Silviase/jgov_v1.4_full_ann huggingface dataset:
## く付注2＞ 本文（3）式の導出プロセス

本文（2）式の予算制約のもとで、（1）式の目的関数を最大化するという制約付き最適化問題を想定する。この時、最適化の必要条件は、以下の通りである。

$$ U^{^{\prime}}\big(C_{t}\big)-\lambda_{t}=0 $$

$$ -\lambda_{t}V_{t}+\beta E_{t}\lambda_{t+1}\big(V_{t+1}+d_{t+1}\big)=0 $$

$$ -\lambda_{_{t}}+\beta E_{_{t}}\lambda_{_{t+1}}\big(1+r\big)=0 $$

ここで $ \lambda_{t} $ はラグランジュ乗数を示している。(A-1-2)式、(A-1-3)式より、以下のような安全資産と株式の間に成立する裁定条件を得る。

$$ 1+r=\frac{E_{t}\left(V_{_{t+1}}+d_{_{t+1}}\right)}{V_{_{t}}} $$

条件付期待値の情報集合は一定のもとで、(A-1-4)式の諸変数を1期後方へずらす。さらに、同式の両辺に $ x_{t} $ を掛けると以下の式を得る。

$$ V_{t}x_{t}+d_{t}x_{t}=\left(1+r\right)V_{t-1}x_{t} $$

また、本文（2）式の予算制約式の右辺 $ \left(A_{t+1}+V_{t}x_{t+1}\right) $ を $ Q_{t+1} $ とおくと、

$$ \left(1+r\right)Q_{t}=\left(1+r\right)A_{t}+\left(1+r\right)V_{t-1}x_{t} $$

という関係が成立する。(A-1-6) 式の右辺第2項は、(A-1-5) 式の右辺と等しくなるので、

$$ \left(1+r\right)Q_{t}=\left(1+r\right)A_{t}+V_{t}x_{t}+d_{t}x_{t} $$

という形に整理することができる。(A-1-7) 式の右辺は、予算制約式（本文（2）式）の右辺第1項から第3項に他ならないので、（2）式は、以下のように、 $ Q_{t} $ に関する一階の定差方程式として表現できる。

$$ Q_{t+1}=\left(1+r\right)Q_{t}+WL_{t}-C_{t} $$

（A-1-8）式を前向きに逐次代入し、整理することによって、本文（3）式を得ることができる。
## く付注3＞本文(15)式の導出プロセス

（10）式の消費関数に、α、λ、θ、γのパラメータ、及び誤差項を付加すると、以下の推定式を得る。

$$ C_{t}=\alpha\Bigg[W_{t}+\gamma E_{t}\sum_{s=t}^{\infty}\beta^{s-t}\big(T H_{s}+T O_{s}-G_{s}\big)+\theta E_{t}\sum_{s=t}^{\infty}\beta^{s-t}\big(\pi_{s}-d_{s}\big)+E_{t}\sum_{s=t}^{\infty}\beta^{s-t}W L_{s}\Bigg]+\lambda Y D_{t}+v_{t} $$

$$ W_{t}=\left(1+r\right)B_{t}^{p}+d_{t} $$

$$ \alpha>0,\beta=\frac{1}{1+\mu},E\big(\nu_{t}\big)=0,E\big(\nu_{t}^{2}\big)=\sigma_{\nu}^{2} $$

人的資産（ $ HW_{t} $ ）、企業貯蓄の将来値（ $ SFW_{t} $ ）、政府貯蓄の将来値（ $ SGW_{t} $ ）を以下のように定義する。

$$ H W_{t}=E_{t}\sum_{s=t}^{\infty}\beta^{s-t}W L_{s} $$

$$ S F W_{t}=E_{t}\sum_{s=t}^{\infty}\beta^{s-t}\big(\pi_{s}-d_{s}\big)=E_{t}\sum_{s=t}^{\infty}\beta^{s-t}S_{s}^{f} $$

$$ S G W_{t}=E_{t}\sum_{s=t}^{\infty}\beta^{s-t}\big(T H_{s}+T O_{s}-G_{s}\big)=E_{t}\sum_{s=t}^{\infty}\beta^{s-t}S_{s}^{g} $$

さらに、人的資産、企業貯蓄、政府貯蓄について、t期までの情報集合による予想と、t-1期までの情報集合による予想の差を、予測誤差（forecast error）として以下のように定義する。

$$ e_{t}^{h}=\sum_{s=t}^{\infty}\beta^{s-t}\left[E_{t}WL_{s}-E_{t-1}WL_{s}\right] $$

$$ e_{t}^{f}=\sum_{s=t}^{\infty}\beta^{s-t}\left[E_{t}S_{s}^{f}-E_{t-1}S_{s}^{f}\right] $$

$$ e_{t}^{g}=\sum_{s=t}^{\infty}\beta^{s-t}\Big[E_{t}S_{s}^{g}-E_{t-1}S_{s}^{g}\Big] $$

$ e_{t}^{h}, e_{t}^{f}, e_{t}^{g} $ は人的資産、企業貯蓄、政府貯蓄の予測誤差を示している。

次に（A-2-5）、（A2-6）、（A-2-7）式を、（A-2-2）、（A-2-3）、（A-2-4）式に代入、整理していく。以下では人的資産を例にとり、説明しておく。まず（A-2-2）式を1期後方にずらすと、

$$ H W_{_{t-1}}=E_{_{t-1}}\sum_{s=t}^{\infty}\beta^{s-t}W L_{_{s-1}} $$

となる。したがって、

$$ E_{t-1}\sum_{s=t}^{\infty}\beta^{s-t}WL_{s}=\big(1+\mu\big)\big(HW_{t-1}-WL_{t-1}\big) $$
という関係式が得られる。（A-2-9）式を（A-2-5）式に代入、整理すると、 $ HW_{t} $ に関する一階の定差方程式を得る。

$$ H W_{_{t}}=\big(1+\mu\big)\big(H W_{_{t-1}}-W L_{_{t-1}}\big)+e_{_{t}}^{^{h}} $$

同様の手続きを $ SFW_{t} $ 、 $ SGW_{t} $ についても施すことができるので、

$$ SFW_{t}=\big(1+\mu\big)\big(SFW_{t-1}-S^{f}{}_{t-1}\big)+e_{t}^{f} $$

$$ S G W_{_{t}}=\big(1+\mu\big)\big(S G W_{_{t-1}}-S^{g}{}_{_{t-1}}\big)+e_{_{t}}^{g} $$

という関係式を得る。

ここで、(A-2-1)式と、(A-2-1)式の一期ラグ× $ 1+\mu $ の差を求めておく。

$$ C_{t}=\big(1+\mu\big)C_{t-1}+\alpha\big[W_{t}-\big(1+\mu\big)W_{t-1}\big]+\alpha\big[HW_{t}-\big(1+\mu\big)HW_{t-1}\big]+\alpha\gamma\big[SGW_{t}-\big(1+\mu\big)SGW_{t-1}\big]+ $$

$$ \alpha\theta\big[S F W_{_{t}}-\big(1+\mu\big)S F W_{_{t-1}}\big]+\lambda\big[Y D_{_{t}}-\big(1+\mu\big)Y D_{_{t-1}}\big]+\nu_{_{t}}-\big(1+\mu\big)\nu_{_{t-1}} $$

（A-2-13）式に、（A-2-10）、（A-2-11）、（A-2-12）式を代入、整理することによって推定の対象となる式（本文（15）式）が得られる。

$$ C_{t}=\big(1+\mu\big)C_{t-1}+\alpha\big[W_{t}-\big(1+\mu\big)\big(W_{t-1}+WL_{t-1}\big)\big]-\alpha\gamma\big(1+\mu\big)S^{g}{}_{t-1}-\alpha\theta\big(1+\mu\big)S^{f}{}_{t-1} $$

$$ +\lambda\big[Y D_{t}-\big(1+\mu\big)Y D_{t-1}\big]+u_{t} $$

$$ W_{t}=\left(1+r\right)B_{t}^{p}+d_{t} $$

$$ u_{_{t}}=\alpha\Big(e_{_{t}}^{^{h}}+\theta e_{_{t}}^{^{f}}+\gamma e_{_{t}}^{^{g}}\Big)+v_{_{t}}-(1+\mu)v_{_{t-1}} $$
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ESRI Discussion Paper Series No.101

How Do People Cope With Natural Disasters?

Evidence from the Great Hanshin-Awaji Earthquake

by

Yasuyuki Sawada and Satoshi Shimizutani

April 2004

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
How Do People Cope With a Natural Disaster?

Evidence from the Great Hanshin-Awaji Earthquake $ ^{1} $

by

Yasuyuki Sawada $ ^{2} $ and Satoshi Shimizutani $ ^{3} $

April 2004
## Abstract

We investigate how people coped with unexpected losses caused by the 1995 Hanshin-Awaji earthquake by using an unusually rich household data. Several empirical findings emerged. We found that the coping means were specific to the nature of the loss caused by the earthquake. For example, borrowing was extensively used to recover the damages to housing, whereas dissavings were utilized to compensate for the loss to assets. Our analysis in this paper contains important policy implications in the preparation of well-designed social safety nets against future natural disasters. Since the economic losses caused by natural disasters are often too large for the government to support effectively, its role is to facilitate the self-insurance of the victims of the disasters. Our empirical results suggest that provisions of the subsidized loan programs to the victims can be a good example.

Keywords: Natural disasters; Risk-coping strategies.
### 1. Introduction

In the early morning of January 17, 1995, a major earthquake hit the Hanshin area of Japan, causing the losses of US114 billion to capital stock, the largest economic damage in the human history [Horwich (2000)]. It is fair to say that the earthquake was totally unexpected in this area, unlike in Tokyo, which was hit by a massive earthquake in 1923. This is reflected in the fact that only 3 percent of the property in Hyogo Prefecture (where Kobe is located) was covered by earthquake insurance [Skidmore (2001)]. $ ^{4} $ However, in retrospect, the negative impact of the earthquake on households’ economic welfare was smaller than was originally expected, and recovery from the earthquake proceeded with unexpected speed. The sensible responses of households played an important role in coping with the shocks caused by the earthquake. The government, too, played an important role in providing public safety nets ex ante and ex post in the form of the safety infrastructure and temporal housing.

As an ex ante measure against economic losses from unexpected future events, Japanese households hold significant amounts of precautionary savings [Horioka and Watanabe (1997)]. Some researchers attributed the high frequency of catastrophes such as earthquakes, volcanic eruptions, landslides, and typhoons to the Japanese high propensity to save [Bronfenbrenner and Yasuba (1987); Skidmore (2001)]. Self-insurance through private savings seems to have become a major source of individual self-protection from natural disasters in Japan. Skidmore (2001) estimated that almost a third of Japan's private savings can be explained as a precautionary device to the unexpected losses from natural disasters. Moreover, a reduction in unnecessary expenditures, borrowing, and private transfers should have been a part of important risk-coping strategies. Yet, the role of self-insurance was not recognized as a major source of ex post disaster management [Horwich (2000)]. The only related paper known to us is by Horioka et al (2002), which found that Japanese households cope with risk primarily by drawing down their own savings.

While natural disasters are thought to be a correlated shock, there is an important heterogeneity among households with different vulnerabilities. Some households were insulated from the shocks, while the physical and human assets of others were seriously damaged. It is entirely an empirical question for whom, which, and how risk-coping devices worked against the negative shocks caused by the earthquake. In this paper, armed with a unique household-level data collected in Kobe shortly after the earthquake in 1995, we investigate how people coped with unexpected resource losses caused by the sudden natural disaster. Particularly, we compare the
effectiveness of the four risk-coping strategies quantitatively, i.e., a reduction in unnecessary expenditures, dissaving, borrowing, and receiving private transfers.

We believe that this study is the first to address these questions, investigating the relative effectiveness of different risk-coping devices against natural disasters. While the market might respond effectively to the risk of damage from natural disasters in the Untied States [Brookshire et al. (1985)], there are serious limitations in private insurance markets for earthquakes in Japan. Zeckhouser (1996) pointed out that the costs generated by natural disasters can be reduced with effective policies for insurance and government regulation. However, the government, in its attempt to provide ex post public support after a natural disaster, may create social costs that reduce or offset the effectiveness of its program if it fails to consider other risk-coping devices employed by its target group. It is therefore important to examine whether a government program crowds out existing private self- and mutual-insurance mechanisms and whether its coverage of public eligibility is limited only to those unprotected. Moreover, if substantial compensation were to be expected in future disasters, it could encourage people to place themselves in harm's way more than they might otherwise do. This is a moral hazard problem pointed out by Horwich (2000). In this context, we believe our integrated analysis of risk-coping devices has important policy implications in the preparation of well-designed social safety nets against future natural disasters.

The rest of this paper is composed of three sections. Section 2 sets up our theoretical and econometric framework. In Section 3, after a brief overview of our data set, we summarize the empirical findings. The final section summarizes with some concluding remarks.

### 2. The Model Framework

People in developed and developing countries alike are confronted by ex post shocks in their day-to-day lives. For example, crops and livestock—the sources of income of most farmers—may be destroyed by natural hazards such as hurricanes, floods, fire, and serious drought. There are also serious risks in business activities, since sales and prices of production inputs fluctuate even in developed countries. Moreover, accidents, sickness, or sudden death may disable a household head or an entire family. Macroeconomic instabilities or recessions, which tend to generate harsh inflation and widespread unemployment, may also significantly reduce the real value of household resources. Yet, among these unexpected shocks, natural disasters are the most serious.

Under these uncertainties, households face a problem of how to reconcile income fluctuations with a desired stable consumption. This problem can be theoretically captured as a
problem of intertemporal consumption smoothing under a stochastic income process. Based on such a framework, the recent literature addresses the effectiveness of formal and informal risk-mitigating mechanisms of households [Besley (1995), Hayashi (1996), Townsend (1994, 1995)]. Households have developed several ways, such as those involving self-insurance and mutual insurance, to cope with the ex-post risks of negative-income shocks and to protect their levels of consumption [Hayashi (1996)]. In other words, we can define risk-coping strategies as ex-post strategies to reduce consumption fluctuations, provided income fluctuations due to these ex-post risks.

The existing literature identifies the following four household risk-coping strategies. First, a household can change the quality and composition of expenditures by reducing unnecessary expenditures, such as those for luxuries. As revealed in recent studies on the aftermath of the currency crisis in Korea, Indonesia, and Thailand, consumption reallocation is indeed an important coping strategy [Kang and Sawada (2003), Frankenberg, Thomas, and Beegle (1999)]. Interestingly, Olney (1999) showed that cutting consumption was the only viable strategy of American households against a recession in 1930, given the high default cost on their loans. Accordingly, consumer spending collapsed in 1930, turning a minor recession into the Great Depression.

Second, households can use credit to smooth consumption by reallocating future resources to current consumption. It is straightforward to show theoretically that the lack of consumption insurance can be compensated by the access to the credit market [Eswaran and Kotwal (1989)]. In fact, the use of credit for consumption is the basic logic of the LC-PIH interpretation of household-consumption smoothing. However, households often have only a limited access to credit markets and are constrained from borrowing for a variety of reasons [Jappelli (1990)]. This can be due to high information cost, lack of assets for collateral, or policy-induced financial repression [Stiglitz and Weiss (1981), McKinnon (1973)]. In either case, the existence of credit constraints has important negative impacts on risk-coping abilities of poor households. However, Horioka and Kohara (1999) and Sawada et. al (2003) found that less than fewer than 10 percent of households face credit constraints in Japan.

Third, households can accumulate financial and physical assets as precautionary means against unexpected income shortfalls [Guiso et al. (1992), Caroll and Samwick (1998)]. Theoretically, positive precautionary savings exist when the third derivative of a utility function is positive [Leland (1968)]. The forms of precautionary savings include bank deposits, cash holdings, and jewelry.

Finally, formal or informal transfers can serve as self-insurance or mutual-insurance mechanisms. Even when a natural disaster occurs, a household can still hedge downside risk by
receiving remittances from family members who are altruistically linked [Altonji, et al. (1997), Cox and Jimenez (1990, 1992)]. These transfers can be interpreted as self-insurance behavior of a dynastic family which is composed of altruistically linked generations. Moreover, through informal arrangements of state-contingent mutual transfers among relatives, friends and neighbors, a household can also achieve consumption smoothing [Hayashi et al. (1996), Kohara et al. (2002), Townsend (1994, 1995)]. It is also important to note that the self-enforcement mechanisms of this informal self-interested mutual-insurance scheme could be sustained as sub-game perfect Nash equilibria in a repeated game framework [Coate and Ravallion (1993); Kocherlakota (1996)].

In addition to the above coping strategies, the government can also complement the risk-coping behaviors of households in various ways. Direct public transfers through means-tested targeting or geographical/group targeting can act as a formal safety net for vulnerable households who face temporary difficulties. Moreover, a provision of self-targeting workfare programs can be used as a self-insurance of poor households.

## The Theoretical Framework

To illustrate the role of different household responses in coping with unexpected damages caused by a natural disaster, we follow Zeldes (1989) and Deaton (1991) and construct a model that provides optimal consumer behavior under uncertain income and possible credit constraints. Suppose a household decision maker has a concave instantaneous utility, $ U(\bullet) $ , of the household consumption, $ C_{t} $ . The household decision is then to choose $ C_{t} $ , which maximizes the conditional expectation of discounted lifetime utility with a subjective discount rate, $ \delta $ , subject to intertemporal budget constraints:

$$ \begin{aligned}Max_{\{C_{t}\}}&\quad E_{t}\sum_{j=0}^{T}\left(\frac{1}{1+\delta}\right)^{t+j}U(C_{t+j})\\s.t.\quad&A_{t+1}=(1+r_{t})(A_{t}+y_{t}-C_{t})\\&A_{t}+y_{t}-C_{t}+z_{t}\geq0,\\&z_{t}\geq0\\&A_{0}\ given\\&A_{T}\geq0,\end{aligned} $$

where A is the household asset at the beginning of the period. The maximum amount of credit possible for this household is represented by $ z^{5} $ . Note that r and y represent the interest rate and
stochastic household income, respectively.

When income is stochastic, analytical solutions to this problem cannot generally be derived [Zeldes (1989)]. However, we can derive a set of first-order necessary conditions by forming a value function and Bellman equation to obtain an optimum solution. Let $ \lambda $ represent the Lagrange multiplier associated with credit constraint $ A+y-C+z \geq 0 $ . Combining the envelope condition derived from the first-order conditions, we obtain a consumption Euler equation, which is augmented by the possibility of a binding credit constraint:

$$ \begin{align*}U^{\prime}(C_{t})&=E_{t}\Bigg[U^{\prime}(C_{t+1})\Bigg(\frac{1+r_{t}}{1+\delta}\Bigg)\Bigg]+\lambda_{t},\\A_{t}+y_{t}-C_{t}+z_{t}&\geq0\text{if}\lambda_{t}=0,\\A_{t}+y_{t}-C_{t}+z_{t}&=0\text{if}\lambda_{t}>0.\end{align*} $$

Note that this augmented Euler equation was first derived by Zeldes (1989). We can interpret the Lagrange multiplier, $ \lambda $ , as an indicator of negative welfare effects generated by binding credit constraints. $ ^{6} $ Note that the Lagrange multiplier $ \lambda_{t} $ is a negative function of the current asset, income, and the maximum value of borrowing. It is straightforward to show that, given other variables, a decrease in these variables of a credit-constrained household leads the marginal utility of current consumption to increase, causing the Lagrange multiplier to increase.

## The Econometric Framework

The aim of our econometric framework is to test the implications of the augmented Euler equation (1). When the credit constraint is binding, we have:

$$ U^{\prime}(C_{i t})=E_{t}\Biggl[U^{\prime}(C_{i t+1})\Biggl(\frac{1+r_{i t}}{1+\delta_{i}}\Biggr)\Biggr]+\lambda_{i t}\left(A_{i t},y_{i t},z_{i t}\right), $$

where i is the household index. In equation (2), recall that $ \lambda $ is a negative function of the current asset, income, and the maximum value of borrowing. Hence, given the first term of the right-hand side of equation (2), i.e., the expected value of the marginal utility of the targeted consumption at