RDP 8602: ShortTerm Interest Rates, Weekly Money Announcements and Rational Forecasts Appendix
May 1986
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ANALYSIS IN GROWTH RATES
Period  n  Start  End  Reasons for Break from Previous Period 

1  104  10/13/77  10/04/79  
2  17  10/11/79  01/31/80  Fed switched to nonborrowed reserves 
3  101  02/08/80  01/08/82  Switch to MIB, release day now Fridays 
4  38  01/15/82  10/01/82  Definition changed to “new” MI 
5  71  10/08/82  02/10/84  Fed switched to borrowed reserves 
Period  df1  df2  FA^{2,3}  F^{3}  A  R_{1}  R_{2}  R_{3}  R_{4}  R_{5}  R_{6}  R_{7}  

1  14  74  .19  .12  .85  .50  .78  .37  1.01  .19  .22  .25  
23  14  88  .62  .56  .63  .46  .46  .46  .67  .52  .43  .57  
45  14  79  1.22  1.06  1.64°  1.48  1.48  .98  .82  1.85^{*}  .82  .82  
Notes: 1. These are the F statistics for testing the null hypothesis
that the coefficients of the revisions, lagged once and twice, are zero in each of
the forecasting equations for each period indicated. Under the null, these
statistics have an Fdistribution with df1 and df2 degrees of freedom. An * (°)
denotes rejection of the null hypothesis at the 5% (10%) level of significance,
respectively. 
H_{0}  df1  df2  FA^{2}  F  A  R_{1}  R_{2}  R_{3}  R_{4}  R_{5}  R_{6}  R_{7}  

1=12  17  88  .40^{3}  .33  1.17  2.79^{*}  1.51  .15  .19  .07  .15  5.13^{*}  
23=3  17  85  1.04^{3}  .51  .39  2.48^{*}  .70  .10  .15  .13  .11  3.30^{*}  
1=23  16  190  .65  1.22  2.49^{*}  .94  .41  .31  .82  .32  .28  .14  
3=4  16  107  2.03^{*}  .88  .71  .37  1.71  3.75^{*}  3.32^{*}  1.19  .91  1.93^{*}  
23=4  16  124  1.79^{*}  .85  .66  .43  1.86^{*}  4.37^{*}  3.92^{*}  1.27  1.04  1.49  
4=5  16  77  1.26^{4}  .55^{5}  1.45  .70  1.32  1.48  1.53  .93  1.40  1.69°  
23=45  16  195  1.85^{*}^{6}  .91^{6}  1.05  .70  2.09^{*}  4.35  3.95^{*}  1.98^{*}  1.53°  1.88^{*}  
Notes: 1. These are the F statistics for testing the null hypothesis
that the coefficients of each forecasting equation are the same in the two periods indicated. Under the null, these statistics have an Fdistribution with df1 and df2 degrees of freedom. An * (°)
denotes rejection of the null hypothesis at the 5% (10%) level of significance,
respectively. 
Period  R_{1}  R_{2}  R_{3}  R_{4}  R_{5}  R_{6}  R_{7}  

1  R^{2} dw 
.10 2.02 
.17 1.76° 
.07 2.07 
.14 2.01 
.05 2.01 
.04 2.04 
.04 2.04 

23  R^{2} dw 
.19° 2.09 
.06 1.94 
.08 2.12 
.11 2.00 
.17 2.10 
.15 2.05 
.03 2.41° 

45  R^{2} dw 
.19 2.01 
.34^{*} 2.14 
.44^{*} 2.29° 
.45^{*} 2.14 
.36^{*} 1.94 
.46^{*} 2.20° 
.47^{*} 2.24° 

Notes: 1. An * (°) next to an R^{2} denotes rejection of the null hypothesis that the explanatory power of the equation is zero at the 5% (10%) level of significance, respectively. An * next to a DurbinWatson (dw) statistic denotes rejection of the null hypothesis of no autocorrelation at the 5% level of significance; a ° indicates that the dw statistic falls within the inconclusive region. 
F: Final before announcement^{2,4}  A: Announced^{2}  

Period  df2  R^{2}  dw  H_{0}1  H_{0}2  H_{0}3  R^{2}  dw  H_{0}1  H_{0}2  H_{0}3  
df1  16  15  14  16  15  14  
1  88  .11  2.66^{*}  7.76^{*}  8.03^{*}  .42  .58^{*}  1.86  2.09^{*}  1.71°  1.71°  
23  102  .31^{*}  2.05  9.52^{*}  9.90^{*}  3.33^{*}  .46^{*}  1.97  2.11^{*}  2.20^{*}  2.02^{*}  
45  93  .41  2.29°  3.85^{*}  3.70^{*}  1.02  .58^{*}  2.06  1.82°  1.63°  1.73°  
FA: Final after announcement^{3,4}  
Period  df^{2}  R^{2}  dw  H_{0}4  H_{0}5  H_{0}6  H_{0}7  
df1  24  23  15  14  
1  80  .22  2.81^{*}  14.01^{*}  14.39^{*}  .25  .23  
23  94  .50^{*}  2.13  21.25^{*}  22.17^{*}  2.93^{*}  1.70°  
45  28  .79^{*}  2.11  5.64^{*}  5.88^{*}  1.41  1.12  
Notes: 1. An * (°) next to an R^{2} denotes rejection of
the null hypothesis that the explanatory power of the equation is zero at the 5% (10%) level of significance, respectively. An *
next to a DurbinWatson (dw) statistic denotes rejection of the null hypothesis of
no autocorrelation at the 5% level of significance; a ° indicates that the dw
statistic falls within the inconclusive region. The remaining entries are F
statistics for testing the relevant null hypothesis. Under the null, these
statistics have an Fdistribution with df1 and df2 degrees of freedom. An * (°)
denotes rejection of the null hypothesis at the 5% (10%) level of significance,
respectively. 
Federal Funds Rate  TBill Rate  

H_{0}  m,  k  F^{2}  FR^{3}  A^{2}  AR^{3}  S^{2}  F^{2}  FR^{3}  A^{2}  AR^{2}  S^{2}  
df1  17  17  17  17  17  17  17  17  17  17  
1=12  101,  14  39.63^{*}  34.00^{*}  40.76^{*}  34.48^{*}  40.15^{*}  7.43^{*}  5.13^{*}  7.37^{*}  4.86^{*}  7.66^{*}  
23=3  98,  14  .58  .94  .66  .95  .62  .65  .77  .53  .65  .72  
df1  3  17  3  17  3  3  17  3  17  3  
1=23  216,  28  2.81^{*}  1.54  3.36^{*}  1.84^{*}  1.93  5.12^{*}  2.00^{*}  5.21^{*}  1.58°  8.79^{*}  
3=4  133,  28  1.30  .88  .05  .75  .32  6.48^{*}  2.45^{*}  1.20  1.54°  1.62  
23=4  150,  28  1.62  .92  .11  .77  .34  6.40^{*}  2.25^{*}  1.22  1.46  1.27  
4=5  103,  28  4.29^{*}  1.19  2.03  1.25  2.97^{*}  4.15^{*}  2.45^{*}  .97  1.76^{*}  1.27  
Notes: 1. The entries are F statistics for testing the null
hypothesis that the coefficients of each equation are the same in the two periods
indicated. An * (°) denotes rejection of the null
hypothesis at the 5% (10%) level of significance, respectively. 
Federal Funds Rate  TBill Rate  

Model AR  Model FR  Model AR  Model FR  
Period  df2  H_{0}8  H_{0}9  H_{0}8  H_{0}9  H_{0}8  H_{0}9  H_{0}8  H_{0}9  
1  87  .50  1.05  .45  1.05  .75  .35  .37  .36  
23  101  1.33  1.14  1.09  1.10  2.07°  1.04  2.88^{*}  .57  
4  21  .69  .36  .52  .37  1.21  .79  1.20  .69  
5  54  .73  .20  .80  2.50^{*2}  .33  .32  .666  1.11^{2}  
Notes: 1. The entries are F statistics for testing the relevant null
hypothesis. Under the null, these statistics have an Fdistribution with 7 and df2
degrees of freedom for H_{0}8, and 7 and (df2+8) degrees of freedom for
H_{0}9. H_{0}8 is the hypothesis that the surprise parts of the
revisions are jointly orthogonal, H_{0}9 is the hypothesis that the expected
parts of the revisions are jointly orthogonal. An * (°) denotes rejection of the
null hypothesis at the 5% (10%) level of significance, respectively. (These tests
are independent.) 
Model& Period 
Federal Funds Rate  TBill Rate  

nk  α  β  γ  R^{2}  dw  α  β  γ  R^{2}  dw  
F  1 
101 
−.002 [.018]  .058 [.104]  .034 [.100]  .00 
1.93 
.021 [.019]  .313^{*} [.109]  .010 [.109]  .08^{*} 
1.71 

F  23 
115 
.033 [.078]  1.761^{*} [.455]  .319 [.374]  .12^{*} 
2.50^{*} 
−.005 [.040]  1.176^{*} [.227]  .663^{*} [.191]  .26^{*} 
2.17 

F  4 
35 
.089 [.128]  .857^{*} [.333]  −.525 [.467]  .19^{*} 
2.56° 
.068 [.097]  .585^{*} [.243]  −. 478 [.377]  .20^{*} 
1.81 

F  5 
68 
.094° [.055]^{2}  .062 [.082]  −.112 [.157]^{2}  .02 
1.61 
.004 [.030]^{2}  .086° [.448]  .009 [.086]^{2}  .05 
2.01 

A  1 
101 
.004 [.009]  .001 [.024]  −.005 [.020]  .00 
1.90 
.023^{*} [.010]  .058^{*} [.025]  −.009 [.022]  .05° 
1.70 

A  23 
115 
.067 [.067]  .489^{*} [.134]  .021 [.152]  .10^{*} 
2.44^{*} 
.065° [.036]  .367^{*} [.069]  .058 [.081]  .20^{*} 
1.91 

A  4 
35 
.022 [.100]  .508^{*} [.202]  −.071 [.193]  .16° 
2.67^{*} 
.020 [.074]  .276° [.151]  −.150 [.144]  .12° 
1.76 

A  5 
68 
.055^{*} [.027]  .093 [.065]  −.013 [.060]  .03 
1.69 
.005 [.018]  .109^{*} [.034]  −.044 [.039]  .15^{*} 
2.09 

S  1 
101 
.010 [.011]  .013 [.021]  − .025 [.026]  .01 
1.89 
.039^{*} [.011]  .062^{*} [.022]  −.044 [.027]  .09^{*} 
1.69° 

S  23 
115 
.055 [.066]  .354^{*} [.121]  −.005 [.253]  .07^{*} 
2.44^{*} 
.079^{*} [.031]  .394^{*} [.057]  −.356^{*} [.119]  .31^{*} 
2.08 

S  4 
35 
−.014 [.080]  .479^{*} [.160]  −.237 [.175]  .24^{*} 
2.79^{*} 
−.006 [.060]  .248^{*} [.121]  −.264° [.132]  .20^{*} 
1.84 

S  5 
68 
.048° [.025]  .083 [.062]  −.028 [.071]  .03 
1.73 
−.003 [.013]  .114^{*} [.031]  −.090^{*} [.036]  .20^{*} 
2.06 

Notes: 1. Estimated standard errors are given in square brackets. An
* (°) next to a parameter estimate or R^{2} denotes rejection of the
null hypothesis that the corresponding population value is zero at the 5% (10%)
level of significance, respectively. An * next to a DurbinWatson (dw) statistic
denotes rejection of the null hypothesis of no autocorrelation at the 5% level of
significance; a ° indicates that the dw statistic falls within the inconculsive
region. 
Final  Announced  Survey  

Period  obs  mean  variance  mean  variance  mean  variance  
1  104  1.547  7.306  .935  35.208  2.068  12.419  
23  118  1.148  9.827  1.064  40.600  .654  6.608  
4  38  1.240  14.886  1.256  42.912  .130  20.254  
5  71  2.237^{2}  11.492^{2}  1.983  30.172  1.297  11.382  
Notes: 1. These values refer to the percentage change in the money supply
multiplied by a factor of ten. 