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]
91 We can substitute (6.53) into (6.51) to obtain pf = £ 2"1 + (I  )~ fEtzmt + YTUPt + Pt (6.54) 1+ 1+ Solving this expression for pf yields simply pf = Efznif. (6.55) We can now combine the results and describe the equilibrium. Substituting (6.55) into (6.52) and simphfying gives pI = £f2fnf + (Et imtEt ) (6.56) I + Finally, substituting (6.55) and (6.56) into the expressions for the price level and output, Pt = {pj + pf)/2 and yt = mt  Pt, implies Pt = Etzrrit + 7{Et imt  Et 2mt). (6.57) I + Yt = Ti7(£tifnt  £f2fn,) + (mt  E{ imt). (6.58) L + Implications Equation (6.58) shows the models mam implications. First, as in the Lucas model, unanticipated aggregate demand shifts have real effects; this is shown by the mt ~ £tif"t term. Because pricesetters are assumed not to know mt when they set their prices, these shocks are passed oneforone into output. Second, and crucially, aggregate demand shifts that become anticipated after the first prices are set affect output. Consider information about aggregate demand in ( that becomes available between period t  2 and period f 1. In practice, this might correspond to the release of survey results or other leading indicators of future economic activity, or to indications of likely shifts in monetary policy. As (6.57) and (6.58) show, proportion 1/(1 + ) of a change in m that becomes expected between f  2 and t  1 is passed into output, and the remainder goes into prices. The reason that the change is not neutral is straightforward: not all prices are completely flexible in the short run. An immediate corollary is that policy rules can stabihze the economy. As in Section 6.4, suppose that mt equals m* + Vf, where m* is controlled by policy and Vf represents other aggregate demand movements. Assume that the policymaker is subject to the same informational constraints as price
6.8 Fixed Prices The Model We now change the model of the previous section by assuming that when an individual sets prices for two periods, he or she must set the same price Haltiwanger and Waldman (1989) show more generally how a small fraction of agents who do not respond to shocks can have a disproportionate effect on the economy. setters, and must therefore choose m* before the exact value of Vt is known. Nonetheless, as long as the poUcymaker can adjust in response to information learned between t  2 and r 1, there is a role for stabilization policy. From(6.58), when , = mf* + Vf,yf dependson(m*+Vf)£ti(m* + Vt)and on£f!(m,* + Vf) Et2(m* + Vf). By adjusting m* to offset £f iv, £f2Vf, the policymaker can offset the effects of these changes in v on output, even if this information about v is publicly known. An additional implication of these results is that interactions among pricesetters can either increase or decrease the effects of microeconomic price stickiness. Consider an aggregate demand shift that becomes known after the first prices are set. One might expect that since half of prices are already set and the other half are free to adjust, half of the shift is passed into prices and half into output. Equations (6.57) and (6.58) show that in general this is not correct. The key parameter is : the proportion of the shift that is passed mto output is not but 1/(1 + ) (see [6.58]). Recall from equation (6.45) that is the responsiveness of pricesetters desired real prices to aggregate real output: p*, pt = c + ,. A lower value of therefore corresponds to greater real rigidity (BaW and D. Romer, 1990). Real rigidity alone does not cause monetary disturbances to have real effects: if prices can adjust freely, money is neutral regardless of the value of . But real rigidity magnifies the effect of nominal rigidity: given that pricesetters do not adjust their prices freely, a higher degree of real rigidity (that is, a lower value of ) increases the real effects of a given monetary change. The reason for this is that a low value of implies that pricesetters are reluctant to allow variations in their relative prices. As a result, the pricesetters that are free to adjust their prices do not allow their prices to differ greatly from the ones already set, and so the real effects of a monetary shock are large. If exceeds 1, in contrast, the later pricesetters make large price changes, and the aggregate real effects of changes in m are small.!* Finally, the model implies that output does not depend on £t 2f"t (given the values of £f ifn,  £t~2"i( and ,  E, iirit). That is, any information about aggregate demand that all pricesetters have had a chance to respond to has no effect on output.
for botfi periods; in tfie terminology introduced earlier, prices are not just predetermined, but fixed. We make two other, less significant changes to the model. First, an individual setting a price in period t now does so for periods t and f  1 rather than for periods f i 1 and t i 2. This change simplifies the model without affecting the main results. Second, the model is much easier to solve if we posit a specific process for m. A simple assumption is that m is a random walk: mt = mti t Uf, (6.59) where is white noise. The key feature of this process is that an innovation lo m (the term) has a longlasting effect on its level (indeed, with the randomwalk assumption, the effect is permanent). Let Xf denote the price chosen by individuals who set their prices in period f. We make the usual certaintyequivalence assumption that pricesetters try to gel their prices as close as possible to the optimal prices. Here this implies Xf = (p* + £fp*i) (6.60) = \[[ 1  (1  )Pt] + [ Etmt+l  (1  )EtPt+l] where the second line uses the fact that p* =  (1  ) . Since half of prices are set each period, pt is the average of Xf and Xfi. In addition, since m is a random walk, £f frif+i is frif. Substituting these facts into (6.60) gives us Xf = mt + (1  )[Xfi + 2xf + £fXf+i]. (6.61) Solving for Xf yields Xf = A(Xfi + £fXf+i) b (1  2A)mf, 11 (6.62) "21+ Equation (6.62) is the key equation of the model. Equation (6.62) expresses Xt in terms of frif, Xfi, and the expectation of Xf+i. To solve the model, we need to eliminate the expectation of Xf+i from this expression. We will solve the model in two different ways, first using the method of undetermined coefficients and then using lag operators. The method of undetermined coefficients is simpler. But there are cases where it is cumbersome or intractable; in those cases the use of lag operators is often fruitful.
[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]
