HIAS-E-88

Forecasting Public Investment Using Daily Stock Returns
Hiroshi Morita
Institute of Comparative Economic Studies, Hosei University

August, 2019

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
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http://hias.ad.hit-u.ac.jp/
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Forecasting Public Investment Using Daily Stock Returns✩
Hiroshi Morita∗
Institute of Comparative Economic Studies, Hosei University
4342 Aihara, Machida, Tokyo 194-0298, Japan

Abstract
This paper investigates the predictability of public investment in Japan using the daily excess
stock returns of the construction industry, to contribute to the recent discussion on fiscal foresight. To examine the relationship between monthly public investment and daily stock returns
without any prior time aggregation, we employ the VAR model with MIDAS regression andestimate the optimal weights for connecting high-frequency and low-frequency data in addition to VAR coeﬃcients and the variance-covariance structure. We find that the VAR modelwith MIDAS regression reduces the mean square prediction error in out-of-sample forecastingby approximately 15% and 2.5% compared to the no-change forecast and VAR model forecasting with prior time aggregation, respectively. Moreover, using the local projection method, we
find evidence of the fiscal news shock estimated in our proposed model delaying positive eﬀects
on output, consumption, hours worked, and real wage when news shocks actually result in increasing public investment. This finding suggests the New Keynesian structure of the Japanese
economy.
JEL classification: C22, C53, E62
Keywords: MIDAS regression, fiscal foresight, stock returns, local projection method.

✩

I am grateful to Etsuro Shioji, Toshiaki Watanabe, Naoko Hara, and seminar participants at The 5th Hitotsubashi Summer Institute for their helpful comments and suggestions. This study is part of an ongoing research
project with Etsuro Shioji (Hitotsubashi University). The research has been funded by Grant-in-Aid for Young
Scientists 19K13652 and Nomura Foundation. Errors, if any, are entirely the author’s responsibility.
∗
Email: morita-h@hosei.ac.jp, T el: +81-42-783-2558.

1. Introduction
Financial market variables contain much information to help forecast variations in macroeconomic data. Taking advantage of this desirable property of financial data, we investigate thepredictability of public investment in Japan using the daily excess stock returns of the construction industry. This paper contributes to the recent discussion on fiscal foresight, where thefocus is on fiscal policy foreseeability and to understand how it aﬀects the economy (Mertens
and Ravn, 2010; Leeper et al., 2012, 2013). That is, this paper tries to identify the series offiscal news shocks and reveal their eﬀect on macroeconomic variables by forecasting public investment using the daily stock returns of the construction industry. To achieve our purpose,
we develop a model that directly connects monthly public investment with daily stock returns
using mixed-frequency data.
The literature has been continually examining the eﬀect of government spending and public
investment shocks (hereinafter, fiscal policy shock), but there is little consensus on its macroeconomic eﬀect. Two strands of time series analysis exist in the literature on the eﬀect of fiscal
policy, the VAR-based analysis conducted by Blanchard and Perotti (2002), Galı́ et al. (2007),and Mountford and Uhlig (2009), and the narrative approach adopted by Ramey and Shapiro(1998), Burnside et al. (2004), and Ramey (2011). The narrative approach mainly adopts war
dummies to capture fiscal policy shock, because war is closely related to increases in government(military) spending. VAR analyses document the positive eﬀects of government spending on
consumption and real wage as well as output, while the narrative approach shows that fiscal
policy shocks induce a decline in consumption and real wage. Ramey (2011) states that the two
strands diﬀer in the timing of identifying fiscal policy shock. Furthermore, the VAR approach
might fail to capture the true timing of innovation because changes in government spending are
anticipated before they actually occur owing to implementation lag. Following Ramey (2011),
this paper focuses on fiscal news shocks to show the true eﬀect of fiscal policy shock. Moreover, we need to understand its true eﬀect in terms of evaluating the role of economic stimulus
packages as well as distinguishing the competing macroeconomic models.
This paper considers the Japanese economy. The Japanese government implemented numerous fiscal stimulus packages after their bubble economy collapsed in the early 1990s and the
2007–08 global financial crisis. More recently, they adopted large-scale fiscal expansion policies as part of Prime Minister Abe’s economic reforms, the so-called Abenomics; this included
the reconstruction of Japan after the earthquake disaster. Therefore, we consider the Japanese
economy a suitable subject for study in that it presents scores of fiscal events to be forecasted.
In addition, the Japanese fiscal policy has been mainly analyzed using the VAR model, which2does not consider fiscal foresight. Only a few recent studies have examined fiscal news shocks
in Japan; for example, Fukuda and Yamada (2011), Morita (2017), Shioji (2017) and Kanazawa(2018). Thus, we consider it worthwhile to study the eﬀect of fiscal news shocks in the Japanese
economy.
This paper follows the method of Fisher and Peters (2011), who used the stock returns oflarge military contractors to identify the anticipated US military spending shocks. The method
they used to identify fiscal news shocks could resolve the shortcomings of the narrative approach,where the number of fiscal innovations captured by war dummies are limited; they addressed
this issue by extracting fiscal news shocks from time series of stock returns. The strategy ofFisher and Peters (2011) presumes that the financial market variables reflect almost all thecurrent available information. Morita (2017) applies this method to the Japanese economy byreplacing the military industry with the construction industry, because fiscal policy for economic
stimulus is executed via public works in Japan.1 Here, we need to purify fiscal news shocks fromraw stock returns shocks because not all stock return variations are due to fiscal news shocks.
Fisher and Peters (2011) propose the use of excess stock returns obtained by eliminating themarket returns, while Morita (2017) uses the excess stock returns and then adopts the robust
sign restriction method; fiscal news shocks are identified by imposing sign restrictions derived
from the theoretical model.
The aforementioned studies consider the contamination of information in stock returns
caused by factors other than fiscal news, but pay little attention to attenuate the information due to time aggregation of the data. Previous studies generally examine the eﬀects of fiscal
news shock on macroeconomic variable using the information of stock returns. Of course, stock
returns is high-frequency data collected at (intra-)daily frequency, whereas the macroeconomic
variables such as output and consumption are low-frequency data released at monthly or quarterly frequencies. If the data frequencies in the analysis are mixed, the high-frequency data (i.e.,
stock returns) will be normally integrated with the low-frequency data through time aggregation.
In this case, the information originally contained in the high-frequency data might be discarded
by such time aggregation, as pointed out in the forecasting literature (e.g., Ghysels et al., 2007).
In particular, we can reasonably assume that such time aggregation of stock returns can dilute
the information from noisy variation in stock returns. Hence, we use mixed frequency analysis
to examine the relationship between monthly public investment and daily stock returns; this is1

Shioji (2017) and Kanazawa (2018) also use the stock returns of construction industry to identify the fiscal

news shocks eﬀect in Japan.

3

known as Mixed Data Sampling (MIDAS) regression.2 MIDAS regression is widely accepted inoil price forecasting analysis using financial market variables (Baumeister et al., 2015) or nowcasting macroeconomic data (Foroni et al., 2015; Ghysels and Ozkan, 2015). To the best of ourknowledge, few studies have used MIDAS regression to analyze macroeconomic policy; Francis
et al. (2011) focus on the eﬀect of monetary policy. Thus, this paper can be said to establish a
novel method, at least in this literature, to refine fiscal shock from a diﬀerent standpoint.
The outline of this paper is summarized as follows. We first examine the predictability of
public investment using the construction industry’s daily stock returns to check whether they
can be considered as a proxy for fiscal news shocks. For this, we build the VAR model with
MIDAS regression by including both monthly public investment and daily stock returns in asingle VAR system. We then compare the mean square prediction error (MSPE) in the VAR
model with MIDAS regression with those obtained from other possible models. We first confirm
that the stock returns of construction industry can forecast a variation in public investment in
the future, and then compute the impulse responses of some macroeconomic variables to fiscal
news shock.
Our main finding in this study is that a variation in public investment is predicted by thestock returns of construction industry in Japan. The MIDAS specification significantly improves
the predictability by as much as 2.5% compared to using time-aggregated monthly stock returns.
We also find delayed positive responses of output, consumption, hours worked, and real wage tofiscal news shocks. This finding supports the evidence that the Japanese economy is consistent
with the New Keynesian structure.
The remainder of this paper is structured as follows. Section 2 explains the structure andestimation method for VAR models with MIDAS regression employed in this paper. Section 3
presents our data description, with the empirical results presented in two parts: out-of-sample
forecasting, and impulse responses of macroeconomic variables. Section 4 concludes the paper.

2

An alternative procedure with mixed data frequency is the mixed-frequency(MF-) VAR model proposed by

Schorheide and Song (2015). In this model, the unobserved high-frequency data originally published at low
frequency are regarded as latent variables and estimated using the Kalman filter. In our case of relating monthly
and daily data, however, we need to estimate a lot of latent variables because over twenty daily latent observations
need to be estimated by the month. Moreover, Bai et al. (2013) document little to choose between MIDAS
regression and the MF-VAR model for accuracy of predictability. Therefore, we adopt MIDAS regression in thispaper.

4

2. Estimation model
2.1. VAR model with MIDAS regression
We first explain the VAR model with MIDAS regression; this allows us to directly deal withtime series data sampled at diﬀerent frequencies in a single VAR system. We then use a simple
two-variable VAR model allowing for forecasting public investment using excess stock returnsof the construction industry (hereinafter, stock returns).
Let ytM denote a vector of endogenous variables at monthly frequency consisting of public
investment (gtM ) and stock returns (ertM ) in this order. The VAR system is written as
M + · · · + Φ yM + u ,ytM = Φ1 yt−1
p t−p
t

(1)

ut ∼ N (0, Σ),
where Φs (s = 1, · · · , p) is a coeﬃcient matrix with lag order s and Σ is a variance-covariancematrix for the reduced-form residuals vector denoted by ut . Following MIDAS regression, weconstruct the monthly stock returns in the VAR system as a weighted average of daily returns
as follows:
ertM =d!

Dωj (γ1 , γ2 )ert,j−1
,

(2)

j=1

"
#
exp γ1 j + γ2 j 2

ωj (γ1 , γ2 ) = $d2
j=1 exp {γ1 j + γ2 j }

,

(3)

D
where ert,j−1
denotes the daily stock returns at the j − 1st business day before the month-end

t, and the form of weighting function ωj (γ1 , γ2 ) is the exponential Almon lag polynomial, as in
Baumeister et al. (2015).3 Note that MIDAS regression is a data-driven aggregation scheme
because the shape of the weighting function is estimated using available information (Francis etal., 2011). In other words, the weights on daily stock returns are estimated to improve the fitnessof the entire monthly VAR system, and hence ertM can be an appropriate monthly stock returns
series in that they can be adjusted to explain the variation in endogenous variables better than
the series obtained by way of an arithmetic average.
3

Foroni et al. (2015) propose the unrestricted(U-) MIDAS regression, where the counterparts of eq. (2) aresimply described as
ertM =d!

D
αj ert,j−1.

j=1

Although this model can be conveniently estimated because of its linearity, the number of parameters to be
estimated (i.e., αj ) will be relatively large in our case if we adopt U-MIDAS specification instead of the exponential
Almon lag polynomial.

5

2.2. Bayesian inference% M&
M
We define XtM = I ⊗ yt−1
, · · · , yt−pand Φ = [vec(Φ1 )′ , · · · , vec(Φp )′ ]′ , where the vec

operator creates a column vector from Φs (s = 1, · · · , p), by stacking the column vectors of Φs ,and ⊗ denotes the Kronecker product. Then, eq. (1) can be rewritten as
ytM = XtM Φ + ut ,(4)

ut ∼ N (0, Σ).
The parameters to be estimated here are summarized in Θ = [Φ, Σ, γ1 , γ2 ]. We estimate theseparameters using the random-walk Metropolis-Hastings (RW-MH) algorithm of the BayesianMarkov Chain Monte Carlo (MCMC) method. Since the RW-MH algorithm samples parameters
by drawing candidates from the proposal distribution, we can estimate the VAR model with
MIDAS regression relatively easily even with the nonlinearity in eq. (3). Given the data Y andprior distribution π(Θ), we sample from the posterior distribution π(Θ | Y ) as follows:
1. Find the posterior mode Θ̂ of ln π(Θ | Y ).
2. Set Θ(0) = Θ̂ and n = 1.
(n)

(n)

3. Sample Θproposal from Θproposal = Θ(n) + νt , νt ∼ N (0, cH).
' !
"
(n)

4. Calculate the acceptance probability q = minf Θproposal |Yf (Θ(n−1) |Y )

(

,1 .

(n)

5. Accept Θproposal w.p. q and reject w.p. 1 − q.
(n)6. Set Θ(n) = Θproposal if it is accepted, and Θ(n) = Θ(n−1) otherwise.
7. Return to step 3 until N iterations have been completed.
In the process above, N is set to 20, 000 and the initial 10, 000 samples are discarded as a burn-in.
Also, H is the inverse of a Hessian matrix of ln π(Θ | Y ) multiplied by −1. We set c = 2.382 /q,
where q is the number of parameters in Θ, as proposed in Roberts and Rosenthal (2001).
2.3. Prior distributions
Our model is basically equal to a traditional VAR model, except for aggregating the daily
data presented in eqs. (2) and (3). Therefore, we assume the prior distributions for Φ and Σ tobe multivariate normal and inverse Wishart distributions; that is,Φ | Σ ∼ N (Φ0 , Σ ⊗ Ω0 ), Σ ∼ iW (Σ0 , k + 2).

(5)Here, k is the number of endogenous variables in the VAR model (k = 2). As in Kadiyala andKarlsson (1997), the diagonal elements of Σ0 are set to residual variances of the correspondingp−lag univariate autoregressions, while the diagonal elements of Ω0 are constructed such thatthe prior variance of VAR coeﬃcients on the s lagged j’th variables in the i’th equation equals6σi2 /sσj2 . These are set according to the Minnesota prior. Therefore, the coeﬃcients attachedto the first own lag in Φ0 are set to unity, while the remaining coeﬃcients are set to zero. As
regards the priors for γ1 and γ2 , we simply adopt the standard normal distribution given byγi ∼ N (0, 1), i = 1, 2.

(6)

In this setting, each observation of stock returns is presumed to be assigned equal weights inthe prior (Ghysels, 2016).

3. Empirical results
3.1. Data and specification
In what follows, we show the empirical results of out-of-sample forecasting and the impulse
responses of macroeconomic variables to public investment news shocks. Throughout the two
exercises, the lag length in VAR model is set to two (i.e., p = 2) and the monthly stock returns
in eq. (2) is constructed using the daily stock returns from the end of month to the twenty-fifthbusiness day before the end of month (i.e., d = 26).4 As for the data, the monthly series ofpublic investment are taken from the Quick Estimate of Construction Investment published by
the Ministry of Land, Infrastructure, Transport and Tourism in Japan. The public investment
used here are a nominal series of construction work conducted by the government, defined as
the sum of government building and government civil engineering work. The seasonality of theoriginal series is eliminated by using X-12-ARIMA. The daily stock returns of the constructionindustry is calculated by taking the log diﬀerentials of closing price and multiplying them by
100. To control for the factors that might aﬀect the stock prices of the construction industry
other than fiscal news, we build the excess stock returns by subtracting the Nikkei average
returns (market returns) from the construction industry returns. Moreover, the accumulated
excess stock returns is employed in the estimation because of the noisy fluctuation in originalexcess stock returns, as pointed out in Fisher and Peters (2010).
In analyzing the macroeconomic eﬀect of fiscal news shock, we focus on the impulse responsesof consumption, hours worked, and real wage as well as output to find the macroeconomic
models supported by the Japanese data. For monthly real consumption, we employ the index
of consumption expenditure level obtained from the Family Income and Expenditure Survey
published by the Ministry of Internal Aﬀairs and Communication. This index is adjusted tocontrol for the eﬀects of diﬀerence in household size, number of days in the month, and changes
4

All the daily data including in a month can be covered by tracking the daily data back to twenty-fifth businessdays from the end of month.

7

in price level. Thus, the index is a real series. The hours worked and real wage are obtained
from the Monthly Labor Survey of the Ministry of Health, Labour and Welfare. The data
source originally provided the average hours worked, employment, and real wage per worker forestablishments with over five employees. We obtain the total hours worked by multiplying thehours worked by employment. We construct the hourly real wage by dividing the real wage
by hours worked. For output, we employ indices of all industry activity (IAA) released by
the Ministry of Economy, Trade and Industry as a proxy for output. As regards covering theconstruction, mining and manufacturing, and tertiary industry activities, the IAA is consideredmore suitable as a proxy of output rather than industrial production index, which captures only
the mining and manufacturing activities. All the data employed here are seasonally adjusted in
the data source.
3.2. Out-of-sample Forecasting
The total sample period in out-of-sample forecasting is from January 1987 to March 2017.
This period is restricted by the data availability of public investment. For correspondence withthis period, we use the daily stock returns from December 23, 1986, to March 31, 2017. For the
April 2010 to March 2015 period (60 months), we recursively conduct 24 periods ahead out-ofsample forecasting. In other words, we repeat the estimation and forecasting by updating theestimation period on a monthly basis. That is, for initial estimation, we use the data from the
beginning to March 2010 to forecast the April 2010 to March 2012 monthly data. Subsequently,
we add the April 2010 data to the estimation and shift the forecasting period one month ahead forthe second estimation. We iterate this process 60 times until the end of estimation period reaches
to March 2015. Figure 1 displays the data for out-of-sample forecasting. The series of public
investment is taken by a natural logarithm multiplying by 100. The shaded area corresponds
to the forecasting period, which shows rapid increases in public investment stemming from therecovery from the Great East Japan Earthquake and fiscal expansion policies due to Prime
Minister Abe’s Abenomics.
[Figure 1 about here.]
To show the importance of information contained in daily stock returns in forecasting public
investment, we calculate the MSPE of no-change forecast, the monthly AR and VAR models, andthe VAR model with MIDAS regression. The monthly AR model includes the monthly public
investment, while the monthly VAR model includes the monthly public investment and excess
stock returns constructed using the month-end stock price only. That is, the diﬀerence between
the monthly VAR model and the VAR model with MIDAS regression is whether the daily stock8

returns is assigned an optimal weight or not when they translate into monthly returns. The
MSPE is computed at the h−period ahead forecasting as
T

2
!
)
*2
1
M SP E(h) =ŷ¯t+h − yt+h ,T2 − T1 + 1

(7)

t=T1

where T1 and T2 correspond to April 2010 and March 2015, respectively. In addition, ŷ¯t+h =
$N
(n)
(n)
n=N0 +1 ŷt+h /(N − N0 ), where ŷt+h denotes the prediction value of public investment at t + hcalculated using the parameters drawn at the n-th MCMC iteration.

Following Baumeister and Kilian (2012) and Baumeister et al. (2015), we report the relative
MSPE ratio to no-change forecast as well as the success ratio in Table 1. The success ratio
indicates direction accuracy, and is defined as the proportion of forecasts correctly predicting
the direction of change in public investment. The model is considered to perform well compared
to no-change forecasting when the MSPE ratio takes a value less than unity, while the model
forecast is considered reliable compared to the forecast using coin toss when the success ratio
takes a value greater than 0.5. The significance of the MSPE ratio and success ratio is tested
using the Diebold and Mariano (1995) test modified by Harvey et al. (1997) and the Pesaran
and Timmermann (2009) test, respectively. Moreover, column (iv) in Table 1 shows the MSPEof the VAR model with MIDAS regression relative to the monthly VAR model to confirm theusefulness of MIDAS regression.
[Table 1 about here.]
From Table 1, the forecasts using the AR model shown at column (i) indicate lower MSPEs
than the no-change forecasts throughout the horizon, with most of the success ratios below 0.5.
However, the monthly VAR model and VAR model with MIDAS shown at columns (ii) and(iii), respectively, significantly improve the forecastability of public investment compared to the
no-change forecast in terms of both the MSPE and success ratios. Thus, the stock returns of theconstruction industry contains information about a future variation in public investment, thus
indicating that the construction industry stock returns can be regarded as a proxy for public
investment news shock in Japan, as in Morita (2017) and Shioji (2017). The result also illustrates
that the MPSEs derived from models using stock returns take the minimum values at aroundhorizons eight and nine. The VAR model with MIDAS regression reduces the MPSE by about
15% at horizons eight and nine compared to no-change forecasting. The MSPE in the monthly
VAR model also lowers by almost 12% at horizon eight. Similarly, the direction accuracy exceeds
0.5, with statistical significance at around horizon eight in both models. From these results, we
can conjecture that the actual increase in public investment occurs at approximately eight ornine months after the news is announced.
9

Next, we consider the usefulness of daily data. Column (iv) in Table 1 displays the MSPEof the VAR model with MIDAS relative to the monthly VAR model. From the MSPE ratios incolumns (ii) and (iii), the VAR model with MIDAS regression reduces the MSPEs by around
2.5% compared to the monthly VAR model for all horizons. Thus, the null hypothesis that
the MSPE in the VAR model with MIDAS is greater than that in the monthly VAR model isrejected at the 10% significance level in horizons nine to twelve. Consequently, the stock returnsof the construction industry is a good predictor for public investment, with its daily information
improving the predictability of public investment even more than the monthly data.
3.3. Macroeconomic eﬀects
The stock returns of the construction industry includes information about the future fiscal
policy in the above exercise, and so we can examine the eﬀects of fiscal news shock on macroeconomic variables. After estimating the VAR model with MIDAS regression, we can identify
the fiscal news shock, denoted by vtnews , from the reduced-form residuals ut in eq. (1) througha recursive restriction as follows:
⎛
⎞ ⎛
⎞⎛
⎞
ugt
a11 0
vtg
⎝
⎠=⎝
⎠⎝
⎠.
news
uer
a
a
v
21
22
t
t

(8)

Here, we adopt this identification presuming that the news cannot materialize in the same month.
Another structural shock, denoted by vtg , is a surprising fiscal policy shock. We will not discuss
this here.
As noted above, we analyze the eﬀects on consumption, hours worked, real wage, and output,
to detect a macroeconomic model supported by the data. This choice of variables is consistent
with Fisher and Peters (2010) and Ramey (2011). Before introducing the method and result
described here, we briefly review the prediction obtained from two theoretical models located in
the opposite polar. First, the neoclassical model, as in Aiyagari et al. (1992) and Baxter andKing (1993), shows that a government spending shock decreases consumption but increases thelabor supply due to negative wealth eﬀect, and the real wage then declines along with a fall inmarginal productivity of labor.5 In contrast, the New Keynesian model with the rule-of-thumbhousehold, as in Galı́ et al. (2007), demonstrates that an increase in government spending raises
the consumption, labor, and real wage. Therefore, the response of consumption and real wage
is a key to distinguish the macroeconomic model.
5

Strictly, public investment, which we consider in this paper, is diﬀerent from government spending in terms of

productivity, because public investment contributes to increase output by incorporating public capital at a futuredate. However, the model prediction mentioned here is qualitatively unchanged even when public capital has a
productive eﬀect, as in Baxter and King (1993).

10

To obtain the dynamic responses of each variable to fiscal news shock, we employ the local
projection method proposed by Jordá (2005), instead of adding endogenous variables into the
VAR model with MIDAS regression, because the value of the weights estimated in eq. (3) may
also trace the variations in other variables besides public investment by incorporating additionalvariables into the VAR system. Another reason is the easiness to obtain the impulse responses,
as pointed out in Ramey and Zubairy (2018). To obtain the impulse response function at horizonh, we estimate the single equation
xt+h = ψh1 zt−1 + · · · + ψhp zt−p + βh vtnews + et+h ,)*2
et+h ∼ N 0, σv,h,(9)where xt is a scalar of monthly macroeconomic variable of interest, and zt is a vector of covariate
including gtM , erMt , output, and xt . In this specification, we can interpret the coeﬃcient associated with vtnews , represented as βh , as the response of x at horizon h to the shock occurred athorizon 0. To calculate the dynamic responses, we estimate the above single equation for eachhorizon. In addition to the responses of consumption, hours worked, real wage, and output,
we compute the responses of public investment and excess stock returns in the same manner.
As regards the estimations for public investment and stock returns, we exclude xt from zt . We
repeatedly estimate eq. (9) by changing h from 0 to 47 for each macroeconomic variable.6
We estimate the parameters in eq. (9) and Θ in eqs. (1) and (3) simultaneously using
the Bayesian method as follows. First, we draw Θ as described in steps 1 to 6 in Subsection
2.2. We then extract the fiscal news shock vtnews from the reduced-form residuals ut which is
2 ,calculated using the sampled Θ. Thereafter, we randomly draw Ψh = [ψh1 , · · · , ψhp , βh ]′ , and σv,hplacing the calculated vtnews on the right-hand side of eq. (9). For sampling simplicity, we set a
2 .7 In short, we insert the sampling step for Ψ andconjugate prior distribution for Ψh and σv,hh
2 between steps 6 and 7 in the MCMC iteration shown in Subsection 2.2.
σv,hFigure 2 gives the data needed to examine the macroeconomic eﬀects of fiscal news shock.
Note that the sample period in this exercise is slightly diﬀerent from the out-of-sample forecasting
period. The sample period here is from January 1990 to March 2017 because the data for thelabor market (i.e., hours worked and real wage) starts from January 1990. Similar to the outof-sample forecasting analysis, all the data are taken by a natural logarithm multiplied by 100
and the estimation is carried out in level.
[Figure 2 about here.]6

However, to estimate the response of public investment, we set h from 1 to 47 because one can reasonably

assume that fiscal news shock has no eﬀect on public investment in the impact period.
7
2
The prior and posterior distributions for Ψh and σv,hare discussed in Appendix A.

11

The impulse responses of macroeconomic variables to fiscal news shocks are given in Figure
3. While the monthly responses of each variable are obtained in the estimation of eq.(9), Figure
3 is drawn by centering on the quarterly responses for the purpose of making it simply tointerpret the results. This is because monthly responses are highly irregular presumably fromthe high-frequency fluctuation in the monthly data displayed in Figure 2. Quarterly responses
are computed as the average of the monthly responses for every three months. In Figure 3, thequarterly and monthly median responses are depicted by a solid line with circles and a thinline, respectively, with the shaded area indicating 90% credible intervals corresponding to thequarterly responses. Since monthly responses are basically within the credible intervals, thistransformation hardly changes the qualitative and quantitative interpretation of our results.
[Figure 3 about here.]First, Figures 3(a) and (b) illustrate that fiscal news shocks involve a significant increase inpublic investment with a persistent positive eﬀect on excess stock returns. These results confirm
that stock returns of the construction industry is tied to a future public investment, as discussed
in out-of-sample forecasting. Also, public investment exhibits a significant response around one
year after a shock in accordance with the exposition of out-of-sample forecasting, where MSPEs
are minimized at eight- or nine-months ahead forecasting.
Figures 3(c)–(f) exhibit a delayed significant positive eﬀect of fiscal news shocks on output,
consumption, hours worked, and real wage. As regards output and consumption, the responses
are positive and significant for a few quarters after a significant increase in public investment.8
Compared to output and consumption, hours worked takes some more quarters to become significant, while real wage becomes significantly positive before the fiscal news shock embodies as an
actual change in public investment. From these results, we can conclude that an increase in public investment raises the output, consumption, hours worked, and real wage, although the timeof significant increase depends on the variable. As regards distinguishing the macroeconomic
model, the result clearly supports the New Keynesian model with some additional frictions (i.e.,liquidity constraint and labor union), as proposed by Galı́ et al. (2007), for the Japanese economy. Moreover, our result emphasizes the role of fiscal policy as an economic stimulus packagein that a fiscal news shock has a positive eﬀect on consumption as well as output.

8Morita (2017) shows an immediate positive responses of consumption and output in contrast to our results,

although both studies are similar in that consumption and output become positive when public investment
increases. The diﬀerence in results suggests the possibility of too restrictive sign restriction based on theoreticalprediction.

124. Conclusion
In order to obtain the fiscal news shock series and gauge their macroeconomic eﬀects, weanalyzed the predictability of public investment from the daily stock returns of the constructionindustry in Japan. To improve predictive accuracy, we used the proposed VAR model with
MIDAS regression, connecting the monthly series of public investment with daily stock returns
in a single VAR system. Moreover, we examined the eﬀects of fiscal news shock on output,
consumption, hours worked, and real wage based on the local projection method developed by
Jordá (2005).
The results in out-of-sample forecasting clearly show that stock returns in the constructionindustry contains information about future changes in public investment. The models considering stock returns significantly improve the predictability of public investment. Moreover, theVAR model with MIDAS significantly reduces the MSPEs compared to a model using monthly
data. Thus, this result suggests that simple time aggregation might deteriorate the quality of
information contained in high-frequency data, as pointed out in Ghysels et al. (2007). The
finding also shows that fiscal news shocks involve an actual increase in public investment about
one year after the news is announced. This empirical fact contributes to specify the exogenous
process of government spending in the theoretical analysis.
Our analysis of macroeconomic eﬀects shows that Japanese data appear to support the New
Keynesian framework. More precisely, we find that fiscal news shock has a significantly positiveeﬀect on output, consumption, hours worked, and real wage almost when the shock materializes
an increase in public investment. Although the timing of the responses becoming significantly
positive slightly diﬀer between the variables, the responses are generally consistent with thosederived from the ultra-Keynesian model, as presented in Galı́ et al. (2007). From the economic
policy perspective, our findings also highlight the importance of fiscal policy as an economic
stimulus package.
Finally, we suggest a foreseeable extension of this research. This paper has shown how toaggregate time series data using the proposed MIDAS model. However, sectoral stock price also
constitutes aggregate data constructed from summing up the stock prices of individual firms.
Therefore, the predictability of public investment can be further improved by aggregating thestock returns of each construction firm optimally. Also, cross-sectional aggregation might enable
us to obtain fiscal news shocks series that are more clear than the ones presented in this paper.
In a future work, we would like to develop a model where the stock returns can be integrated
optimally in both time series and cross-sectional dimensions.

13Appendix A. Estimation for the local projection method
Since eq. (9) is a linear regression model, we can rewrite it as the matrix representation of2
Xh = Wh Ψh + eh , eh ∼ N (0, σv,hIT −p−h ), ;

(A.1)

)
*
′
news ,
here, Xh = (xh+p+1 , · · · , xT )′ , and Wh = (wh+p+1, · · · , wT′ )′ , where wt = zt−h−1 , · · · , zt−h−p , vt−heh = (eh+p+1 , · · · , eT )′ , and T is the total number of observations. For the priors of Ψh and−2σv,h, we set the Normal-Gamma conjugate priors specified as−2−22
Ψh | σv,h∼ N (0, σv,hIm ), σv,h∼ Gamma/

4 0.04,2 2

0,where m is the number of coeﬃcients included in Ψh . These priors lead to the posterior distributions as follows:1

4 + (T − p − h) 0.04 + e′ e + Ψ̂′h Wh′ Wh Ψ̂h − Ψ̃′h M −1 Ψ̃
,
2
2
3
4
−2
2
Ψh | σv,h, Xh ∼ N M −1 Ψ̃h , (σv,hM )−1 ,−2σv,h
| Xh ∼ Gamma2,where Ψ̂h is an ordinary least squares (OLS) estimator of Ψh , e = Xh −Wh Ψ̂h , M = Im +Wh′ Wh ,and Ψ̃h = Wh′ Wh Ψ̂h .

−2
An important point to note here is that the posterior distribution of σv,his conditional only−2
on the data. In other words, the sampling for Ψh and σv,hcan be proceeded without relying

on the MCMC method, where parameter sampling is implemented using information from theprevious iteration. Consequently, we can mitigate the computational burden for estimating our−2model, because the previous iteration values for the Ψh and σv,hneed not be saved. Thus, we−2
can easily incorporate the sampling for Ψh and σv,hinto the VAR model estimation with MIDAS

regression.
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17excess stock returns

50

0

-50

-100

-150

Jan, 90

Jan, 95

Jan, 00

Jan, 05

Jan, 10

Jan, 15

Figure 1: Data for out-of-sample forecasting

Notes: The figure shows the public investment (top) and excess stock returns time series of
the construction industry (bottom) for the period from January 1987 to March 2017. Public
investment are collected from the Quick Estimate of Construction Investment, and include thetotal government building and civil engineering investment. The data are seasonally adjusted byusing X12-ARIMA and obtained by multiplying a natural logarithm by 100. The shaded area
corresponds to the period from April 2010 to March 2015; this period is used for out-of-sample
forecasting. The excess stock returns of the construction industry is obtained by subtracting themarket returns from stock returns of the construction industry, computed using the daily closing
price log diﬀerentials. Moreover, note that the data shown here relate to the accumulated excess
stock returns.

18

470

output480

consumption

475

465

470
460
465
455
450
1990

460
2000

455
1990

2010

hours worked

780

2000

2010

real wage

2268
2266

775

2264

770

2262
765

2260
2258
1990

2000

760
1990

2010

2000

2010

Figure 2: Data for analyzing the macroeconomic eﬀects of fiscal news shocks

Notes: The sample period is from January 1990 to March 2017. All the data are seasonallyadjusted series obtained by multiplying a natural logarithm by 100. Output is the Indices of
All Industry Activity released by METI. Consumption is obtained from the Family Income andExpenditure Survey. Hours worked and real wage are collected from the Monthly Labour Survey.
Hours worked are obtained by multiplying the total hours worked and regular employment, while
the real wage give the hourly wage constructed by dividing the real wage by hours worked.

19

Figure 3: Impulse responses of macroeconomic variables to fiscal news shock

Notes: This figure shows the impulse responses of each variable to fiscal news shocks. Since
the monthly responses, denoted by a thin line, appear highly irregular, the figure centers on thequarterly responses denoted by solid lines with circles. The quarterly response is computed as
the average of the monthly responses for every three months. The shaded area indicates the
90% credible intervals corresponding to quarterly responses.

20

Table 1: Relative MSPE ratio

horizon(months)
1
2
3
4
5
6
7
8
9
10
11
12
15
18
21
24

Relative to no-change forecasting(i) Monthly AR (ii) Monthly VAR
MSPE success MSPE
success
ratio
ratio
ratio
ratio
1.033
0.55
1.010
0.63
1.029
0.48
0.969∗
0.72∗∗
∗∗
1.024
0.57
0.929
0.75∗∗
1.030
0.55
0.915∗∗ 0.83∗∗
1.033
0.48
0.897∗∗ 0.80∗∗
1.041
0.53
0.888∗∗ 0.83∗∗
1.047
0.48
0.883∗∗ 0.80∗∗
1.055
0.52
0.878∗
0.83∗∗
1.061
0.50
0.879∗
0.82∗∗
1.068
0.43
0.885
0.73∗∗
1.071
0.47
0.882
0.77∗∗
1.076
0.42
0.888
0.73∗∗
1.095
0.33
0.931
0.62
1.113
0.28
0.974
0.57
1.134
0.18
1.014
0.47
1.148
0.12
1.048
0.40

(iii) MIDAS VAR
MSPE
success
ratio
ratio
1.003
0.67∗∗∗∗
0.952
0.73∗∗∗∗
0.911
0.77∗∗
0.896∗∗ 0.82∗∗
0.875∗∗ 0.80∗∗
0.867∗∗ 0.83∗∗
0.860∗
0.80∗∗∗
0.855
0.85∗∗
0.855∗
0.83∗∗
0.862
0.77∗∗
0.858
0.80∗∗
0.863
0.77∗∗
0.908
0.68∗
0.951
0.60
0.993
0.50
1.030
0.43

to Monthly VAR(iv)MIDAS VAR
MSPE
ratio
0.993
0.982
0.980
0.979
0.976
0.976
0.975
0.974
0.973∗
0.974∗
0.972∗
0.971∗
0.976
0.976
0.980
0.983

Notes: The success ratio denotes the proportion of forecasts correctly predicting the directionof change in public investment. The null hypothesis that the prediction error in each modelis greater than the error in no-change forecast is tested by the Diebold and Mariano (1995)
test modified by Harvey et al. (1997). The direction accuracy is tested using the Pesaran andTimmermann (2009) test. In this table, ∗∗ and ∗ indicate significance at the 5% and 10% levels,
respectively.

21