back start next
[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [ 144 ] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183]
144 01 92 9m FIGURE 9.8 How seignorage needs determine inflation where = e" Ye". The impact of a change in money growth on seignorage is therefore given by = " = (1  ". (9.38) This expression is positive for 0 < 1 / and negative thereafter. Cagans estimates suggest that b is between and . This imphes that the peak of the inflationtax Laffer curve occurs when g is between 2 and 3. This corresponds to a continuously compounded rate of money growth of 200% to 300% per year, which implies an increase in the money stock by a factor of between e 7.4 and e 20 per year. Cagan, Sachs and Larrain (1993), and others suggest that for most countries, seignorage at the peak of the Laffer curve is about 10% of GDP. Now consider a government that has some amount of real purchases, G, that it needs to finance with seignorage. Assume that G is less than the maximum feasible amount of seignorage, denoted 5*. Then, as Figure 9.8 shows, there are two rates of money growth that can finance the purchases. With one, inflation is low and real balances high; with the Figure 9.8 implicitly assumes that the seignorage needs are independent of the inflation rate. This assumption omits an important effect of inflation: because taxes are usually specified in nominal terms and collected with a lag, an increase in inflation typically reduces real tax revenues. As a result, seignorage needs are likely to be greater at higher inflation rates. This Tanzi (or OliveraTanzi) effect does not require any basic change in our analysis;
we only have to replace the horizontal hne at G with an upwardsloping line. But the effect can be quantitatively significant, and is therefore Important to understanding high inflation in practice. other, inflation is high and real balances low. The highinflation equihbrium has peculiar comparativestatics properties; for example, a decrease in the governments seignorage needs raises inflation. Since we do not appear to observe such situations in practice, we focus on the lowinflation equihbrium. Thus the rate of money growthand hence the rate of inflationis given by 01. This analysis provides an explanation of high inflation: it stems from governments need for seignorage. Suppose, for example, that b = and that seignorage at the peak of the Laffer curve, S*, is 10% of GDP. Since seignorage is maximized when = 1/b, (9.37) implies that S* is Ce/b. Thus for S* to equal 10% of GDP when fois i, must be about 9% of GDP. Straightforward calculations then show that raising 2% of GDP from seignorage requires ~ 0.24, raising 5% requires ~ 0.70, and raising 8% requires  1.42. Thus moderate seignorage needs give rise to substantial inflation, and large seignorage needs produce high inflation. Seignorage and Hyperinflation This analysis seems to imply that even governments need for seignorage cannot accoimt for hyperinflations: if seignorage revenue is maximized at inflation rates of several hundred percent, why do governments ever let inflation go higher? The answer is that the preceding analysis holds only in steady state. If the public does not immediately adjust its money holdings or its expectations of inflation to changes in the economic enviroimient, then in the short run seignorage is always increasing in money growth, and the government can obtain more seignorage than the maximum sustainable amount, S *. Thus hyperinflations arise when the governments seignorage needs exceed S* (Cagan, 1956). Gradual adjustment of money holdings and gradual adjustment of expected inflation have similar implications for the dynamics of inflation. We focus on the case of gradual adjustment of money holdings. Specificahy, assume that individuals desired money holdings are given by the Cagan moneydemand function, (9.36). In addition, continue to assume that the real interest rate and output are fixed at F and F: although both variables are likely to change somewhat over time, the effects of those variations are likely to be smaU relative to the effects of changes in inflation. Thus desired real money holdings are m*(t) = Ce (9.39) The key assumption of the model is that actual money holdings adjust gradually toward desired holdings. Specifically, our assumption is Inm(f) = /3[lnm*(t)lnm(t)L (9.401
= p\lnm*(t)~lnm(t)] (941) = iS[lnC  Mf)lnm(f)], where the second hne uses (9.39) to substhute for In m * (r). The idea behind this assumption of gradual adjustment is that it is difhcult for individuals to adjust their money holdings; for example, they may have made arrangements to make certain types of purchases using money. As a result, they adjust their money holdings toward the desired level only gradually. The specihc functional form is chosen for convenience. Finally, p is assumed to be positive but less than 1 / fothat is, adjustment is assumed not to be too rapid. As before, seignorage equals M/P, or {M/M){MIP); thus S(t) = gM(t)m{t). (9.42) Suppose that this economy is initially in steady state with G less than S*, and that G then increases to a value greater than S*. If adjustment is instantaneous, there is no equilibrium with positive money holdings. Since S* is the maximum amount of seignorage the government can obtain when individuals have adjusted their real money holdings to their desired level, the government cannot obtain more than this with instantaneous adjustment. As a result, the only possibility is for money to immediately become worthless and for the government to be unable to obtain the seignorage it needs. With gradual adjustment, on the other hand, the government can obtain the needed seignorage through increasing money growth and inflation. With rising inflation, real money holdings are falling. But because the adjustment is not immediate, the real money stock exceeds Ce "; as a result (as long as the adjustment is not too rapid), the government is able to obtain more than S *. But with the real money stock falling, the required rate of money growth is rising. The result is explosive inflation. To see the dynamics of the economy formally, it is easiest to focus on the dynamics of the real money stock, m. Equation (9.41) gives rh/m in terms of TT and m. Thus to characterize the behavior of m,we need to eliminate TT from this equation. To do this, note that the growth rate of real money, rh/m, equals the growth rate of nominal money, , minus the rate of inflation, . Rewriting The assumption that the change in real money holdings depends only on the current values of m * and m implies that individuals are not forwardlooking. A more appealing assumption, along the lines of the q model of investment m Chapter 8, is that individuals consider the entire future path of inflation in deciding how to adjust their money holdings. This assumption comphcates the analysis greatly without changing the imphcations for most of the issues we are interested m (but see n. 9, below).
[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [ 144 ] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183]
