Macroeconomic Disasters and the Equity Premium Puzzle: Are Emerging Countries Riskier?

Macroeconomic Disasters and the Equity Premium Puzzle: Are Emerging Countries Riskier?

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Macroeconomic Disasters and the Equity Premium Puzzle: Are Emerging Countries Riskier? Jaroslav Horvath PII: DOI: Reference:

S0165-1889(20)30022-1 https://doi.org/10.1016/j.jedc.2020.103852 DYNCON 103852

To appear in:

Journal of Economic Dynamics & Control

Received date: Revised date: Accepted date:

6 August 2019 6 December 2019 6 January 2020

Please cite this article as: Jaroslav Horvath, Macroeconomic Disasters and the Equity Premium Puzzle: Are Emerging Countries Riskier?, Journal of Economic Dynamics & Control (2020), doi: https://doi.org/10.1016/j.jedc.2020.103852

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Macroeconomic Disasters and the Equity Premium Puzzle: Are Emerging Countries Riskier?∗ Jaroslav Horvath† December 2, 2019

Abstract

Not necessarily. I provide evidence that advanced countries’ equity premium and consumption growth differ significantly from those of emerging countries. I then estimate distinct disaster risk parameters for these two country groups. My Bayesian analysis demonstrates that in some aspects advanced countries are more exposed to disaster risk, while in others their exposure is smaller. Disasters are estimated to be more severe and uncertain in advanced countries, but are on average less persistent. Advanced countries are also more likely to experience a global disaster, whereas disasters in emerging countries tend to be more idiosyncratic. I show that country-group heterogeneity in disaster length and magnitude has the largest impact on equity premium. JEL classification: C11; E21; E44; G12. Keywords: Consumption Disasters; Equity Premium; Bayesian Markov-Chain Monte Carlo.

[email protected]. Department of Economics, University of New Hampshire, 10 Garrison Avenue, Durham, NH 03824. Office Phone: 603-862-0867. † A previous version of this paper was circulated under the title “Macroeconomic Disasters and the Equity Premium Puzzle in Developing and High-Income Countries.” I am highly indebted to Pok-sang Lam for his guidance. I would like to thank Paul Evans, Yin Germaschewski, Michael Goldberg, Zhaozhao He, Xiang Hui, Paulina Restrepo-Echavarria, Frank Schorfheide, Andrew Seal, Byoung Hoon Seok, and seminar participants at various institutions and conferences for useful comments and suggestions. ∗

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Introduction

Rietz (1988), Barro (2006), and Barro and Ursua (2008) report evidence that the longstanding equity premium puzzle, discovered by Mehra and Prescott (1985), can be explained as compensation for the risk of rare events that lead to “disastrous” falls in income and consumption. The work of Barro (2006) and Barro and Ursua (2008) assumes that the fall in output and consumption during disasters is permanent and instantaneous – occurs over one period (year). Nakamura et al. (2013) extend their work by allowing for a multiperiod nature of disasters and for disaster recoveries, and conclude that disaster risk is still important in resolving the equity premium puzzle. Their analysis delivers a coefficient of relative risk aversion that is lower than in models without disaster risk, but at 6.4, is higher than in Barro (2006) and Barro and Ursua (2008). In this paper, I extend the disaster risk framework, in particular the model of Nakamura et al. (2013), to address another concern: it assumes a common risk premium and a common probability and magnitude of disasters across all countries. The extension is motivated by documenting that, in the long-run international data, the consumption growth and equity premium in emerging market economies (EMEs) are significantly different from their counterparts in advanced economies (AEs).1 More specifically, consumption growth in AEs exhibits, on average, larger kurtosis (“fatter tails”), while the average equity premium is found to be considerably larger in EMEs – I find the average equity premium to be 4.9 and 9.7 percent in AEs and EMEs, respectively.2 This evidence leads me to estimate distinct disaster risk parameters for these two country groups. Like Nakamura et al. (2013), I use a Bayesian analysis and allow for both permanent 1

Several other studies report that, compared to advanced countries, emerging countries are characterized by a significantly higher equity risk premium and by more volatile business cycles. For example, Neumeyer and Perri (2005) and, more recently, Horvath (2018), document a larger volatility of consumption in emerging economies, whereas Shackman (2006) documents a considerably higher equity risk premium in emerging countries compared to advanced countries. 2 Because of the large volatility of stock returns, the use of long-term financial data is critical for accurately assessing the value of the equity premium in both groups of countries. Dimson et al. (2006) highlight numerous periods of extraordinarily high and low returns for 17 countries over the last 100 years and emphasize the danger of extrapolating future equity returns based on a small sample window.

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and temporary disasters that can unfold over multiple years. But, my analysis uses a larger and longer sample of countries and estimates group-specific disaster magnitudes and probabilities.3 In addition, my model accounts for correlation in the timing of both permanent and temporary disaster drops in consumption within each group of countries. The Bayesian analysis reveals that in some dimensions AEs are more exposed to disaster risk, while in other dimensions their exposure is smaller. More specifically, my empirical estimates demonstrate that disasters are larger (in magnitude) and more uncertain in AEs. However, EMEs face, on average, a higher probability of entering a disaster on their own – they are six times more likely to enter an individual disaster – and exhibit a larger disaster persistence – a typical disaster lasts on average 50 percent longer. In addition, the Bayesian estimation finds a large correlation of permanent consumption drops in disasters across AEs and of temporary consumption drops in disasters across EMEs. Overall, the estimation results show that AEs tend to enter global events with more disastrous consequences such as the Great Depression, while EMEs more frequently experience isolated disasters, such as civil wars and coups, which are usually of a smaller magnitude. I show that the distinct exposure of AEs and EMEs to disaster risk has several implications for asset prices. As in earlier studies, I adopt an endowment economy with a representative consumer that has Epstein-Zin-Weil (EZW) preferences in each country group. Given the estimated disaster parameters, matching the equity premia in the group of advanced and emerging countries requires a coefficient of relative risk aversion (CRRA) of 4.4 and 6.2, respectively. The lower CRRA value in AEs than in EMEs is in line with empirical evidence provided by Falk et al. (2018), who use “an experimentally validated survey data set” to measure risk taking behavior in individual countries. Nakamura et al. (2013) arrive at a CRRA of 6.4 to match the mean of the observed equity premia across all countries in their sample. Barro and Jin (2016) require a CRRA value of 5.9 when jointly estimating disasters 3

Ideally, one would want to let the disaster parameters be time-varying and country-specific instead of group-specific. However, given the rare nature of disasters, there is a need to pool information over time and across countries within each group to allow for an accurate parameter estimation.

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and long-run risks, first introduced by Bansal and Yaron (2004), in a unified framework. Different from previous studies, my work allows for disaster contagion and importantly for country-group heterogeneity in disaster parameters and equity premia. This yields the fact that to match the equity premium the model requires a lower CRRA for AEs, compared to EMEs and to other related works that allow for recoveries in consumption during disasters. My framework also allows me to quantify the contribution of the differences in groupspecific disaster parameters to the equity premium. I find that differences in disaster duration and in permanent disaster shocks to consumption contribute the most to the equity premium in both groups of countries. Specifically, for AEs it is the difference in disaster duration that leads to the largest change in the equity premium. Setting the mean AE disaster length to the mean EME disaster length of six years (instead of the estimated four years for AEs) increases the equity premium for AEs by approximately 35 percent, relative to its observed and baseline model value. For EMEs, it is the difference in the long-run disaster impact on consumption that contributes the most to the equity premium. The EME equity premium increases by 29 percent when EMEs face the long-run disaster shocks estimated for AEs. Lastly, in line with data, the model generates higher correlations of cross-country consumption growth, equity returns, and risk-free rates for AEs than for EMEs. This result is driven by the more “global” nature of disasters in AEs (for example, the World Wars) compared to the more “idiosyncratic” nature of disasters in EMEs (for example, the Asian Financial Crisis). To maintain accuracy of the parameter estimation, the probability of disasters is assumed to be constant over time in each country group. Gourio (2012) calibrates a time-varying disaster probability in a real business cycle framework to account for the co-movements of asset prices and macroeconomic aggregates in the United States. Similarly, Wachter (2013) models a stochastic disaster probability to account for several U.S. asset pricing features such as the long-run predictability and high volatility of stock returns. In contrast, my research targets distinct equity premia in AEs and EMEs, and uses Bayesian analysis to estimate a 3

non-stochastic disaster probability and other group-specific disaster risk parameters for the two country groups. My paper contributes to the vast literature trying to explain the equity premium puzzle. Instead of trying to provide an exhaustive list of possible explanations for the puzzle, I focus on listing a few seminal works including the literature on habit formation, long-run risks, disasters, agent heterogeneity, and behavioral explanations. The habit formation work is exemplified by Campbell and Cochrane (1999), who, building on the work of Abel (1990) and Constantinides (1990), show that their model can replicate the observed equity premium under the assumption that agents care about the value of their current consumption relative to its past. A possibility that the consumption growth contains a small persistent growth component and stochastic volatility has been put forward by Bansal and Yaron (2004), later followed by Hansen et al. (2008), Bansal et al. (2010), and Constantinides and Ghosh (2011). In contrast, Constantinides and Duffie (1996) argue that consumption heterogeneity across agents is key in resolving the equity premium puzzle, while Barberis et al. (2001) utilize prospect theory to offer a behavioral explanation – agents’ risk aversion varies based on past outcomes – to the puzzle. My work is in line with the disaster literature introduced by Rietz (1988) and later extended by Barro (2006) and Nakamura et al. (2013), which states that the equity premium is a compensation for infrequent, but disastrous events that lead to large consumption drops. However, in contrast to the previous disaster studies, my work estimates group-specific disaster parameters and quantifies the impact of differences in countries’ disaster parameters on the distinct equity premium in advanced and emerging countries. The rest of the paper is organized as follows. Section 2 describes the data and stylized facts of consumption growth and equity premium in advanced and emerging countries. Section 3 lays out the empirical model of consumption disasters. The Bayesian estimation method is outlined in Section 4. Section 5 presents the estimates of group-specific disaster parameters. Section 6 analyzes the asset pricing implications of the differences in countries’ 4

disaster parameters on the equity premium. Section 7 concludes.

2

Data and Stylized Facts

The aim of this section is to describe the data and methods used to classify countries into two groups. The section documents significant differences in the moments of the consumption growth distribution and equity premium between the two country groups and, thus, provides prima facia evidence that disaster parameters may potentially differ across the country groupings.

2.1

Country Classification

As is commonly done in the literature (see, e.g., Akinci and Olmstead-Rumsey, 2018; CarriereSwallow and Cespedes, 2013; Ilzetzki et al., 2013; Kose et al., 2012; Miyamoto and Nguyen, 2017), I classify countries into groups based on their level of economic development. However, in contrast to this line of work, I employ several standard clustering methods, including the k-means clustering and partitioning around medoids, to divide countries into two groups. These methods divide data (countries) into clusters (groups) based on their “similarity,” which is defined to be country’s economic development in my context. Specifically, I use long-run output per capita data to keep track of countries’ relative development over the last 100 years.4 The main advantage of the clustering approach is that it not only allows me to use statistical procedures to determine the optimal number of country groupings, but it also takes into account the historical evolution of a country’s relative economic development. In other words, clustering accounts for the fact that the ranking of countries based on their GDP per capita may change over time. 4 I consider all countries included in my consumption sample, used for Bayesian analysis, which spans from 1890 to 2016. Output data is sourced from the Barro and Ursua (2008) dataset and is extended using the PPP real GDP per capita data from the World Bank. The sample window is 1911-2016 to achieve a balanced panel required by the clustering methods. More details on the datasets and country selection criteria are provided in Subsection 2.2 and in the Appendix.

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The number of country groupings is motivated by the following two reasons. First, it is the optimal number of clusters determined by various cluster selection criteria such as the Silhouette and Gap Statistic Methods. Second, given that disasters occur infrequently, there is a need to pool information across countries (and over time) in a given group in order to increase the statistical accuracy of the estimation.5 Having a large number of country groupings would lead to a small number of countries in some groups and, thus, to an imprecise estimation of disaster parameters. Based on the countries’ relative economic development over the last century, the clustering methods yield the following two groupings.6 The first consists of 14 countries – Argentina, Brazil, Chile, Colombia, Egypt, India, Korea, Mexico, Peru, Portugal, Russia, Taiwan, Turkey, and Venezuela – while the second group is comprised of 17 countries – Australia, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, the UK, and the US. As a result, I label these two country groupings as the emerging market economies (EMEs) and advanced economies (AEs), respectively. Naturally, there are some borderline cases. For example, Portugal and Taiwan are classified as EMEs.7 This stems from the fact that for the most part of the sample, especially in the first half of the 20th century, the two countries were, relative to AEs, much poorer than in the recent years. The Appendix shows that the estimation results are robust to including Portugal and Taiwan in the AE group.

2.2

Consumption Data

This paper employs long-run consumption data and Bayesian analysis to examine the impact of rare consumption disasters on asset pricing. The Bayesian estimation utilizes consumption data from the macroeconomic dataset constructed by Barro and Ursua (2008). The dataset contains long-term annual per capita real GDP and consumption (personal consumer expen5

Similar rationale applies for having time-invariant disaster parameters. The classification results are insensitive to the choice of the distance measure including the Euclidean and Manhattan distance measures. 7 Using post-1990 quarterly data, Carriere-Swallow and Cespedes (2013) also classify Portugal as an EME. 6

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ditures) series for over 40 countries.8 The focus on long-run consumption data is key for an accurate parameter estimation, because it ensures that the data series contains information on the evolution of consumption during disasters. The dataset ends in 2006, so I follow Barro and Ursua’s data source documentation to extend the dataset until year 2016 to account for the most recent financial crisis. The most common data source is the World Bank’s World Development Indicators Database. A country is included in my sample as long as its uninterrupted consumption series commences between 1890 and 1925 to avoid poor data quality and a sample selection bias.9 The sample of consumption data consists of an unbalanced panel of 31 countries with an average starting year of approximately 1904 for emerging countries and 1892 for advanced countries.10 The ending year is 2016 for each country, which yields a total of 3713 observations. To shed light on potential differences in disaster characteristics between AEs and EMEs, Table 1 reports the first four moments of the consumption per capita growth distribution for individual countries. The numbers in parentheses denote standard errors obtained with bootstrapping, while the numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of country group means and medians, respectively. Three observations are worth noting. First, EMEs exhibit, on average, a significantly larger mean and volatility in their consumption growth. This is in line with the literature examining business cycles in EMEs, exemplified by, e.g., Neumeyer and Perri (2005) and Aguiar and Gopinath (2007), which using post-1990 quarterly data shows that consumption tends to be more volatile in EMEs than in AEs. In contrast, I demonstrate that this finding is robust to annual data frequency and to considering a much longer sample window. Second, the 8

Barro and Ursua (2008) apply several treatments to the historical data. For example, when it comes to changes in country’s borders, Barro and Ursua smoothly paste multiple consumption series together to avoid discrete shifts in the data. These might be otherwise identified as disasters by the model, although that was likely not the case. 9 There are some countries such as Austria or Singapore whose consumption data starts between 1890 and 1925, but they have missing data during the WWII. Including them would likely underestimate the effects of disasters. 10 The Appendix shows that the estimates of group-specific disaster parameters remain very similar when dropping countries (Colombia, India, Venezuela), whose consumption data starts after World War I.

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Table 1: Consumption Per Capita Growth Emerging Argentina Brazil Chile Colombia Egypt India Korea Mexico Peru Portugal Russia Taiwan Turkey Venezuela Mean Median Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

Mean

Volatility

Skewness

Kurtosis

Start

1.60 (0.68) 2.67 (0.70) 2.08 (0.81) 2.21 (0.66) 1.91 (0.57) 1.78 (0.45) 2.89 (0.64) 1.64 (0.58) 2.01 (0.42) 2.48 (0.43) 2.24 (0.89) 3.29 (0.77) 2.06 (0.62) 3.46 (1.06) 2.31 2.21

7.80 (0.68) 7.50 (0.67) 8.76 (0.76) 6.36 (0.91) 6.26 (0.70) 4.46 (0.52) 6.49 (0.73) 6.34 (1.17) 4.60 (0.44) 4.42 (0.31) 10.07 (1.42) 8.36 (1.23) 7.08 (0.68) 10.36 (0.92) 7.06 7.06

0.45 (0.36) 0.72 (0.28) -0.80 (0.28) 1.08 (0.72) 0.76 (0.62) 0.68 (0.64) -0.66 (0.57) 2.18 (1.47) -0.82 (0.40) -0.37 (0.18) 0.13 (1.10) -1.10 (1.03) -0.54 (0.51) 0.46 (0.28) 0.15 0.15

4.84 (0.69) 4.62 (0.61) 4.54 (0.64) 8.35 (2.09) 7.07 (1.85) 6.45 (1.82) 6.26 (1.13) 17.99 (7.38) 5.38 (1.28) 3.15 (0.32) 11.22 (2.65) 11.39 (2.76) 5.82 (1.57) 3.89 (0.50) 7.21 6.26

1890 1901 1900 1925 1894 1919 1911 1900 1896 1910 1890 1901 1890 1923

1.54 (0.46) 1.76 (0.84) 1.97 (0.39) 1.55 (0.47) 2.39 (0.51) 1.73 (0.59) 1.86 (0.51) 1.80 (0.34) 2.39 (0.60) 1.80 (0.77) 1.51 (0.52) 2.01 (0.35) 1.90 (0.65) 1.88 (0.38) 1.46 (0.40) 1.47 (0.26) 1.78 (0.30) 1.81 [0.009] 1.80 [0.005]

4.87 (0.56) 8.60 (1.62) 4.43 (0.46) 5.33 (0.76) 5.72 (0.65) 6.67 (0.99) 5.84 (0.60) 3.83 (0.45) 6.93 (1.24) 8.77 (1.69) 5.90 (0.64) 3.97 (0.57) 7.27 (1.11) 4.29 (0.53) 4.61 (0.76) 2.91 (0.35) 3.33 (0.26) 5.49 [0.024] 5.41 [0.029]

-0.58 (0.65) 0.43 (1.70) -1.08 (0.39) -0.06 (1.06) -0.68 (0.73) -0.03 (1.15) -0.10 (0.51) 0.38 (0.78) 0.20 (1.76) 1.31 (1.80) -0.28 (0.63) 0.22 (1.14) -1.53 (1.15) 0.90 (0.75) 2.40 (0.93) -0.10 (0.83) -0.24 (0.29) 0.07 [0.796] -0.04 [0.769]

7.29 (1.57) 15.36 (4.63) 6.32 (1.27) 11.13 (2.07) 7.79 (1.67) 12.06 (2.60) 6.27 (0.93) 8.04 (1.99) 17.62 (4.86) 19.35 (5.58) 6.97 (1.46) 11.43 (2.90) 13.36 (5.19) 8.83 (1.85) 15.22 (4.34) 8.68 (1.52) 4.04 (0.56) 10.58 [0.033] 9.70 [0.002]

1901 1913 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890

Notes: The table shows summary statistics of consumption per capita. The consumption series is in growth rates and percentages. Standard errors in parentheses are obtained by bootstrapping. The numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of means and medians, respectively, in advanced and emerging countries. End year is 2016.

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distribution of consumption growth in EMEs appears to be slightly more positively skewed, albeit the difference is not statistically significant. Third, and most importantly, the kurtosis is significantly larger in AEs than in EMEs. This is of interest, because, as Martin (2012) states, “fat tails” generally indicate presence of disasters.11 Overall, Table 1 shows that although the EME consumption growth tends to be, on average, higher and more volatile, it is the distribution of consumption growth in AEs that tends to exhibit “fatter tails.” As a result, Table 1 provides suggestive evidence that disaster characteristics may differ considerably between the two groups of countries.

2.3

Financial Data

Following Barro and Ursua (2008), I use the Global Financial Database to construct annual long-term financial series of total stock and bill returns for over 20 countries. Unfortunately, the coverage of financial data is not as substantial as the one of consumption data. For this reason, a country is included in the sample of financial returns if (1) it has at least 50 years of equity premium data available, and (2) its consumption series commences between 1890 and 1925. This yields 17 advanced countries and 6 emerging countries. The starting year of 1870 and the ending year of 2017 lead to a sample size of 2989 observations. I use end-of-year values of stock and bill price indexes to compute arithmetic averages of returns on the corresponding securities. To obtain real returns, the indexes are deflated by the end-of-year values of the country’s consumer price index. Importantly, I use total returns on stock market indexes and government bills with maturity of three months as proxies for stock market returns and the risk-free rate, respectively.12 As in Barro and Ursua (2008), I set the returns in years with missing data to the average of a multi-year cumulative real 11

The Appendix provides analogous tables to Table 1 using output (instead of consumption) per capita for the baseline country groupings, and also for an extended and more comprehensive sample of countries comprised of 19 AEs and 20 EMEs. The key finding of AEs exhibiting significantly fatter tails (larger kurtosis) remains. 12 For example, I use the S&P 500 index, CDAX index, and Bombay SE sensitive index as proxies of the U.S., German, and Indian stock market returns, respectively. The data is extended in some cases with stock market returns when total returns are unavailable.

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Table 2: Equity Premium and Bill Return Emerging Chile India Korea Mexico Portugal Venezuela Mean Median Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

E(Rep )

σ(Rep )

E(Rf )

σ(Rf )

Start

12.1 (4.6) 2.3 (2.4) 11.4 (4.7) 5.4 (2.5) 7.4 (3.7) 19.4 (8.9) 9.7 9.7

48.1 (13.4) 23.6 (2.1) 34.7 (3.8) 27.4 (2.8) 34.0 (5.0) 73.5 (16.3) 40.2 34.7

-1.7 (1.6) 1.7 (0.8) 4.2 (0.8) -0.6 (0.8) -0.3 (0.5) -3.1 (1.2) 0.0 -0.3

17.3 (2.1) 7.8 (1.0) 6.1 (0.6) 9.1 (0.9) 4.9 (0.4) 9.8 (1.2) 9.2 9.1

1909 1921 1963 1902* 1932* 1948

4.5 (1.3) 3.3 (1.5) 3.7 (1.5) 2.8 (1.6) 10.0 (3.1) 7.1 (1.9) 6.5 (2.2) 4.8 (2.4) 7.8 (2.4) 3.8 (1.7) 2.0 (2.2) 4.9 (2.9) 2.2 (1.8) 6.4 (1.6) 3.3 (1.8) 3.5 (1.5) 7.1 (1.5) 4.9 [0.112] 4.6 [0.052]

16.2 (1.2) 17.8 (1.2) 18.3 (1.2) 19.1 (1.9) 30.4 (4.1) 23.5 (3.4) 26.5 (3.0) 25.7 (2.3) 28.0 (2.7) 20.1 (1.6) 21.4 (3.1) 28.9 (4.5) 20.8 (1.5) 18.9 (1.3) 19.6 (1.4) 17.7 (2.4) 18.5 (1.1) 21.9 [0.058] 20.5 [0.001]

4.2 (0.3) 0.5 (0.6) 2.2 (0.5) 3.0 (0.5) 1.2 (0.9) -0.8 (0.8) -1.2 (1.4) -1.1 (1.2) -0.3 (1.1) 0.7 (0.4) 2.3 (0.5) 0.5 (0.7) 1.3 (0.5) 1.5 (0.5) 0.8 (0.4) 1.3 (0.5) 1.2 (0.4) 1.0 [0.420] 1.1 [0.354]

3.5 (0.3) 7.4 (0.6) 6.0 (0.6) 5.8 (0.5) 8.8 (1.9) 9.6 (1.1) 16.3 (3.4) 12.6 (2.5) 13.0 (2.3) 4.7 (0.4) 5.0 (0.4) 7.5 (0.9) 5.8 (0.4) 6.4 (1.1) 4.9 (0.7) 5.7 (1.1) 4.7 (0.4) 7.5 [0.428] 6.2 [0.256]

1870 1870* 1872 1874 1921 1870 1870 1906 1887 1891* 1927 1915 1883* 1871 1900 1870 1870

Notes: The table shows in percentages the mean and volatility of equity premium (Rep ) and bill return (Rf ). Standard errors in parentheses are obtained by bootstrapping. The numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of means and medians, respectively, in advanced and emerging countries. End year is 2017. * denotes missing data: 1941 - 1946 for Belgium, 1914 - 1918 for Mexico, 1945-1946 for Netherlands, 1975 - 1977 for Portugal, and 1914 - 1920 and 1937 - 1940 for Spain. Returns are computed using end-of-year values of total equity and bill indexes deflated by the end-of-year values of country’s consumer price index. Short-term government bonds (maturity of three months) are used for computation of bill returns. The data is sourced from the Global Financial Data and for Mexico for 1902 - 1929 years from Haber, Razo, and Maurer (2003).

return during the given period. 10

Table 2 reports in percentages the mean and standard deviation of equity premium and bill returns for individual countries. It documents that the equity premium is about two times larger in EMEs, on average, than in AEs. This difference is statistically significant when comparing group medians (p-value of 0.052) and marginally statistically insignificant for group means (p-value of 0.112).13 In addition, Table 2 shows that EMEs tend to exhibit a substantially larger equity premium volatility, while it can be seen that there is no significant difference in the first two moments of the risk-free rate. Table 2 reveals that the financial sample of EMEs is usually shorter and consists of only six out of the 14 countries used for estimation of the consumption disaster model. Potential candidates for extending the sample are Argentina, Brazil, Colombia, and Peru. However, all of these countries lack early data on bill returns. Moreover, central bank discount rates or deposit rates are highly volatile in these economies due to the large changes in the inflation rate, and hence they are not appropriate proxies for the risk-free rate return. Table A4 in the Appendix, however, shows that the difference in equity premium between the two country groups is robust to using postwar financial data. The p-values for difference in equity premium group means and medians are, respectively, 0.087 and 0.030. Furthermore, I expand the baseline sample of financial returns for EMEs by considering additional countries, not included in the consumption sample, that have at least 40 years of data for both financial series. The inclusion of additional six countries (Greece, Malaysia, Philippines, South Africa, Sri Lanka, and Taiwan) slightly decreases the mean equity premium in EMEs, but the higher statistical power allows me to reject the null hypothesis of the equity premium being identical between the two country groups at a higher confidence level. The p-values, reported in Table A5, for equality of country group means and medians are 0.008 and 0.003, respectively.14 13

In the Appendix, I show that the difference in group equity premium means becomes statistically significant when extending the EME group with additional countries that are not included in the consumption sample and when considering a postwar sample window. For completeness, the Appendix also provides higher order moments (skewness and kurtosis) of the equity premium and bill returns. 14 These results are robust again to considering postwar financial return data.

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3

Disaster Model

The empirical model of consumption disasters builds on the work of Nakamura et al. (2013) and decomposes observed consumption into three unobservable components, while allowing for gradual recoveries, to isolate the contribution of disasters to consumption movements.15 Similarly to Barro (2006) and Barro and Ursua (2008), Nakamura et al. (2013) assume common disaster magnitudes and probabilities across countries and, in turn, target one equity premium, which they compute by taking an average of equity premia over all countries in their sample. In contrast, motivated by the evidence that AEs display a consumption growth distribution with relatively “fatter” tails, my model allows disaster parameters to differ between the country groups. This also allows me to target two distinct equity premia, which is important given that EMEs deliver, on average, a significantly higher equity premium. However, due to the infrequent nature of disasters, I pool information about disasters across time and across countries within each group – disaster parameters are assumed to be group-specific – to maintain accuracy of the Bayesian estimation. Summarizing, the proposed model in this paper deviates from the one of Nakamura et al. (2013) in two main aspects. First, the sample of countries is divided into two groups to capture the differences in consumption and equity premium distributions between AEs and EMEs. Second, the model accounts for correlation of temporary and permanent drops in consumption during disasters among countries within each group. The consumption and disaster evolution are assumed to be symmetric across the two groups of countries, and, hence, for convenience they are described from a perspective of AEs. Analogous expressions with group-specific disaster parameters apply to EMEs. As in Nakamura et al. (2013), the dynamics of the observed log per capita consumption, ci,t , for a country i at time t is given by the following processes: ci,t = xi,t + zi,t + i,t , 15

Figure 3 shows the estimated evolution of consumption during disasters in AEs and EMEs.

12

(1)

4xi,t = µi,t + Ii,t θi,t + ηi,t ,

(2)

zi,t = ρz zi,t−1 + Ii,t φi,t − Ii,t θi,t + νi,t .

(3)

xi,t denotes the long-run (potential) level of consumption, zi,t captures a disaster gap, i.e., the difference between actual and long-run consumption that arises due to disasters, and i,t denotes an independently and identically distributed shock that is normally distributed 2 .  is meant to capture measurement errors in observed with mean zero and variance σ,i,t

consumption. σ2 takes two values: the first stands for the period before 1946, while the second one stands for the period after 1946 to capture the drop in consumption volatility after World War II.16 This assumption ensures that the model does not overestimate the effects of disasters. Equation (2) models the first difference in long-run consumption, 4xi,t ≡ xi,t − xi,t−1 ,

as the sum of three components: a country-specific and time-varying mean of consumption

growth, µi,t ; an independently and identically distributed temporary shock, ηi,t , following a 2 ; and a product of a disaster indicator, normal distribution with mean zero and variance ση,i

Ii,t , and a permanent drop in consumption during disasters, θi,t . Following Nakamura et al. (2013), µi,t takes three different values for each country over time to capture the fast economic growth that many countries exhibited during the 1946-1972 period: one value for the period before 1946, one for the period between 1946 and 1972, and one for the period after 1972. As evidenced in in equation (3), the disaster gap, zi,t , follows a modified autoregressive distributed process, where ρz ∈ [0, 1) represents the persistence of the disaster gap, φi,t

denotes a temporary consumption drop during disasters, and νi,t is a normal shock that is 2 independently and identically distributed with mean zero and variance σν,i introduced solely

to facilitate convergence of the Bayesian algorithm. θi,t is assumed to have no initial effect on 16

Romer (1986) attributes the drop in volatility to changes in the measurement of national accounts. Amir-Ahmadi et al. (2016) offer empirical evidence for this assumption for the US. Moreover, this modeling assumption is in line with Nakamura et al. (2013) and Barro and Jin (2016), and importantly, Nakamura et al. (2013) show that the results are robust to using the year 1951 for the structural break in consumption growth volatility instead of the year 1946.

13

actual consumption at the onset of a disaster and is, therefore, subtracted from the disaster gap. In addition to modeling group-heterogeneity in disaster parameters, this paper also allows for spatial correlation in disaster shocks. Specifically, the permanent (θi,t ) and temporary (φi,t ) drops in consumption during disasters depend on group-specific and country-specific components, and are assumed to be governed by: C , θi,t = θtG + θi,t

(4)

C φi,t = φG t + φi,t .

(5)

θtG denotes the group-specific permanent drop in consumption during disasters. It is dis2 tributed as θtG ∼ N (θG , σθ,G ) and captures correlation in permanent consumption drops

among countries in a given group. Put differently, θtG allows for a possibility that an ad-

vanced country may be prone to a large long-run disaster shock, if the AE group is subject to C represents the country-specific component and follows a large long-run disaster shock.17 θi,t C 2 θi,t ∼ N (0, σθ,C ).18 It captures the idiosyncrasy of long-run disasters across individual coun-

tries in a given group. An example of a permanent drop in consumption during disasters could include a long-run destruction of structures due to a war. Note that the permanent disaster magnitude components are not restricted to be negative to reflect the fact that sometimes, perhaps due to a favorable change in institutions, disasters might actually have positive effects on consumption in the long run.

The group-specific and country-specific temporary consumption drops during disasters C are denoted, respectively, by φG t and φi,t . This specification allows for correlation in the

short-run consumption drops during disasters between countries within each group. φG t 17

I have also considered the inclusion of a world (instead of a group-specific) component in the temporary and permanent consumption drops during disasters. However, the DIC model selection criterion suggested the baseline model with group-specific components to be the preferred model. This was further corroborated by the world component estimates that revealed no significant correlation in the long-run and short-run consumption drops during disasters between AEs and EMEs. 18 C Notice that the mean of θi,t is set to zero in order to achieve model identification.

14

?G 2 19 is distributed as φG Similarly, φC t ∼ tN (φ , σφ? ,G , −∞, 0). i,t follows a truncated normal

distribution on the support [−∞, 0], but with mean zero (to achieve identification) and

variance σφ2 ? ,C . The stars on the parameters denote the mean and variances of the normal distribution before truncation. Notice that the temporary disaster magnitude components can only take non-positive values implying that disasters, such as a temporary weakness of the financial system, have only negative effects on the consumption in the short-run. Following Nakamura et al. (2013), country-specific consumption disasters are denoted with an indicator variable Ii,t , which follows a Markov process. Consequently, each country can be in one of two states in period t: a disaster state (Ii,t = 1) and normal times (Ii,t = 0). Furthermore, each country can enter a disaster in two different ways. First, a country can enter a disaster on its own, i.e., individually, such as through a sovereign debt crisis. The probability of entering an individual disaster is denoted with pCbI . Second, countries can enter a disaster through a world disaster. The probability of entering a disaster conditional on a world disaster is captured by pCbW . World disasters, such as the World Wars or the Great Depression, are represented with a Bernoulli process ItW , where the world disaster indicator ItW = 1 with probability pW . The Markov process for Ii,t can be summarized as follows:

P r{Ii,t = 1 | Ii,t−1 , ItW } =

     pCbW,     

pCbI ,         1 − pCbe ,

if Ii,t−1 = 0, ItW = 1, if Ii,t−1 = 0, ItW = 0,

(6)

if Ii,t−1 = 1.

As a result, a country has the probability pCbI (1 − ItW ) + pCbW ItW of entering a disaster in

period t, given that the country is not in a disaster in period t − 1. If a country currently faces a disaster state, it will remain in a disaster state with probability (1 − pCbe ), i.e., pCbe 19

tN stands for a truncated Normal distribution.

15

denotes the probability of exiting a disaster.

4

Bayesian Estimation

The goal of this section is to summarize all disaster and non-disaster parameters that are estimated via the Bayesian approach. In addition, the section describes the estimation method and then discusses the prior distributions.20 Since disasters occur rarely, calibration of disaster parameters is challenging and requires a stand on the definition of disasters. For example, Barro and Ursua (2008) define disasters as peak-to-trough declines in per capita consumption of at least 10%. Bayesian estimation avoids taking a stand on a particular definition of disasters by estimating posterior probability for each country being in a disaster state in a given year. Moreover, the Bayesian approach allows for an accurate estimation of disaster parameters and provides measures of parameter uncertainty.

4.1

Parameters

To allow for an efficient estimation of the model, I employ Bayesian Markov Chain Monte Carlo methods and pool the information across countries within each group and across time. In other words, each group of countries (AEs and EMEs) possesses the following group2 2 2 2 specific disaster parameters: pCbW , pCbI , pCbe , ρz , θG , σθ,G , σθ,C , φG , σφ,G , and σφ,C . The

world disaster process is common to both country groups and is governed by pW . The non2 2 disaster parameters are country-specific and potentially time-varying: µk,t , σ,k,t , ση,k , and 2 σν,k , where k denotes an advanced or an emerging country. 20

The Bayesian method has been widely used in the asset pricing literature. See Schorfheide et al. (2018) for a recent example.

16

4.2

Prior distributions

The results in this paper are based on running four independent Markov chains using overdispersed sets of initial values. Each Markov chain pair is started from a different set of initial values. One set of initial values attributes all variation in actual consumption to potential consumption, and Ii,t = 0 for all countries and time periods. In the other set of initial values, Ii,t = 1 for all i and t, and variation in the disaster gap is set to explain most of the variation in the consumption data. Each chain is iterated two million times with the first million iterations dropped as a burn-in sample. Conjugacy and Gibbs sampling are exploited whenever possible. Otherwise, the Metropolis-Hastings algorithm with a normal proposal density is used to sample from the joint posterior distribution.21 Another attractive feature of the Bayesian approach is that the MCMC algorithm converges under very general conditions. To monitor convergence and ensure good mixing of the MCMC chains, I use trace and autocorrelation plots.22 I also experiment with the burn-in size and chain length to ensure robustness of the posterior estimates. The prior distributions are symmetric across the two groups of countries to let the data themselves drive potential differences in the disaster parameters. Moreover, for comparison purposes the set of priors is mostly based on Nakamura et al. (2013) and Barro and Jin (2016). The prior distributions used for each country group are reported in Table 3. The priors are generally flat and uninformative to let the data mainly pin down the posterior disaster parameters. For example, the prior for the probability of entering a disaster conditional on world disaster, pCbW , and for the probability of exiting a disaster, pCbe , follows a uniform distribution U (0, 1). Priors on the probability of world disasters, pW , and on the probability for an advanced country entering a disaster on its own, pCbI , reflect the fact that disasters occur rarely and, thus, follow a uniform distribution ranging from zero to ten percent. 21 22

More details about the estimation can be found in the Online Appendix of Nakamura et al. (2013). These can be found in the appendix.

17

Parameter θG σθ,G σθ,C φ?G σφ? ,G σφ? ,C pCbI pW

∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼

Table 3: Prior Distributions Distribution Parameter N(0, 0.2) σ,i,t U(0.01, 0.25) ση,i U(0.01, 0.25) σν,i U(-0.25, 0) µi,t U(0.01, 0.25) ρz U(0.01, 0.25) pCbW U(0, 0.1) 1 − pCbe U(0, 0.1)

∼ ∼ ∼ ∼ ∼ ∼ ∼

Distribution U(0, 0.15) U(0, 0.15) U(0, 0.015) N(0.02, 1) U(0, 0.9) U(0, 1) U(0, 1)

Notes: The table reports the prior distributions used for each country group. * indicates parameters before truncation. The probability of world disasters, pW , is common to both country groups.

The prior for the permanent drop in consumption during a disaster, θG , follows a normal distribution, which is symmetric around zero and highly dispersed. This specification allows not only for negative, but also for positive disaster consequences in the long run.23 φ?G prior embeds the assumption that disasters can have only negative effects on consumption in the short run. Priors on the standard deviations are overall fairly agnostic. The exception is the tight prior on σν,i to ensure that νi aids the simulation convergence only and does not affect the simulation results. The prior for the disaster gap persistence parameter, ρz , restricts the half-life of disasters to guarantee that past disasters do not explain current consumption changes. The prior on µi,t follows N (0.02, 1), where the prior mean is set to the average consumption growth across countries. I use the posterior mean as the point estimate of each parameter to analyze the estimation results and asset pricing implications.

5

Estimation Results

This section presents the empirical estimates of the disaster and country-specific parameters. The section also documents consumption dynamics during disasters in the model and in the data. The overall message of the section is that in certain dimensions AEs are more exposed to disaster risk than EMEs, while in other dimensions AEs’ exposure to disaster risk is 23

This makes the model more conservative and captures a potential situation, in which a disaster could lead, say, to an economic reform, which in the long run could have a positive impact on consumption.

18

smaller. For comparison purposes, I estimate not only the baseline model, but also the NSBU (Nakamura et al., 2013) model using the same set of countries and sample windows as for the baseline model.24 Recall that the NSBU model deviates from the baseline model in two main respects. First, the model assumes common disaster parameters for all countries. Second, the NSBU model abstracts from cross-country correlation in consumption drops during disasters. More specifically, θi,t ∼ N (θ,σθ2 ) and φi,t ∼ tN (φ? , σφ2 ? , −∞, 0) for all

countries. In comparison, the baseline model equations (4) and (5) imply that the correlation of disaster severity in the long run and short run in a given country group can be obtained, 2 2 2 2 2 2 respectively, as ρθ = σθ,G /(σθ,G + σθ,C ) and ρφ = σφ,G /(σφ,G + σφ,C ).25

Table 4 displays the posterior estimates of disaster parameters. To compare the relative model fit, the last row of Table 4 reports the deviance information criterion (DIC) for the baseline and NSBU models. The DIC is computed based on the likelihood function, penalizes for model complexity, and is often times the preferred selection criterion over the Bayes factor. Common cited reasons include the fact that the Bayes factor searches for a “true” model and is difficult, and sometimes even impossible, to compute for complex models. Table 4 shows that the DIC is considerably lower for the baseline model, indicating the baseline model to be the preferred model specification. Importantly, Table 4 highlights several key differences in AE and EME disaster dynamics. First, I find that disasters are more severe, both in the long run and in the short run, in AEs as evidenced by the more negative estimates of θ and φ. In particular, AEs experience during disasters an average long-run consumption decrease of 3 percent per annum and a short-run decrease of 11.4 percent per annum. Second, the estimates of σθ and σφ are found to be larger for AEs, implying that the more severe disasters in AEs are also accompanied by higher uncertainty. The higher long-run and short-run disaster uncertainty in AEs 24

The NSBU model uses priors laid out in Nakamura et al. (2013) and are identical for common parameters. Since the distributions of θ and φ are not necessarily independent, I use their joint posterior distribution to compute the posterior means and standard deviations of individual correlations. 25

19

Table 4: Posterior Estimates of Disaster Parameters Definition (parameter) temporary disaster shock (φ) permanent disaster shock (θ) group-specific SD of φ (σφ,G ) country-specific SD of φ (σφ,C ) overall SD of φ (σφ ) group-specific SD of θ (σθ,G ) country-specific SD of θ (σθ,C ) overall SD of θ (σθ ) disaster gap persistence (ρz ) world disaster prob. (pW ) country dis. prob. given world disaster (pCbW ) country prob. of individual disaster (pCbI ) country prob. of exiting disaster (1 − pCbe ) country overall prob. of entering disaster (pCbO ) deviance information criterion (DIC)

Baseline AEs Baseline EMEs -0.114 -0.072 (0.007) (0.013) -0.030 -0.013 (0.013) (0.008) 0.008 0.016 (0.002) (0.006) 0.077 0.033 (0.005) (0.011) 0.078 0.038 (0.005) (0.009) 0.148 0.051 (0.030) (0.020) 0.061 0.144 (0.022) (0.020) 0.162 0.153 (0.030) (0.019) 0.668 0.332 (0.029) (0.093) 0.060 0.060 (0.019) (0.019) 0.725 0.393 (0.074) (0.101) 0.003 0.019 (0.002) (0.008) 0.746 0.826 (0.053) (0.039) 0.046 0.042 (0.014) (0.012) -26602.2

NSBU model -0.087 (0.011) -0.016 (0.007) – – – – 0.065 (0.009) – – – – 0.141 (0.013) 0.457 (0.055) 0.048 (0.018) 0.618 (0.071) 0.008 (0.003) 0.833 (0.024) 0.036 (0.011) -26476.1

Notes: The table reports posterior mean and standard deviation (in parentheses) of disaster parameters in AEs (Advanced Economies) and in EMEs (Emerging Market Economies) for the baseline model and the NSBU (Nakamura et al., 2013) model, which considers common disaster parameters across all countries and abstracts from correlation in θi,t and φi,t . θ, σθ , φ, and σφ are the posterior means and standard deviations of θi,t and φi,t , respectively. SD stands for standard deviation. pW is common for both country groups. DIC reports the deviance information criterion for the baseline and NSBU models.

stems, respectively, from larger AE group-specific and country-specific disaster uncertainty estimates. Disaster uncertainty plays an important role in asset pricing, as agents at the onset of a disaster account for the substantial risk represented by disasters. Third, I find a sizeable correlation in the temporary consumption drops during disasters in the emerging 20

E countries (ρAE = 0.012 versus ρEM = 0.244) and in the permanent consumption drops in φ φ E the advanced countries (ρAE = 0.838 versus ρEM = 0.123). These results stem from the θ θ

larger group-specific estimates for the standard deviation of the temporary disaster shock for EMEs (σφ,G ) and of the permanent disaster shock for AEs (σθ,G ). This suggests that uncertainty about the temporary disaster effects tends to be more similar in EMEs likely due to the localized nature of these events such as the Asian Financial Crisis, while the uncertainty about the permanent disaster effects tends to be more similar in AEs likely due to the global nature of these events such as the World Wars. Lastly, Table 4 documents considerable differences in disaster probabilities. Although, AEs are more likely to enter a disaster EM E conditional on a world disaster (pAE CbW = 0.725 versus pCbW = 0.393), EMEs are more than EM E = 0.019). six times more likely to enter a disaster on their own (pAE CbI = 0.003 versus pCbI

The posterior mean of the probability of exiting a disaster, pCbe , implies that disasters last on 26 E average longer, roughly 6 years (= 1/pEM Cbe ), in EMEs compared to about 4 years in AEs.

The intuition behind these results follows from the fact that EMEs tend to experience more idiosyncratic events–such as currency or sovereign default crises–that occur less frequently in AEs. On the other hand, AEs more often enter widely-spread and severe disasters such as the World Wars, which tend to affect EMEs less. These results are consistent with a recent evidence presented by Epstein et al. (2019) who show that, over the 2002-2016 period encompassing mainly the recent global financial crisis, small-open advanced economies (SOAEs) are much more affected by global financial risk (proxied by the VIX index) shocks than EMEs.27 As presented in Table 4, the mean probability of a world disaster, pW , is estimated to be 0.06 per year. Figure 1, in turn, plots the evolution of world disasters over time. Specifically, it plots the posterior mean of ItW , i.e. the probability of a world disaster, in each year from 1890 to 2016. Figure 1 shows that the world disasters are mostly pinned down by global 26

Although beyond the scope of the paper, this disaster risk heterogeneity has implications on potentially distinct welfare costs across the two groups of countries. For more details, see Barro (2009). 27 Gourio et al. (2013) demonstrate that equity volatility, captured for example by the VIX index, is a reasonable proxy of disaster probability.

21

0.0

0.2

0.4

0.6

0.8

1.0

Figure 1: Evolution of World Disaster Probability

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

2010

Notes: The figure plots the probability (posterior mean) of the world, ItW , being in a disaster in each year from 1890 to 2016.

events. The model identifies three major disasters: World War I, World War II, and the Great Depression. The model also partially identifies the Great Recession as a disaster. More specifically, the probability of the world being in a disaster in 2009 is approximately 0.3.28 Given the joint posterior distribution of the estimated group-specific and world disaster probabilities, the overall probability of a country to enter a disaster, pCbO , is computed as: pCbO = pW pCbW + (1 − pW )pCbI .

(7)

The overall probability is on average somewhat larger for the advanced group of countries. EM E Table 4 shows that pAE CbO = 0.046 and pCbO = 0.042. This finding may seem counterintuitive,

but, for a given country groupings and sample windows, it stems from a combination of the estimates for country and world disaster probabilities. More specifically, given the estimate 28

This probability might seem relatively low and is brought about by the fact that most countries experienced only a mild decrease in consumption per capita. For example, real consumption per capita in the U.S. dropped by only about four percent (at annual frequency) during the Great Recession.

22

of the world disaster probability (pW ), equation (7) shows that although the probability of entering an individual disaster (pCbI ) is six times higher for EMEs, the much larger (in absolute terms) probability of entering a disaster conditional on a world disaster (pCbW ) for AEs leads to a higher overall disaster probability in AEs.29 Several AEs have not experienced a disaster since the World War II. However, the model implies a non-negligible disaster probability of observing no disaster in a panel of 31 countries over the span of 71 years (the number of years in the sample since World War II). In particular, the model estimates this probability to be 0.08. The model also implies that the probability of at least one country experiencing no disaster over the 71-year span is about 0.60, i.e., the probability of a randomly selected country entering no disaster is relatively high, which captures the postwar experience of many AEs. How does a representative disaster for AEs and EMEs look like? Using the group-specific posterior estimates of θ, φ, and ρz , Figure 2 answers this question by plotting a typical disaster for AEs (blue solid line) and for EMEs (green dashed line). All other shocks of the consumption process are set to zero. Figure 2 shows that a typical disaster is longer for EMEs. Disasters on average last for 6 years in EMEs, while the average disaster duration in AEs is estimated to be 4 years. However, it can be seen that disasters in EMEs are on average less severe, both in the short and long run. The cumulative temporary fall in consumption is around 32 percent in AEs and 17 percent in EMEs, whereas the permanent fall in consumption is about 12 percent in AEs and 8 percent in EMEs. For both groups of countries, Figure 2 also presents evidence that disasters unfold over several years and that disasters are followed by recoveries. Specifically, 63 percent of the short-run drop in consumption is recovered in AEs compared to only 53 percent in EMEs, suggesting that AEs might have institutions and policies that respond more effectively to disasters. This is in 29

Additional results reported in the Appendix for alternative country groupings and a more comprehensive sample of countries, when using output data, show that EMEs typically face a larger overall disaster probability. Importantly, I show in the Asset Pricing Section in Table 8 that (counterfactually) setting the overall disaster probability for AEs to the estimate for EMEs (and vice versa) has a small impact on the equity premium; the differences in country’s conditional disaster probabilities, pCbW and pCbI , are found to be more important.

23

−0.20

Emerging Countries Advanced Countries

−0.30

log(C)

−0.10

0.00

Figure 2: Evolution of log Consumption During a Typical Disaster

0

1

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3

4

5

6

7

8

9

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11

12

13

14

15

16

17

18

19

20

Years

Notes: The figure plots the evolution of detrended log consumption during a typical disaster, which is four years for advanced and six years for emerging countries. θ, φ, and ρz are set to their group-specific posterior means. All other shocks of the consumption process are set to zero.

contrast to Cerra and Saxena (2008), who use postwar data for 190 countries and document a lack of recovery in output following financial and political crisis; the difference in findings might stem from distinct sample and country coverage. To illustrate disaster episodes in individual countries, Figure 3 depicts consumption dynamics in two selected countries: Argentina and the United States.30 The black line represents actual consumption, while the light green line represents potential consumption. The red bars display the posterior mean of Ii,t , i.e., the probability of a country i being in a disaster in year t. It can be seen that due to a sovereign default Argentina exhibits a prolonged episode of turmoil at the beginning of its sample period. Figure 4 shows that Argentina faced five disasters, but was not affected by the world disasters as much as the United States. For example, World War II had only a minor impact on Argentine consumption. However, after the Great Depression Argentina experienced a couple of idiosyncratic disasters: one in 1985 30

A complete set of figures for emerging and advanced countries is included in the Appendix.

24

Figure 3: Evolution of Consumption Disasters in Argentina and in the United States

4.5 4.0

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3.5

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Notes: The bars plot the posterior mean of Ii,t , i.e., the probability of country being in a disaster in each year. The light green line depicts the log per capita potential consumption and the black line displays the evolution of actual log per capita consumption.

due to a hyperinflation crisis and the other one in 2000 because of the extreme level of country’s debt that eventually led to another sovereign default. The Argentine story highlights that EMEs, relative to AEs, tend to experience more often individual disasters that are usually less severe. In comparison to Argentina, the United States experienced only three disasters, all of which can be contributed to world disasters. The model identifies World War I and the Spanish Flu as one single disaster that lasted nine years. The largest disaster in the United States was the Great Depression, during which consumption decreased by roughly 30 percent in the short run and 10 percent in the long run over a span of five years. Note that the characteristics of this disaster are similar to those of a typical disaster in AEs. Lastly, the model does not classify the Great Recession as a disaster. The probability of the United States being in a disaster in 2009 is estimated to be less than a third. One of the advantages of the Bayesian approach, relative to calibration, is that it allows me to estimate the posterior probability of a country being in a disaster, without requiring me to take a stand on whether a country was in a disaster during the given time period. However, to be able to analyze how closely the model tracks the consumption behavior during disaster episodes in the data, it is helpful to identify periods during which a country 25

Figure 4: Consumption Dynamics during Disasters in the Model and Data Emerging Market Economies 0.4

log C during disaster episodes −0.2 0.0 0.2 0.4

Advanced Economies

−0.4

−0.4

−0.2

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data median C model median C model IQR C

2

4

6 years

8

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8

10

Notes: The figure plots the change in consumption over 10 years after a disaster start in AEs (left panel) and EMEs (right panel). I simulate the model 5000 times to obtain distribution of consumption disasters. The dashed black line denotes the median of the simulated distribution of consumption disasters, while the dot-dashed green lines denote the 25th and 75th percentiles. For the data, I identity disasterPepisodes as the number of consecutive years Ti for country i, such that each year P r{Ii,t = 1} > 0.1 and t∈Ti P r{Ii,t = 1} > 1. The red solid line plots the corresponding median of consumption change relative to its pre-disaster value in the data.

can be considered to be in a disaster. To this end, I follow the disaster definition introduced in Nakamura et al. (2013) and define a disaster episode as the period during which the probability of being in a disaster for a country is high.31 More specifically, a disaster episode is defined as the number of consecutive years for a country i (Ti ) such that the probability of being in a disaster in each year is greater than 10 percent (P r{Ii,t = 1} > 0.1) and the P

sum of these probabilities during a disaster is larger than one (

t∈Ti

P r{Ii,t = 1} > 1).32

Based on the above definition of a disaster episode, Figure 4 contrasts the consumption dynamics during disaster episodes in the data and in the model to demonstrate how well the model tracks the observed consumption.33 For the data, I utilize the identified disaster episodes to plot in each year the median change in consumption across group-specific episodes relative to the year before the disaster started. The model is simulated 5000 times to generate 31

This definition of disasters serves mainly for expositional purposes and it does not influence the asset pricing results, which are based on the posterior estimates reported in Table 4. 32 Results are robust to reasonable changes in these cutoffs. 33 Tables A6 and A7 in the Appendix display the identified disaster episodes and the corresponding cumulative temporary and permanent drops in consumption for individual countries.

26

Table 5: Nondisaster Parameters: Mean and Standard Deviation of Consumption Growth

Advanced Mean Median Emerging Mean Median

µ pre-1946 Mean SD

µ 1946-1972 Mean SD

µ post-1973 Mean SD

σ pre-1946 Mean SD

σ post-1946 Mean SD

ση Mean SD

0.013 0.004 0.011 0.004

0.035 0.005 0.030 0.005

0.016 0.003 0.016 0.003

0.023 0.006 0.021 0.005

0.003 0.002 0.002 0.002

0.020 0.003 0.018 0.002

0.018 0.009 0.017 0.008

0.027 0.008 0.025 0.007

0.026 0.006 0.022 0.006

0.035 0.013 0.029 0.011

0.006 0.004 0.004 0.003

0.035 0.006 0.033 0.005

Notes: The table reports posterior means and standard deviations. µ denotes the country-specific mean of consumption growth for pre-1946, 1946-1972, and post-1973 periods. σ denotes the standard deviation of the transitory shock to consumption. ση denotes the standard deviation of the permanent shock to consumption.

a model-implied distribution of consumption disasters and, then, to plot the corresponding median together with the 25th and 75th percentiles of the distribution. Figure 4 shows that the model is able to track the consumption behavior during disasters in the data relatively well, as the data-implied consumption path is, in general, well within the inter-quartile range for the model-implied consumption path. Moreover, it can be seen that the model performs somewhat better for AEs, especially in terms of capturing the median temporary drop in consumption during disasters. Lastly, the Bayesian estimation also produces estimates of nondisaster parameters that are country-specific. The averages of these estimates are presented in Table 5.34 Although the priors for the parameters across the two groups of countries are identical, the groupspecific values differ on average. I find that the mean consumption growth in 1946-1972 is higher in AEs than in EMEs, while the opposite situation prevails for the pre-1946 and post-1973 periods. The standard deviation estimates of the transitory shock to consumption are on average larger for EMEs for both, pre-1946 and post-1946, periods. Importantly, the estimates are lower for the post-1946 relative to the pre-1946 period for both groups of countries on average, providing suggestive evidence for a break occurrence in the standard deviation of the transitory shock and are, moreover, consistent with the evidence provided 34

The estimates of the non-disaster parameters for individual countries can be found in the Appendix.

27

in Romer (1986).35

6

Asset Pricing Implications

This section follows the approach of Mehra and Prescott (1985) and Nakamura et al. (2013) to analyze the equity premium puzzle in AEs and EMEs. Specifically, I use the posterior estimates of the consumption disaster parameters reported in Table 4 and assume that each group of countries consists of a representative agent endowment economy. I follow the recent work in assuming that asset markets are complete in both country groups, but frictions in the goods market prevent any net trade of goods, which allows for a separate solution of allocation in each group of countries.36

6.1

Model

Nakamura et al. (2013) show that disaster recoveries have counterfactual asset pricing implications under a power utility and demonstrate that there is actually a boom in the stock market at the onset of a disaster due to the agents’ large savings motive. For this reason, I decouple the inverse relationship between the coefficient of relative risk aversion (CRRA) and the intertemporal elasticity of substitution (IES) by assuming that the representative agent has Epstein and Zin (1989) and Weil (1990) (EZW) preferences. Following Epstein and Zin (1989), the gross return on any asset k in country i from period t to period t + 1, Rk,i,t+1 , is found as a solution to the following fundamental asset pricing equation: 

Et β

ξ

Ci,t+1 Ci,t

!(−ξ/ψ)



−(1−ξ) Rw,i,t+1 Rk,i,t+1 

= 1.

(8)

Rw,i,t+1 represents the gross return on agent’s endowment, which equals to the consumption stream in the model. β denotes the agent’s subjective discount factor, ψ captures the in35

Nakamura et al. (2013) show that the estimates of disaster parameters remain virtually unchanged when considering 1951 as the structural break year. 36 See for example Verdelhan (2010) and Gourio et al. (2013).

28

tertemporal elasticity of substitution, and ξ =

1−γ . 1−1/ψ

γ denotes the coefficient of relative risk

aversion and Ci,t represents the consumption of country i in period t. The country-specific components of the consumption process take average values for the given country group.37 I focus on calculating returns on a one-period bond and, similarly to Barro and Jin (2016), on a levered claim on consumption process using a debt-equity ratio of 0.5.38 The use of EZW preferences implies no analytical solution. Therefore, I follow the method of Nakamura et al. (2013) and employ numerical methods to solve the integral in equation (8) on a grid over the state space. First, I rearrange equation (8) into a recursive form for the consumption price-dividend ratio. I iterate this recursive equation until it converges to a fixed point. Then, the consumption price-dividend ratio can be used to solve for a fixed point of a price-dividend ratio of any other asset such as a one-period risk-free bond, which can be used further to compute other asset pricing statistics.

6.2

Calibration

To calculate the model’s implied equity premium, values to the remaining model parameters ψ, β, and γ need to be assigned. Since agents anticipate future decreases in consumption at the start of a disaster, they have a strong desire to save, and therefore the IES parameter ψ plays an important role in the model. In the long-run risk literature, which decomposes the consumption process into low-frequency changes in consumption growth and consumption volatility, Bansal and Yaron (2004) and Bansal et al. (2012) show that their asset pricing model needs an IES greater than one to avoid generating counterfactual behavior of asset prices. Recently, using the generalized method of moments approach developed by Hansen (1982), in their long-run risk model, Bansal et al. (2016) estimate the IES to be 2.2, while Schorfheide et al. (2018) estimate it to be roughly 2. In the disaster literature, Gourio (2008), Barro (2009), and Nakamura et al. (2013) demonstrate that if the IES is less than one and 37

2 As in Nakamura et al. (2013), µi,t and σ,i,t are assumed to take the post-1973 and post-1946 values, respectively. 38 Due to data limitations and for comparison with the related literature, the U.S. corporate leverage ratio is used to compute the levered model-implied equity premium for both groups of countries.

29

the model allows for recoveries, the strong savings motive dominates the negative effect that disasters have on expected future dividends, and, as a result, the stock prices counterfactually increase at the onset of a disaster, providing evidence against low IES values. There is little consensus regarding the value of the IES in the empirical literature. By regressing consumption growth on a risk-free rate, Hall (1988) finds the IES to be less than one. Recently, Gruber (2013) notes that Hall’s approach may be biased downward due to fluctuations in the risk-free rate. Gruber employs a tax-based approach to identify movements in the risk-free rate and finds an IES value of around two. For this reason, many subsequent studies use Gruber’s estimate in their models. To be consistent with the recent empirical and theoretical literature, I consider a value of the IES greater than one. In particular, I set the IES (ψ) to 2 for both groups of countries. Due to the lack of relevant data on the subjective discount factor (β), I choose it such that the model accounts for the observed risk-free rate in the data.39 Lastly, as commonly done in the literature, the value of the CRRA (γ) is pinned down to replicate the observed equity premium in both groups of countries.40

6.3

Results

Table 6 presents the CRRA values for which the model replicates the mean equity premium and risk free rate in AEs and EMEs. In brackets the table lists the 90 percent confidence interval for the equity premium and risk-free rate. For the data, the interval is computed for each group of countries based on country means of equity premium and risk-free rate, while for the model it is estimated using the posterior distribution of disaster parameters. Table 6 shows that the baseline model requires a CRRA value of 4.4 with β = exp(−0.018), to generate the observed equity premium and risk-free rate in AEs. For EMEs, the implied CRRA is 6.2 and β = exp(−0.023). The “no disasters” baseline model – agents expect disasters to 39

Variations in the subjective discount factor mostly affect the risk-free rate and have a negligible impact on the equity premium. 40 This yields a distinct CRRA value for AEs and EMEs. The robustness section below shows the implications of assuming identical CRRA for both country groups.

30

Table 6: Asset Pricing: Model versus Data

Data

CRRA –

Baseline

4.4

Baseline: No disasters

4.4

Advanced E(Rep ) E(Rf ) 4.9 1.0

[2.1, 8.3] [-1.1, 3.1]

CRRA –

4.9

1.0

6.2

4.7

1.1

6.2

[2.0, 8.3] [-0.9, 1.9] [1.7, 8.1] [-0.5, 1.9]

Emerging E(Rep ) E(Rf ) 9.7 0.0

[3.1, 17.5] [-2.6, 3.4]

9.7

0.0

9.2

0.1

[6.5, 14.3] [-2.6, 1.5] [5.8, 14.2] [-2.7, 1.6]

Notes: The table shows in percentages the mean of equity premium, E(Rep ), and risk-free rate, E(Rf ). “No disasters” denotes a model in which agents expect disasters to occur, but none actually occurs. The IES (ψ) is set to 2 for both groups of countries in all models. The subjective discount factor (β) is calibrated such that the model replicates the observed risk-free rate, implying β = exp(−0.018) for AEs and β = exp(−0.023) for EMEs. Brackets denote the 90 percent confidence interval. For the data, the interval is based on the country group means. For the model, the interval is estimated using posterior distribution of disaster risk parameters and baseline values for β, γ, and ψ.

occur as usual but no disaster actually occurs – delivers a slightly lower equity premium. This case is meant to represent the post-WWII experience of most AEs in the sample and shows that the equity premium and risk-free rate remain similar to the baseline case, when disasters occur with their estimated frequency. Regarding the sampling uncertainty, Table 6 reveals that although the rare nature of disasters makes an accurate estimation of disaster risk parameters challenging, the baseline model attaches a 90 percent probability on the equity premium being between 2.0 and 8.3 percent for AEs, and between 6.5 and 14.3 percent for EMEs. Table 6 shows that the larger and more uncertain disasters in AEs yield a lower value of CRRA to replicate the equity premium in these countries. This value is smaller not only compared to the CRRA value for EMEs, but also compared to the related literature. Nakamura et al. (2013) use a value of 6.4 to replicate the mean of equity premia across countries in their sample. Barro and Jin (2016) estimate disasters and long-run risks in a unified framework and conclude that a CRRA value of around 5.9 is sufficient to generate the mean of observed equity premia in their sample of countries. In comparison, my work shows that allowing for differences in disaster parameters between the two country groups brings down the CRRA value needed to replicate the observed equity premium, especially 31

for AEs. However, the model also implies that agents in EMEs are, on average, more risk averse and less patient (have lower β) than in AEs. In light of this finding, I use the new comprehensive data set on risk aversion and time preference, constructed by Falk et al. (2018), to provide empirical evidence that agents in my sample of AEs tend to be less risk averse and more patient than in EMEs. Specifically, Falk et al. (2018) use “an experimentally validated survey data set” from the Global Preference Survey to provide, among other things, cross-country estimates of patience and willingness to take risks (WTTR), where a lower value of WTTR implies a higher risk aversion. I use the latter variable to qualitatively compare the observed risk aversion in AEs and EMEs included in my consumption sample in Table 1. I find that the mean (median) WTTR in AEs and EMEs is, respectively, -0.020 (-0.019) and -0.119 (-0.045), which provides suggestive evidence of typically higher risk aversion in EMEs.41 Similarly, using the Falk et al. (2018) data on time preference, I find significantly higher values of patience for AEs. The mean (median) patience in AEs and EMEs is, respectively, 0.570 (0.624) and -0.153 (-0.155).42 Figure 5 plots the evolution of asset returns and detrended log consumption during a typical disaster in AEs (left panel) and EMEs (right panel) for the baseline model. It can be seen, that at the start of a disaster, stock prices relative to bills plummet and consumption declines. Since stocks, compared to bills, perform poorly when the marginal utility of consumption is high, agents require high equity premium in normal times as a compensation for the risk associated with holding equity. As the consumption recovers, the asset returns temporarily increase. The evolution of asset returns during disasters depicted in Figure 5 is consistent with empirical evidence provided by Barro (2006), who documents that disaster episodes tend to be accompanied with relatively low equity and bill returns, while documenting that international financial markets tend to deliver relatively high returns 41

This yields a sample of 13 AEs and 13 EMEs, because there is no data on WTTR for Belgium, Denmark, New Zealand, Norway, and Taiwan. The difference is not statistically significant, due to perhaps a small sample size, but the results also hold when considering countries in the extend output sample shown in Table A2. 42 See the Online Appendix of Falk et al. (2018) on more details about the construction of patience and willingness to take risks measures.

32

Figure 5: Evolution of Returns and Consumption in AEs and EMEs

0.3 0.2 0.1 0.0 −0.3

−0.2

−0.1

Returns and log(C)

0.1 0.0 −0.1 −0.3

−0.2

Returns and log(C)

0.2

0.3

0.4

Emerging Market Economies

0.4

Advanced Economies

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

Equity Return Bill Return log Consumption

−0.4

−0.4

Equity Return Bill Return log Consumption 20

1

Years

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Years

Notes: The figure plots the evolution of returns and detrended consumption during a typical disaster, which starts in period four and lasts for four years in AEs (left panel) and six years in EMEs (right panel). All other shocks are set to zero.

during recoveries. Comparison of the two panels in Figure 5 highlights the fact that a typical disaster is less severe and longer in EMEs, implying a lack of coincidence between the stock market crash and the consumption drop. The drop in consumption during the first disaster year is about 11 percent in AEs, while it is only 7 percent in EMEs. This, in turn, makes it more difficult for the model to replicate the larger equity premium in the EMEs, i.e., the model requires a higher CRRA to explain the observed equity premium in EMEs. In addition, Figure 5 implies that the model delivers, during consumption disasters, a stock market crash of roughly 25 and 21 percent in AEs and EMEs, respectively. To analyze the stock market behavior during disasters in the data, I compute stock market returns during the disaster start year and adjacent years to the disaster start year.43 More specifically, across all countries in each group I sum negative returns during the three-year window centered on the disaster start year. If there are no negative returns during the three-year window, the stock market return is set to the minimum return during this time span. I find that the size of a typical stock market crash in the data lines up well, not just qualitatively but also quantitatively, with model predictions. In particular, the mean negative equity return 43

The start years correspond to the beginning years of disaster episodes listed in Tables A7 and A8 in the Appendix.

33

Table 7: Country-Group Correlations

corr(4ci , 4cj ) corr(Rie , Rje ) corr(Rif , Rjf )

Advanced Data Model 0.20 0.19 0.40 0.25 0.44 0.32

Emerging Data Model 0.06 0.03 0.16 0.04 0.13 0.03

Notes: The table shows averages of pair-wise (within-group) country correlations of consumption growth (4c), equity returns (Re ), and bill returns (Rf ) for AEs and EMEs in the data and in the baseline model. Data sample windows are reported in Tables 1 and 2. The model parameters β, γ, and ψ are set to their baseline values.

during disaster episodes in AEs and EMEs in the data is, respectively, 24 and 22 percent. The distinct country-group nature of disaster dynamics has implications for correlations of consumption growth, equity returns, and bill returns. Table 7 reports within-group crosscountry correlations implied by the baseline model for AEs and EMEs, together with their empirical counterparts, where the data statistics are averages of (within-group) pair-wise country correlations across AEs and across EMEs.44 Table 7 reveals that the model does a good job of replicating the relatively higher correlations in AEs, reflecting the fact that AEs are more likely to experience global disasters that tend to affect countries similarly, while disasters in EMEs tend to be more idiosyncratic.

6.4

Disaster Risk Heterogeneity and Equity Premium

Given the differences in disaster parameters between AEs and EMEs, a natural question to ask is to what extent is the level of the equity premium driven by the group heterogeneity in disaster magnitude, probability, and persistence. I address this question in Table 8 through the lens of a counterfactual experiment. In particular, Table 8 contrasts the baseline model equity premium with the model-generated equity premium and risk-free rate, when setting a particular disaster parameter of one country group to the estimated parameter value for the other group.45 For example, to investigate the impact of country group differences in disaster duration on the equity premium, “prob. of exiting disaster: pCbe ” sets the probability 44 45

See Tables 1 and 2 for sample windows. β, γ, and ψ are set to their baseline values.

34

EM E of exiting a disaster for AEs to the corresponding estimate for EMEs (pAE Cbe = pCbe ). This

implies that a typical disaster in AEs is counterfactually set to last 6 years instead of the estimated 4 years, and vice versa for EMEs. In this case, the equity premium increases from 4.9 to 6.6 percent for AEs due to the increased disaster length, which leads to a larger cumulative temporary drop in consumption. For EMEs, the disasters become shorter, implying a faster recovery, and, hence, a less risky world, which decreases the equity premium from 9.7 to 7.8 percent. In the case when AEs face the estimated probability of entering an individual disaster for EM E EMEs (pAE CbI = pCbI ), the equity premium jumps to 5.3 percent, since now, all else equal,

AEs are more likely to enter a disaster. On the other hand, EMEs become less likely to enter a disaster, which yields a lower equity premium. Similar intuition applies to the case for the probability of entering a disaster conditionally on a world disaster (pCbW ). The equity premium decreases to 4 percent in AEs and increases to 9.9 percent in EMEs. Lastly, the differences in the overall country disaster probability (pCbO ) seem to play a minor role, as the equity premium changes little in both country groups under this specification. Regarding the disaster magnitude, it can be seen that differences in the long-run shocks play a more important role in driving the equity premium than differences in the short-run shocks. Moreover, Table 8 reveals that it is the long-run drop in consumption during disasters that contributes more to the equity premium in both groups of countries than the uncertainty about the long-run drop. Under the long-run drop scenario, the equity premium decreases (increases) to 3.3 (11.4) percent in AEs (EMEs), while under the long-run uncertainty case the equity premium decreases (increases) to 4.4 (10.7) percent in AEs (EMEs).46 Overall, Table 8 shows that the differences in disaster duration and long-run shock magnitude affect equity premium the most in both groups of countries. For AEs it is the difference in disaster duration that leads to the largest change in the equity premium. The premium 46

It is not possible to disentangle the effect of the short-run drop versus short-run uncertainty, because the value of the truncated parameter φ (and σφ ) depends on the estimated values of both φ? and σφ? , which are the parameters before truncation of the normal distribution.

35

Table 8: Equity Premium: Contribution of Differences in Group-Specific Disaster Parameters Advanced E(Rep ) E(Rf ) 4.9 1.0

Baseline Model

Emerging E(Rep ) E(Rf ) 9.7 0.0

Disaster Persistence prob. of exiting disaster: pCbe

6.6

-0.1

7.8

0.8

Disaster Probability cond. on world disaster: pCbW cond. on no world disaster: pCbI uncond. prob. of entering disaster: pCbO

4.0 5.3 4.7

1.1 0.5 0.8

9.9 9.5 9.8

0.0 -0.1 0.0

Disaster Magnitude short-run: φ, σφ long-run: θ, σθ long-run drop: θ long-run uncertainty: σθ

4.1 3.3 3.8 4.4

1.0 1.4 1.2 0.9

10.8 12.5 11.4 10.7

-0.7 -1.6 -1.1 -0.5

Notes: The table shows the contribution of differences in disaster parameters between AEs and EMEs to the group-specific baseline equity premium, E(Rep ), and risk-free rate, E(Rf ). For example, “prob. of exiting disaster pCbe ” sets the estimate of the probability of exiting a disaster for AEs to the corresponding estimate EM E for EMEs (pAE Cbe = pCbe ), i.e., AEs remain in a disaster on average for 6 years instead of 4 years. β, γ, and ψ are set to their baseline model values.

increases by approximately 35 percent, relative to its baseline value. For EMEs, it is the difference in the long-run disaster impact that changes the equity premium the most. The premium increases by 29 percent in this case.

6.5

Robustness

Table 9 compares the equity premium of the baseline model with related literature. “One period permanent” specification is meant to represent the Barro (2006) framework, in which disasters are permanent and occur instantaneously. In other words, the probability of exiting a disaster is equal to zero and the entire temporary drop in consumption occurs over one period and also pins down the long-run drop in consumption. The one-period nature of disasters eliminates the strong savings motive that agents exhibit when disasters unfold over several periods and substantially increases the exposure to disaster risk. The large increase 36

Table 9: Equity Premium: Disaster Characteristics and Sensitivity to CRRA and IES

Baseline Model

Advanced E(Rep ) E(Rf ) 4.9 1.0

Emerging E(Rep ) E(Rf ) 9.7 0.0

Disasters One period permanent None

28.7 0.3

-16.6 2.5

76.3 1.2

-47.0 3.0

Sensitivity Low CRRA High CRRA Common CRRA Common parameters Low IES High IES

1.6 10.2 6.8 7.2 4.3 5.2

1.9 -1.8 1.0 0.1 1.2 0.4

4.8 14.9 7.6 7.4 8.5 10.4

2.0 -2.8 0.0 0.7 1.1 -0.7

Notes: “One period permanent” denotes the case when disasters are permanent and occur in one year as in Barro (2006). “None” denotes the case with no disasters as in Mehra and Prescott (1985), i.e., all disaster probabilities are set to zero. Unless otherwise noted, β, γ, and ψ are set to their baseline model values. “Common CRRA” sets γ = 5.3 for both country groups, while β = exp(−0.030) and β = exp(−0.013) for AEs and EMEs to replicate the risk-free rate. “Common parameters” sets γ = 5.3 and β = exp(−0.0205) for both country groups. Low (high) CRRA sets γ to 2.6 (6.2) for AEs and 4.4 (8.0) for EMEs, respectively. Low (high) ψ sets IES to 1.5 (2.5) for both groups of countries.

of the equity premium is brought about by a near-perfect synchronization of the drop in consumption and stock prices, as all of the consumption drop occurs in one period. Allowing for recoveries under the baseline scenario breaks down this synchronization of the stock market crash and consumption drop. “None” denotes a model without disaster risk in the spirit of Mehra and Prescott (1985). In this case, the conditional probabilities of entering a disaster are set to zero. Similarly to Mehra and Prescott (1985), the equity premium in both groups of countries becomes negligible due to the fact that agents face no risk of disasters, which substantially decreases the volatility of the consumption process. Table 9 also considers alternative preference parameter values. The “low CRRA” case sets γ = 4.4 for EMEs, which is the CRRA value for AEs in the baseline model, and γ = 2.6 for AEs. The equity premium decreases to 1.6 percent and 4.8 percent in AEs and EMEs, respectively. The “high CRRA” case, delivers an equity premium of 10.2 percent in AEs (with γ = 6.2, which is the EME CRRA value in the baseline model) and an equity premium of 37

14.9 percent in EMEs (with γ = 8.0). Note that the model generates a slightly higher equity premium in AEs than in EMEs for identical CRRA of 4.4 or 6.2 for both groups. However, the risk-free rates are not in line with the data. To address this, the “Common CRRA” case sets γ = 5.3, which is the average of the AEs and EMEs baseline model CRRA values, and finds values for the subjective discount factor that replicate the observed risk-free rate in each group of countries, implying β = exp(−0.030) and β = exp(−0.013) for AEs and EMEs, respectively. This yields a lower equity premium in AEs (6.8 percent) than in EMEs (7.6 percent). The model-generated equity premium remains also lower, albeit slightly, in AEs under the “Common parameters” case, when γ = 5.3 and β = exp(−0.0205), which is the average of the baseline β values, for both country groups. However, the model overestimates (underestimates) the equity premium for AEs (EMEs). In summary, under the assumption of common preference parameters for AEs and EMEs, the model leaves room for some other factors (such as the long-run risks – see Nakamura et al. (2017) for estimation of long-run risks for a sample of advanced countries using long-run consumption data) to play a role in explaining the difference in equity premium between AEs and EMEs. The last two cases in Table 9 recompute the asset pricing statistics for low (ψ = 1.5) and high (ψ = 2.5) IES values. The “low IES” value yields an equity premium of 4.3 percent in AEs and 8.5 percent in EMEs. The “high IES” case raises the equity premium to 5.2 percent and 10.4 percent in advanced and emerging countries, respectively. Overall, the specifications show that a higher value of IES diminishes agents’ savings motive, which increases the magnitude of the stock crash at the onset of a disaster, and consequently raises the equity premium.47 On the other hand, a higher CRRA value makes agents more risk averse, implying that stocks must offer a higher premium relative to bills to compensate agents for the disaster risk. 47

one.

See Nakamura et al. (2013) for an extensive discussion on asset price behavior when IES is less than

38

7

Conclusion

I document that consumption per capita growth is less volatile, but exhibits larger kurtosis in advanced economies (AEs) compared to emerging market economies (EMEs). Moreover, I show that EMEs reward investors with a significantly larger equity premium, on average. The Bayesian analysis finds considerable disaster risk heterogeneity between the emerging and advanced country groups. More specifically, the estimation results show that disasters in AEs tend to be shorter, but more severe and uncertain. I find that group heterogeneity in disaster risk exposure has important implications for contribution to the equity premium.48 Accounting for the asymmetry in disaster parameters between the two groups of countries implies that to match the distinct equity premia the model requires a lower CRRA for advanced countries compared to emerging countries. A potential concern may be the fact that the bill returns, especially in EMEs, are not completely risk-free. To address this issue, one could introduce a partial default on bills. However, an accurate approximation of a group-specific default probability on bills would be difficult due to the lack of long-run financial data, particularly for EMEs. The consumption process also implies a non-trivial term structure. With improvements in data quality, it would be interesting to introduce long-term bonds and compare the implied term premia between the country groups. The rare nature of disasters has led me to assume a constant probability of disasters over time to increase the precision of the Bayesian estimation. Future research, could leverage a time-varying probability of disasters to explain the equity volatility puzzle since, EMEs exhibit an equity premium that is significantly more volatile than the one in AEs. Several authors (e.g. Gourio, 2012 and Wachter, 2013, among others) show that a calibrated time-varying disaster risk is essential to generate sufficient volatility and long-run predictability of stock returns observed in the U.S. data. 48

Disaster risk heterogeneity has also implications for potentially distinct welfare costs of uncertainty in AEs and EMEs. See Barro (2009) for more details.

39

Appendix The Appendix lists various tables and figures to provide supplemental material to the main results in order to document their robustness.

A.1 Output Data In general, the use of consumption is more appropriate for asset pricing than output as theory relates asset returns to consumption. Additionally, output dynamics might capture disasters less accurately, since output might not decrease as much (or it might even go up) during disasters such as the world wars due to increased government spending. Nevertheless, for completeness and robustness, Tables A1 and A2 report the first four moments and start years of output (instead of consumption) per capita growth. Table A1 considers identical composition (but with longer sample windows given the better availability of output data) of advanced economies (AEs) and emerging market economies (EMEs) as in the baseline consumption disaster model. Table A2 extends the baseline sample of countries with additional countries that have at least 100 years of uninterrupted output data available. Countries are classified into groups again based on clustering methods, which yield 19 AEs and 20 EMEs. It can be seen that AE output growth still exhibits significantly larger kurtosis (fat tails), which typically indicates presence of disasters.

A.2 Additional Financial Data Table A3 provides the first four moments (mean, standard deviation, skewness, and kurtosis) for the distributions of equity premium and bill returns in the baseline sample. Tables A4 and A5 show that the difference in equity premium remains significant when considering a balanced postwar sample (1950-2017) of financial data, and also when extending the baseline sample of EMEs with additional EMEs (Greece, Malaysia, Philippines, South Africa, Sri Lanka, Taiwan), which have at least 30 years of financial data, but are not included in the 40

consumption sample due to insufficient long-term consumption data.

A.3 Country-Specific Parameters Table A6 displays the estimates of country-specific parameters for all countries included in the baseline consumption sample, since the main text only shows the group means and medians.

A.4 Disaster Episodes Tables A7 and A8 display the identified disaster episodes for individual countries and also the estimates of cumulative temporary and permanent drops in consumption during these disasters. As in Nakamura et al. (2013), a disaster episode is defined as the number of consecutive years for a country i (Ti ) such that the probability of being in a disaster in each year is greater than 10 percent (P r{Ii,t = 1} > 0.1) and the sum of these probabilities during P

a disaster is larger than one (

t∈Ti

P r{Ii,t = 1} > 1). The identified disaster episodes are

used to assess how well the model tracks the consumption dynamics during disasters in the data (see Figure 4 in the main text). Tables A7 and A8 show that the classification of disaster episodes yields 44 events in AEs and 38 events in EMEs. The medians of the temporary and permanent drop in consumption during these episodes in AEs are 29 percent and 10 percent, respectively. The median short-run and long-run fall in consumption in EMEs is 17 percent and 3 percent, respectively. Thus, when compared to the estimated parameters of a typical disaster in emerging and advanced countries, the definition of disaster episodes captures the drops in consumption relatively well. In addition, Tables A7 and A8 confirm the fact that disasters tend to be more severe in AEs and that EMEs are more prone to enter a disaster on their own. In some instances, the model is unable to distinguish between two individual events and lumps them into one big disaster. For example, the model identifies World War I and the Great Influenza Epidemic in the U.S. as one disaster that lasts from 1914-1922.

41

A.5 Estimates of Disaster Parameters: Additional Results Table A9 contrasts the posterior estimates of disaster parameters for the baseline model with four alternative models. Baseline PtTw model includes Portugal and Taiwan in AEs (instead of EMEs). Baseline CoInVe model drops Colombia, India, and Venezuela from the EME group. Output model uses output (instead of consumption) per capita data for the baseline sample of countries - see Table A1 for the corresponding sample windows, which are usually longer and yield a more balanced panel countries. Output extended model uses output per capita data for an extended sample of countries - see Table A2 for included countries and their sample windows. pW is common for both country groups. Overall, Table A9 demonstrates that the disaster parameter estimates imply very similar differences in group-specific disaster parameters as in the baseline model. Specifically, disasters tend to be larger and more uncertain in the short- and long-run in AEs, while they tend to be longer in EMEs. Also, AEs have a higher probability of entering a disaster conditional on a world disaster, wheres EMEs are more likely to face idiosyncratic disasters. The main difference between the baseline model and alternative models is that given the estimates of conditional and world disaster probabilities, the alternative models deliver a higher estimate of the overall (unconditional) disaster probability for EMEs than for AEs.

A.6 Country-Specific Consumption Dynamics Figures A1 through A5 plot the evolution of actual consumption (the black line) and potential consumption (the green line) for all countries included in baseline the sample. The bars in the figures show the posterior mean of a country’s probability being in a disaster in each year.

42

A.7 MCMC Convergence Figures A6-A9 provide the autocorrelation plots of the thinned time-series, after discarding the burn-in sample, for individual disaster parameters for the baseline and NSBU - Nakamura et al. (2013) models, while Figures A10-A13 display the trace plots for disaster parameters. Both sets of plots indicate good mixing of the MCMC algorithm.

43

Table A1: Output Per Capita Growth: Baseline Sample of Countries Emerging Argentina Brazil Chile Colombia Egypt India Korea Mexico Peru Portugal Russia Taiwan Turkey Venezuela Mean Median Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

Mean

Volatility

Skewness

Kurtosis

Start

1.29 (0.56) 2.28 (0.43) 2.08 (0.52) 2.42 (0.21) 1.64 (0.43) 1.84 (0.40) 3.64 (0.65) 1.77 (0.36) 2.25 (0.43) 2.14 (0.39) 2.17 (0.75) 3.64 (0.72) 2.39 (0.63) 2.18 (0.80) 2.27 2.18

6.36 (0.48) 5.00 (0.40) 5.87 (0.51) 2.25 (0.18) 4.81 (0.60) 4.49 (0.38) 6.74 (0.88) 4.12 (0.41) 4.71 (0.45) 4.41 (0.35) 8.42 (0.80) 7.78 (1.47) 7.30 (0.71) 9.02 (0.78) 5.81 5.81

-0.51 (0.29) -0.30 (0.36) -0.88 (0.31) -0.52 (0.31) 1.33 (0.70) -0.06 (0.40) -1.03 (0.74) -1.10 (0.41) -1.13 (0.28) 0.12 (0.31) -0.26 (0.47) -2.38 (1.32) -0.09 (0.53) 0.73 (0.34) -0.43 -0.43

3.84 (0.71) 4.27 (0.66) 4.95 (0.80) 3.93 (0.87) 9.06 (2.83) 4.70 (0.73) 8.22 (1.85) 5.69 (1.68) 5.32 (0.86) 4.16 (0.53) 5.56 (0.98) 18.04 (6.77) 5.80 (1.09) 4.75 (1.09) 6.31 5.32

1890 1890 1890 1905 1894 1890 1911 1895 1896 1890 1890 1901 1890 1890

1.45 (0.36) 2.03 (0.76) 2.06 (0.44) 1.87 (0.33) 2.38 (0.41) 2.06 (0.56) 2.16 (0.74) 2.11 (0.44) 2.81 (0.55) 1.88 (0.69) 1.44 (0.35) 2.33 (0.33) 1.86 (0.38) 2.23 (0.29) 1.48 (0.32) 1.49 (0.27) 2.07 (0.44) 1.98 [0.169] 2.04 [0.161]

3.91 (0.39) 8.69 (1.86) 4.90 (0.45) 3.83 (0.42) 4.65 (0.50) 6.50 (0.86) 8.44 (2.13) 4.91 (0.70) 6.23 (0.83) 7.82 (2.26) 3.93 (0.32) 3.69 (0.40) 4.32 (0.59) 3.38 (0.38) 3.67 (0.28) 2.98 (0.27) 5.03 (0.42) 5.11 [0.306] 4.77 [0.215]

-0.85 (0.45) 2.88 (1.76) -0.61 (0.38) -0.76 (0.55) -0.52 (0.62) 0.18 (0.95) -4.23 (2.00) -0.66 (1.11) -1.52 (0.79) 3.85 (3.22) 0.25 (0.31) -0.49 (0.56) -1.65 (0.90) -1.32 (0.46) -0.19 (0.29) -0.77 (0.36) 0.14 (0.33) -0.37 [0.895] -0.56 [0.830]

5.95 (1.18) 23.53 (7.53) 5.16 (0.89) 7.05 (1.40) 6.82 (1.29) 10.25 (2.19) 35.38 (14.44) 11.59 (2.50) 10.33 (3.24) 42.79 (15.70) 4.50 (0.54) 6.92 (1.03) 11.37 (4.46) 7.46 (1.48) 3.89 (0.55) 5.18 (0.89) 4.61 (0.55) 11.93 [0.068] 7.26 [0.036]

1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890

Notes: The table shows summary statistics of output per capita. The output series is in growth rates and percentages. Standard errors in parentheses are obtained by bootstrapping. The numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of means and medians, respectively, in advanced and emerging countries. End year is 2016.

44

Table A2: Output Per Capita Growth: Extended Sample of Countries Emerging Argentina Brazil Chile China Colombia Egypt Greece India Indonesia Korea Mexico Peru Portugal Russia South Africa Sri Lanka Taiwan Turkey Uruguay Venezuela Mean Median Advanced Australia Austria Belgium Canada Denmark Finland France Germany Iceland Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

Mean

Volatility

Skewness

Kurtosis

Start

1.29 (0.56) 2.28 (0.44) 2.08 (0.52) 3.48 (0.62) 2.42 (0.21) 1.64 (0.44) 2.03 (0.91) 1.84 (0.40) 1.90 (0.48) 3.64 (0.65) 1.77 (0.38) 2.25 (0.42) 2.14 (0.39) 2.17 (0.75) 1.26 (0.45) 1.88 (0.37) 3.64 (0.71) 2.39 (0.64) 1.70 (0.61) 2.18 (0.80) 2.20 2.14

6.36 (0.47) 5.00 (0.40) 5.87 (0.52) 7.02 (0.46) 2.25 (0.18) 4.81 (0.61) 10.31 (1.17) 4.49 (0.39) 5.50 (0.74) 6.74 (0.88) 4.12 (0.41) 4.71 (0.45) 4.41 (0.34) 8.42 (0.79) 4.64 (0.72) 4.22 (0.33) 7.78 (1.46) 7.30 (0.71) 6.92 (0.49) 9.02 (0.76) 5.99 5.87

-0.51 (0.29) -0.30 (0.35) -0.88 (0.31) -0.61 (0.18) -0.52 (0.31) 1.33 (0.72) -0.75 (0.60) -0.06 (0.40) -1.89 (0.57) -1.03 (0.75) -1.10 (0.40) -1.13 (0.27) 0.12 (0.32) -0.26 (0.48) -0.92 (1.15) -0.24 (0.33) -2.38 (1.34) -0.09 (0.51) -0.50 (0.22) 0.73 (0.35) -0.55 -0.52

3.84 (0.69) 4.27 (0.66) 4.95 (0.79) 3.20 (0.42) 3.93 (0.88) 9.06 (2.87) 7.67 (1.27) 4.70 (0.74) 10.19 (2.74) 8.22 (1.81) 5.69 (1.66) 5.32 (0.87) 4.16 (0.52) 5.56 (0.97) 11.41 (3.65) 4.05 (0.60) 18.04 (6.84) 5.80 (1.09) 3.59 (0.44) 4.75 (1.08) 6.42 5.32

1890 1890 1890 1890 1905 1894 1890 1890 1890 1911 1895 1896 1890 1890 1911 1890 1901 1890 1890 1890

1.45 (0.34) 2.20 (0.65) 2.03 (0.77) 2.06 (0.44) 1.87 (0.34) 2.38 (0.41) 2.06 (0.57) 2.16 (0.75) 2.66 (0.45) 2.11 (0.43) 2.81 (0.55) 1.88 (0.69) 1.44 (0.35) 2.33 (0.33) 1.86 (0.39) 2.23 (0.30) 1.48 (0.32) 1.49 (0.27) 2.07 (0.44) 2.03 [0.345] 2.06 [0.667]

3.91 (0.39) 7.30 (1.72) 8.69 (1.84) 4.90 (0.45) 3.83 (0.41) 4.65 (0.49) 6.50 (0.88) 8.44 (2.15) 5.09 (0.39) 4.91 (0.71) 6.23 (0.84) 7.82 (2.24) 3.93 (0.33) 3.69 (0.40) 4.32 (0.60) 3.38 (0.38) 3.67 (0.28) 2.98 (0.27) 5.03 (0.43) 5.22 [0.204] 4.91 [0.175]

-0.85 (0.46) -3.39 (2.10) 2.88 (1.78) -0.61 (0.38) -0.76 (0.55) -0.52 (0.62) 0.18 (0.97) -4.23 (1.99) -0.21 (0.32) -0.66 (1.11) -1.52 (0.78) 3.85 (3.18) 0.25 (0.31) -0.49 (0.57) -1.65 (0.89) -1.32 (0.48) -0.19 (0.29) -0.77 (0.36) 0.14 (0.33) -0.52 [0.947] -0.56 [0.989]

5.95 (1.19) 30.78 (12.05) 23.53 (7.70) 5.16 (0.90) 7.05 (1.39) 6.82 (1.30) 10.25 (2.12) 35.38 (14.50) 3.95 (0.68) 11.59 (2.53) 10.33 (3.25) 42.79 (15.73) 4.50 (0.56) 6.92 (1.05) 11.37 (4.44) 7.46 (1.52) 3.89 (0.55) 5.18 (0.89) 4.61 (0.54) 12.50 [0.041] 7.26 [0.038]

1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890 1890

Notes: The table shows summary statistics of output per capita. The baseline sample of countries is extended to 19 advanced and 20 emerging market economies. End year is 2016.

45

Table A3: Equity Premium and Bill Return: Baseline Sample Emerging Chile India Korea Mexico Portugal Venezuela Mean Median Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

E(Rep )

σ(Rep )

12.1 (4.6) 2.3 (2.4) 11.4 (4.7) 5.4 (2.5) 7.4 (3.7) 19.4 (8.9) 9.7 9.7

48.1 (13.4) 23.6 (2.1) 34.7 (3.8) 27.4 (2.8) 34.0 (5.0) 73.5 (16.3) 40.2 34.7

4.5 (1.3) 3.3 (1.5) 3.7 (1.5) 2.8 (1.6) 10.0 (3.1) 7.1 (1.9) 6.5 (2.2) 4.8 (2.4) 7.8 (2.4) 3.8 (1.7) 2.0 (2.2) 4.9 (2.9) 2.2 (1.8) 6.4 (1.6) 3.3 (1.8) 3.5 (1.5) 7.1 (1.5) 4.9 [0.112] 4.6 [0.052]

16.2 (1.2) 17.8 (1.2) 18.3 (1.2) 19.1 (1.9) 30.4 (4.1) 23.5 (3.4) 26.5 (3.0) 25.7 (2.3) 28.0 (2.7) 20.1 (1.6) 21.4 (3.1) 28.9 (4.5) 20.8 (1.5) 18.9 (1.3) 19.6 (1.4) 17.7 (2.4) 18.5 (1.1) 21.9 [0.058] 20.5 [0.001]

S(Rep )

K(Rep )

σ(Rf )

S(Rf )

4.6 (1.9) 36.1 (14.7) -1.7 (1.6) 0.8 (0.3) 4.2 (0.6) 1.7 (0.8) 0.7 (0.3) 3.6 (0.9) 4.2 (0.8) 1.6 (0.3) 6.0 (1.1) -0.6 (0.8) 1.8 (0.5) 8.6 (2.6) -0.3 (0.5) 3.1 (0.7) 13.7 (5.2) -3.1 (1.2) 2.1 12.0 0.0 1.8 8.6 -0.3

17.3 (2.1) 7.8 (1.0) 6.1 (0.6) 9.1 (0.9) 4.9 (0.4) 9.8 (1.2) 9.2 9.1

-0.9 (0.6) -0.2 (0.7) -0.4 (0.3) 0.1 (0.5) -0.6 (0.3) -1.3 (0.3) -0.6 -0.6

-0.8 (0.2) 0.1 (0.2) 0.2 (0.3) 1.1 (0.5) 1.4 (0.6) 2.0 (1.0) 1.4 (0.6) 0.8 (0.3) 1.1 (0.4) 0.3 (0.3) 1.0 (0.9) 1.9 (0.8) 0.6 (0.2) 0.1 (0.2) 0.3 (0.2) 1.5 (1.0) -0.2 (0.2) 0.8 [0.083] 0.8 [0.044]

3.5 (0.3) 7.4 (0.6) 6.0 (0.6) 5.8 (0.5) 8.8 (1.9) 9.6 (1.1) 16.3 (3.4) 12.6 (2.5) 13.0 (2.3) 4.7 (0.4) 5.0 (0.4) 7.5 (0.9) 5.8 (0.4) 6.4 (1.1) 4.9 (0.7) 5.7 (1.1) 4.7 (0.4) 7.5 [0.428] 6.2 [0.256]

1.9 (0.2) 0.1 (0.3) 1.3 (0.4) -0.4 (0.4) -3.1 (1.1) -1.4 (0.6) -4.3 (0.8) -3.1 (1.0) -3.1 (0.7) 0.1 (0.5) 0.3 (0.3) 0.4 (0.7) -0.2 (0.3) 0.0 (1.8) 0.6 (1.1) 2.6 (2.0) -0.4 (0.4) -0.5 [0.915] -0.1 [0.354]

4.2 (0.5) 3.7 (0.4) 3.4 (0.6) 7.0 (1.6) 8.0 (3) 14.1 (5.9) 8.6 (2.4) 4.6 (0.8) 5.9 (1.5) 3.9 (0.5) 9.1 (2.6) 11.3 (4.1) 3.7 (0.6) 3.8 (0.4) 3.6 (0.4) 12.4 (4.8) 3.1 (0.3) 6.5 [0.325] 5.2 [0.354]

E(Rf )

4.2 (0.3) 0.5 (0.6) 2.2 (0.5) 3.0 (0.5) 1.2 (0.9) -0.8 (0.8) -1.2 (1.4) -1.1 (1.2) -0.3 (1.1) 0.7 (0.4) 2.3 (0.5) 0.5 (0.7) 1.3 (0.5) 1.5 (0.5) 0.8 (0.4) 1.3 (0.5) 1.2 (0.4) 1.0 [0.420] 1.1 [0.354]

K(Rf )

Start

7.7 (1.6) 1909 7.2 (1.4) 1921 3.5 (0.6) 1963 5.7 (1.0) 1902* 3.8 (0.6) 1932* 4.9 (1.2) 1948 5.5 5.5

6.6 (1.2) 4.7 (0.5) 7.1 (1.7) 5.1 (0.7) 19.1 (6.8) 8.3 (1.6) 25.1 (9.4) 19.0 (6.6) 17.1 (4.7) 5.5 (1.3) 3.5 (0.5) 7.1 (1.4) 3.8 (0.7) 18.5 (4.5) 11.1 (2.8) 27.0 (10.9) 5.8 (0.8) 11.4 [0.008] 7.7 [0.117]

1870 1870* 1872 1874 1921 1870 1870 1906 1887 1891* 1927 1915 1883* 1871 1900 1870 1870

Notes: The table shows in percentages the mean, volatility, skewness, and kurtosis of equity premium (Rep ) and bill return (Rf ). Standard errors in parentheses are obtained by bootstrapping. The numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of means and medians, respectively, in advanced and emerging countries. End year is 2017. * denotes missing data: 1941 - 1946 for Belgium, 1914 - 1918 for Mexico, 1945-1946 for Netherlands, 1975 - 1977 for Portugal, and 1914 - 1920 and 1937 - 1940 for Spain. Returns are computed using end-of-year values of total equity and bill indexes deflated by the end-of-year values of country’s consumer price index. Short-term government bonds (maturity of three months) are used for computation of bill returns. The data is sourced from the Global Financial Data and for Mexico for 1902 - 1929 years from Haber, Razo, and Maurer (2003).

46

Table A4: Equity Premium and Bill Return: Postwar Sample (1950-2017) Emerging Chile India Korea Mexico Portugal Venezuela Mean Median Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

E(Rep )

σ(Rep )

S(Rep )

K(Rep )

E(Rf )

σ(Rf )

S(Rf )

K(Rf ) Start

20.6 (6.9) 5.7 (3.0) 11.4 (4.7) 10.2 (3.8) 8.4 (4.4) 20.0 (9.0) 12.7 11.4

58.0 (17.1) 25.0 (2.5) 34.7 (3.8) 31.3 (3.6) 36.4 (5.7) 74.6 (16.5) 43.3 36.4

3.8 (1.6) 0.8 (0.3) 0.7 (0.3) 1.1 (0.3) 1.8 (0.6) 3.1 (0.6) 1.9 1.8

25.1 (9.9) 3.8 (0.7) 3.6 (0.8) 4.5 (0.9) 7.9 (2.4) 13.3 (5.0) 9.7 7.9

-2.6 (2.5) 1.0 (0.6) 4.2 (0.8) 0.0 (0.8) -0.2 (0.5) -3.1 (1.2) -0.1 -0.1

20.5 (2.8) 5.1 (0.6) 6.1 (0.6) 6.7 (0.8) 4.6 (0.5) 9.9 (1.2) 8.8 6.7

-0.8 (0.6) -0.2 (0.5) -0.4 (0.3) -0.6 (0.4) -1.2 (0.2) -1.3 (0.3) -0.8 -0.8

6.0 (1.4) 4.8 (0.8) 3.5 (0.6) 4.3 (0.8) 4.5 (1.0) 4.8 (1.2) 4.7 4.7

1950 1950 1963 1950 1950 1950

2.5 (2.5) 5.5 (2.2) 5.8 (2.0) 6.8 (3.0) 11.2 (4.0) 8.0 (2.9) 8.8 (3.1) 5.5 (3.1) 10.3 (3.6) 8.7 (2.6) 3.4 (2.9) 7.3 (4.0) 7.5 (2.8) 9.8 (2.8) 6.6 (2.6) 7.9 (2.7) 8.2 (2.1) 7.3 [0.087] 7.4 [0.030]

21.1 (1.8) 18.5 (1.6) 16.6 (1.3) 25.2 (2.7) 32.9 (5.1) 24.0 (1.8) 25.8 (2.3) 26.2 (2.7) 29.2 (4.3) 21.3 (2.0) 23.8 (3.7) 33.1 (5.7) 23.5 (2.0) 23.0 (1.9) 21.3 (1.7) 22.5 (3.7) 17.1 (1.5) 23.8 [0.053] 23.6 [0.001]

-0.4 (0.2) -0.3 (0.3) -0.3 (0.2) 0.6 (0.4) 1.5 (0.7) 0.1 (0.2) 0.4 (0.2) 0.6 (0.3) 1.4 (0.6) 0.0 (0.3) 0.9 (0.8) 1.8 (0.8) 0.4 (0.3) -0.1 (0.2) 0.0 (0.2) 1.1 (1.0) -0.3 (0.3) 0.4 [0.041] 0.4 [0.008]

2.8 (0.4) 3.0 (0.6) 2.6 (0.3) 4.4 (0.9) 8.0 (2.8) 2.6 (0.3) 3.3 (0.4) 3.9 (0.7) 7.0 (2.1) 3.4 (0.5) 7.8 (2.2) 9.3 (3.3) 2.9 (0.5) 2.9 (0.4) 2.7 (0.4) 9.1 (3.1) 3.1 (0.5) 4.6 [0.201] 3.3 [0.044]

6.1 (0.5) 2.2 (0.4) 1.7 (0.4) 2.9 (0.5) 1.9 (0.5) 1.2 (0.4) 1.3 (0.3) 1.2 (0.4) 1.0 (0.5) 0.5 (0.4) 2.2 (0.5) 0.3 (0.5) 0.4 (0.5) 1.3 (0.4) 0.4 (0.2) 0.8 (0.5) 0.8 (0.3) 1.6 [0.194] 1.2 [0.052]

4.3 (0.4) 2.9 (0.2) 3.0 (0.3) 4.4 (0.3) 4.5 (0.5) 3.5 (0.6) 2.4 (0.3) 3.6 (0.3) 4.0 (0.5) 3.2 (0.3) 4.5 (0.4) 4.2 (0.4) 4.1 (0.3) 3.7 (0.5) 1.9 (0.3) 3.7 (0.4) 2.3 (0.2) 3.5 [0.085] 3.6 [0.000]

1.0 (0.2) -0.5 (0.2) -0.5 (0.4) 0.5 (0.2) -0.3 (0.4) -1.2 (0.9) -0.7 (0.6) -0.1 (0.3) -0.7 (0.6) -0.1 (0.2) -0.4 (0.2) -0.2 (0.3) -0.3 (0.2) -0.5 (0.8) -1.2 (0.5) -0.8 (0.3) 0.1 (0.3) -0.3 [0.079] -0.4 [0.117]

3.3 (0.7) 2.9 (0.4) 4.1 (0.9) 2.6 (0.4) 3.9 (0.7) 8.8 (3.2) 5.5 (1.8) 3.4 (0.6) 5.8 (1.1) 2.7 (0.3) 3.1 (0.4) 3.1 (0.4) 2.6 (0.3) 6.6 (2.0) 6.2 (1.6) 4.1 (0.9) 3.2 (0.4) 4.2 [0.435] 3.6 [0.177]

1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950

Notes: The table shows in percentages the mean, volatility, skewness, and kurtosis of equity premium (Rep ) and bill return (Rf ). Standard errors in parentheses are obtained by bootstrapping. The numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of means and medians, respectively, in advanced and emerging countries.

47

Table A5: Equity Premium and Bill Return: Extended Sample of Emerging Countries Emerging Chile Greece India Korea Malaysia Mexico Philippines Portugal South Africa Sri Lanka Taiwan Venezuela Mean Median Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland UK US Mean Median

E(Rep )

σ(Rep )

12.1 (4.6) 11.3 (5.5) 2.3 (2.4) 11.4 (4.6) 5.4 (2.5) 8.3 (4.5) 5.2 (5.5) 7.4 (3.6) 6.0 (2.1) 9.7 (7.9) 14.0 (5.6) 19.4 (8.9) 9.4 9.4

48.1 (13.2) 44.4 (7.2) 23.6 (2.2) 34.7 (3.8) 27.4 (2.8) 30.5 (4) 44.9 (8.4) 34 (5.0) 19.3 (1.7) 47.4 (8.8) 39.8 (4.3) 73.5 (16.5) 39.0 39.0

4.5 (1.3) 3.3 (1.5) 3.7 (1.5) 2.8 (1.6) 10.0 (3.1) 7.1 (1.9) 6.5 (2.2) 4.8 (2.4) 7.8 (2.4) 3.8 (1.7) 2.0 (2.2) 4.9 (2.9) 2.2 (1.8) 6.4 (1.6) 3.3 (1.8) 3.5 (1.5) 7.1 (1.5) 4.9 [0.008] 4.6 [0.003]

16.2 (1.2) 17.8 (1.2) 18.3 (1.2) 19.1 (1.9) 30.4 (4.1) 23.5 (3.4) 26.5 (3.0) 25.7 (2.3) 28.0 (2.7) 20.1 (1.6) 21.4 (3.1) 28.9 (4.5) 20.8 (1.5) 18.9 (1.3) 19.6 (1.4) 17.7 (2.4) 18.5 (1.1) 21.9 [0.002] 20.5 [0.000]

S(Rep )

K(Rep )

K(Rf )

Start

4.6 (1.8) 36.1 (14.5) -1.7 (1.7) 17.3 (2.2) -0.9 (0.6) 1.8 (0.6) 8.0 (2.7) 1.3 (0.6) 5.1 (0.6) -1.1 (0.5) 0.8 (0.3) 4.2 (0.6) 1.7 (0.8) 7.8 (1.0) -0.2 (0.7) 0.7 (0.3) 3.6 (0.9) 4.2 (0.8) 6.1 (0.6) -0.4 (0.3) 1.6 (0.3) 6.0 (1.1) -0.6 (0.8) 9.1 (0.9) 0.1 (0.5) 0.6 (0.5) 4.2 (1.1) 0.6 (0.4) 2.9 (0.6) -2.3 (0.8) 2.0 (0.8) 10.2 (3.5) 1.8 (0.8) 6.9 (0.8) 0.0 (0.5) 1.8 (0.5) 8.6 (2.6) -0.3 (0.5) 4.9 (0.4) -0.6 (0.3) 0.6 (0.3) 3.6 (0.7) 0.1 (0.4) 4.2 (0.3) 0.2 (0.2) 1.4 (0.6) 5.7 (1.9) 3.1 (0.8) 4.4 (0.5) 0.3 (0.3) 0.7 (0.3) 3.3 (0.7) 1.0 (0.6) 4.4 (0.9) -2.0 (0.8) 3.1 (0.7) 13.7 (5.3) -3.1 (1.2) 9.8 (1.2) -1.3 (0.3) 1.6 8.9 0.7 6.9 -0.7 1.6 6.0 0.7 6.1 -0.6

7.7 (1.5) 5.5 (1.8) 7.2 (1.4) 3.5 (0.6) 5.7 (1.0) 10.4 (3.9) 4.6 (0.8) 3.8 (0.6) 3.2 (0.4) 2.7 (0.5) 9.2 (2.8) 4.9 (1.1) 5.7 5.5

1909 1953 1921 1963 1973 1902* 1953 1932* 1936 1985 1968 1948

-0.8 (0.2) 0.1 (0.2) 0.2 (0.3) 1.1 (0.5) 1.4 (0.6) 2.0 (1.0) 1.4 (0.6) 0.8 (0.3) 1.1 (0.4) 0.3 (0.3) 1.0 (0.9) 1.9 (0.8) 0.6 (0.2) 0.1 (0.2) 0.3 (0.2) 1.5 (1.0) -0.2 (0.2) 0.8 [0.040] 0.8 [0.043]

6.6 (1.2) 4.7 (0.5) 7.1 (1.7) 5.1 (0.7) 19.1 (6.8) 8.3 (1.6) 25.1 (9.4) 19.0 (6.6) 17.1 (4.7) 5.5 (1.3) 3.5 (0.5) 7.1 (1.4) 3.8 (0.7) 18.5 (4.5) 11.1 (2.8) 27.0 (10.9) 5.8 (0.8) 11.4 [0.010] 7.7 [0.034]

1870 1870* 1872 1874 1921 1870 1870 1906 1887 1891* 1927 1915 1883* 1871 1900 1870 1870

4.2 (0.5) 3.7 (0.4) 3.4 (0.6) 7.0 (1.6) 8.0 (3) 14.1 (5.9) 8.6 (2.4) 4.6 (0.8) 5.9 (1.5) 3.9 (0.5) 9.1 (2.6) 11.3 (4.1) 3.7 (0.6) 3.8 (0.4) 3.6 (0.4) 12.4 (4.8) 3.1 (0.3) 6.5 [0.395] 5.2 [0.777]

E(Rf )

4.2 (0.3) 0.5 (0.6) 2.2 (0.5) 3.0 (0.5) 1.2 (0.9) -0.8 (0.8) -1.2 (1.4) -1.1 (1.2) -0.3 (1.1) 0.7 (0.4) 2.3 (0.5) 0.5 (0.7) 1.3 (0.5) 1.5 (0.5) 0.8 (0.4) 1.3 (0.5) 1.2 (0.4) 1.0 [0.633] 1.1 [0.811]

σ(Rf )

3.5 (0.3) 7.4 (0.6) 6.0 (0.6) 5.8 (0.5) 8.8 (1.9) 9.6 (1.1) 16.3 (3.4) 12.6 (2.5) 13.0 (2.3) 4.7 (0.4) 5.0 (0.4) 7.5 (0.9) 5.8 (0.4) 6.4 (1.1) 4.9 (0.7) 5.7 (1.1) 4.7 (0.4) 7.5 [0.669] 6.2 [0.499]

S(Rf )

1.9 (0.2) 0.1 (0.3) 1.3 (0.4) -0.4 (0.4) -3.1 (1.1) -1.4 (0.6) -4.3 (0.8) -3.1 (1.0) -3.1 (0.7) 0.1 (0.5) 0.3 (0.3) 0.4 (0.7) -0.2 (0.3) 0.0 (1.8) 0.6 (1.1) 2.6 (2.0) -0.4 (0.4) -0.5 [0.734] -0.1 [0.394]

Notes: The table shows in percentages the mean, volatility, skewness, and kurtosis of equity premium (Rep ) and bill return (Rf ). Standard errors in parentheses are obtained by bootstrapping. The numbers in brackets denote p-values for the Student’s t-test and Mann-Whitney test for equality of means and medians, respectively, in advanced and emerging countries. End year is 2017. * denotes missing data: 1941 - 1946 for Belgium, 1914 - 1918 for Mexico, 1945-1946 for Netherlands, 1975 - 1977 for Portugal, and 1914 - 1920 and 1937 - 1940 for Spain.

48

Table A6: Nondisaster Parameters: Mean and Standard Deviation of Consumption Growth Country Advanced Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands New Zealand Norway Spain Sweden Switzerland United Kingdom United States Mean Median Emerging Argentina Brazil Chile Colombia Egypt India Korea Mexico Peru Portugal Russia Taiwan Turkey Venezuela Mean Median

µ pre-1946 Mean SD

µ 1946-1972 Mean SD

µ post-1973 Mean SD

σ pre-1946 Mean SD

σ post-1946 Mean SD

ση Mean SD

0.011 0.004 0.023 0.020 0.020 0.002 0.011 0.011 0.004 0.009 0.023 0.017 0.008 0.025 0.011 0.010 0.016 0.013 0.011

0.005 0.006 0.004 0.004 0.006 0.003 0.004 0.003 0.004 0.004 0.007 0.005 0.005 0.003 0.003 0.003 0.003 0.004 0.004

0.025 0.031 0.027 0.022 0.039 0.038 0.048 0.048 0.073 0.039 0.021 0.027 0.054 0.026 0.030 0.022 0.026 0.035 0.030

0.006 0.005 0.004 0.005 0.007 0.003 0.004 0.005 0.005 0.006 0.010 0.005 0.009 0.004 0.003 0.004 0.004 0.005 0.005

0.019 0.016 0.017 0.009 0.020 0.016 0.015 0.016 0.019 0.013 0.011 0.023 0.017 0.012 0.008 0.021 0.019 0.016 0.016

0.003 0.003 0.003 0.003 0.005 0.002 0.003 0.004 0.003 0.003 0.004 0.004 0.004 0.003 0.002 0.003 0.003 0.003 0.003

0.037 0.030 0.032 0.006 0.018 0.030 0.019 0.010 0.018 0.023 0.039 0.004 0.048 0.021 0.040 0.003 0.021 0.023 0.021

0.007 0.016 0.007 0.004 0.007 0.004 0.006 0.004 0.004 0.006 0.015 0.003 0.008 0.004 0.005 0.002 0.004 0.006 0.005

0.004 0.002 0.002 0.004 0.004 0.002 0.002 0.002 0.003 0.002 0.005 0.005 0.003 0.002 0.001 0.002 0.002 0.003 0.002

0.003 0.002 0.002 0.003 0.003 0.001 0.002 0.002 0.002 0.002 0.004 0.003 0.002 0.002 0.001 0.002 0.002 0.002 0.002

0.016 0.017 0.018 0.020 0.029 0.014 0.017 0.020 0.021 0.021 0.029 0.023 0.024 0.017 0.011 0.017 0.016 0.020 0.018

0.004 0.002 0.002 0.003 0.004 0.001 0.002 0.002 0.002 0.003 0.005 0.003 0.004 0.003 0.001 0.002 0.002 0.003 0.002

0.015 0.023 0.019 0.016 0.002 -0.001 0.017 0.007 0.021 0.016 0.020 0.006 0.023 0.073 0.018 0.017

0.009 0.008 0.009 0.015 0.004 0.007 0.006 0.008 0.006 0.009 0.009 0.007 0.009 0.024 0.009 0.008

0.018 0.035 0.024 0.021 0.019 0.008 0.034 0.026 0.031 0.042 0.033 0.059 0.023 0.004 0.027 0.025

0.010 0.009 0.009 0.006 0.006 0.006 0.007 0.007 0.006 0.007 0.005 0.009 0.011 0.016 0.008 0.007

0.008 0.014 0.043 0.021 0.023 0.034 0.043 0.016 0.027 0.025 0.018 0.047 0.018 0.022 0.026 0.022

0.009 0.007 0.007 0.004 0.003 0.004 0.005 0.007 0.006 0.006 0.005 0.005 0.007 0.013 0.006 0.006

0.023 0.063 0.048 0.054 0.044 0.010 0.025 0.032 0.008 0.024 0.040 0.021 0.019 0.072 0.035 0.029

0.014 0.011 0.016 0.022 0.009 0.007 0.007 0.008 0.005 0.008 0.014 0.018 0.011 0.022 0.013 0.011

0.014 0.007 0.012 0.004 0.006 0.004 0.003 0.004 0.004 0.004 0.003 0.003 0.009 0.011 0.006 0.004

0.009 0.005 0.008 0.003 0.004 0.003 0.002 0.003 0.003 0.003 0.002 0.002 0.006 0.008 0.004 0.003

0.049 0.039 0.038 0.024 0.018 0.028 0.029 0.034 0.032 0.033 0.017 0.034 0.044 0.066 0.035 0.033

0.008 0.005 0.007 0.003 0.005 0.003 0.003 0.005 0.003 0.004 0.011 0.004 0.005 0.013 0.006 0.005

Notes: The table reports posterior means and standard deviations. µ denotes the country-specific mean of consumption growth for pre-1946, 1946-1972, and post-1973 periods. σ denotes the standard deviation of the shock to observed consumption. ση denotes the standard deviation of the shock to potential consumption growth.

49

Table A7: Disaster Episodes in Advanced Economies Advanced Australia Australia Australia Belgium Belgium Canada Canada Canada Denmark Denmark Finland Finland Finland Finland Finland France France Germany Germany Germany Germany Italy Italy Japan Japan Japan Netherlands Netherlands New Zealand New Zealand New Zealand Norway Norway Spain Spain Sweden Sweden Switzerland Switzerland United Kingdom United Kingdom United States United States United States

Start Date 1914 1930 1940 1913 1940 1914 1930 1943 1914 1940 1890 1914 1930 1940 1944 1914 1940 1914 1930 1940 1944 1930 1940 1914 1940 1944 1914 1940 1890 1914 1944 1914 1944 1914 1930 1914 1940 1914 1940 1914 1940 1914 1930 1943

End Date 1922 1932 1958 1919 1951 1925 1935 1948 1926 1951 1893 1921 1933 1942 1947 1920 1948 1928 1933 1942 1949 1931 1950 1917 1942 1950 1920 1952 1898 1935 1962 1925 1947 1921 1960 1923 1951 1921 1951 1921 1948 1922 1934 1948

Mean Median

Temp. Drop -0.31 -0.27 -0.37 -0.47 -0.73 -0.43 -0.34 -0.04 -0.20 -0.35 -0.16 -0.48 -0.27 -0.28 -0.10 -0.23 -0.81 -0.58 -0.18 -0.31 -0.32 -0.11 -0.41 -0.05 -0.35 -0.58 -0.58 -0.79 -0.14 -0.66 -0.33 -0.19 -0.04 -0.13 -0.83 -0.22 -0.33 -0.17 -0.24 -0.23 -0.23 -0.26 -0.30 -0.04

Perm. Drop -0.07 -0.14 -0.13 0.16 -0.24 -0.14 -0.27 0.04 -0.10 -0.18 0.01 -0.10 -0.07 -0.23 0.17 0.12 -0.06 -0.02 -0.11 -0.31 0.00 -0.11 -0.22 0.18 -0.35 -0.09 0.04 -0.21 -0.02 -0.37 -0.22 -0.08 0.04 0.10 -0.67 -0.13 -0.19 0.00 -0.20 -0.09 -0.14 -0.09 -0.10 0.01

-0.33 -0.29

-0.10 -0.10

Notes: Disaster P episode is defined as the number of consecutive years for country i, Ti such that P r{Ii,t = 1} > 0.1 and t∈Ti P r{Ii,t = 1} > 1. Temp. drop is the posterior mean of the cumulative temporary drop in consumption during the disaster. Perm. drop is the posterior mean of the cumulative permanent drop in consumption during the disaster.

50

Table A8: Disaster Episodes in Emerging Market Economies Emerging Argentina Argentina Argentina Argentina Argentina Brazil Brazil Brazil Brazil Chile Chile Chile Colombia Colombia Egypt Egypt Egypt India Korea Korea Mexico Mexico Peru Peru Peru Portugal Portugal Russia Russia Russia Russia Russia Taiwan Taiwan Turkey Turkey Venezuela Venezuela

Start Date 1890 1914 1930 1988 2000 1911 1930 1940 1968 1914 1953 1970 1929 1940 1914 1940 1973 1940 1940 1997 1910 1930 1913 1930 1976 1914 1969 1890 1904 1914 1930 1990 1901 1939 1914 1940 1930 2001

End Date 1907 1918 1933 1991 2005 1919 1932 1944 1977 1935 1959 1986 1938 1951 1924 1960 1980 1951 1954 1999 1917 1936 1916 1933 1990 1922 1976 1893 1907 1926 1951 2016 1915 1955 1936 1953 1958 2012

Mean Median

Temp. Drop -0.16 -0.11 -0.17 -0.07 -0.15 -0.05 -0.09 -0.06 -0.09 -0.72 -0.15 -0.94 -0.19 -0.22 -0.09 -0.16 -0.08 -0.14 -0.77 -0.20 -0.18 -0.27 -0.05 -0.17 -0.72 -0.31 -0.04 -0.10 -0.14 -0.90 -0.88 -0.28 -0.22 -0.83 -0.82 -0.41 -0.60 -0.08

Perm. Drop 0.12 -0.03 -0.13 0.04 0.00 0.08 -0.05 0.01 0.25 -0.46 -0.04 -0.91 0.06 0.12 0.02 0.14 0.23 -0.06 -0.51 -0.10 0.21 -0.08 0.07 -0.08 -0.71 -0.15 -0.02 0.10 -0.13 -0.79 0.02 0.23 -0.03 -0.63 -0.43 -0.04 -0.10 0.16

-0.31 -0.17

-0.10 -0.03

Notes: Disaster P episode is defined as the number of consecutive years for country i, Ti such that P r{Ii,t = 1} > 0.1 and t∈Ti P r{Ii,t = 1} > 1. Temp. drop is the posterior mean of the cumulative temporary drop in consumption during the disaster. Perm. drop is the posterior mean of the cumulative permanent drop in consumption during the disaster.

51

Table A9: Posterior Estimates of Disaster Parameters: Robustness

φ θ σφ,G σφ,C σφ σθ,G σθ,C σθ ρz pW pCbW pCbI 1 − pCbe pCbO

Baseline AEs EMEs -0.114 -0.072 (0.007) (0.013) -0.030 -0.013 (0.013) (0.008) 0.008 0.016 (0.002) (0.006) 0.077 0.033 (0.005) (0.011) 0.078 0.038 (0.005) (0.009) 0.148 0.051 (0.030) (0.020) 0.061 0.144 (0.022) (0.020) 0.162 0.153 (0.030) (0.019) 0.668 0.332 (0.029) (0.093) 0.060 0.060 (0.019) (0.019) 0.725 0.393 (0.074) (0.101) 0.003 0.019 (0.002) (0.008) 0.746 0.826 (0.053) (0.039) 0.046 0.042 (0.014) (0.012)

Baseline PtTw AEs EMEs -0.117 -0.071 (0.006) (0.014) -0.030 -0.011 (0.012) (0.008) 0.008 0.018 (0.001) (0.007) 0.080 0.027 (0.005) (0.011) 0.081 0.034 (0.005) (0.008) 0.164 0.046 (0.029) (0.018) 0.053 0.141 (0.020) (0.018) 0.173 0.150 (0.029) (0.018) 0.693 0.360 (0.031) (0.086) 0.068 0.068 (0.018) (0.018) 0.685 0.378 (0.085) (0.101) 0.004 0.028 (0.003) (0.009) 0.671 0.809 (0.052) (0.040) 0.050 0.051 (0.014) (0.012)

Baseline CoInVe AEs EMEs -0.116 -0.088 (0.007) (0.019) -0.031 -0.012 (0.012) (0.009) 0.008 0.015 (0.002) (0.007) 0.079 0.048 (0.006) (0.018) 0.079 0.052 (0.005) (0.015) 0.141 0.073 (0.026) (0.049) 0.035 0.120 (0.015) (0.031) 0.146 0.138 (0.025) (0.037) 0.654 0.624 (0.038) (0.113) 0.073 0.073 (0.016) (0.016) 0.684 0.318 (0.062) (0.103) 0.003 0.037 (0.002) (0.013) 0.683 0.788 (0.059) (0.065) 0.053 0.058 (0.012) (0.017)

Output AEs EMEs -0.139 -0.086 (0.015) (0.009) -0.050 -0.016 (0.018) (0.011) 0.065 0.010 (0.025) (0.003) 0.040 0.054 (0.021) (0.006) 0.095 0.055 (0.026) (0.006) 0.209 0.153 (0.030) (0.073) 0.122 0.169 (0.044) (0.039) 0.246 0.241 (0.028) (0.029) 0.683 0.788 (0.075) (0.033) 0.084 0.084 (0.013) (0.013) 0.653 0.330 (0.077) (0.078) 0.005 0.051 (0.003) (0.013) 0.426 0.578 (0.089) (0.080) 0.059 0.074 (0.009) (0.015)

Output AEs -0.107 (0.008) -0.040 (0.017) 0.010 (0.003) 0.071 (0.006) 0.072 (0.006) 0.161 (0.044) 0.148 (0.025) 0.221 (0.024) 0.600 (0.042) 0.076 (0.015) 0.717 (0.059) 0.003 (0.002) 0.482 (0.050) 0.058 (0.011)

extended EMEs -0.082 (0.009) -0.026 (0.011) 0.009 (0.002) 0.052 (0.007) 0.053 (0.006) 0.069 (0.037) 0.197 (0.023) 0.212 (0.036) 0.763 (0.061) 0.076 (0.015) 0.362 (0.066) 0.053 (0.012) 0.562 (0.069) 0.076 (0.013)

Notes: The table reports posterior mean and standard deviation (in parentheses) of disaster parameters in AEs (Advanced Economies) and in EMEs (Emerging Market Economies) for the baseline model and alternative models. Baseline PtTw model includes Portugal and Taiwan in the AE group (instead of in the EME group). Baseline CoInVe model drops Colombia, India, Venezuela from the EME group. Output model uses output (instead of consumption) per capita data for the baseline sample of countries - see Table A1 for sample windows. Output extended model uses output (instead of consumption) per capita data for an extended sample of countries - see Table A2 for included countries and their sample windows. pW is common for both country groups.

52

Figure A1: Evolution of Disasters and Consumption: Advanced Countries (Panel 1)

1920

1940

1960

1980

2000

2020

4.5 4.0 3.5 3.0

4.5 4.0 3.5 3.0 1900

0.0 0.2 0.4 0.6 0.8 1.0

Belgium

0.0 0.2 0.4 0.6 0.8 1.0

Australia

1920

1940

1920

1940

1960

1980

2000

2020

4.5 4.0 3.5 1920

1960

1980

2000

2020

1960

2020

1920

1940

1960

1980

2000

2020

1980

2000

2020

1980

2000

2020

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

2.5 3.0 3.5 4.0 4.5 1940

2000

Italy

0.0 0.2 0.4 0.6 0.8 1.0

1920

1980

2.5 3.0 3.5 4.0 4.5 1900

Germany

1900

1960

0.0 0.2 0.4 0.6 0.8 1.0

4.0 3.0 2.0 1940

1940

France

0.0 0.2 0.4 0.6 0.8 1.0

1920

2020

3.0 1900

Finland

1900

2000

0.0 0.2 0.4 0.6 0.8 1.0

2.5 3.0 3.5 4.0 4.5 1900

1980

Denmark

0.0 0.2 0.4 0.6 0.8 1.0

Canada

1960

1900

53

1920

1940

1960

Figure A2: Evolution of Disasters and Consumption: Advanced Countries (Panel 2)

1920

1940

1960

1980

2000

2020

4.5 4.0 3.5 3.0 2.5

4.5 3.5 2.5 1.5 1900

0.0 0.2 0.4 0.6 0.8 1.0

Netherlands

0.0 0.2 0.4 0.6 0.8 1.0

Japan

1900

1920

1920

1940

1960

1980

2000

2020

1920

1960

1980

2000

2020

1960

2000

2020

1980

1980

2000

2020

2000

2020

4.5 4.0 3.5 3.0 1920

1940

1960

2000

2020

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

4.5 4.0 3.5 3.0 1940

1980

United Kingdom

0.0 0.2 0.4 0.6 0.8 1.0

1920

1960

2.5 1900

Switzerland

1900

1940

0.0 0.2 0.4 0.6 0.8 1.0

4.5 4.0 3.5 3.0 2.5 1940

2020

Sweden

0.0 0.2 0.4 0.6 0.8 1.0

1920

2000

2.5 3.0 3.5 4.0 4.5 1900

Spain

1900

1980

0.0 0.2 0.4 0.6 0.8 1.0

4.5 4.0 3.5 3.0 1900

1960

Norway

0.0 0.2 0.4 0.6 0.8 1.0

New Zealand

1940

1900

54

1920

1940

1960

1980

Figure A3: Evolution of Disasters and Consumption: Advanced Countries (Panel 3)

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

United States

1900

1920

1940

1960

1980

2000

2020

55

Figure A4: Evolution of Disasters and Consumption: Emerging Countries (Panel 1)

1920

1940

1960

1980

2000

2020

4.0 3.0 2.0

4.5 4.0 3.5 1900

0.0 0.2 0.4 0.6 0.8 1.0

Brazil

0.0 0.2 0.4 0.6 0.8 1.0

Argentina

1900

1920

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0 1900

1920

1940

1960

1980

2000

4.5 4.0 3.5 3.0 1940

5.0

Egypt

2020

2020

1920

1940

1960

1980

2000

1980

2000

2020

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

4.0 3.0 2.0 1960

2000

Mexico

0.0 0.2 0.4 0.6 0.8 1.0

1940

1980

India

Korea

1920

1960

5.0

2000

4.5

1980

4.0

1960

2020

3.5

1940

2000

0.0 0.2 0.4 0.6 0.8 1.0

1920

1980

0.0 0.2 0.4 0.6 0.8 1.0

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0 1900

1960

Colombia 5.0

Chile

1940

1900

56

1920

1940

1960

1980

2000

2020

Figure A5: Evolution of Disasters and Consumption: Emerging Countries (Panel 2)

2.0

3.0

4.0

0.0 0.2 0.4 0.6 0.8 1.0 1900

1920

1940

1960

1980

2000

4.0 3.0 1920

5.0

Russia

2020

1940

2020

1900

1960

2020

1920

1940

1960

1980

2000

2020

1980

2000

2020

1920

57

2.5

3.5

4.5

0.0 0.2 0.4 0.6 0.8 1.0

2.5 3.0 3.5 4.0 4.5 1940

2000

Venezuela

0.0 0.2 0.4 0.6 0.8 1.0

1920

1980

Taiwan

Turkey

1900

1960

4

2000

3

1980

2

1960

1

1940

0.0 0.2 0.4 0.6 0.8 1.0

1920

2.0

5.0 4.5 4.0 3.5 3.0 1900

0.0 0.2 0.4 0.6 0.8 1.0

Portugal

0.0 0.2 0.4 0.6 0.8 1.0

Peru

1940

1960

1980

2000

Figure A6: Autocorrelation Plots - Baseline Model (Part 1)

15

5

15

0.8 0.4 0.0

autocorrelation

0.8 0

25

0

5

15

25

pCbW_AE

rhoZ_AE

meanPhiG_AE

15

25

0

5

15

0.4 0.0

autocorrelation

0.4 0.0

autocorrelation

0.4

5

0.8

lag

0.8

lag

0.8

lag

25

0

5

15

25

lag

sigmaPhiG_AE

sigmaPhiC_AE

meanThetaG_AE

15

25

0

5

15

lag

lag

58

25

0.4 0.0

autocorrelation

0.4 0.0

autocorrelation

0.4

5

0.8

lag

0.8

lag

0.0 0

0.4

25

0.8

0

1−pCe_AE

0.0

autocorrelation

0.8 0.4

5

0.0

autocorrelation

0

autocorrelation

pCbI_AE

0.0

autocorrelation

pW

0

5

15 lag

25

Figure A7: Autocorrelation Plots - Baseline Model (Part 2)

5

15

0

5

15

0.8 0.4 0.0

0.4

autocorrelation

0.8

pCbI_EME

25

0

5

15

25

1−pCe_EME

pCbW_EME

rhoZ_EME

15

25

0

5

15

0.4 0.0

autocorrelation

0.4 0.0

autocorrelation 5

0.8

lag

0.8

lag

0.8

lag

0.4 0

0.0

25

0.0

25

0

5

15

25

meanPhiG_EME

sigmaPhiG_EME

sigmaPhiC_EME

5

15

25

0

5

15

lag

lag

59

25

0.4 0.0

autocorrelation

0.4

autocorrelation

0.4 0.0 0

0.8

lag

0.8

lag

0.8

lag

0.0

autocorrelation

0

autocorrelation

sigmaThetaC_AE

autocorrelation

0.8 0.4 0.0

autocorrelation

sigmaThetaG_AE

0

5

15 lag

25

Figure A8: Autocorrelation Plots - Baseline Model (Part 3)

0

5

15

25

5

15

lag

lag

60

25

0.4 0.0

0.4 0.0 0

0.8

sigmaThetaC_EME

autocorrelation

0.8

sigmaThetaG_EME

autocorrelation

0.8 0.4 0.0

autocorrelation

meanThetaG_EME

0

5

15 lag

25

0.4

0.8

0

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15

25 0

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5 15

5

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lag

lag

61

25 0.4

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15

0.0

5

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25 autocorrelation

0.0 0

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0.0

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autocorrelation

0.0

autocorrelation

0.0

autocorrelation

pW

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15 25

autocorrelation

5 15

0.8

0 5

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autocorrelation

0.0

autocorrelation

0

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autocorrelation

0.0

autocorrelation

Figure A9: Autocorrelation Plots - NSBU Model pCbI 1−pCe

25 0

25 0

0

5

5

5

15

lag lag lag

pCbW rhoZ meanPhi

15

15

lag

25

25

lag lag lag

sigmaPhi meanTheta sigmaTheta

25

Figure A10: Trace Plots - Baseline Model (Part 1) pCbI_AE

1−pCe_AE

3000

0

1000

0.7

3000

0

1000

3000

iterations

iterations

iterations

pCbW_AE

rhoZ_AE

meanPhiG_AE

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−0.010

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sigmaPhiG_AE

sigmaPhiC_AE

meanThetaG_AE

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iterations

0

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3000

iterations

62

−0.10

meanThetaG_AE

0.14 0.10

0.12

sigmaPhiC_AE

0.020

1000

0.00

iterations

0.16

iterations

0.030

iterations

0.010 0

−0.020

meanPhiG_AE

0.60

0.70

rhoZ_AE

0.9 0.7 0.5

pCbW_AE

0

sigmaPhiG_AE

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0.9 1000

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1−pCe_AE

0.000

0.010

pCbI_AE

0.06 0.02

pW

0.10

pW

0

1000

3000

iterations

Figure A11: Trace Plots - Baseline Model (Part 2)

1000

3000

0.06 0.03 0.00

0.02

0.06

pCbI_EME

pCbI_EME

0

1000

3000

0

1000

3000

iterations

iterations

iterations

1−pCe_EME

pCbW_EME

rhoZ_EME

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0.5 0.1

0.3

rhoZ_EME

0.6 0.2

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meanPhiG_EME

sigmaPhiG_EME

sigmaPhiC_EME

1000

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iterations

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iterations

63

0.06 0.02

0.05 0.03 0.01

sigmaPhiG_EME

−0.04 0

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iterations

sigmaPhiC_EME

iterations

0.00

iterations

−0.08

meanPhiG_EME

0.4

pCbW_EME

0.85 0.75 0.65

1−pCe_EME

0.8

0

0.10

sigmaThetaC_AE sigmaThetaC_AE

0.20 0.10

sigmaThetaG_AE

sigmaThetaG_AE

0

1000

3000

iterations

Figure A12: Trace Plots - Baseline Model (Part 3)

0

1000

3000

iterations

1000

3000

iterations

64

0.20 0.15 0.10

0.10 0.06 0.02 0

0.25

sigmaThetaC_EME sigmaThetaC_EME

sigmaThetaG_EME sigmaThetaG_EME

0.02 −0.02 −0.06

meanThetaG_EME

meanThetaG_EME

0

1000

3000

iterations

Figure A13: Trace Plots - NSBU Model 1−pCe

1−pCe

0.015 0.005

pCbI

0.06 0.02

1000

3000

0

1000

3000

0

3000

iterations

iterations

pCbW

rhoZ

meanPhi

−0.05

0.30 1000

3000

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sigmaPhi

meanTheta

sigmaTheta

sigmaTheta

3000

iterations

0.10

−0.04

−0.02

meanTheta

0.10

1000

0.18

iterations

0.00

iterations

0.14

iterations

0.06 0

−0.02

meanPhi

0.40

0.6

rhoZ

0.50

0.8

0.00

iterations

0.4

pCbW

0

sigmaPhi

1000

0.14

pW

0

0.75 0.80 0.85 0.90

pCbI

0.10

pW

0

1000

3000

iterations

65

0

1000

3000

iterations

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