HIAS-E-122

The Efficiency of the Government’s
Revenue Projections

Natsuki Arai(a) , Nobuo Iizuka(b) , Yohei Yamamoto(c)
(a)
(b)
(c)

National Chengchi University
Kanagawa University
Hitotsubashi University

September 2022

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8668 http://hias.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:https://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

The Efficiency of the Government’s Revenue Projections∗Natsuki Arai† Nobuo Iizuka‡ Yohei Yamamoto§
September 2, 2022∗
The authors are grateful to Shunichiro Bessho, Neil Ericsson, Masayoshi Hayashi, Yasushi Iwamoto, Jaime
Marquez, Hikaru Ogawa, Tara Sinclair, and the seminar participants at George Washington University and the
University of Tokyo for their helpful comments. Arai gratefully acknowledges financial support from the Taiwanese
Ministry of Science and Technology’s grant (110-2410-H-004-183). All errors are the sole responsibility of the authors.
†
Corresponding author. Department of International Business, National Chengchi University. Address: No. 64,
Sec. 2, Tz-nan Rd., Wenshan, Taipei 11605, Taiwan. E-mail: narai@nccu.edu.tw.
‡
Department of Economics, Kanagawa University, Japan: nobuo-iizuka-0915@kanagawa-u.ac.jp.
§
Department of Economics, Hitotsubashi University, Japan: yohei.yamamoto@r.hit-u.ac.jp1Abstract
This paper evaluates the efficiency of the Japanese fiscal authority’s revenue projections
from 1960 to 2020 using real-time data. Revenue projections are not efficient, primarily due
to the conditioning projections of output growth. By adjusting the forecasts based on the
results of real-time forecast evaluations, this paper finds that the out-of-sample accuracy of the
one-year-ahead projections could be significantly improved by a magnitude of up to 10 percent
in root mean squared errors. The analysis of the disaggregated series suggests that corporate
tax projections are the least efficient. The fiscal authority’s loss function is estimated to beasymmetric, making the underprediction of revenues more common.

Keywords: Revenue Projections, Japan, Forecast Evaluation, Real-Time Data, Out-of-Sample
Forecast Accuracy
J.E.L. codes: C53, E62, H682

1

Introduction

Governments produce fiscal projections in their national budgets to maintain accountability for theuse of public funds. As noted by Elmendorf (2015), fiscal projections are essential inputs to debates
about national budgets and play a critical role in the formulation of fiscal policy. Although theaccuracy of fiscal projections has a substantial impact on a nation’s economic well-being, evaluationsof fiscal projections are scarce compared to those of macroeconomic projections, perhaps due to theirpolitical nature and short sample period. This issue has been widely recognized in the literature,
and a growing number of papers focus on evaluations of fiscal projections.1 However, these analyses
primarily focus on US data, and international evidence remains limited.
To fill this gap, this paper evaluates the efficiency of revenue projections made by Japan’s fiscal authority. Japan has a relatively long sample of fiscal projections from 1960 to 2020, withcorresponding real-time data, which enables us to make a fair comparison with evaluations of
the US. We primarily focus on revenue projections for two reasons. First, although the public
pays particular attention to deficit projections due to concerns about fiscal sustainability, errors
in deficit projections are largely driven by errors in revenue projections. The findings in the literature suggest that forecasting fiscal revenue is inherently more difficult than outlays because revenues depend on macroeconomic fundamentals that become nearly unpredictable, as documented
in Buettner and Kauder (2010).2 Second, many fiscal authorities make systematic mistakes in theirrevenue forecasting, often overestimating revenue.3 Investigating whether the Japanese fiscal authority has similar tendencies in its revenue projections is an interesting, but as yet unanswered,question.
To answer this question, this paper employs the standard methods of forecast evaluations proposed by Mincer and Zarnowitz (1969) and Patton and Timmermann (2012), which test whether
1

For example, Kliesen and Thornton (2001, 2012) evaluate fiscal projections made by the Congressional Budget
Office (CBO), and Croushore and van Norden (2018, 2019) analyze fiscal projections made by the Federal Reserve.
Ericsson and Martinez (2019) and Martinez (2015) provide evaluations of projections for federal debt in the US. See
Auerbach (1999) and Campbell and Ghysels (1995) for earlier studies.
2
For example, it has been extremely difficult to outperform simple reduced-form models forecasting output growth
in recent decades, as documented in Edge and Gürkaynak (2010), Faust and Wright (2013), and Tulip (2009).
3
For example, Booth et al. (2015) find that the CBO’s revenue projections have an upward bias, and Leal et al.
(2008) document similar overoptimism in a study of EU member countries. See Frankel (2011) for cross-country
evidence of overoptimism.

3

forecast errors and forecast revisions are predictable. This paper also uses the additional methodology proposed by Faust and Wright (2008) to control the effects of conditioning variables. The
analysis is based on a recently built real-time data set, which is critical for forecast evaluation, as
documented in Cimadomo (2016) and Croushore (2006).
The results of forecast evaluations show that the efficiency of revenue projections is significantly
rejected, particularly for one-year-ahead forecasts, with a positive bias and slope coefficient significantly smaller than unity. Unlike the US or EU member countries, the Japanese fiscal authority
tends to underestimate revenues. This inefficiency seems to be primarily due to projections madeduring recessions. However, efficiency is accepted once output growth projections are controlled asa conditioning variable.
Based on the rejection of forecast efficiency, this paper employs a method proposed by Croushore(2012) to adjust the systematic errors of forecasts in real time. The rejection of forecast efficiency
implies that a forecaster makes systematic mistakes. Since forecast evaluations incorporate thesesystematic mistakes, forecast accuracy could potentially be improved by collecting the predictedvalues, which effectively corrects past systematic mistakes in real time. We show that the out-ofsample accuracy of one-year-ahead revenue projections can be significantly improved by a magnitude of up to 10 percent in root mean squared errors (RMSEs) in recursive and rolling methods.
However, there is no significant improvement in nowcasts, perhaps because the forecast errors are
not systematic.
This paper provides two additional exercises to shed light on the sources of inefficiency. It
analyzes the disaggregated series of revenues—income, corporate, and consumption taxes—between
1989 and 2020. The efficiency of corporate tax projections is rejected, while those of income tax
and consumption tax are not. We also estimate the asymmetry of a forecaster’s loss function
by applying the methods proposed by Elliott et al. (2005). The fiscal authority’s loss function isestimated to be asymmetric, showing a greater aversion to negative forecast errors and implyingthat the underprediction of revenues is more common.
The contribution of this paper is twofold. First, it provides the first comprehensive assessmentof fiscal projections in Japan, employing methods of forecast evaluations based on real-time data.
The results are consistent with the literature documenting problems in official Japanese macroeco-

4

nomic forecasts—strong inefficiency and inferior performance relative to private forecasters.4 These
results could be interpreted as evidence of manipulations in budgetary projections based on political motives, such as in Paleologou (2005) for the UK, Pina and Venes (2011) for EU countries, andMaekawa and Fukushige (2012) for Japan.
Second, this paper provides additional evidence that the results of forecast evaluations could
be used to improve the accuracy of forecasts in real time, particularly when efficiency is rejected.
Several studies find that policy institutions’ forecasts can be improved in real time by adjusting
systematic errors,5 which is also the case for the Japanese fiscal authority.
The remainder of this paper is organized as follows: Sections 2 and 3 set out the data andmethods used. Section 4 presents the results of the efficiency evaluation. Section 5 provides theextensions, and Section 6 offers concluding remarks.

2

Data

In this paper, we focus on Japanese revenue projections normalized by real-time nominal output
from 1960 to 2020. The revenue projections are based on a fiscal year in Japan (from April to
March), and the timing is illustrated in Figure 1. The first projections are released before the fiscal
year starts, typically in December of the previous year, together with a proposal for the annual
budget. Then, the fiscal authority updates its projections in the middle of the fiscal year, typicallybetween October and December, which can be regarded as nowcasts. After the fiscal year ends,
the government publishes the realized values of revenues, typically in November.
Nominal output is obtained from the real-time data set compiled by Komaki (2009) and theTokyo Foundation for Policy Research. The base of output is GNP before 1990 and GDP thereafter.
The data between 1960 and 1968 are based on the vintage observed in 1969 due to the lack of older
vintages. The level of nominal GDP in a fiscal year is computed by adding the corresponding
quarterly GDP observed two quarters after the end of the fiscal year, following the convention
proposed by Reifschneider and Tulip (2007) and Faust and Wright (2009).6
4

For example, see Ashiya (2003, 2007), and Tsuchiya (2016).
For example, Arai (2014, 2020) finds significant improvement in out-of-sample forecast accuracy in the Federal
Reserve’s inflation forecasts and the CBO’s revenue projections.
6
More recently, Reifschneider and Tulip (2019) adopt an adjustment based on the current vintage, which has only55

We also use real output growth as the conditioning variable, which is computed by taking
percentage change relative to the previous year. The rationale for this computation is consistency
with the government’s output growth projections. As for nominal GDP, the computation is basedon the vintage observed two quarters after the fiscal year ends. Election and recession dummies
are used as additional control variables. Election dummies take the value of 1 when a lower houseelection is held during a fiscal year. For the recession dummies, we use the number of months
classified as a recession in a fiscal year, normalized by 12 months. The classification of businesscycles is based on official releases by the Economic and Social Research Institute of the Cabinet
Office.
Figure 2 shows the time series of forecast errors of one-year-ahead projections and nowcasts.
As is evident from the figure, the variation in one-year-ahead forecast errors is substantially larger
than that of nowcasts, ranging between -2.5 and 2 percent of nominal GDP.

3

Methodology

The methodology used in this paper is threefold: (1) forecast evaluation with a symmetric loss function, (2) conditional forecast evaluation, and (3) real-time adjustment based on forecast evaluation.
The notation follows Arai (2020).

3.1

Forecast Evaluation with a Symmetric Loss Function

We start with the Mincer-Zarnowitz (MZ) evaluation based on the assumption of a symmetric loss
function. Let yt+h be a variable at time t + h to be forecasted and let ŷt+h|t+j be a forecast of yt+h∗
at time t + j for any 0 < j < h. An optimal forecast, ŷt+h|t+j, should minimize the expected loss ofthe forecasts, L(·), which is a function of the forecast errors in the available information set Ωt+j
as follows:∗ŷt+h|t+j= arg min E[L(et+h|t+j )|Ωt+j ],ŷt+h|t+jmodest implications in terms of magnitude.

6(1)

where et+h|t+j ≡ yt+h − ŷt+h|t+j . By assuming the mean squared error loss function and taking thefirst-order condition,7 we derive the following optimality condition:∗ŷt+h|t+j= E[yt+h |Ωt+j ].

(2)This condition implies that the optimal forecasts should be the conditional mean of the series. Based on this implication, Mincer and Zarnowitz (1969) proposed the following regression toevaluate the efficiency of forecasts:

yt+h = α + β ŷt+h|t+j + εt+h ,(3)thereby jointly testing the null hypothesis that there is no bias in the forecasts (α = 0) and thatthe relationship between the forecasts and the realized values is one-to-one (β = 1).
More recently, Patton and Timmermann (2012) (PT) proposed a more powerful forecast efficiency evaluation at multiple horizons, testing the internal consistency of the forecasts. We first
define the forecast revision for period t + h between t and t + j, as rt+h|t,t+j ≡ ŷt+h|t+j − ŷt+h|t .
By replacing the forecast in Equation (3) with the sum of the forecast at a longer horizon andP
subsequent revisions, ŷt+h|t+j = ŷt+h|t + jk=1 rt+h|t+k−1,t+k , Equation (3) can be rewritten as
follows:
yt+h = α + β ŷt+h|t +jXγk rt+h|t+k−1,t+k + εt+h ,

(4)

k=1

with the null hypothesis of [α, β, γ1 , . . . , γj ] = [0, 1, 1, . . . , 1], where j denotes the number of forecast
revisions included in the regression. Unlike the MZ regression, this PT regression jointly tests theimplications of forecast efficiency that both forecast errors and forecast revisions are orthogonal topast forecasts.

3.2

Conditional Forecast Evaluation

The forecast evaluations discussed in the previous subsection assume that forecasters make unconditional forecasts, allowing us to test the unpredictability of forecast errors and revisions. However,7

For details, see Chapter 15 of Elliott and Timmermann (2016).

7

many economic forecasts are conditional in nature, in the sense that they are based on a particularpath of conditioning variables. For example, revenue projections may need to be consistent withgovernment’s official macroeconomic projections, which are revised slowly. Such restrictions on
conditioning forecasts may lead to endogeneity issues in forecast evaluations.
To mitigate these issues, we employ the method of conditional forecast evaluation proposed by
Faust and Wright (2008) (FW). We decompose the observed conditional forecasts into two components: optimal forecasts and the deviation in the conditioning assumptions from the optimal
forecasts. After controlling for the differences in the conditioning assumptions, we test the unpredictability of unconditional forecast errors.
Suppose that the fiscal variable yt depends on the m × 1 vector of conditioning macroeconomiccvariables, zt . The conditional forecasts for yt+h and zt+h at time t are denoted as ŷt+h|tandẑct+h|t , respectively. For simplicity, assume that the deviation of conditional fiscal forecasts from theoptimum is linearly associated with the corresponding deviations in the conditioning macroeconomic
forecasts as follows:c∗ŷt+h|t+j− ŷt+h|t+j= θ ′ (ẑct+h|t+j − ẑ∗t+h|t+j ).

(5)

In other words, the observed conditional forecasts deviate from the optimal forecasts becauseof the deviation in the conditioning assumptions. By combining this decomposition with the MZ
forecast evaluation in Equation (3), the baseline regression is rewritten as follows:cyt+h = α + β ŷt+h|t+j+ δ ′ (ẑct+h|t+j − ẑ∗t+h|t+j ) + εt+h ,(6)where δ = −βθ, with a null hypothesis of α = 0 and β = 1. As in the MZ evaluation, this null
hypothesis jointly tests whether there is no bias and the relationship between the forecasts andthe realized values is one-to-one. The only difference from the MZ evaluation is that we control
the deviation from the optimal forecasts in the path of conditioning assumptions to effectively test
the unpredictability of unconditional forecast errors. Note that there is no testable implicationfor δ, as it simply controls the deviations in the conditioning assumptions. Since the availabilityof unconditional conditioning forecasts (ẑ∗t+h|t+j ) is limited, we replace it with the realized value
8

(zt+h|t ) for the estimation.

3.3

Real-Time Adjustment Based on Forecast Evaluation

Based on the results of the forecast evaluation, we conduct a real-time forecasting exercise to see
whether the evidence against efficiency can be used to improve the accuracy of forecasts. Supposethat we run the MZ evaluation described in Equation (3) at time t. Then, we define the adjusted
forecast ỹt+h|t as the predicted value of forecast evaluation as follows:ỹt+h|t ≡ α̂t + β̂t ŷt+h|t ,(7)where α̂t and β̂t are the estimates based on the data vintage available at time t.8 The idea behind
this adjustment is that the regression coefficients of the forecast evaluation capture the systematic
mistakes that a forecaster made in the past, which can be used to correct the systematic tendency
in the most recent forecast. We form the adjusted forecast in real time by repeating this procedure
for every period to obtain predictions from the forecast efficiency evaluation.

4

Empirical Results

The results of the MZ evaluation are summarized in Table 1. The efficiency of the one-year-ahead
forecast is strongly rejected by the MZ evaluation, with positive biases and slopes significantly
smaller than 1 for multiple specifications. This result suggests that revenue projections tend tobe systematically smaller than realized values. In other words, the Japanese fiscal authority tends
to underestimate revenues, unlike the CBO in the US or the fiscal authorities of EU member
states. Although the additional control variables of election or recession months are not statisticallysignificant, the bias (2.11) and the coefficient on forecasts (0.83) in no recession periods are notsignificantly different from the values in the null hypothesis in the specification with recession
dummies. In contrast, the bias (3.34) and the coefficient on forecasts (0.62) in recession periods
further deviate from the values in the null hypothesis. This result sugges1ts that the projections
8
Since annual nominal GDP is available approximately two years after the first revenue forecasts are released, we
conduct the forecast evaluations using the data until period t − 2 to adjust the forecast made at period t.

9made during recessions may contribute to inefficiency.
For nowcasts, the overall efficiency is rejected, although individual coefficients are not statistically different from the values in the null hypothesis. Figure 3 compares the scatterplots of forecasts,
nowcasts, and realized values to show the contrast between forecasts and nowcasts. As is evident
from the figure, the deviation of the estimated slope from the 45-degree line is larger for forecasts
than for nowcasts, and the fluctuations of forecasts are substantially larger than those of nowcasts,
which likely reflects the information advantage in nowcasts.9
Table 2 provides the results of the PT and FW evaluations. The joint efficiency of revenue
projections that combine forecast errors and forecast revisions are strongly rejected by the PT
evaluation. The results of the FW evaluation show that both forecasts and nowcasts become
efficient once the forecast errors of the corresponding output growth projections are controlled.
These results imply that the inefficiency of revenue projections is mainly due to the inefficiency ofoutput growth projections, which are conditioning variables for revenue projections. These results
are similar to those of Arai (2020), which analyzes the CBO’s budgetary projections.
Table 3 presents the relative RMSEs of the different forecasting models compared to the original
forecast: the random walk model, the AR(1) model, the adjusted forecasts based on the MZ
evaluation, and the adjusted forecasts based on the vector-MZ evaluation. The most recent realized
value is treated as a forecast for the random walk model. The AR(1) model is estimated using
the vintage of realized values, and we take the prediction from the most recent observation as
the forecast. The MZ-adjusted forecasts are based on the MZ evaluation of revenue projections
described in Equation (7). The vector-MZ-adjusted forecasts are based on the joint MZ evaluationof revenue and output growth projections—we extend the framework in Equation (3) into multiple
series. Then, we take the prediction of revenue projections as the adjusted forecast. The first 31
years are used as a training period, and we compare the out-of-sample forecasting performance after
the training period with recursive and rolling estimations. The results show that the adjustment
significantly improves the accuracy of the one-year-ahead forecasts by a magnitude of up to 10
percent in RMSEs. These results imply that the fiscal authority makes a systematic mistake forthe one-year-ahead revenue projections and that correcting such mistakes makes the forecasts more
9This result is consistent with the discussion in Faust and Wright (2013) and Bańbura et al. (2013), which highlightthe different natures of forecasts and nowcasts in practice.

10

accurate in real time.
In contrast, the adjustment does not improve the accuracy of nowcasts. This is because theinefficiency of nowcasts is neither strong nor systematic, and the adjustment based on forecast
evaluations cannot improve forecast accuracy. In fact, the original nowcasts are far more accurate
than the random walk or the AR(1) model, suggesting that the fiscal authority successfully exploits
the information advantage of nowcasts to produce more accurate forecasts. The recursive and rolling
estimations lead to similar results, which implies that the results are robust.

5

Extensions

To shed light on the source of inefficiency, we provide two extensions to the main results: anevaluation of disaggregated revenue projections and an estimation of the asymmetry of the fiscal
authority’s loss function.

5.1

Evaluation of Diaggregated Revenue

We present the results of the MZ evaluation of the disaggregated series of revenues from 1989 to2020 in Table 4—income, corporate, and consumption taxes. The analysis of the disaggregatedseries suggests that the efficiency of corporate tax is significantly rejected, while those of income
tax and consumption tax are not. Although none of these tax projections has significant biases,
the slope of the corporate tax projections is 0.69 for forecasts and 0.85 for nowcasts, which leads
to the rejection of efficiency.10 The inefficiency of corporate tax projections is consistent with theresults of the conditional forecast evaluations—corporate tax is more sensitive to macroeconomic
conditions than the other taxes, and the inefficiency of macroeconomic projections leads to theinefficiency of corporate tax projections. This result is similar to results in the US, where corporate
tax projections exhibit the largest forecast errors, as discussed by Booth et al. (2015).
10

The rejection of efficiency is less severe relative to the whole sample, which is likely due to the lower power of
the tests with the short sample.

11

5.2

Estimation of an Asymmetric Loss Function

We then estimate the asymmetry of a forecaster’s loss function using the methodology proposed
by Elliott et al. (2005). Suppose that the forecaster has a piecewise asymmetric loss function as
follows:
L(et+h|t+j ) ≡ [α + (1 − 2α)1(et+h|t+j < 0)]|et+h|t+j |p ,(8)

where a larger deviation of α from 0.5 indicates a greater aversion to positive forecast errors.
Elliott et al. (2005) assume that a forecaster follows a systematic forecasting rule, f (θ), where θ
governs the weights of the variables in the information set. A simple example is the linear forecasting
rule f (θ) = θ ′ Vt+j , where Vt+j are the variables in the information set at t + j. By following asimilar discussion of the MZ evaluation and deriving the first-order condition, the optimal forecast
to minimize the expected loss leads to the following moment condition :E[Vt+j (1(et+h|t+j < 0) − α)|et+h|t+j |p−1 ] = 0.
|
{z
}

(9)

≡gt+j (α)

By exploiting this moment condition,11 α can be estimated by the generalized method of moments(GMM) as follows:α̂ = arg min gT (α)′ WgT (α),

(10)

α

where gT (α) =PT

t=1 gt+j (α), and W is an appropriate weighting matrix.

Table 5 shows the GMM estimates of an asymmetric loss function based on a different combination of instruments, including constant, past forecasts, past forecast errors, and past output growthforecasts. The null hypothesis of the symmetric loss function is significantly rejected in all specifications, with estimates smaller than 0.5. Based on the results of the J-statistics, we do not reject
the null that our instruments are exogenous. The estimated parameters of the loss function imply
that a forecaster shows a greater aversion to negative forecast errors, which is consistent with theresults of the MZ evaluation with positive biases. This result also suggests that the Japanese fiscal
authority tends to underpredict revenues and avoid a projection of surplus, unlike the authorities
11

Vt+j is replaced by f ′ (θ) if the forecasting rule is nonlinear.

12

in the US or in EU member countries who tend to be overoptimistic.

6

Conclusion

In this paper, we provide a comprehensive evaluation of the Japanese fiscal authority’s revenue
projections from 1960 to 2020 and find several sets of results. First, the efficiency of revenue
projections is strongly rejected, particularly for the one-year-ahead forecast, which is likely due
to inefficiency in conditioning forecasts. Then, we show that evidence against efficiency can beused to improve the accuracy of forecasts in real time by correcting past systematic mistakes. By
studying disaggregated projections, we find that corporate tax projections are the least efficient.
Finally, the Japanese fiscal authority’s loss function is estimated to be asymmetric, preferring theunderprediction of revenues.
Given the highly political nature of revenue projections that involve the discussion of the national budget, it may be possible that the Japanese fiscal authority has a particular preference forunder/over predictions of revenue, which leads to the rejections of efficiency revealed in this paper.
However, maintaining such systematic errors may undermine the credibility of revenue projectionsin the long run. Providing a comprehensive evaluation of forecast efficiency is crucial to controlling the quality of forecasts. Since the proposed adjustment based on forecast evaluations is fairly
straightforward to implement, policy institutions could consider this adjustment a viable option for
their forecasting and evaluations.

13

References
Arai, Natsuki, “Using Forecast Evaluation to Improve the Accuracy of the Greenbook Forecast,”
International Journal of Forecasting, January 2014, 30 (1), 12–19.
, “Investigating the Inefficiency of the CBO’s Budgetary Projections,” International Journal of
Forecasting, 2020, 36 (4), 1290–1300.
Ashiya, Masahiro, “Testing the Rationality of Japanese GDP Forecasts: the Sign of Forecast
Revision Matters,” Journal of Economic Behavior & Organization, 2003, 50 (2), 263–269.
, “Forecast Accuracy of the Japanese Government: Its Year-Ahead GDP Forecast Is Too Optimistic,” Japan and the World Economy, 2007, 19 (1), 68–85.
Auerbach, Alan J., “On the Performance and Use of Government Revenue Forecasts,” National
Tax Journal, December 1999, 52 (4), 765–82.
Bańbura, Marta, Domenico Giannone, Michele Modugno, and Lucrezia Reichlin, “NowCasting and the Real-Time Data Flow,” in Graham Elliott and Allan Timmermann, eds., Handbook of Economic Forecasting, Vol. 2, Elsevier, 2013, chapter 4, pp. 2–56.
Booth, Mark, Logan Timmerhoff, and David Weiner, “CBO’s Economic Forecasting Record:
Forecast Errors for CBO’s and the Administration’s Two-Year Revenue Projections,” Congressional Budget Office 2015.
Buettner, Thiess and Bjoern Kauder, “Revenue Forecasting Practices: Differences acrossCountries and Consequences for Forecasting Performance,” Fiscal Studies, 2010, 31 (3), 313–
340.
Campbell, Bryan and Eric Ghysels, “Federal Budget Projections: A Nonparametric Assessment of Bias and Efficiency,” The Review of Economics and Statistics, February 1995, 77 (1),
17–31.
Cimadomo, Jacopo, “Real-Time Data and Fiscal Policy Analysis: A Survey of the Literature,”
Journal of Economic Surveys, 2016, 30 (2), 302–326.
14Clark, Todd E. and Kenneth D. West, “Approximately Normal Tests for Equal Predictive
Accuracy in Nested Models,” Journal of Econometrics, May 2007, 138 (1), 291–311.
Croushore, Dean, “Forecasting with Real-Time Macroeconomic Data,” in G. Elliott, C. Granger,
and A. Timmermann, eds., Handbook of Economic Forecasting, Vol. 1, Elsevier, 2006, chapter 17,
pp. 961–982.
, “Comment on ‘Forecast Rationality Tests Based on Multi-Horizon Bounds’,” Journal of Business and Economic Statistics, January 2012, 30 (1), 17–20.
and Simon van Norden, “Fiscal Forecasts at the FOMC: Evidence from the Greenbooks,”
The Review of Economics and Statistics, December 2018, 100 (5), 933–945.
and, “Fiscal Surprises at the FOMC,” International Journal of Forecasting, 2019, 35 (4),1583–1595.
Edge, Rochelle M. and Refet S. Gürkaynak, “How Useful Are Estimated DSGE Model
Forecasts for Central Bankers?,” Brookings Papers on Economic Activity, Fall 2010, 2.
Elliott, Graham, Allan Timmermann, and Ivana Komunjer, “Estimation and Testing of
Forecast Rationality under Flexible Loss,” The Review of Economic Studies, 2005, 72 (4), 1107–
1125.
and

, Economic Forecasting, Princeton University Press, 2016.

Elmendorf, Douglas W., “‘Dynamic Scoring’: Why and How to Include Macroeconomic Effects
in Budget Estimates for Legislative Proposals,” Brookings Papers on Economic Activity, Fall
2015.
Ericsson, Neil R. and Andrew B. Martinez, “Evaluating Government Budget Forecasts,”in Daniel Williams, ed., The Palgrave Handbook of Government Budget Forecasting, Palgrave
Macmillan, 2019, chapter 3, pp. 37–69.
Faust, Jon and Jonathan H. Wright, “Efficient Forecast Tests for Conditional Policy Forecasts,” Journal of Econometrics, October 2008, 146 (2), 293–303.
15

and

, “Comparing Greenbook and Reduced Form Forecasts using a Large Realtime Dataset,”

Journal of Business and Economic Statistics, October 2009, 27 (4), 468–479.
and, “Forecasting Inflation,” in Graham Elliott and Allan Timmermann, eds., Handbook of

Economic Forecasting, Vol. 2, Elsevier, 2013, chapter 3, pp. 2–56.
Frankel, Jeffrey, “Over-Optimism in Forecasts by Official Budget Agencies and Its Implications,”
Oxford Review of Economic Policy, December 2011, 27 (4), 536–562.
Kliesen, Kevin L. and Daniel L. Thornton, “The Expected Federal Budget Surplus: How
Much Confidence Should the Public and Policymakers Place in the Projections?,” Federal Reserve
Bank of St. Louis Review, 2001.
and, “How Good Are the Government’s Deficit and Debt Projections and Should We Care?,”Federal Reserve Bank of St. Louis Review, 2012.
Komaki, Yasuyuki, “The Construction of the Real-Time Data Set and an Evaluation of Market
Expectation with the Data Set,” 2009. Grant-in-Aid for Scientific Research (C), Japan Society
for Promotion of Science.
Leal, Teresa, Javier J. Pérez, Mika Tujula, and Jean-Pierre Vidal, “Fiscal Forecasting:Lessons from the Literature and Challenges,” Fiscal Studies, 2008, 29 (3), 347–386.
Maekawa, Satoko and Mototsugu Fukushige, “Tax Projections and Economic Forecasts by
Government Bureaucrats: Hidden Manoeuverings Behind Fiscal Reconstruction in Japan,” The
Japanese Economic Review, December 2012, 63 (4), 528–545.
Martinez, Andrew B., “How Good Are US Government Forecasts of the Federal Debt?,” International Journal of Forecasting, 2015, 31 (2), 312 – 324.
Mincer, Jacob A. and Victor Zarnowitz, “Economic Forecasts and Expectations: Analysis of
Forecasting Behavior and Performance,” in Jacob A. Mincer, ed., The Evaluation of Economic
Forecasts, NBER, 1969, pp. 3–46.

16

Paleologou, Susanna-Maria, “Political Manoeuvrings as Sources of Measurement Errors in Forecasts,” Journal of Forecasting, 2005, 24 (5), 311–324.
Patton, Andrew J. and Allan Timmermann, “Forecast Rationality Tests Based on MultiHorizon Bounds,” Journal of Business and Economic Statistics, 2012, 30 (1), 1–17.
Pina, Alvaro M. and Nuno M. Venes, “The Political Economy of EDP Fiscal Forecasts: An
Empirical Assessment,” European Journal of Political Economy, 2011, 27 (3), 534–546.
Reifschneider, David and Peter Tulip, “Gauging the Uncertainty of the Economic Outlook
from Historical Forecasting Errors,” November 2007. Working Paper.
and, “Gauging the Uncertainty of the Economic Outlook Using Historical Forecasting Errors:

The Federal Reserve’s Approach,” International Journal of Forecasting, 2019, 35 (4), 1564–1582.
Tsuchiya, Yoichi, “Assessing Macroeconomic Forecasts for Japan under an Asymmetric Loss
Function,” International Journal of Forecasting, 2016, 32 (2), 233–242.
Tulip, Peter, “Has the Economy Become More Predictable? Changes in Greenbook Forecast
Accuracy,” Journal of Money, Credit and Banking, 2009, 41 (6), 1217–1231.

17

Fiscal Year
Year 1

April

Forecast(December)Year 2

March

Nowcast(October-December)Realized Value(November)

Note: This figure illustrates the timeline of revenue projections made by the Japanese fiscal authority and its relationship with the Japanese fiscal year.

Figure 1: Timeline of Revenue Projections18

2

Forecast
Nowcast1.5

Forecast Errors (ratio to GDP)

1

0.5

0

-0.5

-1

-1.5

-2

-2.5
1960

1970

1980

1990

2000

2010

Fiscal Year

Figure 2: Forecast Errors of Revenue Forecasts

19

2020

14
1988

1990

1989

1987

13

1991

Realized Value

1986
12
1985
1983
1984
2020
1980
1974
2014
2018
2017 1995
1997
1994
2015
1979
1978
1996
2016 2019
1972
1961
1962
1970
1960
1998
1963 2000 1964 1971
2007
2005
2013
1969
2006
2001
1965
1968
2012
1976
1975
1999
2004
1967
1977
2008
19662011
2002
2010 2003
1973

11

10

9

8

1981

19931992
1982

13

14

2009

7
7

8

9

10

11

12

Forecasts

14
1988
1987

13

1990
1989

1991

Realized Value

1986
12

11

10

9
2010
2003
8

1985
1992
1983
1984 1993
1982
1981
2020 19731980
2014 2018 197420171994 1997
1995
2015
1979
1978
1996
2016 20191961 1972 1970
1962
1964
19602000
1998
1963
2007
1971
2005
2013
1969
2006
2001
1965
1968
2012
1976
1975
1999
2004
1967
1977
2011
2008
1966
2002

2009

7
7

8

9

10

11

12

13

14

Nowcasts

Note: The black dotted line is the 45-degree line, and the red solid line is the linear fitted line.

Figure 3: Forecasts, Nowcasts, and Realized Values

20Specification(1)

Estimates:
Constant

3.49∗∗( 1.05)0.67∗∗( 0.11)

Forecasts
Election
Election×Forecasts

Forecasts(2)3.65∗∗( 1.13)0.65∗∗( 0.11)−1.03( 1.22)0.13( 0.12)

Recession
Recession×Forecast
Wald Statistic
Adjusted R2

15.38∗∗
0.59

20.09∗∗
0.59

(3)
2.11
( 1.10)0.83( 0.12)

1.23( 1.57)−0.21( 0.15)49.09∗∗
0.66

(1)

(
(

0.59
0.56)
0.95
0.06)

Nowcasts
(2)
0.46
0.72)
0.96
( 0.04)0.26( 0.60)−0.01( 0.06)
(

(3)

(
(

0.05
0.44)
1.01
0.05)

1.65
1.00)
−0.16
( 0.10)16.40∗∗
0.92(

12.58∗∗
0.92

a.

36.59∗∗
0.92

This table shows the results of the MZ forecast evaluation in Equation (3) with the additional control variables of election
and recession dummies.
b.
Heteroscedasticity and autocorrelation robust (HAC) standard errors are listed in parentheses. ∗∗ denotes the significanceat the level of 1 percent.

Table 1: MZ Evaluations of Revenue Projections (1960–2020)

21

PT Evaluation
Estimates:
Constant

0.64
0.51)
0.95
( 0.05)1.05( 0.09)17.30∗∗
0.92(

Forecasts
Revisions
Wald Stat.
Adjusted R2

FW Evaluation
Forecasts
Nowcasts

(
(

0.55
1.23)
0.96
0.12)

0.96
0.44

(
(

0.41
0.60)
0.97
0.06)

3.17
0.92

a.

This table shows the results of the PT evaluation in Equation (4)and the FW evaluation in Equation (6).
b.
As for the note in Table 1.

Table 2: PT and FW Evaluations of Revenue Projections (1960–2020)22

Random Walk
Recursive
Forecasts
1.07
Nowcasts
2.57
Rolling with Window of 30 Years
Forecasts
1.07
Nowcasts
2.57

AR(1)

MZ-Adjusted

Vector-MZ-Adjusted

1.07
2.58

0.90∗∗
1.02

0.91∗∗
1.04

1.11
2.67

0.93∗∗
1.06

0.94∗∗
1.16

a.

This table shows the out-of-sample RMSEs relative to the original revenue projections. We use
the first 31 years as a training period to compare the forecast accuracy in the next 30 years.
b. ∗∗denotes the significance level at 1 percent based on Clark and West (2007).

Table 3: Comparison of Out-of-Sample RMSEs

23

Series

Income Tax

Corporate Tax

Consumption Tax

Panel A: Forecasts
Estimates:
Constant
Forecasts
Wald Statistic
Adjusted R2

0.00( 0.00)0.87( 0.12)
1.84
0.80

(
(

0.01
0.00)
0.69∗∗
0.13)
5.89∗
0.68

(
(

0.00
0.00)
0.99
0.03)
1.54
0.99

Panel B: Nowcasts
Estimates:
Constant
Forecasts
Wald Statistic
Adjusted R2

0.00( 0.00)1.01( 0.06)
4.18
0.97

(
(

0.00
0.00)
0.85∗∗
0.05)
8.35∗
0.92

(
(

0.00
0.00)
1.04∗
0.02)
4.08
0.99

a.

This table shows the results of the MZ forecast evaluation in Equation (3) for
the disaggregated series of revenue projections.
b.
Heteroscedasticity and autocorrelation robust (HAC) standard errors are listed
in parentheses. ∗ and ∗∗ denote the significance at the level of 5 percent and 1
percent, respectively.

Table 4: MZ Evaluations of Disaggregated Revenue Projections (1989–2020)24

Forecasts
p=1
p=2

Nowcasts
p=1
p=2

Panel A: Constant and Past Forecast Errors
Estimate
J-Statistic

0.28∗∗( 0.06)3.62

0.24∗∗( 0.08)4.73∗

0.29∗∗( 0.05)2.39

0.38( 0.08)3.43

0.29∗∗( 0.05)0.35

0.21∗∗( 0.06)
1.87

Panel B: Constant and Past Forecasts
Estimate
J-Statistic

0.27∗∗( 0.05)3.22

0.30∗∗( 0.08)
3.69

Panel C: Constant, Past Forecasts, and Forecast Errors for Growth
Estimate
J-Statistic

0.28∗∗( 0.05)3.24

0.30∗∗( 0.08)3.71

0.29∗∗( 0.05)1.61

0.16∗∗( 0.06)
4.70∗

a.

This table shows the estimates of alpha in Equation (10) with different sets of
instruments.
b.
The test is based on the null hypothesis of α = 0.5. Inference is based on HAC
standard errors. ∗ and ∗∗ denote the significance at the level of 5 percent and
1 percent, respectively.

Table 5: Estimates of Asymmetric Loss Function

25