An evaluation of federal reserve forecasting: Reply

DENNIS W. JANSEN Texas A&M University College Station, Texas

RUBY P. KISHAN Southwest Texas State University San Marcos, Texas

An Evaluation of Federal Reserve Forecasting: Reply* Thispaper explainswhyJansenand Kishan(1996)and Joutzand Steklerdifferin theirevaluation of Federal Reserveforecasts.We showthat these differencesare due to differencesin the data employedin the two papers, and point out some featuresof the raw data.

1. Our Response Joutz and Stelder (js) make several claims in their comment. Their basic point is that, using a different set of data, they found results that differ from those we reported in Jansen and Kishan (JK 1996). Perhaps this is not surprising. It does raise an interesting question, which is why the results differ. JS claim that they want to answer this question. The usual suspects in a situation like this are differences in data, differences in specification, and differences in methodology. Given that JK and JS used different data and different samples, data differences must be a prime suspect. JS investigate this to an extent, trying to match their data to ours in some ways. However, they never took the obvious step of asking for our data. Doing so would have helped them answer the question they claim to want to answer. One result they report (in their Table 1) is that, using a data set that extends 11 quarters longer than the sample we used, they find evidence of 12th order serial correlation in one-quarter ahead Fed forecasts of the GNP deflator. We did not test for 12th order serial correlation, and did not have data that extends to 1989, so their Table 1 is not comparable to our results. However, their result raises an interesting question, and in our Table 1 we report the Box-Ljung Q-statistic for the one-quarter ahead inflation forecasts using our specification, and using both our data and the JS data. In both cases the sample period corresponded to our original sample period, 1966.i*We thank Fred Joutz for providinghis data. Jansen thanks the Private EnterpriseResearch Center for its support. Journal of Macroeconomics, Winter 1999, Vol. 21, No. i, pp. 189-203

Copyright © 1999 by LouisianaState UniversityPress 0164-0704/99/$1.50

189

Dennis W. Jansen and Ruby P. Kishan TABLE 1.

One-Quarter-Ahead Inflation Forecast Results Dependent Variable: nt +1 - nt +1/t"

Regressors constant 7~t + 1/t'

--

~t/t'

~t/t' - nt-1 MA(1) term R.squared standard error

Our Data 0.262 (0.240) 0.177 (0.163) -0.134 (0.125) 0.374 (0.124) 0.125 1.585 -

Joutz-Stekler Data 0.000 (0.001) - 0.139 (0.137) -0.112 (0.122) 0.424 (0.123) 0.149 3.611E-3

-

Ljung-Box Q Statistics Number of Lags Up to and Including 1 2 3 4 5 6 7 8 9 10 11 12

Q-statistic and probability value 0.053 0.173 3.156 4.316 4.374 4.689 9.233 9.323 12.895 13.414 13.488 20.491

(0.678) (0,206) (0,229) (0,358) (0.455) (0.161) (0.230) (0.116) (0.145) (0.198) (0.039)

0.065 0.933 4.560 4.583 5.485 5.566 11.929 12.629 16.130 17.190 18.110 22.777

(0.334) (0.102) (0.205) (0.241) (0.351) (0.064) (0.082) (0.041) (0.046) (0.053) (0.0]9)

NOTE: *Unless otherwiseindicated,all sampleperiods are 1966:i-1986:iv. Givenour two data sets, this is the largestpossiblecommonsampleperiod across all specifications.

1986:iv. Regardless of the data used, it is clear that the Box-Ljung statistic at 12 lags is significant at the 5% level. However, there is more to report, For our data the Box-Ljung statistic is insignificant at even the 10% level until we test for 12th order serial correlation. The closest we come is a probability value of 11.6% when we look at 9 lags. Using the JS data, the Box-Ljung statistic is significant at the 5% level when we include 9, 10 or 190

An Evaluation of Federal Reserve Forecasting: Reply 12 lags, and at the 10% level the statistic is significant when we include 7 or more lags. These results show that, had we tested for 12th order serial correlation using the Box-Ljung test, we would have found a significant test statistic. However, given the long number of lags needed for this statistic to indicate a problem, it is not immediately clear how this should be interpreted. It is well known that statistically significant Box-Ljung statistics may indicate problems other than serial correlation. JS next present a series of estimation results in their Tables 9.a-2d. The first two columns of each of these tables contain specifications we never estimated. The third column presents the specification that is comparable to the ones we estimated in our original work. This column uses our specification but not our data, and while it does not exactly replicate our results it does come close. Our main qualitative results for the real GNP and inflation forecasts were that the current quarter output forecast appears biased and that the other forecasts appear unbiased. 1 JS's qualitative findings agree with ours, except that they find substantially weaker evidence pointing to bias in the current quarter output forecast. While we could reject the hypothesis of an unbiased forecast at less than a 1% significance level, they report that this hypothesis can be rejected at the 10% (but not 5%) significance level. As an aside on the serial correlation issue, we note that their 4th order serial correlation test in Table 2b does not indicate serial correlation in the one-quarter ahead inflation forecast errors, a result in accord with what we reported. js question our methodology in several respects. They wonder which specification we estimated and question the appropriateness of our choice. To repeat our original paper, we were interested in an equation of the form: A , = a + bF~ + e , ,

(1)

where A is the actual value and F the forecast of one of the following variables: the inflation rate, the growth rate of real GNP, or the unemployment rate. The standard test for an unbiased forecast is a test of the hypothesis a = 0, b = 1. (Tests for serial correlation and possible significance of other explanatory variables are also of interest.) It bears emphasis that here, as in our original paper, we take A and F to be the inflation rate or the output growth rate. In eontrast, JS define A and F as the level of the real GNP deflator or the level of real GNP. Thus their use of these symbols is not equivalent to our use of them, which can 1We also report that the unemploymentforecastswere biased at both horizons. 191

Dennis W. Jansen and Ruby P. Kishan

cause confusion when examining their Equations (1)-(4). For example, their Equation (2) is equivalent to our Equation (1). For our data on inflation and the unemployment rate it was not possible to reject the null hypothesis of a unit root, at least over our sample period 1965:iv-1986:iv. We know that failure to reject does not lead to a conclusion that there is a unit root, but to avoid the possibility of a unit root and the accompanying problems of inference 2 we made the following transformations to Equation (1): At - At-1 = a + bFt

-

At_l

-b

et,

(2)

which under the null hypothesis a = 0, b = 1 is equivalent to At

-

At-1

=

a

q-

b(F t

-

At-l) + et.

(3)

Equation (3), with A measured as the inflation rate, the unemployment rate, or the rate of GNP growth, is the basic equation we estimated, a We also added additional lagged explanatory variables, and for the one-quarter ahead forecasts we decomposed the explanatory variable (Ft - At-1) into two terms, one measuring the difference between the forecast one quarter ahead and the forecast of the current quarter, and one measuring the difference between the current quarter forecast and the lagged actual value. Constraining the coefficient on these two terms to be the same would result in an equation like (3). Of course, Equation (3) can be rewritten as At = a + bF~ + (1 -

b)&_l

+ et

(4)

and respecified by relaxing the constraint on the explanatory variables as ZOf course, overdifferencing can induce a MA error term, and this possibility represents the potential cost of differencing the data. Our transformation is not differencing the data. Instead it is a transformation that is correct only under the null hypothesis. It has the benefit of regressing forecast errors (which we presume to be stationary even if the forecasted series is nonstationary) on differences between forecast values and lagged actual values (which we again presume to be stationary even if the forecasted series is nonstationary). If the null hypothesis is rejected, then our Equations (1) and (3) are not equivalent, and estimated parameters in (3) do not correspond to parameters of (1). This does not invalidate the rejection of the null hypothesis, however. aWe actually transformed Equation (3) into the mathematically identical equation A t - F t = a + c ( F t - At-l) + et, by subtracting (F, - At-l) from both sides of (3). This makes no difference to the results, except that c = b - 1.

192

An Evaluation of Federal Reserve Forecasting: Reply At = a + bFt + cAt-1 + et.

(5)

JS suggest that we estimated an equation that they label (4), which we translate here (using P for the log level of prices and Pf for forecasts of the log price level) as [(e, - e,_l) - (e, 1 - Pt-2)] = a + b[(N- i°(-1) - (i%1 - e,_2)] + e,.

(6)

This is not what we estimated. We never differenced the forecast variable. Our F is the forecasted rate of inflation, Pft - Pt- 1, not the difference in the forecasted levels. Table 2 presents estimates of specification (3), (1), and (5) using both our data and the JS data for the current-quarter output growth forecast. We do not present results for the other three forecasts because, despite the differences in quantitative results, specification, and data, the conclusions we reach concerning the lack of bias in the Fed forecasts are the same. In Table 2, the first and fourth columns present estimates of specification (3), using our data and the js data, respectively. Our data results in a strong rejection of the hypothesis a = 0, b = 1, while the JS data results in a weaker rejection of this hypothesis, at the 10% significance level. In fact, the marginal probability value for this hypothesis is 0.1% using our data and 7.2% using the JS data. We also look at two alternatives. The second and fifth columns present estimates of specification (1), and for both our data and the js data the hypothesis a = 0, b = 1 is not rejected. The third and sixth columns present estimates of the less constrained alternative, specification (5). Here use of our data leads to a strong rejection of a = 0, b = 1, c = 0, while use of the JS data does not lead to a rejection at a 10% significance level or higher. The conclusion from our Table 2 is that the data differences between JK and js are responsible for the differences in results, and that JS do not control for these differences in their comment. What are the data differences? js use data released by the Commerce Department 45 days after the end of the quarter, and they gather forecast data from the Fed's Greenbook. We use data on actual series and forecast data gathered from the Fed's Greenbook. We provide an example of our data-gathering procedures in Table 3, where we reproduce data from the March i4, 1979, FOMC Greenbook. Data in the Greenbook includes historical data from 1978:i to 1978:iv and forecasts for 1979:i through 1979:iv. The top 3 rows reproduce the raw Creenbook data on growth rates in GNP, real GNP (labeled AY), and the inflation rate (~). Values for 1978:i through

193

Z"

I

~5 C~

~o I v

i

~

~

m~

~'~

~5~5v v

i

v

v

~

v

i0 ~

v

g.

~.~

v

v

~ ~ .~'-~

~3

~.~

o

e.i I

194

~'~

An Evaluation of Federal Reserve Forecasting: Reply 1978:iv are historical values known to the Fed on or before March 14, 1979, and values for 1979:i through 1979:iv are forecasts. We label the forecast for 1979:i as the current-quarter forecast, and the forecast for 1979:ii as the one-quarter-ahead forecast. We also include in rows 4 and 5 the values for the levels of GNP and real GNP." These are tile raw data used by JS, who calculated the GNP deflator and transformed the data to growth rates to generate their series for forecasts of real GNP growth and inflation. JS used the Greenbook strictly to garner the forecast data. In addition to the forecast data, JK gathered their data on actual values of the growth rate of real GNP and of the inflation rate from the Greenbook itself. In fact, we took as the actual value for a series at time t the value listed for that time period in the FOMC Greenbook at time t + 2 quarters. Another way to say this is that we used the March 14, 1979, Greenbook to obtain our value for actual real GNP growth and the actual inflation rate in 1978:iii. By using data listed in the Greenbook itself, we were sure that this was a value that was known to the Fed and of enough interest to be printed in the Greenbook at some point approximately six months after the forecast was made. By having this 2-quarter lag, we sought to avoid problems of data availability and data revisions in the releases of GNP data. For 1978:iii, the 75-day release should occur sometime late in the fourth quarter of 1978. By late in the first quarter of 1979, the 75-day release was certainly known and available. Note, however, that we were assuming that the value the FOMC Greenbook lists at time t plus 2 quarters for period t is the value the Fed was trying to forecast at time t. In contrast, JS make the assumption that the value the Commerce Department releases as the 45-day value for time t is the value the Fed was trying to forecast at time t. We take one additional set of information from the Greenbook forecasts. In judging forecast bias we regress (A - F), where A and F are the actual and forecast values at time t as garnered from the Greenbook, on (F At-l) and other lags such as (At-1 - At-s). Clearly measures of At_ 1 and At-~ should be known to the Fed at the time the forecast is made. JS question whether we were careful in this regard. We were. All lagged values of A were taken from the FOMC Greenbook. Thus, for March 14, 1979, we took the first lag of inflation, the value for 1978:iv, as 8_1%, as listed in the Greenbook historical series. We took the second lag of inflation, the value for 1978:iii, as 6.9%, and so on. Thus we clearly used data known to the Fed at the time the forecast was made, since the Fed printed the forecast at the same time they printed the data we used for lags of A! This brings us to another point of clarification. Our forecasts were taken from the last meeting of the FOMC for the quarter, except that this meeting also had to occur in the last month of the quarter. When this was -

195

Dennis W. Jansen and Ruby P. Kishan not possible, we took the data from the first meeting of the following quarter, as long as this meeting took place in the first two weeks of that quarter. This occurred in 79.2 (we took data from the July 3 meeting as 2na-quarter data), 79.4 (we took January 4, 1980, data as 4th-quarter data), 80.2 (July 2 data), 81.2 (July 1), 83.2 (July 6), 84.2 (July 11), 85.2 (July 3), and 86.9. (July 9.). In all cases we reasoned that the Fed forecasts and the lagged actual values reported would make use of data only up to the end of the previous quarter, since the FOMC meeting took place so early (literally days in most cases) in the quarter. Recall that even the 45-day release would not be available until the middle of the second month in the quarter, and in all cases we used data from an FOMC meeting less than two weeks into the following quarter. The alternative, which was used by JS, is to use data from the FOMC meeting in the middle of these quarters. For example, 79.2 (May 16), 79.4 (November 14), 80.2 (May 14), 81.2 (May 13), 83.2 (May 18), 84.2 (May 16), 85.2 (May 15), and 86.2 (May 14). There is another difference in the two datasets, a difference that explains a small part of the discrepancy in results. 4 In the 79:i data, which both JK and JS gather from the March 14 FOMC meeting, the Fed Greenbook has a discrepancy between the levels data on real GNP and the growth rate data. This can be seen in Table 3. In rows 6-9 we calculate the GNP deflator, the inflation rate, the growth rate of real GNP and of nominal GNP. These calculations reproduce the steps of JS in transforming the data to growth rates. Of course, these transformations should give the same values as the inflation rate and growth rate data presented separately by the Fed. However, for 79:i our value for the forecast of the growth rate of real GNP was 3% for the current quarter and 1.9% for one-quarter ahead. Our value for the inflation forecast was 8.9% for the current quarter and 8.3% one-quarter ahead. JS used the levels data to calculate the forecast of the growth rate of real GNP to be 5.6% for the current quarter and - 0.6% one-quarter-ahead. Meanwhile, their inflation forecast was 6.2% for the current quarter and 11.1% one-quarter ahead. Interestingly, the forecasted growth rates of nominal GNP are in agreement in both our data and the JS data, 12.2% for the current-quarter and 10.4% one-quarter ahead. The entire discrepancy appears to be in the split of nominal GNP growth between real GNP and 4We found what appear to be two typos in the JS data used to calculate real GNP growth rates. In 1967:iv, js calculated a value for lagged actual real GNP growth rates as 3.2%, based on levels of real GNP of 666.7 in 1967:ii and 672.0 in 1967:iii. In the FOMC Greenbook the real GNP value for 1967:ii is listed as 664,7. Correcting this would change their lagged actual growth rate for 1967:1v from 3.2% to 4.4%. Then in 1970:i, the lagged actual real GNP growth rate was calculated from levels of real GNP of 730.8 in 1969:iii and 729.8 in 1969:iv, yet the FOMC Greenbook reports the 1969:iii value of real GNP as 730.6. Correcting this would change the lagged actual growth rate for 1970:i from - 0 . 5 % to -0.4%,

196

~-'q O

O

c4~

l'--. 0 0

~c,5

1/3 ~q O

,---~ o o

cq

co

c6~5

cO t"3 c,3 " ~ o,1 ,-~

t¢'3 ",~

~Sc,i

oo

t,-cq

1/3 ¢.D o ~

~7'~ c q

©

~'q o'3

i

©

c,D O

t¢'3 ¢.D

¢.D t-.- O ~ o o ~-..~ O

O

c'3

r....I

O r-..q I'--

O

t"--

c4~

I

r..-4

~ O

c6

Z

197

Dennis W. Jansen and Ruby P. Kishan TABLE 4. ]outz-Stekler Results with Jansen and Kishan's Real GNP Growth Rate Forecast in 1979:i Joutz-Stekler Data Except for Forecast Value in 1979:i

Regressors constant

AYt - dYt/t, - 1.03E-4

(4.90E-4) AYt/t, - AYt-1

0.134

(0.056) R-squared standard error LM test (4 lags) (probability value) Wald Chi-Square

0.066 4.491E-3 4.749 (0.314) 5.856 (0.054)

inflation. It deserves emphasis that the problem here is entirely an issue of the internal inconsistency of the Fed's Greenbook data. However, the forecasts we used are closer to the actual values realized ex-post than are the forecasts calculated by JS. If they had used our data on forecasted growth rates, which would change only the forecast data, and only this one observation, they would have obtained the results we present in Table 4. Note that they still would not reject the null of unbiased forecasts at 5%, but just barely. The probability value attached to the hypothesis has fallen from 7.2% (see Table 2) to 5.4%. Finally, JS ask if the differences are due toour actual data. This turns out not to be so important. We reran the tests using our forecast data with the js 45-day data. These results are in Table 5. The results are in striking accord with results using our forecast data and our actual data as presented in Table 2. For the ist and 3rd row of results, we strongly reject the hypothesis of unbiased forecasts. Thus the differences in results appear to be due to the differences in the forecast series. These differences are the differences due to the FOMC Greenbook inconsistancy in March 1979, and the differences in the meetings selected to represent the forecasts for the various quarters. These differences are presented in Table 6, along with differences in the data on actual values between JK and iS. The table lists forecasts and actual values used by JK and JS. The actual values differ, as is to be expected when js use 45-day releases from the Commerce Department and we use data for the actual values that are 198

An Evaluation of Federal Reserve Forecasting: Reply 5. Joutz-Stekler Data on Actual Values with Jansen-Kishan Forecast Data TABLE

Dependent Variable

Joutz-Stekler 45-day actual values with our forecast values Regressors constant

AYt/t, - AYt-1

3Y, - 3L/~,

3L

3L

- 0.025 (0.168) 0.143 (0.047)

- 0.201 (0.216)

- 0.076 (0.213)

AYt/,, --

-1.064 (0.047)

AYt 1 --

R-squared standard error LM test (4 lags) (probability value) Wald Chi-Square

0.103 (1.539) 0.711 (0.950) 9.428 (0.009)

-0.861 1.607 1.586 (0.811) 1.843 (0.398)

-1.155 (0.056) -0.136 (0.050) 0.872 1.547 0.836 (0.934) 9.483 (0.024)

printed in the Fed Greenbook over 150 days after the end of the quarter. Still, as Table 5 shows, the differences in values used as aetual data do not determine the differences in results. The forecast differences in Table 6 ean be substantial, and not just for the 79:i data that was discussed above. The main issue is how to deal with situations in which FOMC meetings did not occur in the last month of the quarter. Is it better to use forecasts made for FOMC meetings held at midquarter or to use forecasts made for FOMC meetings held in the first week or two of the following quarter? The decision is important. If you choose the latter, as we did, then you will judge the Fed forecast of current quarter real GNP growth to be biased. If you choose the former, as did js, you will judge the Fed forecast of current quarter real GNP growth to be unbiased (using a 5% significance level). It is difficult to draw further inferences from Table 6. It is true that in Table 6 the forecast values we used are always closer to the actual values used by either ourselves or JS. But that is to be expected since our forecasts for the observations listed in this Table were made 30--45 days after the forecasts used for these observations by JS. It is

199

Dennis W. Jansen and Ruby P. Kishan TABLE 6.

Main Differences in Forecasts Data Differences in Forecasts and Actual Values for Current Quarter Output Growth

Forecast8 "'Actual Value" Date for year (FOMCmeeting date) and quarter Jansen-Kishan Joutz-Stekler Jansen-Kishan Joutz- Stekler 79_1 79.2 79.4 80.2 81.2

83.2 84.2 85.2

3.0

(.3/14/79)

- 1.5 (7/3/79) 1.5 (1/3/80) -8.8 (7/2/80)

2.2 (5/16/79) -2.7 (11/14/79) -5.9 (5/14/80)

0.2

(7/1/81) 7.5 (7/6/83) 6.7 (7/11/84) 2.1

(7/3/85) 86.2

5.6

(3/14/79)

1.5

(7/2/86)

1.0

(5/13/81) 5.4 (.5/18/83) 4.9

1.1

0.5

- 2.3

- 2.4

2.0

2.1

-9.6

-9.1

- 1.6

- 2.4

9.7

9.1

7.1

7.6

1.9

1.9

0.6

0.6

(5/16/84) 2.3

(5/15/85) 2.1

(5/14/86)

a bit puzzling that using more accurate forecasts results in a conclusion that the current quarter real GNP growth forecast is biased, but it may just be that the greater precision reduces the otherwise large forecast error variance and allows a more precise judgment about the bias. Interestingly, j s claim to have ruled out differences in results attributable to differences in the data used to measure Fed forecasts. We think Tables 4 and 5 indicate that just the opposite conclusion is warranted. Finally, Table 7 gives a list of FOMC meeting dates and our assignment of FOMC meeting dates to our quarterly observations. This information was offered upon request in our original article. We provide it here so that it is clear how we tied FOMC Greenbook forecasts and other data to quarters.

200

TABLE 7_ Our Assignment of Data from FOMC Meeting Dates to

Quarterly Forecast Data Meeting Quarter Meeting Quarter Meeting Quarter Meeting Quarter

12/8/65 1/3/66 1/26/66 2/24/66 3/15/66 4/5/66 5/4/66 6/22/66 7/20/66 8/17/66 9/28/66 10/26/66 11/15/66 12/17/66 1/5/67 2/1/67 3/1/67 3/29/67 4/26/67 5/17/67 6/14/67 7/12/67 8/9/67 9/7/67 9/27/67 10/18/67 11/8/67 12/6/67

10/9/74 11/13/74

12/11/74 1/15/75 2/12/75 3/12/75 4/9/75 5/1 4/75

65.1

66.1

1/4/68 1/31/68 2/6/68 2/28/68 3/1/68 3/27/68 4/24/68

5/22/68 6/12/68 7/10/68 66.3 8/7/68 9/4/68 10/2/68 66.4 10/25/68 11/20/68 12/11/68 1/8/69 67.1 1/29/69 2/26/69 3/24/69 67.2 4/23/69 5/21/69 6/18/69 7/9/69 67.3 8/6/69 9/4/69 10/1/69 67.4 10/22/69 11/19/69 12/10/69 6/15/77 7/13/77 74.4 8/10/77 9/14/77 10/12/77 75.1 11/9/77 12/14/77 1/11/78

68.1

66.2

68.2

68.3

68,4

69,1

69.2

69.3

69.4 77.2

77.3

77.4

1/7/70 2/4/70 3/4/70 4/6/70 4/29/70 5/20/70 6/17/70 7/15/70 8/12/70 9/9/70 10/14/70 11/11/70 12/8/70 1/6/71

2/9/71 3/3/71 3/31/71 4/28/71 6/2/71 6/23/71 7/21/71 8/18/71 9/15/71 10/13/71 11/10/71 12/8/71 1/7/72 2/9/72 3/15/72 7/2/80 8/6/80 9/10/80 10/15/80 11/12/80 12/12/80 1/28/81 3/25/81

70,1

70.2

70.3

70.4

71,1

71.2

71.3

71,4

72.1 80.2 80.3

80.4 81.1

4/12/72 5/17/72 6/14/72

7/12/72 8/9/72 9/13/72 10/11/72 11/15/72 12/13/72 1/10/73 2/7/73 3/14/73 4/11/73 5/9/73 6/13/73 7/11/73 8/15/73 9/12/73 10/10/73 11/14/73 12/12/73 1/16/74 2/13/74 3/13/74 4/10/74 5/15/74 6/12/74 7/10/74 8/14/74 9/4/74 3/21/84 ,5/16/84 7/11/84 8/15/84 9/26/84 10/31/84 12/12/84 2/6/85

72.2

72.3

72.4

73.1

73.2

73.3

73.4

74.1

74.2

74.3 84.1 84.2 84,3 84.4

201

Dennis W. Jansen and Buby P. Kishan Our Assignment of Data from FOMC Meeting Dates to Quarterly Forecast Data (continued)

TABLE 7.

Meeting Quarter Meeting Quarter Meeting Quarter Meeting Quarter 6/11/75 7/9/75 8/13/75 9/10/75 10/15/75 11/12/75 12/10/75

75.2

75.3

75.4

1/14/76 2/11/76 3/10/76 4/14/76 5/12/76 6/16/76 7/14/76 8/11/76 9/15/76 10/13/76 11/10/76 12/15/76 1/12/77 2/9/77 3/9/77 4/13/77 5/11/77

76.1

76.2

76.3

76.4

77.1

2/22/78 3/15/78 4/12/78 5/10/78/ 6/14/78 7/12/78 8/9/78 9/13/78 10/11/78 11/15/78 12/13/78 1/31./79 3/14/79 4/11/79 5/16/79 7/3/79 8/8/79 9/12/79 11/14/79 1/3/80 1/30/80 3/14/80 4/16/80

5/14/80

78.1

78.2

78.3

78.4 79.1

79.2 79.3 79.4 80.1

5/13/81 7/1/81 8/12/81 9/30/81 11/10/8I 12/16/81 1/27/82 3/24/82 5/12/82 6/23/82 7/23/82 8/18/82 9/29/82 11/10/82 12/15/82 2/2/83 3/23/83 5/18/83 7/6/83 8/17/83 9/28/83 11/9/83 12/14/83 1/25/84

81.2 81.3 81.4 82.1 82.2

82.3 82.4

3/20/85 5/15/85 7/3/85 8/14/85 9/25/85 10/30/85 12/11/85 2/5/86 3/26/86 5/14/86 7/2/86 8/13/86 9/17/86 10/29/86 12/10/86

85.1 85.2 85.3 85.4 86.1 86.2 86.3 86.4

83.1 83.2 83.3 83.4

Conclusion Our conclusion is straightforward. Differences in data and in specification explain all important differences in conclusions. JS use one set of data and get one set of results. JK use a different set of data for both forecasts and actual values, and get a different set of results. It turns out that the differences in forecast data are most important for the differences in results. It remains an open question as to which forecast series provides a better yardstick for measuring Fed forecasting performance. We note that our forecast series is more strongly correlated with the actual series than is their forecast series, whether the actual series is that of JK or JS. However, we readily admit that this is no demonstration of which forecast series is best. 202

An Evaluation of Federal Reserve Forecasting: Reply Received; September 1997 Final version., February 1998

References Jansen, Dennis W., and Ruby Pandey Kishan. "An Evaluation of Federal Reserve Forecasting." Journal of Macroeconomics 18, no. 1 (Winter 1996): 89-109.

203