Silviase/jgov_v1.4_full_ann huggingface dataset:
distribution as $\lambda\rightarrow\infty$. The cdf of SN($\lambda$) is $\forall z\in\mathbb{R}$,

$$ \Phi(z;\lambda):=\Phi(z)-2T(z,\lambda), $$

where $ T(.,.) $ is the function tabulated by Owen (1956). The sn package for R helps to evaluate the cdf and the pdf of SN( $ \lambda $ ).

Let $ Z \sim \mathrm{SN}(\lambda) $ . Then $ -Z \sim \mathrm{SN}(-\lambda) $ , $ Z^{2} \sim \chi^{2}(1) $ , and

$$ \mathrm{E}(Z)=\sqrt{\frac{2}{\pi}}\frac{\lambda}{\sqrt{1+\lambda^{2}}}, $$

$$ \mathrm{var}(Z)=1-\frac{2}{\pi}\frac{\lambda^{2}}{1+\lambda^{2}}. $$

### 2.2 Skew t Distribution

The skew t distribution is due to Azzalini and Capitanio (2003). Let $ Z \sim \mathrm{SN}(\lambda) $ and $ U \sim \chi^{2}(\nu) $ be independent. Then $ Z/\sqrt{U/\nu} $ has a skew t distribution with $ \nu $ degrees of freedom and skewness parameter $ \lambda $ , denoted as $ \mathrm{St}(\nu;\lambda) $ , whose pdf is $ \forall x \in R $ .

$$ f(x;\nu,\lambda)=2F\left(\lambda x\sqrt{\frac{\nu+1}{\nu+x^{2}}};\nu+1\right)f(x;\nu), $$

where $ f(.; \nu) $ is the pdf of $ t(\nu) $ and $ F(.; \nu + 1) $ is the cdf of $ t(\nu + 1) $ . The sn package for R helps to evaluate the cdf and the pdf of $ \mathrm{St}(\nu; \lambda) $ .

Let $ X \sim \mathrm{St}(\nu; \lambda) $ . Then $ -X \sim \mathrm{St}(\nu; -\lambda) $ and $ X^{2} \sim \mathrm{F}(1, \nu) $ . If $ \nu > 1 $ , then

$$ \mathrm{E}(X)=\frac{\Gamma((\nu-1)/2)}{\Gamma(\nu/2)}\sqrt{\frac{\nu}{\pi}}\frac{\lambda}{\sqrt{1+\lambda^{2}}}, $$
and if $ \nu > 2 $ , then

$$ \mathrm{v a r}(X)=\frac{\nu}{\nu-2}-\left(\frac{\Gamma((\nu-1)/2)}{\Gamma(\nu/2)}\right)^{2}\frac{\nu}{\pi}\frac{\lambda^{2}}{1+\lambda^{2}}. $$

## 3 THE CARLSON–PARKIN METHOD

The C–P method is estimation of an ordered probit model applied to inflation expectations data with particular identification restrictions. Let y be a random sample of size n. Assume that for $ i = 1, \ldots, n $ ,

$$ \begin{aligned}&y_{i}:=\left\{\begin{aligned}\\ &1&if y_{i}^{*}\leq a\\&2&if a
## 4 INTERVAL REGRESSION

Assume a normal interval regression model, i.e., an ordered probit model with known boundaries, for $ y_{i} $ such that

$$ \begin{aligned}&y_{i}:=\left\{\begin{aligned}\\ &1\quad if c_{0}
where $ n_{j} := \sum_{i=1}^{n}[y_{i} = j] $ . Let $ \alpha := 1/\sigma $ , $ \beta := \mu/\sigma $ , and $ \mathbf{c} := (c_{1}, \ldots, c_{J-1})' $ . Then the log-likelihood function is concave in $ (\alpha, \beta, \mathbf{c}) $ and hence unimodal in $ (\mu, \sigma, \mathbf{c}) $ ; see Pratt (1981). ML estimation of a normal interval regression model (with known boundaries) is easy on some econometric software packages; e.g., gretl and Stata have a command intreg.

An SN interval regression model assumes that $ u_{i} \sim \mathrm{SN}(\lambda) $ . An St interval regression model assumes that $ u_{i} \sim \mathrm{St}(\nu; \lambda) $ . The sn package for R helps to evaluate the cdf in the log-likelihood function. Note that the log-likelihood function may not be unimodal.

## 5 APPLICATION

### 5.1 Data

The Economic and Social Research Institute (ESRI) of the Cabinet Office, Government of Japan, integrated three old surveys to renew the Monthly Consumer Confidence Survey in April 2004. The survey covers 6,720 households selected by stratified sampling, and asks about various perceptions, price expectation a year ahead, and the state of the household. Individual data are not available. Aggregate data are downloadable from the ESRI's home page. Some disaggregate data are also available; e.g., by household type (one person or not), by sex and age of the head of the household, by income, by region, etc. The response rates were almost 100% by March 2006, and then dropped to around 75% in 2007.

The respondents select their price expectations a year ahead from the
following seven categories (excluding “don’t know”):

1. go down by 5% or more,

2. go down by 2% or more, but less than 5%,

3. go down by less than 2%.

4. stay the same (0%),

5. go up by less than 2%.

6. go up by 2% or more, but less than 5%,

7. go up by 5% or more.

Thus except between 3, 4, and 5, i.e., the indifference interval, the questionnaire gives the boundaries between the categories. We exclude “don’t know” from the sample in the following analysis. Two more categories, “go up/down by 10% or more,” appeared since April 2009, but we maintain the above seven categories as released in the summary report of the Survey. Figure 1 plots the sample size for each month, which is decreasing over time but still quite large.

Figure 2 plots the relative frequencies of the categories for each month. The expectations are heterogeneous, but on average, household inflation expectations in Japan rose since 2007, reaching a peak in mid-2008, and then dropped. Note that the number of households expecting deflation (categories 1–3) increased substantially since late 2008.

In the following, we estimate the distributions of household inflation expectations in Japan from April 2004 to March 2010 using three interval re-
Figure 1: Sample Size (Excluding “Don’t Know”).

Figure 2: Relative Frequencies of the Categories.
gression models (normal, SN, and St). We use the bbmle package for R for numerical maximization of the log-likelihood function.

### 5.2 Parameter Estimates

#### 5.2.1 Normal interval regression

Figure 3 plots the ML estimates of the parameters in the normal interval regression model and their asymptotic 95% confidence intervals for each month. Apart from possible misspecification bias, the estimation errors are extremely small, though increasing slightly since 2006 because of the decreasing sample size. As noted in the recent literature on rationally heterogeneous expectations, the mean and the standard deviation of household inflation expectations have positive correlation. The indifference intervals are asymmetric and unstable over time.

#### 5.2.2 SN interval regression

Figure 4 plots the ML estimates of the parameters in the SN interval regression model and their asymptotic 95% confidence intervals for each month. Note that $ \mu $ and $ \sigma $ are location and scale parameters, and not the mean and the standard deviation unless $ \lambda = 0 $ . Until mid-2007, $ \mu $ is negative and $ \lambda $ is positive; then $ \mu $ rises and $ \lambda $ drops to 0. Moreover, $ \lambda $ turns negative occasionally since late 2008. Since the information matrix of an SN distribution is singular when $ \lambda = 0 $ , the estimation errors increase as $ \lambda \rightarrow 0 $ . The indifference intervals are asymmetric and unstable over time.
sigma

indifference interval

Figure 3: ML Estimates of the Parameters in the Normal Model. The dashed lines are asymptotic 95% confidence intervals.
mu

sigma

lambda

indifference interval

Figure 4: ML Estimates of the Parameters in the SN Model. The dashed lines are asymptotic 95% confidence intervals.
#### 5.2.3 St interval regression

Figure 5 plots the ML estimates of the parameters in the St interval regression model and their asymptotic 95% confidence intervals for each month. With six parameters to estimate, the estimation errors increase substantially. Contrary to the SN model, $ \lambda $ remains positive except December 2009 and January 2010. Interestingly, $ \nu $ is small and often below 2, in which case the variance is infinite. The indifference intervals are more symmetric and stable over time than those of the normal and SN models, staying around $ \pm.5-1\% $ .

### 5.3 Model Selection

Figure 5 already suggests that the St model is preferable to the normal and SN models throughout the period studied, since $ \lambda $ is significantly different from 0 and $ \nu $ is small.

To find the best model, one can also use a model selection criterion such as Akaike's information criterion (AIC) or Schwarz's Bayesian information criterion (SBIC). Davidson and MacKinnon (2004, pp. 676–677) define

$$ \begin{aligned}AIC&:=\ell-k,\\ SBIC&:=\ell-\frac{k\ln n}{2},\end{aligned} $$

where $ \ell $ is the log-likelihood, k is the number of parameters estimated, and n is the sample size.

Figure 6 plots AIC and SBIC of the SN and St models relative to those of the normal model, i.e., AIC (SBIC) of the SN (St) model minus that of the
sigma

Iambda

nu

indifference interval

Figure 5: ML Estimates of the Parameters in the St Model. The dashed lines are asymptotic 95% confidence intervals.
AIC

SBIC

Figure 6: AIC and SBIC of the SN and St Models Relative to the Normal Model.

normal model, for each month. We see that the St model is most preferable throughout the period studied.

### 5.4 Inflation Expectations

For the SN model, the mean inflation expectation is

$$ \mathrm{E}(y_{i}^{*})=\mu+\sigma\sqrt{\frac{2}{\pi}}\frac{\lambda}{\sqrt{1+\lambda^{2}}}. $$
For the St model, if $ \nu > 1 $ , then

$$ \mathrm{E}(y_{i}^{*})=\mu+\sigma\frac{\Gamma((\nu-1)/2)}{\Gamma(\nu/2)}\sqrt{\frac{\nu}{\pi}}\frac{\lambda}{\sqrt{1+\lambda^{2}}}. $$

The top panel of Figure 7 compares the mean inflation expectations implied by the three models with the current CPI inflation (12-month growth rate). For the St model, the mean inflation expectations are too high (25%) in 2008 when $ \nu $ is close to 1. The middle panel compares the median inflation expectations implied by the three models with the current CPI inflation. The three median inflation expectations are close to each other, and mostly higher than the current CPI inflation during the period studied. The SN model gives the lowest median inflation expectations until mid-2007. Since then, the St model gives the lowest median inflation expectations. The bottom panel compares the mode inflation expectations implied by the three models with the current CPI inflation. Until 2007, the SN model gives the lowest mode inflation expectations, which are also closest to (sometimes below) the current CPI inflation. Since then, the St model gives the lowest mode inflation expectations.

Let $ \pi_{t} $ be the CPI inflation rate from date t-12 to date t. Let $ \pi_{t+12|t}^{e} $ be a survey expectation of $ \pi_{t+12} $ at date t. Let $ e_{t} := \pi_{t|t-12}^{e} - \pi_{t} $ be a forecast error at date t. Figure 8 plots the forecast errors of the mean, median, and mode inflation expectations of the St model. The three inflation expectations tend to overpredict the actual CPI inflation during the period studied. On average, the mode inflation expectations have the smallest bias. Capistrán and Timmermann (2009) attribute the bias to asymmetric loss. It also arises
Mean

Median

Mode

Figure 7: Current Inflation and the Mean, Median, and Mode Inflation Expectations.
Figure 8: Forecast Errors of the Mean, Median, and Mode Inflation Expectations of the St Model.

from response bias and the CPI inflation bias, though the latter is usually an upward bias relative to the true cost-of-living index inflation; see Hausman (2003) and Lebow and Ruud (2003).

Figure 9 shows the relation between the distribution of household inflation expectations and the current CPI inflation. The median, the IQR, the skewness parameter, and excess kurtosis all increase with the current CPI inflation when the latter is positive (smaller $ \nu $ means higher excess kurtosis); the relations are unclear when the latter is negative. These may arise from sticky information (Mankiw and Reis (2002), Mankiw et al. (2003), Carroll (2003)), model uncertainty (Branch (2004, 2007)), or asymmetric loss (Capistrán and Timmermann (2009)). To study the dynamics of heterogeneous expectations in detail, we need individual data.

A possible use of the estimated inflation expectations is inflation fore-
Figure 9: Current Inflation and the Distribution of Inflation Expectations. The nonparametric regression uses the Nadaraya–Watson estimator with a Gaussian kernel.
casting. Ang et al. (2007) find that survey expectations predict US inflation better than other variables. We try the mean, median, and mode inflation expectations of the normal, SN, and St models for $ \pi_{t+12|t}^{e} $ , and estimate the following predictive regression:

$$ \mathrm{E}(\pi_{t}|I_{t-12})=\alpha\pi_{t-12}+\beta\pi_{t|t-12}^{e}, $$

where $ I_{t} $ is the information available at date t. We use gretl 1.9.0 for OLS. The estimation period is from April 2005 to March 2010 (60 observations).

Table 1 compares the results of predictive regressions using the mean, median, and mode inflation expectations of the SN model and the mean (=median=mode) inflation expectation of the normal model respectively. We see that none of them helps to predict the actual CPI inflation individually beyond the current CPI inflation. Using all three expectation measures of the SN model improves prediction, but this may not work out-of-sample because the estimated coefficients seem unreasonable.

Table 2 compares the results of predictive regressions using the mean, median, and mode inflation expectations of the St model and the mean inflation expectation of the normal model respectively. We see that none of them, even jointly, helps to predict the actual CPI inflation beyond the current CPI inflation.

Note that the estimation period is too short to give a definitive conclusion, covering at most one business cycle. Dropping the last 12 observations, we find that each expectation measure helps to predict the actual CPI inflation beyond the current CPI inflation, with reasonable sign and size of
Table 1: Predictive Regressions for the CPI Inflation (SN vs Normal)

Regressor	SN mean	SN median	SN mode	SN all	Normal
constant	0.10	0.21	0.30	-1.91	0.11
(0.25)	(0.21)	(0.17)	(0.44)	(0.26)
πt-12	-1.11	-0.97	-0.76	-1.09	-1.09
(0.44)	(0.43)	(0.39)	(0.44)	(0.44)
πte	0.10	41.57	0.09
(mean)	(0.25)	(9.80)	(0.26)
πte	0.01	-55.37
(median)	(0.24)	(13.52)
πte	-0.12	14.44
(mode)	(0.20)	(3.82)
adjusted R²	0.38	0.38	0.38	0.67	0.38
AIC	153.61	153.94	153.20	117.31	153.71
SBIC	159.89	160.23	159.48	127.78	159.99

NOTE: Numbers in parentheses are HAC standard errors. In gretl 1.9.0, AIC is $ -2\ell + 2k $ and SBIC is $ -2\ell + k \ln T $ , where $ \ell $ is the log-likelihood, k is the number of parameters estimated, and T is the sample length.

Table 2: Predictive Regressions for the CPI Inflation (St vs Normal)

Regressor	St mean	St median	St mode	St all	Normal
constant	0.26(0.19)	0.18(0.29)	0.22(0.29)	0.16(0.29)	0.11(0.26)
$ \pi_{t-12} $	-0.87(0.27)	-1.00(0.41)	-0.96(0.37)	-1.02(0.44)	-1.09(0.44)
$ \pi_{t|t-12}^{e} $ (mean)	-0.02(0.03)	-0.05(0.04)	0.09(0.26)
$ \pi_{t|t-12}^{e} $ (median)	0.03(0.32)	1.46(1.18)
$ \pi_{t|t-12}^{e} $ (mode)	-0.00(0.39)	-1.67(1.28)
adjusted $ R^{2} $	0.38	0.38	0.38	0.37	0.38
AIC	153.65	153.93	153.95	156.34	153.71
SBIC	159.94	160.21	160.23	166.81	159.99

NOTE: See note to Table 1.
the coefficient. Hence the large positive price shock in 2008 may distort the result. The analysis here only illustrates a possible use of estimated inflation expectations.

## 6 DISCUSSION

Quantification of qualitative survey data requires strong assumptions. Interval-coded data do not require many of them. Less assumptions lead to more reliable measurement of inflation expectations.

A time series of estimated distributions of household inflation expectations have several uses. This paper gives two examples. One is to study the dynamic relation between the current inflation and the distribution of household inflation expectations, which may help to develop the theory of rationally heterogeneous expectations. The other is to use the estimated distributions for inflation forecasting. Thorough studies on these issues, however, require a long time series covering multiple business cycles.

If households report their expectations correctly (though Inoue et al. (2009) give evidences that they do not), then different expectations come from different information sets. An interesting question is why the distribution of household inflation expectations has high skewness and excess kurtosis (during the period studied). This paper does not answer that question. The followings are some ideas for future research:

1. Finite mixture models may help to explain the shape of the distribution; e.g., a mixture of two normal distributions assuming a symmetric indifference interval.
2. Demographic variables may explain the shape of the distribution, though such studies require individual data.

3. Each person has a belief, or subjective pdf, over future inflation, but the Monthly Consumer Confidence Survey asks only about the mean of the pdf. One can ask probabilistic questions to learn more about the pdf; see Manski (2004).

In addition, the Monthly Consumer Confidence Survey in Japan has changed slightly since April 2009, and now there are nine intervals to choose from. Thus one can fit even more general distributions.

Finally, the SN and St distributions, both univariate and multivariate, will have other interesting applications; e.g., one can use the multivariate SN and St distributions instead of copulas.

## ACKNOWLEDGMENTS

I thank Kazumi Asako, Takatoshi Ito, Kosuke Oya, and Akira Terai for useful comments. This work was supported by KAKENHI (19530185).

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# 第3章 循環型社会の形成

## 第1節 循環型社会の形成に向けた法制度の施行について

（1）循環型社会形成推進基本法（循環型社会基本法）

循環型社会基本計画において示された、物質フロー指標に関する目標及び取組指標に関する目標の達成や、低炭素社会・自然共生社会との統合的取組、地域循環圏の構築、国際的な循環型社会の構築へ向けた取組を進めます。

また、廃棄物の焼却や埋立てに伴う温室効果ガスについては、その排出量の抑制を図ります。

(2) 廃棄物の処理及び清掃に関する法律（廃棄物処理法）

平成13年5月に環境大臣は「廃棄物の減量その他その適正な処理に関する施策の総合的かつ計画的な推進を図るための基本的な方針」（基本方針）を決定し公表しています。その中では、まず、できる限り廃棄物の排出を抑制し、次に、廃棄物となったものについては不適正処理の防止その他の環境への負荷の低減に配慮しつつ、再使用、再生利用、熱回収の順にできる限り循環的な利用を行い、こうした排出抑制及び適正な循環的利用を徹底した上で、なお適正な循環的利用が行われないものについては、適正な処分を確保することを基本とすること等を定めています。これにより平成22年12月に改正した基本方針では、平成27年度において一般廃棄物及び産業廃棄物の最終処分量をそれぞれ平成19年度に対し約22%、約12%に削減することとしています。

また、同基本方針において、国は、市町村及び都道府県が行う、その区域内の廃棄物の減量その他その適正な処理の確保のための取組が円滑にできるよう、平成19年6月に策定した「一般廃棄物会計基準」、「一般廃棄物処理有料化の手引き」、「市町村における循環型社会づくりに向けた一般廃棄物処理システムの指針」の更なる普及等を通じた技術的な支援等に努めることとされていることから、このことについて引き続き取り組むとともに、会計基準の活用状況等の把握、優良事例の抽出、課題の検討等を行い、必要に応じてこれらの見直しに向けた検討を進めていきます。

さらに、平成25年度より5年間の新たな「廃棄物処理施設整備計画」を作成し、廃棄物処理における3Rの推進を前提としつつ、一般廃棄物処理における地球温暖化対策や災害対策の強化を実施していきます。

廃棄物系バイオマスについては、分別、収集運搬、再生、利活用を含めたシステム全体について、具体的かつ実践的な再生利用手法を提示し、地域特性に応じた合理的かつ実現可能な廃棄物系バイオマスの大幅な利活用の促進を図ります。

また、産業廃棄物処理施設のモデル的整備事業に対する補助制度により、廃棄物処理センター等の公共関与による産業廃棄物処理施設の整備促進を図ります。

最終処分場の確保が特に困難となっている大都市圏のうち、近畿圏においては、大阪湾広域臨海環境整備センターが行う広域処理場整備を促進して、埋立ての円滑な実施を図ります。また、首都圏においては、必要な広域処理場を確保して、埋立ての円滑な実施を図ります。

産業廃棄物問題の根本的な解決に向け、不法投棄等の不適正処理事案の発生の未然防止や電子マニフェストの普及促進等による廃棄物処理システムの透明性の向上、優良で信頼できる産業廃棄物処理業者の育成を昨年度に引き続き進めてまいります。

石綿を含む廃棄物及び微量のPCBに汚染された廃電気機器等の円滑かつ安全な処理を促進するために、処
理技術に関する検討を行うとともに、無害化処理認定制度により、これらの廃棄物の無害化処理を促進します。

## (3) 資源の有効な利用の促進に関する法律（資源有効利用促進法）

従来進めてきた取組に加え、産業構造審議会において平成20年1月に取りまとめられた報告書に基づいて、世界最高水準の省資源社会の実現を図るため、各種資源の投入量のさらなる低減施策に取り組み、我が国産業の競争力の維持・強化等を図ります。

また、平成20年度から、3R配慮型製品の市場を確保するため、製造事業者による3Rに関する製品設計・製造の取組状況を、消費者に対して正確に、分かりやすく伝えるための評価手法・仕組みの検討を行っています。

## (4) 容器包装に係る分別収集及び再商品化の促進等に関する法律（容器包装リサイクル法）

改正後の容器包装リサイクル法に基づき、容器包装廃棄物の排出抑制を促進するため、容器包装廃棄物排出抑制推進員（愛称：3R推進マイスター）を活用した消費者へのさらなる普及啓発や、小売業に属する事業を行う者（指定容器包装利用事業者）に対して義務付けられた容器包装廃棄物の排出抑制促進措置を着実に実施し、容器包装の使用合理化を図ります。また、容器包装リサイクル法の参加市町村を増加させるための取組についても検討します。

「環境物品等の調達の促進に関する基本方針」の改訂を通じ、国等の各機関による再使用の促進のために容器包装の返却・回収が可能なリユース商品の購入の拡大を検討します。

改正容器包装リサイクル法の施行から5年が経過し、改正法附則に基づく法の見直し時期の到来を受け、制度の評価・検討を進めていきます。

## (5) 特定家庭用機器再商品化法（家電リサイクル法）

家電リサイクル法施行令の改正により平成21年4月から追加された対象機器（液晶・プラズマテレビ、衣類乾燥機）も含めて、引き続き、使用済家電の適正なリサイクルを進めていきます。また、家電リサイクル法ルート以外のルートにおける処理の状況などの使用済家電のフローについて把握し、使用済家電の流通実態・処理実態の透明化を推進します。

不適正な処理ルートの対策に関しましては、環境省から地方自治体宛てに不用品回収業者が取り扱う使用済み家電製品についての通知（「使用済家電製品の廃棄物該当性の判断について」）に基づき、対策を強化していきます。

また、産業構造審議会環境部会廃棄物・リサイクル小委員会電気・電子機器リサイクルワーキンググループ、中央環境審議会廃棄物・リサイクル部会及び家電リサイクル制度評価検討小委員会の合同会合において、平成20年2月に取りまとめられた「家電リサイクル制度の施行状況の評価・検討に関する報告書」に基づき、制度の評価・検討を進めていきます。

## (6) 使用済小型電子機器等の再資源化の促進に関する法律（小型家電リサイクル法）

平成25年4月1日から使用済み小型電子機器等の再資源化の促進に関する法律（平成24年法律第57号）が施行されます。本法律では、使用済小型電子機器等の再資源化を促進するための措置を講じることにより、廃棄物の適正な処理及び資源の有効な利用の促進を推進していきます。

## (7) 食品循環資源の再生利用等の促進に関する法律（食品リサイクル法）

食品廃棄物等の発生量が一定規模以上の食品関連事業者に対する定期報告の義務付け等指導監督の強化、登録再生利用事業者制度及び再生利用事業計画認定制度を通じた再生利用等の円滑な取組等を引き続き推進します。

また、食品循環資源の再生利用等の推進を図るため、食品リサイクル制度の普及啓発を実施するほか、平