Silviase/jgov_v1.4_full_ann huggingface dataset:
$$ TAXA61=TAXA*(YW6064*LERatio6064)/YWW*1000 $$

$$ TAXA62=TAXA*(YW6064*LERatio6064)/YWW*1000 $$

$$ TAXA63{=}TAXA{*}(YW6064{*}LERatio6064)/YWW{*}1000 $$

$$ TAXA64=TAXA*(YW6064*LERatio6064)/YWW*1000 $$

$$ TAXA65{=}TAXA{*}(YW6569{*}LERatio6569)/YWW{*}1000 $$

$$ TAXA66{=}TAXA{*}(YW6569{*}LERatio6569)/YWW{*}1000 $$

$$ TAXA67=TAXA*(YW6569*LERatio6569)/YWW*1000 $$

$$ TAXA68{=TAXA{*}(YW6569{*LERatio6569)/YWW{*1000} $$

$$ TAXA69{=}TAXA{*}(YW6569{*}LERatio6569)/YWW{*}1000 $$

$$ TAXA70=TAXA*(YW7074*LERatio7074)/YWW*1000 $$

$$ TAXA71=TAXA*(YW7074*LERatio7074)/YWW*1000 $$

$$ TAXA72=TAXA*(YW7074*LERatio7074)/YWW*1000 $$

$$ TAXA73{=}TAXA{*}(YW7074{*}LERatio7074)/YWW{*}1000 $$

$$ TAXA74=TAXA*(YW7074*LERatio7074)/YWW*1000 $$

$$ TAXA75{=}TAXA{*}(YW7579{*}LERatio7579)/YWW{*}1000 $$

$$ TAXA76{=}TAXA{*}(YW7579{*}LERatio7579)/YWW{*}1000 $$

$$ TAXA77=TAXA*(YW7579*LERatio7579)/YWW*1000 $$

$$ TAXA78{=TAXA{*}(YW7579{*LERatio7579)}/YWW{*1000} $$

$$ TAXA79=TAXA*(YW7579*LERatio7579)/YWW*1000 $$

$$ TAXA80=TAXA*(YW8084*LERatio8084)/YWW*1000 $$

$$ TAXA81=TAXA*(YW8084*LERatio8084)/YWW*1000 $$

$$ TAXA82=TAXA*(YW8084*LERatio8084)/YWW*1000 $$

$$ TAXA83{=}TAXA{*}(YW8084{*}LERatio8084)/YWW{*}1000 $$

$$ TAXA84=TAXA*(YW8084*LERatio8084)/YWW*1000 $$

$$ TAXA85{=}TAXA{*}(YW8589{*}LERatio8589)/YWW{*}1000 $$

$$ TAXA86{=}TAXA{*}(YW8589{*}LERatio8589)/YWW{*}1000 $$

$$ TAXA87=TAXA*(YW8589*LERatio8589)/YWW*1000 $$

$$ TAXA88{=TAXA{*}(YW8589{*LERatio8589)}/YWW{*1000} $$

$$ TAXA89{=}TAXA{*}(YW8589{*}LERatio8589)/YWW{*}1000 $$

$$ TAXA90=TAXA*(YW9094*LERatio9094)/YWW*1000 $$

$$ TAXA91=TAXA*(YW9094*LERatio9094)/YWW*1000 $$

$$ TAXA92=TAXA*(YW9094*LERatio9094)/YWW*1000 $$

$$ TAXA93=TAXA*(YW9094*LERatio9094)/YWW*1000 $$

$$ TAXA94=TAXA*(YW9094*LERatio9094)/YWW*1000 $$
$$ TAXB41=TAXB*Saving4044/SavingW*1000 $$

$$ TAXB42=TAXB*Saving4044/SavingW*1000 $$

$$ TAXB43=TAXB*Saving4044/SavingW*1000 $$

$$ TAXB44=TAXB*Saving4044/SavingW*1000 $$

$$ TAXB45{=}TAXB*Saving4549/SavingW*1000 $$

$$ TAXB46{=}TAXB{*}Saving4549/SavingW{*}1000 $$

$$ TAXB47{=}TAXB*Saving4549/SavingW*1000 $$

$$ TAXB48=TAXB*Saving4549/SavingW*1000 $$

$$ TAXB49=TAXB*Saving4549/SavingW*1000 $$

$$ TAXB50{=}TAXB{*}Saving5054/SavingW{*}1000 $$

$$ TAXB51=TAXB*Saving5054/SavingW*1000 $$

$$ TAXB52=TAXB*Saving5054/SavingW*1000 $$

$$ TAXB53{=}TAXB{*}Saving5054/SavingW{*}1000 $$

$$ TAXB54=TAXB*Saving5054/SavingW*1000 $$

$$ TAXB55{=}TAXB{*}Saving5559/SavingW{*}1000 $$

$$ TAXB56{=}TAXB{*}Saving5559/SavingW{*}1000 $$

$$ TAXB57{=}TAXB{*}Saving5559/SavingW{*}1000 $$

$$ TAXB58{=}TAXB{*}Saving5559/SavingW{*}1000 $$

$$ TAXB59{=}TAXB{*}Saving5559/SavingW{*}1000 $$

$$ TAXB60=TAXB*Saving6064/SavingW*1000 $$

$$ TAXB61{=}TAXB*Saving6064/SavingW*1000 $$

$$ TAXB62=TAXB*Saving6064/SavingW*1000 $$

$$ TAXB63{=}TAXB{*}Saving6064/SavingW{*}1000 $$

$$ TAXB64=TAXB*Saving6064/SavingW*1000 $$

$$ TAXB65{=}TAXB{*}Saving6569/SavingW{*}1000 $$

$$ TAXB66{=}TAXB{*}Saving6569/SavingW{*}1000 $$

$$ TAXB67{=}TAXB{*}Saving6569/SavingW{*}1000 $$

$$ TAXB68{=}TAXB*Saving6569/SavingW*1000 $$

$$ TAXB69=TAXB*Saving6569/SavingW*1000 $$

$$ TAXB70=TAXB*Saving7074/SavingW*1000 $$

$$ TAXB71{=}TAXB*Saving7074/SavingW*1000 $$

$$ TAXB72=TAXB*Saving7074/SavingW*1000 $$

$$ TAXB73{=}TAXB*Saving7074/SavingW*1000 $$

$$ TAXB74=TAXB*Saving7074/SavingW*1000 $$

$$ TAXB75{=}TAXB{*}Saving7579/SavingW{*}1000 $$

$$ TAXB76{=}TAXB{*}Saving7579/SavingW{*}1000 $$
$$ TAXB77=TAXB*Saving7579/SavingW*1000 $$

$$ TAXB78{=}TAXB{*}Saving7579/SavingW{*}1000 $$

$$ TAXB79{=}TAXB*Saving7579/SavingW*1000 $$

$$ TAXB80=TAXB*Saving8084/SavingW*1000 $$

$$ TAXB81{=}TAXB*Saving8084/SavingW*1000 $$

$$ TAXB82=TAXB*Saving8084/SavingW*1000 $$

$$ TAXB83{=}TAXB*Saving8084/SavingW*1000 $$

$$ TAXB84=TAXB*Saving8084/SavingW*1000 $$

$$ TAXB85{=}TAXB{*}Saving8589/SavingW{*}1000 $$

$$ TAXB86{=}TAXB{*}Saving8589/SavingW{*}1000 $$

$$ TAXB87{=}TAXB{*}Saving8589/SavingW{*}1000 $$

$$ TAXB88{=TAXB*Saving8589/SavingW*1000} $$

$$ TAXB89{=}TAXB{*}Saving8589/SavingW{*}1000 $$

$$ TAXB90=TAXB*Saving9094/SavingW*1000 $$

$$ TAXB91=TAXB*Saving9094/SavingW*1000 $$

$$ TAXB92=TAXB*Saving9094/SavingW*1000 $$

$$ TAXB93=TAXB*Saving9094/SavingW*1000 $$

$$ TAXB94=TAXB*Saving9094/SavingW*1000 $$

＜CAPTAX: 資本化された税＞

CAPTAX=CAPTAXX*GR08

＜CAPTAX00～CAPTAX94:資本化された税(各歳別)＞

$$ CAPTAX00=0 $$

$$ CAPTAX01=0 $$

$$ CAPTAX02=0 $$

$$ CAPTAX03=0 $$

$$ CAPTAX04=0 $$

$$ CAPTAX05{=}0 $$

$$ CAPTAX06=0 $$

$$ CAPTAX07{=}0 $$

$$ CAPTAX08=0 $$

$$ CAPTAX09=0 $$

$$ CAPTAX10=0 $$

$$ CAPTAX11=0 $$

$$ CAPTAX12=0 $$
$$ CAPTAX85=CAPTAX*Saving8589/SavingW*1000 $$

$$ CAPTAX86=CAPTAX*Saving8589/SavingW*1000 $$

$$ CAPTAX87=CAPTAX*Saving8589/SavingW*1000 $$

$$ CAPTAX88=CAPTAX*Saving8589/SavingW*1000 $$

$$ CAPTAX89=CAPTAX*Saving8589/SavingW*1000 $$

$$ CAPTAX90=CAPTAX*Saving9094/SavingW*1000 $$

$$ CAPTAX91=CAPTAX*Saving9094/SavingW*1000 $$

$$ CAPTAX92=CAPTAX*Saving9094/SavingW*1000 $$

$$ CAPTAX93=CAPTAX*Saving9094/SavingW*1000 $$

$$ CAPTAX94=CAPTAX*Saving9094/SavingW*1000 $$

＜TAXC:生産物に課せられる税＞

TAXC=TAXCX*GR08

＜TAXC00～TAXC94：生産物に課せられる税（各歳別）＞

TAXC00=0

TAXC01=0

TAXC02=0

TAXC03=0

TAXC04=0

TAXC05=0

TAXC06=0

TAXC07=0

TAXC08=0

TAXC09=0

TAXC10=0

TAXC11=0

TAXC12=0

TAXC13=0

TAXC14=0

TAXC15=0

TAXC16=0

TAXC17=0

TAXC18=0

TAXC19=0

TAXC20=TAXC*ConsExp2024/consw*1000
$$ CTRLG=CTRLG x*GR08*ExpCut $$

$$ $$

$$ IGVG{=}IGVG{x}{*}GR08{*}ExpCut $$

$$ CGVCG=CGVCG\times GR08\times ExpCut $$

＜TRLG：その他の経常移転・支払(国・地方)＞

TRL $ _{G} $ =TRL $ _{G} $ $ _{x} $ *GR $ _{08} $ *ExpCut

$$ $$

YIGVLG=YIGVLGx*GR08*ExpCut

G:資本移転·支払(一般政府內)(国·地方)>

$$ CTRPLG=CTRPLG\times GR08\times ExpCut $$

＜TRPLG:その他の経常移転・支払(一般政府内)(国・地方)＞

$$ \mathrm{TRPLG}=\mathrm{TRPLG}\times\left(1-\mathrm{D09C}\right)+\left(\mathrm{DFC1}+\mathrm{DFC2}\right)\times\mathrm{D09C} $$

CGVG=CGVIERRG+CGVIEDU+CGVCG

GNETEG=DEPG+CTRLG+IGVG+CGVCG+CGVIEDU+TRLG+YIGVLG+CTRPLG+TRPLG

EXPTG=CGVIERRG+BSSVG+SUB+TRPAGG+GNTEG

$$ $$

$$ YIGVLRG=YIGVLRG\times*(1-D09C)+DEBTG(-1)*(DiscountRate+DRadj)*D09C $$

EXPTG2=YIGVLRG+EXPTG
NETDEBTGaGDP=NETDEBTG/GDPV*100

DFCCAR=CSSVCAR-(CGVICAR+BSSVCAR)

DFCMED=CSSVMED-(CGVIMED+CGVIMEDE+BSSVMED)

DFCERR=(CSSVERRF+TRAF+CTRAF+YIGVAF+CTRPAF)-(BSSVERRF+CGVIERRF)

+DEPF+CTRLF+IGVF+TRL+YIGVLF+CTRPLF+TRPLF+TRPAFF+CGVCF+YIGVLRF)

DFC1=-DFCCAR-DFCMED-DFCERR

DFC2=KFR*BSSVPEN

PB=PBG+PBF

<BGV:財政收支(一般政府)>

BGV=BGGV+BGFV

DEBT=DEBTG+DEBTF

ASSET=ASSETG+ASSETF

NETDEBT2=ASSET-DEBT

PBaGDP=PB/GDPV*100
404	BSSVPENX	現物社会移転以外の社会給付・年金、実績値
405	CAPTAXX	資本化された税、実績値
406	CGVCFX	現実最終消費、実績値
407	CGVCGX	現実最終消費(国・地方)、実績値
408	CGVICARX	現物社会移転(個別消費支出)・介護、実績値
409	CGVIEDUX	現物社会移転(個別消費支出)・教育、実績値
410	CGVIERRGX	現物社会移転・その他(国・地方)、実績値
411	CGVIERRX	現物社会移転(個別消費支出)・その他、実績値
412	CGVIMEDEX	現物社会移転(個別消費支出)・その他医療、実績値
413	CGVIMEDX	現物社会移転(個別消費支出)・医療、実績値
414	CSSVCARX	社会負担・介護、実績値
415	CSSVERRGX	社会負担・その他(国・地方)、実績値
416	CSSVERRX	社会負担・その他、実績値
417	CSSVMEDX	社会負担・医療、実績値
418	CSSVPENX	社会負担・年金、実績値
419	CTRAFX	資本移転・受取(社会保障基金)、実績値
420	CTRAGX	資本移転・受取(国・地方)、実績値
421	CTRLFX	資本移転・支払(社会保障基金)、実績値
422	CTRLGX	資本移転・支払(国・地方)、実績値
423	CTRPLFX	資本移転・支払(一般政府内)(社会保障基金)、実績値
424	CTRPLGX	資本移転・支払(一般政府内)(国・地方)、実績値
425	DEBTGX	負債残高(国・地方)、実績値
426	DEPFX	固定資本減耗(社会保障基金)、実績値
427	DEPGX	固定資本減耗(国・地方)、実績値
428	GDPVX	国内総生産、実績値
429	GRCARX	介護負担伸び率、実績値
430	GRMEDX	医療負担伸び率、実績値
431	IGVFX	総固定資本形成(社会保障基金)、実績値
432	IGVGX	総固定資本形成(国・地方)、実績値
433	NIVX	国民所得、実績値
434	SUBX	補助金、実績値
435	TAXAX	所得富等経常税、実績値
436	TAXBX	資本所得税、実績値
437	TACX	生産物に課せられる税、実績値
438	TCIVX	消費税、実績値
439	TRAFX	その他の経常移転・受取(社会保障基金)、実績値
440	TRAGX	その他の経常移転・受取(国・地方)、実績値
441	TRLFX	その他の経常移転・支払(社会保障基金)、実績値
442	TRLGX	その他の経常移転・支払(国・地方)、実績値
443	TRPAFFX	その他の経常移転(社会保障基金)、実績値
444	TRPAGGX	その他の経常移転(国・地方)、実績値
445	TRPAX	その他の経常移転、実績値
446	TRPLFX	その他の経常移転・支払(一般政府内)(社会保障基金)、実績値
447	TRPLGX	その他の経常移転・支払(一般政府内)(国・地方)、実績値
448	TXFPX	固定資産税等、実績値
449	TXOHX	資本移転(相続税)、実績値
450	YIGVAFX	財産所得・受取(利子除く)(社会保障基金)、実績値
451	YIGVAGX	財産所得・受取(利子除く)、実績値
452	YIGVARFX	財産所得・受取(利子)(社会保障基金)、実績値
453	YIGVARGX	財産所得・受取(利子)、実績値
454	YIGVLFX	財産所得・支払(利子除く)(社会保障基金)、実績値
455	YIGVLGX	財産所得・支払(利子除く)、実績値
456	YIGVLRFX	財産所得・支払(利子)(社会保障基金)、実績値
457	YIGVLRXG	財産所得・支払(利子)、実績値
458	D00C	ダミー変数(2000年以降=1)
459	D00C08	ダミー変数(2000年から2008年まで=1)
460	D09C	ダミー変数(2009年以降=1)
461	D24C	ダミー変数(2024年以降=1)
462	DEBTF	債務残高(社会保障基金)
What Have We Learned from a Survey of Japanese Professional Forecasters?

Taking Stock of Four Years of ESP Forecast Experience

by

Takao Komine, Kanemi Ban, Masaaki Kawagoe and Hiroshi Yoshida

March 2009

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
# What Have We Learned from a Survey of Japanese Professional Forecasters? Taking Stock of Four Years of ESP Forecast Experience *

Takao Komine $ ^{\dagger} $

Kanemi Ban $ ^{\ddagger} $

Masaaki Kawagoe $ ^{\S} $

Hiroshi Yoshida $ ^{\P} $

March, 2009
This paper aims to take stock of four years of ESP forecast experience since its launch in 2004. The consensus performs well, compared to individual forecasters, which is confirmed probably for the first time in Japan. It satisfies the average form of rational expectations hypothesis defined in Pesaran and Weale (2006) at least in short forecast horizon. Remaining promising research agenda includes real-time data analysis of updating forecasters, subjective distribution, non-specialists' forecasts, changes in forecasts due to the Lehman shock.

## Abstract
## 1 Introduction

A monthly survey of Japanese professional forecasters, the ESP Forecast ('ESPF' hereafter) $ ^{1} $ , was launched in 2004. Although similar ad hoc surveys have been conducted in the past, the ESPF may have been the first regular publication to cover forecasts produced by business and academic economists. This initiative was roundly welcomed, and the survey has been established as a valuable information source – the Bank of Japan often presents the results in a figure in its Monthly Report of Recent Economic and Financial Developments, for example.

This paper will provide a bird’s-eye view of a three-year research project funded by the Economic and Social Research Institute (‘ESRI’ hereafter) of the Cabinet Office. The ESRI encourages academics to study ESPF database, hoping to obtain some policy implications.

The structure of the paper is as follows. The following section will examine the details and characteristics of the ESPF. The section 3 will summarise major results of applying an annual performance evaluation scheme to the consensus forecasts. Section 4 will turn to testing the rational expectations hypothesis. Remaining promising research topics are discussed in section 5. Section 6 will conclude the paper.

## 2 What is the ESPF?

### 2.1 Brief History

Before the start of the ESPF, there had been no reliable ‘anchor’ in macroeconomic forecasts. Media provided some information, although they usually cover a small number of economists – about a dozen at most – and is also conducted only on an ad hoc basis. The government’s official outlook might play some role, but it seems to fail to meet business needs because of its ‘official’ nature. For example, it is usually available once a year in late December for the purpose of formulating an annual budget for the next fiscal year (April to March), unless a supplementary budget is planned. It might not be neutral due to intentional optimism in geared towards containing political pressures to increase public expenditures in a recession. In this situation, the launch of the ESPF could be a valuable step to fill the gap.

The ESPF was formally launched in May 2004 after a trial in April. The Economic Planning Association distributes questionnaires to participants around the 25th of each month and publishes the result around the 10th of the following month. The participants are requested to provide their personal $ ^{2} $ forecasts of 16 variables for the current and next fiscal year (March to April) – seven and five of which are GDP and its components, and financial variables, respectively – in addition to three macro variables for quarters during the forecast period $ {}^{3} $ – 10 quarters at longest. They are requested to an
swers to some judgment questions. The number of participants was 38 at the start and, following a few dropouts and new entries every year, it is still the same as of January 2009.

### 2.2 Comparison and Extension

Compared with other surveys of forecasters (Table 1), it is rather obvious that the ESPF and the Blue Chip are similar. In fact, the ESPF was designed to follow a success of Blue Chip Economic Indicators. This is reflected in frequency of monthly publication, choice of forecasted indicators, especially annual forecast, and forecast period of two years. A difference is that variables forecasted quarterly are much fewer in the ESPF than in the Blue Chip. This is because of concerns at the time of the launch of the Survey that heavy burden might discourage forecasters to participate in it, which limits quarterly indicators to essential ones.

Another difference is that the ESPF keeps anonymity, while the Blue Chip does not. We relate this treatment with our request of personal forecasts. Because institutional forecasts may be updated every three months, i.e. less frequently than the ESPF requests, forecasters are likely to add their modifications to their institutional forecasts. It is concerned that if who place what are revealed, this might be embarrassing to forecasters $ ^{4} $ .

Table 1 also shows the ESPF is a medium-sized survey in terms of the number of participants and variables forecasted, i.e. smaller than the Blue Chip, the Survey of Professional Forecasters, and NABE Outlook Survey, but larger than the BOE survey in its Inflation Report.

## (Table 1 Comparison of the ESPF with Other Forecast Surveys)

The ESPF has been expanded with addition of special questions: a question of possible timing and direction of changes in the policy target interest rate was introduced in October, 2006 $ ^{5} $ , which was followed in January, 2008 by a question asking the next turning point of business cycle. These additions were motivated by a desire to address key policy questions. These special questions are extensively utilized in the NABE Outlook as well as the Blue Chip. The latest innovation is to set up questions about subjective distribution of GDP growth rate and CPI inflation, as is observed in the Survey of Professional Forecasters.

What is still missing in the ESPF concerns long-term projections, which are regular questions in the SPF. In particular, taking account of implications for monetary policy, introducing a question about long-term inflation expectation may be worthy of serious consideration. According to Croushore (1993, p.8), obtaining information about long-term inflation expectations is a major motive for FRB Philadelphia to take over the SPF from ASA and NBER in 1990. Although the Bank of Japan has just started to extract
such information from its survey named ‘the Opinion Survey on the General Public’s Views and Behaviour’, asking such a question may still be valuable.

## 3 Annual Performance Evaluation

### 3.1 Evaluation Scheme

The Economic Planning Association evaluates performance of individual forecasters and publicizes names of the best five forecasters every year, thereby encouraging the participants to improve their performance. The evaluation is based on RMSE (Root Mean Squared Error) of five variables $ {}^{6} $ : two for fiscal year, real and nominal GDP growth rates, and three for quarterly developments, real GDP growth rate (s.a.a.r.), CPI y-o-y inflation rate and unemployment rate (s.a.).

First of all, participants’ information sets need to be clear. They can observe March outcomes, say, released late April before submitting their May forecasts, the due date of which is usually around 5th. The time lag is longer for the quarterly estimate for GDP statistics: in the previous example, the last observation is the second estimate of Q4 figures, which is available in mid-March. The Q1 figures are released around 10th of May.

Now our evaluation scheme is shown as follows. Let $ f_{ijt}^{k} $ be a forecast placed by a forecaster i in at time t - j for an economic indicator k of time t, and $ y_{t}^{k} $ its outcome. Figure 1 to 3 provide overall pictures of forecasts and actual values for FY and quarterly GDP growth rate and quarterly CPI inflation rate.

(Figure 1 Forecasts and Actual Values of Fiscal Year Growth Rate)

(Figure 2 Forecasts and Actual Values of Quarterly Growth Rate)

(Figure 3 Forecasts and Actual Values of Quarterly CPI inflation Rate)

The forecast error is represented by:

$$ e_{ijt}^{k}\quad\equiv\quad y_{t}^{k}-f_{ijt}^{k}. $$

The forecasts errors are multiplied by weights, $ w_{jt}^{k} $ , to keep uncertainty faced by forecasters constant across time. For example, forecasting FY 2007 growth rate should be easy in May 2008, because actual values are available up to 2007Q4 and only 2008Q1 has to be forecasted, but difficult in January 2007, because all the four quarterly figures have to be forecasted. The weights are analytically calculated using estimates of dynamic regression models $ ^{7} $ .
The formulae for annual and quarterly figures are shown as follows,

$$ \begin{aligned}RMSE_{it}^{k}\quad&=\quad\left(\frac{1}{17}\sum_{j}(w_{jt}^{k}e_{ijt}^{k})^{2}\right)^{1/2},\quad k=RGDPY,NGDPY.\\RMSE_{it}^{k}\quad&=\quad\left[\frac{1}{4}\sum_{Q\in t}\left(\frac{1}{6}\sum_{j}(w_{jQ}^{k}e_{ijQ}^{k})^{2}\right)\right]^{1/2},\quad k=GDPQ,CPIQ,UNQ.\end{aligned} $$

In order to rank overall performance of a forecaster, it is necessary to aggregate the five RMSEs obtained from the formulae. An RMSE for the fiscal year is calculated based on 17 responses from January to May next year. As for quarterly projections, the last six responses are used while more observations are available. However, note the quarterly growth rate of real GDP is more volatile than CPI inflation. This is why we calculate a mean of T-scores across the five variables for each forecaster to obtain an indicator for total evaluation as below,

$$ \begin{array}{r c l}{T T L_{i t}}&{=}&{\displaystyle\frac{1}{5}\sum_{k}\left(50+10\times\frac{R M S E_{i t}^{k}-M e a n(R M S E_{t}^{k})}{S t d(R M S E_{t}^{k})}\right).}\\ \end{array} $$

Here smaller scores indicate better performances.

Some forecasters do not necessarily submit their projections for all variables each month. If such missing values are often observed in a variable $ {}^{8} $ , it is not evaluated. The overall evaluation for an individual forecaster requires that all five variables be evaluated. Note that if the number of missing values are rather small, evaluation is conducted, and a penalty is noted in the calculation, i.e. one and a half times the average of weighted MSE, $ (w_{jt}^{k}e_{ijt}^{k})^{2} $ , of submitted forecasts.

### 3.2 Evaluating the Consensus Forecast

Application of Eq.(2)-(4) to forecast error of the consensus forecast, $ e_{cjt}^{k} $ , shows it is a good forecast, ranked 5th to 10th place out of around 30 forecasters evaluated every year (Table 2). Kawagoe (2007b) confirmed that this result was robust with regard to changes in weights on forecast errors as well as to variations in ways of aggregating RMSEs of forecasted variables. Relatively good performance of the consensus forecast is a well established finding in the US. But this performance evaluation exercise confirmed this finding probably for the first time in Japan.

## (Table 2 Performance of the Consensus Forecast)

The merit of the consensus is usually explained by appealing to risk diversification, using an analogy common in portfolio investment. There are no perfect forecasts anywhere: each forecast misses something. In this situation, a 'portfolio of forecasts' does
variables. As Table 4 shows, the null is rejected in only one case with the longest forecast horizon. This may illustrate what a misleading result use of the consensus in the unbiasedness test leads to for individual regressions. Nevertheless, we think this result suggests the consensus is still quite useful for forecasting purposes, even though the care is needed for estimation. As for efficiency, the null is rejected in all cases except for those with the three shortest forecast horizons, which is consistent with results from individual regressions. Thus, at least in short forecast horizon, the concensus is likely to satisfy the average form of REH defined in Pesaran and Weale (2006).

## (Table 4 Tests of the Consensus Forecast)

## 5 Promising Research

### 5.1 Real-time Data Analysis

We have assumed there is an actual value. But this is not true. In Japan, the first estimate of quarterly GDP is released a month and a half after the end of the quarter, as explained above. The estimate is subsequently revised with the second estimate a month later and incoming annual statistics in December the following year. Furthermore, re-calculation of seasonal adjustments conducted with every release of new estimates also usually brings about non-negligible changes.

The analyses in the previous sections implicitly assume forecasters try to find the value of the first estimate. This assumption seems plausible as a first approximation to forecasters' behaviour, judging from our experience and anecdotal evidence. However, the revisions to the first estimates are too significant to be ignored.

According to Kawagoe (2007a), MAE of revision from the first to the most recent estimates is larger than 2 percentage points, almost comparable to mean growth rate, 2 and a half per cent (s.a.a.r.) (Table 5). Note that this size of revision is about median for OECD countries, but, alas, it is the largest among the G7 countries $ ^{9} $ .

## (Table 5 Revisions to first quarterly estimates of real GDP growth rate)

The large revisions posed a difficulty in evaluating individual performance last year. A series of strong figures of first quarterly estimates, followed by large downward revisions, ranked optimists high for quarterly, but low for fiscal year forecasts. Are they good forecasters?

As a first step to understand natures of revisions, Kawagoe (2007a) examined whether they are noise or news, following Mankiw and Shapiro (1986) $ ^{10} $ . A modified Eq. $ (5) $ is used,

$$ \begin{array}{r l r}{R_{t}^{i1}}&{{}=}&{\beta_{0}+\beta_{1}y_{t}^{1E}+\beta_{2}Z_{t}+\nu_{t},}\end{array} $$

where $ R_{t}^{i1} $ is a revision from the first estimate, $ y_{t}^{1E} $ to i the estimate, $ y_{t}^{iE} $ . Here two revisions are focused: 1st to 2nd, $ R_{t}^{21} $ and 1st to final (or the most recent), $ R_{t}^{F1} $ . If the