate. A straightforward modification of the model is to allow the velocity of circulation to be increasing in the inflation rate, V = V (π) with V 0 > 0, which may lead to a deteriorating trade-off between the deficit and inflation and to the possibility of instability. See Figure 7.6. If we are initially at point E’ and inflation increases, this will cause velocity to increase since V = V (π). Higher velocity will cause inflation to rise (π = gV ) and the process continues with ever increasing inflation. Point E’ is therefore an unstable equilibrium. Figure 7.6: Activity 7.4 Explain, using Figure 7.6, why point E is a stable equilibrium. (Hint: start by examining what happens when inflation increases slightly from point E.) 95