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] [184] [185] [186] [187] [188] [189] [190] [191] [192] [193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212]


142

Apr.

140.40

31.62

6.36

151.90

33.13

6.46

June

169.20

37.17

7.03

July

189.80

39.98

10.16

Aug.

238.10

56.12

19.20

Sept.

316.90

110.00

28.70

Oct.

469.50

140.80

56.60

Nov.

754.10

241.00

115.10

Dec.

1,280.00

530.50

147.50

1923

Jan.

1,984.00

763.30

278.50

Feb.

3,513.00

1,583.00

588.50

Mar.

5,518.00

2,272.00

488.80

Apr.

6,546.00

3,854.00

521.20

8,564.00

5,063.00

817.00

June

17,290.00

9,953.00

1,938.50

July

43,600.00

27,857.00

7,478.70

Aug.

663,200.00

591,080.00

94,404.00

Sept.

2,823

1,697

X 10"

2,395 X 10

Oct.

2,497

3,868

X 10*

709.5 X 10*

Nov.

4,003

3,740

X 10*

72.6 X 10*

Dec.

4,965

5,480

X 10*

126 X W

1924

Jan.

4,837

2,813

X 10*

117 X 10»

Feb.

5,879

6,505

X 10*

116 X 10*

Mar.

6,899

7,047

X 10*

121 X 10»

Apr.

7,769

8,050

X 10*

124 X 10»

9,269

8,046

X 10*

122 X 10»

June

10,970

7,739

X 10*

116 X 10»

July

12,110

7,430

X 10*

115 X 10»

Aug.

13,920

5,619

X 10*

120 X 10»

Sept.

15,210

6,701

X 10*

127 X 10»

Oct.

17,810

7,087

X 10*

131 X 10»

Nov.

18,630

7,039

X 10*

129 X 10»

Dec.

19,410

8,209

X 10*

131 X 10»

"Money supply is for end of the month and in 10 marks. Since Jan. 1924 the Reischsbank reported money supply in reischmarks. 1 reischmark = 10- old marks. All figures have been converted to old marks and rounded to four significant digits. Thus the money supply is all on a comparable basis for the whole period.

Source: John Parke Young, European Currency and Finance, Commission of Gold and Silver Inquiry, U.S. Senate, Serial 9. Vol. 1, U.S. Government Printing Office, Washington. D.C., 1925.

fable 10.2 (Cont.)

Notes in Wtiolesale

Circulation Total Demand Deposits Price Index



Thus we get

where

= 2a2[yf - y,-i - (y, - y,-i)] iy, - y,-,) = 8(yf - y, ,)

fl, + 02

Note that 0 < 8 < 1 and 8 is close to 1 if the costs of being in disequilibrium are much higher than the costs of adjustments. 8 is close to zero if the costs of adjustment are much higher than the costs of disequilibrium.

change. The partial adjustment model says that the actual change is only a fraction of the desired change, that is,

y, - y,--\ = SCyf -~ y,-i) where 0 < 6 < 1 (10.16)

Note that this equation is similar to the adaptive expectations model (10.12) with y, = x,+, and yf = x,. Thus y, will be a distributed lag of yf with geometrically declining weights. Now suppose that yf is a function of anticipated sales X,; then we can write

yf = oa, + e, where e, ~ IID(0, )

and combining the two equations we get

y, - y,-i = b(ax, + e, - y, ,)

y, = (1 - 6)y, , + :, + 6e,

which can be written as

y, = Piy,-. + ix, + u,

with (B, = 1 - 6, ( 2 = «6, and u, = 6e,. Note that 0 < (B, < I and we need this extra condition for a partial adjustment model. Also note that the properties of the error term u, are the same as those of e,. Thus the partial adjustment model does not change the properties of the error term.

A simple explanation as to why firms make only a partial adjustment to the desired level is as follows. The firm faces two costs: costs of making the adjustment and costs of being in disequilibrium. If the two costs are quadratic and additive, we can write total cost C, as

C, = a,(y, - y,-,) + a2(yf - y,f Given y, and yf we have to choose y, so that total cost C, is minimum. dC,

- = 0 gives 2a,Cy, - y, ,) = 2 { 1 - ,)



I + exp(ao + a,r,)

(we use a subscript / for 8 since it changes over time).

However, there is no reason that the adjustment parameter be between 0 and 1 at all times. In this case we can make 8, a linear function of r,. There are many empirical studies that use partial adjustment models with varying coefficients. Since we have explained the basic idea we will not review them here.*

A more generalized version of the partial adjustment model is the error correction model. This model says that

- -! = - 1 )+ 7(yf-i - y-i) (10.17)

change in the past periods

desired values disequilibrium

where 0 < 8 < 1 and 0 < -y < 1. If 8 = -y, we have the partial adjustment model. Unlike the partial adjustment model, however, this model generates serially correlated errors in the final equation we estimate. Suppose that, as before, we write

yj = ax, + e,

where x, is anticipated sales. Then substituting this in (10.17), we get

(y, - y,-x) = a8(x, - x,„,) + ayx,, - yy,., + 8e, - (8 - 7)e,, (10.18)

The error term is now correlated with y, , and we cannot estimate this equation by ordinary least squares. Again, we can think of using an instrumental variable (say, x,2 for y, ,) and estimate this equation by instrumental variable methods.

Z. Griliches, "Distributed Lags: A Survey," Econometrica, January 1967, pp. 16-49, Sec. 5, "Theoretical Ad-Hockery."

*See M. Nerlove, "Lags in Economic Behavior," Econometrica, March 1972, pp. 221-251, for a survey of the work on adjustment costs and the development of a model with adjustment costs. There are, however, no empirical results in the paper. Nerlove says, "current research on lags in economic behavior is not good because neither is the empirical research soundly based in economic theory nor is the theoretical research very strongly empirically oriented" (p. 246).

For a review of the model up to the early 1970.s, see J. C. R. Rowley and R K. Trivedi, Econometrics of Investment (New York: Wiley, 1975), pp. 86-89 on "variable lags."

Partial ad)ustmei\t models were popular \i\ the 1950s and 1960s but were criticized as being ad hoc The desired level y* is derived independently by some optimization rule and then the adjustment equation is tagged on to it. However, the costs of adjustment and the costs of being in disequilibrium should be incorporated in the optimization rule. There have been many attempts along these lines but they have not resuhed in any tractable estimable equations.*

One refinement that can easily be done is to make the partial adjustment parameter 6 a function of some explanatory variables that are considered important in determining the speed of adjustment (e.g., interest rates). Denoting the interest rate by r„ since 6, is supposed to be between 0 and 1 we can write

exp(ao + ,)

, =



[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] [184] [185] [186] [187] [188] [189] [190] [191] [192] [193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212]