# Time-Varying Skewness and Real Business Cycles.

A growing literature in macroeconomics and finance has found important economic effects of variations in risk, in particular shocks to the volatility of key macroeconomic variables (such as total factor productivity). However, much less is known about the importance of shocks to the skewness of macroeconomic variables. (1)In this paper, we seek to quantify the economic effects of skewness shocks. To this end, we augment a small open economy real business cycle model with a novel feature: discrete regime changes in the higher-order moments of exogenous shocks, modeled as shocks to total factor productivity (TFP). We assume that in each period the economy can be in one of two possible Markov states: an unrest state or a quiet state. The unrest state is assumed to be associated with a substantial increase in volatility and negative skewness of shocks. This assumption is motivated by our empirical findings about the moments of business cycles of many countries that experience political unrest (see the discussion of our calibration below). Hence, unrest is effectively a shock to the second-order and third-order moments of the distribution of economic shocks.

To solve the model, we develop a third-order perturbation method to approximate the endogenous reactions to shocks to the second-order and third-order moments of TFP. Existing methods to solve and simulate models (including global approximations to policy functions as in Judd [1996] or Richter et al. [2014] or perturbation methods as in Andreasen et al. [2017]) rely on Monte Carlo simulations to calculate the dynamics of third-order moments of endogenous quantities such as output and consumption. However, Monte Carlo simulations are problematic for the computation of higher-order moments such as skewness because these higher-order moments are more sensitive to simulation error. (2) To overcome this problem, we build upon the method of Andreasen (2017) to calculate generalized impulse response functions (GIRF) of third-order approximations of third-order moments of endogenous variables. Our solution method exploits computational symbolic algebraic manipulation to calculate the third-order moments without Monte Carlo simulations. This technical innovation is nontrivial, since it requires solving for the dynamics of over 20,000 polynomials, in the presence of a Markov-switching state, that are up to ninth order in the state variables. Furthermore, our approach is readily applicable to other DSGE models, especially those for which the dynamics of higher-order moments of endogenous variables are of interest.

Calibration: To calibrate the model, we document and exploit the substantial changes in higher-order moments of aggregate economic variables during periods of mass political unrest. Unrest episodes, which are well-documented by the political science literature (Chenoweth and Lewis 2013), are helpful in identifying higher-order moment shocks for several reasons. First, we find that these episodes are associated with substantial increases in the volatility and negative skewness of growth rates of output, consumption, and investment. For instance, on average, a year during an unrest episode is associated with a more than 50 percent increase in the volatility and a more than three times increase in the negative skewness of output growth. The changes in higher-order moments of aggregate variables (output growth, consumption growth, and investment growth) associated with an episode of unrest can be estimated with reasonable precision, since the database provides a relatively large number of country-year observations (with eighty-four unrest episodes between 1960 and 2006, each lasting more than five years on average).

Second, since the model assumes that shocks are common knowledge, we ideally want to identify shocks using events that are easily observed for all agents, at home or abroad. Mass unrest episodes are appropriate for this end, as they are major events, and agents in the economy as well as investors abroad do not need to be econometricians to learn that a campaign of mass political unrest is underway. Hence, the onset of an unrest episode is likely to have a direct effect on economic agents' perceptions of risk. Furthermore, since the impulse response exercises assume unanticipated shocks, we ideally want to use events that are ex-ante difficult to predict. Unrest episodes are again appropriate for this end, as it has been well-documented that mass unrest is largely unanticipated because it requires unpredictable shocks that enable a large number of nonstate actors to overcome informational and coordination problems. (3)

Results: Our model shows that the increase in volatility and especially negative skewness when the economy enters an episode of unrest has quantitatively substantial impacts on economic activities. In the baseline calibration, the observed changes in volatility and negative skewness can explain 21 percent of the observed drop in average output growth, 45 percent of the drop in average consumption growth, and 51 percent of the drop in average investment growth during unrest episodes. More importantly, the increase in negative skewness accounts for about half of these drops in growth.

Intuitively, when shocks become more negatively skewed, risk-averse agents know that realizations on the left tail of the distribution of shocks have become more likely. The increase causes agents to shift their portfolios to safer assets abroad and accumulate stocks of these safer assets, leading to capital outflow and drops in domestic investment and output. The consequences of this increased mass on the left tail are heightened under Epstein-Zin preferences. A Taylor expansion of the household's Bellman equation reveals that Epstein-Zin preferences punish and reward, respectively, the second and third central moments of the future value function. To a second-order approximation, Epstein-Zin preferences penalize the second central moment, i.e., variance. To a third-order approximation, the preferences gain an additional term that rewards the third central moment, which is the product of skewness and variance raised to the power of 3/2. Therefore, the quantitative effects of time-varying variance is amplified by time-varying negative skewness.

We demonstrate the quantitative significance of skewness by comparing the losses in economic activities during unrest under a second-order approximation to the same losses under a third-order approximation. The second-order approximation can account for only half of the economic losses that the third-order approximation can. Therefore, negative skewness is revealed as an important component of risk.

Related literature. Our paper is related to several strands of the literature on higher-order moments of business cycles. First, there is a growing body of research that emphasizes the importance of the time-varying volatilities of economic variables (e.g., Justiniano and Primiceri 2008; Caldara et al. 2012; Arellano et al. 2012; Christiano et al. 2014; and Gilchrist et al. 2014. The study that is the closest to ours in quantifying the impact of time-varying higher-order moments is Fernandez-Villaverde et al. (2011). They consider a stochastic volatility process for the real interest rate and explore the impacts of interest rate volatility shocks to economic activities. The primary difference between our paper and this literature is that while they focus only on shocks to second moments, we focus on shocks to both second-order and third-order moments.

Second, there is a related body of macro-finance research that stresses the importance of skewness (e.g., Ranciere et al. 2008; Barberis and Huang 2008; Guvenen et al. 2014; Salgado et al. 2015; Feunou et al. 2015; and Colacito et al. 2015). Our analysis is most related and complementary to that of Colacito et al. (2015), who show the importance of time-varying skewness in a macro-finance model with Epstein-Zin preferences. The major difference is that while they focus on the effects of skewness on financial variables (implied equity Sharpe ratios and equity risk premia), we focus on the effects on real economic variables (the growth rates of output, consumption, and investment). Also, while they focus on the United States, we focus on emerging and developing economies. Finally, while they calibrate the model by looking at analysts' forecasts for the U.S. economy, we look at the changes in higher-order moments of real economic variables during unrest episodes.

Finally, our paper is also related to a body of literature that emphasizes the importance of rare disasters in explaining macroeconomic phenomena (e.g., Barro 2006; Gourio 2012; Andreasen 2012; Gabaix 2012). A key insight from this literature is that variations in the probability of rare disasters, modeled as events on the far left tail of the distribution of shocks, can have first-order macroeconomic effects, as they influence the precautionary behaviors of risk-averse agents. Our paper points out that time-varying negative skewness has similar effects. This is because an increase in negative skewness implies a higher probability of states with very low consumption. However, our estimation approach is different and complementary to existing approaches in this literature. Since rare disasters occur infrequently in data, the literature usually does not estimate the time variation in the probability of disasters from data, (4) or it employs calibrations to proxies such as time-varying volatility of equity returns (e.g., Gourio et al. 2013). In contrast, we exploit the uncertainty associated with episodes of unrest to estimate the time variation in the skewness of economic shocks when the economies enter and exit unrest. (5)

Our paper is organized as follows. Section 1 describes our data sources and documents several stylized facts on business cycles during unrest episodes. Section 2 introduces unrest to a standard small open economy model and calculates how much of the stylized facts can be explained by changes in the distribution of shocks. Section 3 concludes.

1. DATA AND STYLIZED FACTS

Data Sources and Definitions

For economics and other data, we use annual panel macroeconomic data from 154 countries listed in the World Bank's World Development Indicators (WDI) database over the interval 1960-2006. This includes three time series: real output, real investment, and real consumption. We also use WDI data on the Gini coefficient and Alesina et al.'s (2003) data on ethnic, linguistic, and religious fractionalization as control variables

For mass unrest episodes, we use the Nonviolent and Violent Campaigns and Outcomes (NAVCO) dataset, version 2.0 (Chenoweth and Lewis 2013). NAVCO 2.0 provides a "consensus population" of all known continuous and large (having at least 1,000 observed participants) organized unrest campaigns between 1945 and 2006 (6) that satisfy a series of conditions, as detailed in Appendix C. Each episode has an onset year and an end year. The onset year is defined as the first year with a series of coordinated, contentious collective actions with at least 1,000 observed participants. The episode is recorded as over when peak participation drops below 1,000. Overall, the NAVCO dataset provides 157 episodes of nonviolent and violent mass political unrest around the world between 1945 and 2006. Of these, there are eighty-four episodes in the years between 1960 and 2006, the period for which we have both unrest and economic data. Over this period, the average duration of an episode is 5.99 years.

Examples include many pro-democracy movements of civil unrest in Latin America, the Philippines's People Power Revolution (1983-87), Indonesia's civil unrest against Suharto (1997-98), and Mozambique's RENAMO resistance movement (1979-1992); for a complete listing of these episodes, see Appendix A.1. As an illustration, Figure 1 plots the time series of the growth rate in aggregate economic variables for the Philippines around the People's Power Revolution.

Stylized Facts on Business Cycles During Unrest

We now investigate the relationship between unrest and macroeconomic activities. The goal of this section is to arrive at a set of moments that will be used as calibration targets for the structural model of the following section. We focus on the contemporaneous association between unrest in a given country-year and the growth rates of output, consumption, and investment. We follow others in the macroeconomic literature (e.g., Fernandez-Villaverde et al. 2011) and do not explicitly model why the higher-order moments change, nor do we attempt to make any causal claims about the contemporaneous causal impacts of unrest on output or vice versa.

We calculate the growth rates of output, consumption, and investment by the first difference in logs of the variable at constant 2005 USD and then remove a country-specific average growth rate from each series. That is, if the real output for country i in year t is [Y.sub.it], then we calculate the raw growth rate as [DELTA][Y.sub.it] [equivalent to] 100(ln [Y.sub.it] - ln [Y.sub.it-1]). Then we take out the country's average growth rate to yield a demeaned output growth rate of [g.sub.Y,it] [equivalent to] [DELTA][Y.sub.it] - 1/[T.sub.i][[SIGMA].sub.t][DELTA][Y.sub.i]. A similar method is applied to demean consumption and investment growth. We demean to isolate fluctuations at the business cycle frequency and to control for differences in country-specific average growth rates.

We then contrast the distributions of growth rates during unrest ([g.sub.it]|[U.sub.it] = 1) against moments during quiet times of no unrest ([g.sub.it]|[U.sub.it] = 0) in Figure 2. The left column of Figure 2 displays smoothed kernel estimates of the empirical probability density functions for the growth rates of output, consumption, and investment, and the right column displays the corresponding empirical cumulative distribution functions. The probability density functions are estimated by Epanechnikov kernels with a bandwidth of 2 percentage points for output and consumption, and 4 percentage points for investment. The figures suggest that the distributions of the growth rates are more negatively skewed during unrest episodes.

To have numerical comparisons, Table 1 displays the means, standard deviations, skewnesses, and kurtoses of (country-demeaned) output growth, consumption growth, and investment growth during and outside of unrest episodes. All confidence intervals are bootstrapped with 500 replications and are reported at the 95 percent level. The first two columns report the estimated moments. The third column reports the difference in the estimated moments, along with the p-value for a test of the null hypothesis that there is no difference between the corresponding moments. The fourth column reports the ratio of the estimated standard deviations, along with the p-value for the Levene test of the equality of variances. The fifth column reports the p-value for the Kolmogorov-Smirnov test of whether the two distributions of shocks (under unrest and no unrest) are the same.

Table 1 shows that a period of unrest is associated with significant losses in growth. The per-year loss in output growth (relative to periods without unrest) is 1.92 percent, statistically significant at the 1 percent level. This estimated per-year loss is nontrivial, especially given that unrest is persistent once started. The estimated cumulative loss is relatively substantial at 11.50 percent of the base (pre-onset) year's output. (7) The annual loss in consumption growth is 1.22 percent, which is smaller than that of output growth. At the same time, investment growth losses are larger than output growth, at 3.96 percent. In cumulative terms, consumption and investment losses amount to 7.31 percent and 23.71 percent, respectively. Note that this ordering of the loss in investment, output, and consumption is consistent with the permanent income hypothesis, which predicts that investment is more sensitive to shocks than output, which is in turn more sensitive than consumption.

Furthermore, Table 1 shows that the standard deviations of the growth rates of output, consumption, and investment substantially increase during unrest episodes. The fourth column of Table 1 displays the ratio of standard deviations. We can see that the standard deviation of output growth is 53 percent larger in unrest, and the standard deviations of consumption and investment growth are 17 percent and 35 percent larger, respectively. The column also reports the p-values of Levene's test of equality of variances between various forms of unrest against the baseline of no unrest. The p-values show that all of these increases are highly statistically significant: well below 0.01 for all three.

Table 1 also shows that both output and consumption growth becomes more negatively skewed during unrest. The difference in the skewness between unrest and no unrest is -1.57 for output growth and -3.36 for consumption growth. The bootstrapped p-value for the hypothesis that the difference in skewness is equal to zero is 0.15 for output growth and 0.10 for consumption growth. While it is generally difficult to estimate higher-order moments of relatively infrequent events with great confidence, we believe that these differences in skewness are economically significant. The greater variance and larger left tail of many distributions are also visually discernible in Figure 2. (8) This discernible mass on the left tail corresponds to a continuous range from moderately to extremely bad outcomes. The difference between a period of unrest and a period with no unrest then is not the increased probability of a single disaster but an increase in the probability of a whole range of bad outcomes.

Finally, as the fifth column of Table 1 shows, under the Kolmogorov-Smirnov test, we can reject the hypothesis that the two distributions of shocks (under unrest and under no unrest) are the same, as the associated p-value is zero for each series (output growth, consumption growth, or investment growth).

We summarize our results in the following stylized fact: Fact: Episodes of mass political unrest are associated with statistically and economically significant economic costs: the distributions of output, investment, and consumption growth during unrest have lower means and higher variances than the distributions in periods of no unrest. In addition, the distributions of output and consumption growth are more negatively skewed during unrest.

One potential mechanism that could explain the increased volatility and negative skewness in economic activities is that unrest is associated with substantial increases in the probability of institutional disruptions. In Appendix A.3, we document that the probabilities of large political and government changes, including major changes in polity and coups, substantially increase during unrest episodes. Large political changes are often associated with significant changes in legal and economic institutions, such as the protection of property and investment, which are key determinants of investment and growth (Acemoglu and Robinson 2005; and Acemoglu et al. 2014). Therefore, unrest episodes can increase the probability and severity of economic disasters.

2. QUANTITATIVE ANALYSIS

Model

How much of observed declines in average output, consumption, and investment growth during unrest, as reported in the previous section, can be attributed to volatility and skewness shocks? To answer this question, we augment a standard small open economy with a regime-switching process for the volatility and skewness of TFP. We calibrate the regime-switching process to moments that were estimated from data in the previous section.

Consider a canonical small open economy model with a representative household. Domestic firms competitively produce a numeraire good [Y.sub.t] using capital [K.sub.t-1] and labor [H.sub.t], subject to TFP [[zeta].sub.t]:

[Y.sub.t] = [[zeta].sub.t][K.sup.[alpha].sub.t-1][([H.sub.t]).sup.1-[alpha]].

These firms take factor prices [R.sub.t] and [W.sub.t] as given. Their first-order conditions on their optimal choices of capital and labor equate these factor prices with the corresponding marginal products in production:

[W.sub.t] = (1 - [alpha])[zeta.sub.t][K.sup.[alpha].sub.t-1][H.sup.-[alpha].sub.t].

[R.sub.t] = [alpha][[zeta].sub.t][K.sup.[alpha].sub.t-1][H.sup.1-[alpha].sub.t].

Unrest shock. We introduce a regime-switching process. Let [u.sub.t] be an exogenous two-state Markov process, with [u.sub.t] = 1 representing the country being in unrest in period t and [u.sub.t] = 0 representing no unrest, or a quiet time, in period t. Transitional probabilities are calibrated to match the probability of unrest onset and the persistence of unrest observed in data.

To model how unrest affects economic activities in the most tractable way, we assume that unrest affects the TFP process. Intuitively, as unrest episodes are associated with significant economic and political instability, they will affect the productivity of many economic sectors by, for instance, affecting the efficiency of resource allocation (Acemoglu et al. 2014). Such effects can be captured in a reduced form by a wedge to TFP, as in Chari et al. (2007).

Remark. Recall that our goal is to analyze the extent to which the shocks to higher-order moments of aggregate macroeconomic variables that we observe during unrest can explain the observed average losses in output, consumption, and investment growth. To conduct this analysis in the simplest and clearest possible way, we assume that unrest is a shock only to higher-order moments of the TFP process and not to the first moment. Obviously, this is a simplifying assumption and will likely lead to underestimations of the economic impacts of unrest. The model can be extended to allow for the possibility that unrest affects the first moment as well, but this will complicate the analysis. We will show that, even without an immediate associated fall in average productivity, a higher-order moment shock is enough to generate large changes in macroeconomic aggregates in line with the data.

Speciically, assume that TFP [[zeta].sub.t] consists of a growth component [([g.sup.t]).sup.1-[alpha]] and a level component [A.sub.t]:

[[zeta].sub.t] = [([g.sup.t]).sup.1-[alpha]][A.sub.t],

where, for numerical simplicity, we have assumed that growth rate is a constant g. However, level component [A.sub.t] follows an autoregressive process with autoregressive parameter [rho] and i.i.d. shocks [[epsilon].sub.t]:

ln [A.sub.t] = [rho] ln [A.sub.t1] + [[epsilon].sub.t].

The stochastic process for [[epsilon].sub.t] depends on whether the economy is currently experiencing unrest. While in unrest ([u.sub.t] = 1), shock [[epsilon].sub.t] is distributed Normal Inverse Gaussian with mean 0, standard deviation [[sigma].sub.u], skewness [s.sub.u], and kurtosis [k.sub.u]. While not in unrest ([u.sub.t] = 0), shock [[epsilon].sub.t] is distributed Normal Inverse Gaussian with mean 0, standard deviation [[sigma].sub.q], skewness [s.sub.q], and kurtosis [k.sub.q]. The Normal Inverse Gaussian distribution has been used in the finance literature to model skewed distributions with fat tails (e.g. Barndorf-Nielsen 1997; Andersson 2001; and Mencia and Sentana 2012). The fact that the mean of [[epsilon].sub.t] is the same whether [u.sub.t] = 0 or [u.sub.t] = 1 reflects the assumption that unrest only affects higher-order moments of TFP. (9)

Preferences: As is now standard in the macro-finance literature (e.g., Gourio 2012; and Colacito and Croce 2013), we assume the representative household has recursive preferences as in Epstein and Zin (1989). These preferences allow us to distinguish between the intertemporal elasticity of substitution and risk aversion (captured by [zeta] and [gamma] below). Moreover, these preferences nest the standard expected utility with constant relative risk aversion (CRRA) as a special case.

Let [C.sub.t] denote household consumption in period t, and let [[??].sub.t] [equivalent to] [C.sub.t] - [[theta][omega].sup.-1][g.sub.t-1][H.sup.w.sub.t] denote labor-adjusted consumption, where [theta] and [omega] are preference parameters. Then, we follow the sign convention of Rudebusch and Swanson (2012) and define the representative household's preferences as:

[mathematical expression not reproducible] (1)

This convention ensures that the value function and the instantaneous payoff have the same sign.

Households supply capital and labor to the domestic firms, consume domestic goods, invest subject to an adjustment cost in capital, and trade noncontingent bonds in the international credit market:

[mathematical expression not reproducible]

subject to:

[mathematical expression not reproducible]

We assume that the interest rate households borrow at is a function of the aggregate stock of debt [D.sub.t]:

[mathematical expression not reproducible]

where [r.sub.t] is the interest rate, r* is a constant representing the world's risk-free interest rate, and d and [psi] are exogenous constants. This debt-elastic interest rate is a standard assumption to ensure that the equilibrium is stationary (e.g., Schmitt-Grohe and Uribe 2003).

Finally, a recursive equilibrium is defined as a set of policy functions for [C.sub.t], [V.sub.t], [K.sub.t], [D.sub.t], [Y.sub.t], [r.sub.t], [I.sub.t], [H.sub.t], [W.sub.t], and [R.sub.t] as functions of [K.sub.t-1], [D.sub.t-1], [A.sub.t], and [u.sub.t] such that all agent expectations are rational and the optimality conditions, constraints, and laws of motion described above hold.

Solution Method

One way to derive moments of output, consumption, and investment growth from the model is to simulate a very long time series in which the country transitions into and out of unrest with the same probabilities as in the data. But since unrest is rare, we would need an extraordinarily long simulated time series to reduce the Monte Carlo noise around our estimates of those higher-order moments. Instead, we adapt the pruning method from Andreasen et al. (2017) to get closed-form solutions for the paths of conditional moments of endogenous variables, the GIRF. We first describe how we calculate a GIRF and then how we use the GIRF to compare the model against the data. All details on the computational strategy, from approximation to pruning and the GIRF, are given in the Appendix.

We define the GIRF as follows. Let [y.sub.t] denote the log-deviation of output [Y.sub.t] from its steady-state value. Then [DELTA][y.sub.t] is the growth rate of output [Y.sub.t]. Let [X.sub.t] denote a vector of the first three powers of the growth rates of output, consumption, and investment:

[X.sub.t] [equivalent to] ([DELTA][y.sub.t], [DELTA][i.sub.t], [DELTA][c.sub.t], [([DELTA][y.sub.t]).sup.2], [([DELTA][i.sub.t]).sup.2], [([DELTA][c.sub.t]).sup.2], [([DELTA][y.sub.t]).sup.3], [([DELTA][i.sub.t]).sup.3], [([DELTA][c.sub.t]).sup.3]).

The GIRF is the evolution over time of the difference of conditional expectations of [X.sub.t] between two conditioning sets, differing with respect to two given time series of realizations of unrest, u = {[u.sub.t], -[varies] < t < [varies]} and [mathematical expression not reproducible]:

[mathematical expression not reproducible]

The first path, u, represents a country that starts with no unrest and then enters into unrest at t = 1 and stays there. That is, [u.sub.t] = 0 [for all]l [less than or equal to] 0 and [u.sub.t] = 1 [for all]l [greater than or equal to] 1. The second counterfactual path, [mathematical expression not reproducible], is one where the country never enters unrest: [mathematical expression not reproducible].

Remark. The GIRF is useful for our purposes for several reasons. First, we want to calculate the moments that would be uncovered from a simulation. The conditional expectations in the GIRF allow us to consider the effects of shocks over the course of the GIRF. This is important, since under a nonlinear approximation to the policy function, the presence of shocks will cause the ergodic moments of all variables to differ from those in the absence of shocks. Second, since [X.sub.t] contains powers and products of endogenous variables, we can find paths not just for conditional means, but also for conditional variances and skewnesses of the endogenous variables of interest given the paths for the components of [X.sub.t]. Moreover, the GIRF allows us to avoid measurement error, which is a problem for estimating higher-order moments of simulated series from a finite simulation length. While Andreasen et al. (2017) rely on SMM for higher-order moments, we use the computer algebra software Mathematica to calculate GIRFs for these moments symbolically, term by term, and avoid Monte Carlo error.

The GIRF provides the conditional moments in the first year of an unrest episode, the second year, and so on. The moments from the data presented in the previous section are weighted averages over the years in observed unrest episodes because years that are closer to the beginning of an episode are more likely observed than years that are many years after the beginning of an episode. If p = Pr([U.sub.t]|[U.sub.t-1] = 1), then the probability of a given observed year of unrest being the nth year of unrest (n [greater than or equal to] 1) within its respective episode is (1-p)[p.sup.n-1]. Thus, to construct the single value for average value of X on unrest, we take a weighted average of a GIRF where a country enters into unrest and stays there but with smaller and smaller weight given to later periods of unrest. That is, we calculate [mathematical expression not reproducible].

Calibrations

First, we calibrate the model's basic parameters using standard values from the small open economy literature. These numbers are listed in the top panel of Table 2. (10) We allow the values for Epstein-Zin preference parameters to vary within the standard range of values of the literature, surveyed in Table 3. (11)

Second, we calibrate parameters for the unrest process and the higher-order moments of TFP innovation [[epsilon].sub.t] to estimated moments from our empirical analysis in Section 1. Care must be paid to the calibration of the higher-order moments of TFP, both in unrest and in quiet times. The parameters chosen in the model govern the exogenous TFP process, but they are chosen to match the moments of endogenous quantities. It is relatively straightforward (as one could even rely on closed-form solutions) to choose the volatility of a shock process given a desired volatility of an endogenous quantity, such as output growth under a log-linear approximation to equilibrium. However, it is much less straightforward to choose higher-order moments of a shock process to match higher-order moments of a nonlinear approximation of the law of motion for an endogenous variable. Therefore, the parameters [[sigma].sub.q], [[sigma].sub.u], [s.sub.q], and [s.sub.u] are chosen so that the ergodic standard deviation and skewness of output growth, and the average generalized impulse responses of the standard deviation and skewness of output growth, match those in the data. (12)

Results

Model's performance relative to data. We compare the average loss in output, investment, and consumption growth from the GIRF [[infinity].summation over (t=1)](1 - p)[p.sup.t-1][GIRF.sup.2]([DELTA][y.sub.t]) to the corresponding observed average loss in growth as documented in Section 1. Table 4 reports the percentage of observed growth loss that can be explained by the calibrated model. The overall effect is an endogenous response of endogenous variables to an unrest shock that increases the volatility and negative skewness of TFP shocks, with an interplay of capital adjustment costs and preferences over the time resolution of risk. In each panel, we report the percentage obtained by using the first-, second-, and third-order approximations of the solution to the model. Note that by construction, the percentage explained using a first-order approximation is zero, as we assume that unrest does not affect the first moment of TFP shocks. The columns report the results with different preference parameters.

Table 4 shows that, under the baseline specification (the first column), the model explains 21 percent of the average output growth loss, 45 percent of the average consumption growth loss, and 51 percent of the average investment growth loss. This amounts to an output growth loss of 0.40 percent per year, a consumption growth loss of 0.55 percent per year, and an investment growth loss of 2.01 percent per year. In cumulative terms over the average episode duration, this is an output growth loss of 2.41 percent, a consumption growth loss of 3.28 percent, and an investment growth loss of 12.09 percent.

The second column of Table 4 shows that, not surprisingly, the model can explain more with a larger coefficient of risk aversion ([gamma] = 20 instead of [gamma] = 10). There, the fractions of growth losses explained increase to 62 percent for output, 128 percent for consumption and 148 percent for investment (thus this calibration "overexplains" the losses in consumption and investment). On the other hand, when we shut down Epstein-Zin preferences and use a lower coefficient of risk aversion (the third column), the fractions of growth losses explained decrease to 9 percent, 11 percent, and 23 percent for output, consumption, and investment, respectively.

It is not surprising that the model cannot fully explain the observed losses, since we assume that unrest only affects higher-order moments of TFP shocks, and not the first-order moment, thus abstracting away from factors such as reallocation of resources between sectors of the economy that may directly affect the average productivity. (13)

However, the table shows that shocks to the higher-order moments of TFP alone can still explain a substantial fraction of the observed losses, especially in investment. Even without Epstein-Zin preferences and with a relatively low risk-aversion index, the model can still explain around a fourth of the observed loss in investment growth. Intuitively, in the model, when risk increases (either through the second-order or third-order moment of TFP), agents in the country shift away from domestic capital and into the internationally traded asset. This mechanism explains the drop in investment.

Role of negative skewness. One of our main findings is that negative skewness shocks play quantitatively important roles in driving business cycles. To see this, in rows labeled "second order" in Table 4, we show the fractions of observed losses explained under each calibration, but using an approximation of the solution of the model only to the second order, and thus efectively shutting down the endogenous response to the shock to the skewness of TFP. As the baseline column shows, the reaction to skewness is substantial: the fractions of average losses explained in the third-order rows are roughly doubling those explained in the second-order rows. Diferences of comparable magnitudes are also found in the two other calibration columns.

Why does skewness matter? Intuitively, agents in our model dislike negative skewness. To see this, let [mathematical expression not reproducible], the aggregate of utility from consumption and labor to the household. By the definition of household preferences, [mathematical expression not reproducible]. Let [v.sub.t] [equivalent to] [V.sup.1-[zeta].sub.t] so that when [gamma] = [zeta] and thus Epstein-Zin preferences reduce to expected utility preferences, [v.sub.t] is the usual definition of the value function for the household: [mathematical expression not reproducible]. The third-order Taylor approximation for [v.sub.t] around [v.sub.t+1] = [micro] [equivalent to] [E.sub.t][[v.sub.t+1]] is:

[mathematical expression not reproducible] (2)

The first three terms of the continuation payoff are well-known in the literature on Epstein-Zin preferences (e.g., Colacito et al. 2013). The first term is current utility. The second is the same discounted continuation payoff that appears in non-Epstein-Zin expected utility preferences. The third term is a "correction" to expected utility that penalizes future variance of the value function as long as [gamma] > [zeta]. (14) The fourth term is novel to a third-order approximation. Under the same assumption that [gamma] > [zeta] and [zeta] < 1, this term rewards positive skewness of the future value function and penalizes negative skewness. As [gamma] increases, the penalties for both volatility and negative skewness increase.

The term [Skew.sub.t] [[v.sub.t+1]] [Var.sub.t] [[[v.sub.t+1]].sup.3/2] is equal to [E.sub.t][[([v.sub.t+1]-[micro]).sup.3]], the third central moment of the value function. It shows that, for a given amount of skewness, the size of the third central moment increases in the variance. This is why skewness and variance are complementary in giving rise to precautionary motives in equilibrium.

Expression (2) is another way to see how these higher-order moments relate to a disaster risk. A disaster is an outcome on the far left tail. If variance increases, extreme events on both tails become more likely. If in addition skewness becomes more negative, the events far out on the lower tail specifically become more likely. Though we do not calculate a fourth-order approximation to this model, one can easily show that the next term in the above expansion would penalize the fourth central moment of the value function. An increase in the fourth-order moment, like an increase in negative skewness for a given second-order moment, also makes outcomes on the tails more likely. Therefore, by taking a higher-order approximation to the value function and by considering shock distributions with fat and skewed tails, we can recover some of the effects of what has been explored in the rare disaster literature.

Comparison with other studies. How do the results in Table 4 compare with other studies in the literature on the macroeconomic effects of risk? It is well-known that increases in second-order moments lead to economic slowdowns, though the range of models in the literature is wide and none are exactly comparable with the model in this paper in terms of modeling assumptions or forcing processes. For example, while using a very different model (a closed economy with heterogeneous firms, subject to a transitory shock to the second-order moment of a composite of technology and demand, on the monthly frequency), Bloom (2009) obtains effects of risk that are of the same order of magnitude as here, i.e., doubling the standard deviation of the forcing process leads to a decline in the level of output by 2 percentage points within the first six months. For the canonical small open economy model considered here, Fernandez-Villaverde et al. (2011) find that a transitory one-standard-deviation shock to second-order moment of innovations to the global interest rate (the interest rate that households in the small open economy pay on their international debt) can lead to declines in output levels in Argentina of 1.16 percentage points below steady state after sixteen quarters, or an average output growth loss of 0.29 percentage points per year, which is about 73 percent of what our baseline model predicts. Just as in Gourio's (2012) experiment with a transitory increase in the disaster probability, in our model, investment experiences the most significant decline and output contracts by a few percentage points. However, in that model, a disaster also entails some destruction of capital, so it is difficult to directly compare the two sets of numerical results.

Welfare. Finally, we evaluate the welfare loss due to the shock to the distribution of TFP. The change in the value function [V.sub.t] experienced in the first period of an unrest episode corresponds to the welfare loss from facing the more negatively skewed distribution of TFP. The loss can be evaluated by considering the following counterfactual scenario: suppose that household consumption is dictated by a social planner who ensures that households enjoy labor-adjusted consumption [mathematical expression not reproducible] (the steady-state level of labor-adjusted consumption in the model) during each period the economy is not in unrest and [mathematical expression not reproducible], where [[DELTA].sub.C] < 1, during each period the economy is in unrest. Suppose additionally that unrest follows the same stochastic switching process as in the data and the model but there are no other sources of uncertainty to the households. The value function of the household in this scenario takes on two values: [mathematical expression not reproducible] while not in unrest, and [mathematical expression not reproducible], where [[DELTA].sub.V] < 1, while in unrest. The value function takes the following form:

[mathematical expression not reproducible] (3)

The log-linearization of the above:

[mathematical expression not reproducible] (4)

For a given [mathematical expression not reproducible], we can calculate the change in labor-adjusted consumption [mathematical expression not reproducible] that would give rise to a fall of [mathematical expression not reproducible] in the value function below its steady-state value for each period spent in unrest. We take [mathematical expression not reproducible] as calculated from our GIRF.

Our estimates imply a [mathematical expression not reproducible] equal to -6.1 percent. In other words, the welfare loss due to increased volatility and skewness during unrest is equal to the welfare loss if consumption were 6.1 percent lower than its steady-state value in each period of unrest. How does this number compare with those in other studies? Lucas (1987) shows that eliminating all business cycle fluctuations for a representative agent with expected-utility preferences corresponds to 0.1 percent to 0.5 percent of steady-state consumption. Dolmas (1998) finds that the same exercise under Epstein-Zin preferences yields 2 percent to 20 percent of steady-state consumption, depending on the degree of risk aversion.

3. CONCLUSION

We estimate shocks to the volatility and skewness of business cycles by exploiting the uncertainty associated with episodes of political unrest. A small open economy real business cycle model calibrated to the estimated moments from data shows that higher-order moment shocks, especially increased negative skewness, play important roles in explaining the observed average decline in economic activities. In short, the paper demonstrates the quantitative importance of time-varying skewness of shocks in the context of a small open economy real business cycle model. Our paper makes several contributions to different threads of the macroeconomic literature. In the context of real business cycle and DSGE models, the mapping from the higher-order moments of exogenous processes to moments of endogenous variables, such as the mapping studied in this paper, is relatively underexplored. While the literature has deployed a number of mechanisms (e.g., adjustment costs on investment, debt-elastic interest rates, habit in consumption, and interest rate smoothing; see Smets and Wouters 2007) to help log-linearized models better replicate the first-order and second-order moments of observed time series, it is less clear how these mechanisms affect the model's ability to match third-order moments as well. Our paper suggests it may be important to know more about the endogenous mechanisms that help or hinder matching higher-order moments of models, given that these moments could be important for the consequences of aggregate risk. Additionally, our method of accurately calculating the GIRF of third-order moments may help future researchers analyze the dynamics of higher-order moments of macroeconomic aggregates in DSGE models while avoiding Monte Carlo error.

APPENDIX: A. ONLINE APPENDIX: DATA

A.1 Details of NAVCO Unrest Data

NAVCO provides detailed information on 250 nonviolent and violent mass political campaigns between 1945 and 2006. These campaigns constitute a "consensus population" of all known cases satisfying the following conditions. Each episode is a series of observable (i.e., tactics used are overt and documented), continuous (distinguishing from one-of events or revolts) mass tactics or events that mobilize nonstate actors in pursuit of a political objective. The NAVCO dataset also provides, among other information, the country, the main participating groups, the documented objective of the movement in each year of the campaign, the presence of violence in each year of the campaign, and the degree to which the movement was successful at achieving the documented objective. We focus on episodes whose objectives belong to one of the following categories:

(0) Regime change indicates a goal of "overthrowing the state or substantially altering state institutions to the point that it would cause a de facto shift in the regime's hold on power."

(1) Significant institution reform indicates a goal of "changing fundamental political structures to alleviate injustices or grant additional rights."

(2) Policy change indicates a goal of "changes in government policy that fall short of changes in the fundamental political structures, including changes in a state's foreign policy."

For a complete listing of NAVCO unrest episodes, see the Online Appendix C.

A.2 Estimates of Onset and Continuation Probabilities

We investigate how likely unrest is to start and how persistent it is once it starts. We establish that unrest is rare but persistent. These facts are important for understanding the economic consequences of higher-order shocks to business cycles.

Let a dummy variable [U.sub.it] take the value of one during episodes of unrest and zero during years with no unrest, where i denotes a country and t denotes a year. We estimate both the probability of unrest onset (i.e., the probability of unrest conditional on no unrest the previous year) and the probability of unrest continuation (i.e., the probability of unrest conditional on there being unrest in the previous year). To assess whether the probability of unrest is a function of other observable characteristics of a country, we estimate two probit models, one for onset and one for continuation. Each probit predicts [U.sub.it] = 1 as a function of a constant and a vector [Z.sub.it] of control variables, including lagged real GDP growth minus the country-specific average growth rate [mathematical expression not reproducible], religious, ethnic, and linguistic fractionalization (all on a scale of 0 to 1), and income inequality (measured with the Gini coefficient). To control for region-specific factors that might influence the overall probability of a given country experiencing unrest, we include a term [[gamma].sub.Region(i)] as a region-fixed effect. (15) We do not include country-fixed effects because this would effectively exclude any country from our sample that has never experienced unrest. Instead, we want to include all countries in our sample to exploit not just variation within countries but between them as well. The fact that many countries never experience unrest is informative to estimating the probability of onset. The two probit regressions are:

Pr([U.sub.it]|[U.sub.it-1] = 0) = [PHI] ([[gamma].sub.Z0][Z.sub.it] + [[gamma].sub.0] + [[gamma].sub.0,Region(i)]) (onset) (5)

Pr([U.sub.it]|[U.sub.it-1] = 1) = [PHI] ([[gamma].sub.Z1][Z.sub.it] + [[gamma].sub.1] + [[gamma].sub.1,Region(i)]) (continuation) (6)

where [PHI] is the cumulative distribution function of the standard normal distribution.

Our baseline estimations, reported in Table 5, indicate that the onset of unrest is rare: the estimated onset probability is 1.4 percent per year. However, once it starts, unrest tends to last for several years: the estimated continuation probability in Table 6 is 83.3 percent per year. This continuation probability implies that the average duration of unrest episodes is 5.99 (= 1/1-0.833).

In summary, we find that the onset of unrest is rare. But once started, unrest is persistent, leading to relatively lengthy episodes.

A.3 Political Risks Associated with Unrest

We document that the probability of large political changes increases significantly in each year of unrest. To the extent that any large political change entails at least a temporary disruption of the economy, an increase in the probability of disruptive events might help make sense of the increase in the left tail of the distributions of output and consumption growth documented in the next section. We estimate a series of probit regressions to predict a set of political disruptions: (1) coups, (2) positive changes in the Polity index, (3) negative changes in the Polity index, (4) large positive changes in the Polity index (greater than five points), and (5) large negative changes in the Polity index (greater than five points). (16) Each probit regression is specified as in equation (6), as a function of a constant, an indicator for current unrest, the difference between lagged real GDP growth and a country-specific average real GDP growth, and the interaction between current unrest and lagged real GDP growth. Let [X.sub.it] be an indicator for one of the political disruptions. We estimate:

Pr([X.sub.it]) = [PHI] ([[gamma].sub.U][U.sub.it] + [[gamma].sub.Z][Z.sub.it] + [[gamma].sub.zu][Z.sub.it][U.sub.it] + [[gamma].sub.0]) (7)

There are a few differences between this specification and the specification of unrest onset and continuation in equation (6). First, we estimate one probit for each political disruption [X.sub.it]. Second, in equation (6), we estimate the probits conditional on the presence of lagged unrest and the absence of lagged unrest separately. Here, we estimate one probit including both unrest and its interactions with the controls in one step. We do this to test hypotheses that the probability of each political disruption is significantly different in the presence and absence of unrest. Third, for simplicity, we include in the vector of controls [Z.sub.it] just one control: the difference between lagged output growth and country-specific average output growth. We find that unrest is associated with increases in the probability of all kinds of political changes.

APPENDIX: B. ONLINE APPENDIX: MODEL DETAILS

B.1 Derivation of the Household Problem

First, we pose the problem in recursive form

[mathematical expression not reproducible]

The associated first-order conditions and envelope condition are:

[mathematical expression not reproducible].

These lead to:

[mathematical expression not reproducible]

B.2 Full Set of Equilibrium Conditions

The equilibrium conditions are (with additional variables introduced for convenience):

[mathematical expression not reproducible] (8)

[mathematical expression not reproducible] (9)

[mathematical expression not reproducible] (10)

[W.sub.t] = [theta][Z.sub.t-1][H.sup.[[omega]-1.sub.t]] (11)

[mathematical expression not reproducible] (12)

[mathematical expression not reproducible] (13)

[Y.sub.t] = [A.sub.t][K.sup.[alpha].sub.t-1][([Z.sub.t][H.sub.t]).sup.1-[alpha]] (14)

[W.sub.t] = (1-[alpha])[A.sub.t][K.sup.[alpha].sub.t-1][Z.sup.1-[alpha].sub.t][H.sup.[alpha].sub.t] (15)

[R.sub.t] = [alpha][A.sub.t][K.sup.[alpha]-1.sub.t-1][Z.sup.1-[alpha].sub.t][H.sup.1-[alpha].sub.t] (16)

[Y.sub.t] + [D.sub.t]/1+[r.sub.t] = [D.sub.t-1] + [C.sub.t] + [l.sub.t] + [phi]/2[([K.sub.l]/[K.sub.t-1]-[g.sub.t]).sup.2] [K.sub.t-1] (17)

[I.sub.t] = [K.sub.t] - (1 - [delta])[K.sub.t-1] (18)

[mathematical expression not reproducible] (19)

The equilibrium conditions, scaled ([c.sub.t] = [C.sub.t]/[Z.sub.t-1], [mathematical expression not reproducible], [h.sub.t] = [H.sub.t], [w.sub.t] = [W.sub.t]/[Z.sub.t-1], [v.sub.t] = [V.sub.t]/[Z.sub.t-1], [mathematical expression not reproducible], [y.sub.t] = [Y.sub.t]/[Z.sub.t-1], [k.sub.t] = [K.sub.t]/[Z.sub.t], [a.sub.t] = [A.sub.t]) and simplified:

[mathematical expression not reproducible] (20)

[mathematical expression not reproducible] (21)

[mathematical expression not reproducible] (22)

[w.sub.t] = [theta][h.sup.w-1.sub.t] (23)

[[kappa].sub.t] = [k.sub.t]/[k.sub.t-1]-1 (24)

[mathematical expression not reproducible] (25)

[mathematical expression not reproducible] (26)

[y.sub.t] = [a.sub.t][k.sup.[alpha].sub.t-1][([g.sub.t][h.sub.t]).sup.1-[alpha]] (27)

[w.sub.t][h.sub.t] = (1 - [alpha])[y.sub.t] (28)

[R.sub.t][k.sub.t-1] = [alpha][y.sub.t] (29)

[mathematical expression not reproducible] (30)

[i.sub.t] = [k.sub.t][g.sub.t] - (1 - [delta])[k.sub.t-1] (31)

[r.sub.t] = r* + [psi]([e.sup.([d.sub.t]-[bar.d])] - 1) (32)

log([a.sub.t+1]) = [rho]log([a.sub.t]) + [eta]([u.sub.t][[sigma].sub.u] + (1 - [u.sub.t])[[sigma].sub.q])[c.sub.t+1] (33)

log([g.sub.t]) = log([g.sub.q]) + [eta][u.sub.t] log([g.sub.u]) (34)

[[epsilon].sub.t+1] ~ i.i.d.N(0, 1) (35)

[u.sub.t+1] ~ Markov, 0 or 1 with constant transition matrix. (36)

Steady state at [eta] = 0:

[mathematical expression not reproducible] (37) [mathematical expression not reproducible] (38) [mathematical expression not reproducible] (39)

w = 0[h.sup.w-1] (40)

1 = [beta][g.sup.-[zeta]](1 + r) (41)

r = R - [delta] (42)

y = a[k.sup.[alpha]][(gh).sup.1-[alpha]] (43)

wh = (1 - [alpha])y (44)

Rk = [alpha]y (45)

[mathematical expression not reproducible] (46)

i = k(g - 1 + [delta]) (47)

r = r* (48)

a = 1 (49)

[kappa] = 0 (50)

g = [g.sub.q]. (51)

B.3 Notes on Solution Method and GIRFs

To approximate the solution to equilibrium of our model, we use a higher-order perturbation method with the pruning algorithm of Andreasen et al. (2017). Because we calculate GIRFs for higher-order moments of endogenous variables, deriving analytic representations for the GIRFs, as Andreasen et al. (2017) do, would be extremely algebraically tedious. Instead, we rely on the computer algebra software Mathematica to compute these higher-order moments. This section describes our computational strategy.

The equilibrium conditions can be stated in the following form:

0 = [E.sub.t][F([y.sub.t+1], [y.sub.t], [x.sub.t+1], [x.sub.t], [u.sub.t+1], [u.sub.t])]. (52)

The vector of equations F includes all optimality conditions, constraints, and the law of motion for the exogenous process. The vector [y.sub.t] is the vector of control variables: [mathematical expression not reproducible]. The perturbation parameter, [eta], is 1 in the model of interest but set to 0 at the point of approximation. The vector [x.sub.t] is the vector of continuous states, including the perturbation parameter (17): [log([k.sub.t-1]), [d.sub.t-1], log([a.sub.t]), [eta]]. [u.sub.t] is the indicator for unrest, which can only take the values 0 and 1.

The solution to this model is a set of policy functions of the following form, where [mathematical expression not reproducible] and the two shocks [[epsilon].sup.u.sub.t+1] and [[epsilon].sup.q.sub.t+1] follow two i.i.d. Normal Inverse Gaussian processes, described in the text:

[y.sub.t] = g([x.sub.t], [u.sub.t]) (53)

[x.sub.t+1] = h([x.sub.t], [u.sub.t]) + [eta]S([u.sub.t+1])[[epsilon].sub.t+1]. (54)

More specifically, for the state vector,

[mathematical expression not reproducible] (55)

At the point of approximation, the system is at a nonstochastic steady state in [x.sub.t] and [y.sub.t]: [x.sub.t] = [x.sub.ss] = [log([k.sub.ss]), [d.sub.ss], 0, 0] and [y.sub.t] = [y.sub.ss]. Since the unrest and no-unrest states are completely symmetric at [eta] = 0 by construction, the process [u.sub.t] is irrelevant for the steady states of [x.sub.t] and [y.sub.t]. Therefore, the following is true for all values of [u.sub.t+1] and [u.sub.t]:

0 = F([y.sub.ss], [y.sub.ss], [x.sub.ss], [x.sub.ss], [u.sub.t+1], [u.sub.t]).(56)

We use a standard third-order perturbation method (e.g., Judd 1996) to construct Taylor series approximations to h(x, 0), h(x, 1), g(x, 0), and g(x, 1). Those Taylor series approximations yield the coefficients [mathematical expression not reproducible], and [mathematical expression not reproducible], conformably reshaped:

h(x, 0) [approximately equal to] [h.sub.0x]x + 1/2[H.sub.0xx](x [cross product] x) + 1/6[H.sub.0xxx](x [cross product] x [cross product] x).(57)

This implies that the law of motion for [x.sub.t] and [y.sub.t] can be approximated to third order as:

[mathematical expression not reproducible] (58)

[mathematical expression not reproducible] (59)

However, it is well-known (e.g., in Kim et al. 2008; and Den Haan and De Wind 2012) that third-order approximations like the above can have undesirable statistical properties, such as explosive simulated paths and spurious steady states. Andreasen et al. (2017) extend Kim et al. (2008) and use a pruning algorithm to eliminate these undesirable properties. The second-order pruning algorithm separates simulated components of [x.sub.t] and [y.sub.t] into first-order components [x.sup.f.sub.t] and [y.sup.f.sub.t], second-order components [x.sup.s.sub.t] and [y.sup.s.sub.t], and third-order components [x.sup.r.sub.t] and [y.sup.r.sub.t]. The simulated quantities of interest are [x.sup.f.sub.t] + [x.sup.s.sub.t] + [x.sup.r.sub.t] and [y.sup.f.sub.t] + [y.sup.s.sub.t] + [y.sup.r.sub.t], and the components evolve linearly.

Let [mathematical expression not reproducible]. The constant vector [[0, 0, 0, 1].sup.t] reflects the fact that the law of motion for the perturbation parameter is simply [eta] = 1.

Following the approach in Andreasen et al. (2017), we have:

[mathematical expression not reproducible] (60)

[mathematical expression not reproducible] (61)

[mathematical expression not reproducible] (62)

[mathematical expression not reproducible] (63)

[mathematical expression not reproducible] (64)

[mathematical expression not reproducible] (65)

At this point, we deviate from the notation in Andreasen et al. (2017). Let

[mathematical expression not reproducible]

Expanding the above, we find that

[mathematical expression not reproducible]

Remember that [C.sub.t+1] is a function of [[epsilon].sub.t+1].

[mathematical expression not reproducible]

where

[mathematical expression not reproducible] (66)

[mathematical expression not reproducible] (67)

[mathematical expression not reproducible] (68)

[mathematical expression not reproducible]

Similarly, for controls [y.sub.t], we have [mathematical expression not reproducible], where [mathematical expression not reproducible].

In this paper. we are interested in the growth rates of the controls.

[mathematical expression not reproducible]

To calculate the average change in the first three moments of output, investment, and consumption growth during unrest, we use the concept of GIRF from Andreasen et al. (2017) and Koop et al. (1996). In particular, we calculate the unconditional moments of all endogenous variables for two fixed paths for the unrest process. The first path is for a country that starts with no unrest and then enters into unrest at t =1 and stays there. That is, [u.sub.t] = 0 [for all]t [less than or equal to] 0 and [u.sub.t] = 1 [for all]t [greater than or equal to] 1. Denote this path for [u.sub.t] as u. The second counterfactual path is one where the country never enters unrest: [u.sub.t] = 0 [for all]t. Denote this path for [u.sub.t] as [mathematical expression not reproducible]. Andreasen et al. (2017) condition on an initial value of the state vector [z.sub.0]. We instead focus on an unconditional expectation over the entire range of t to be able to arrive at a single path of moments for our exercise. The generalized IRF for the state variables [z.sub.t] is the difference, at each point in time t, of the unconditional mean of [z.sub.t] along the path u and the unconditional mean of [z.sub.t] along the path [mathematical expression not reproducible]:

[mathematical expression not reproducible] (69)

Andreasen et al. (2017) derive separate expressions for the evolution over time of the variances of controls. We take a different approach, which we find to be simpler, especially in dealing with third-order moments. We expand the set of objects we find a GIRF of from [DELTA][y.sub.t] to [mathematical expression not reproducible], so that we can compute one GIRF for all the moments of interest in one pass. For example, vec(Var([DELTA][y.sub.t])) = E[([DELTA][y.sub.t]) [cross product] ([DELTA][y.sub.t])] - E[[DELTA][y.sub.t]] [cross product] E[[DELTA][y.sub.t]], and the skewness of [DELTA][y.sub.t] is similarly a function of E[([DELTA][y.sub.t]) [cross product] ([DELTA][y.sub.t]) [cross product] ([DELTA][y.sub.t])]. Using the expression [mathematical expression not reproducible] and expanding the Kronecker products in [X.sub.t], we have matrices [mathematical expression not reproducible] and [mathematical expression not reproducible] such that

[mathematical expression not reproducible] (70)

where [mathematical expression not reproducible]

To calculate the law of motion for [Z.sub.t], we expand the Kronecker products in the definition of [Z.sub.t] using the law of motion [mathematical expression not reproducible] and arrive at the law of motion [mathematical expression not reproducible] for matrices [mathematical expression not reproducible] and [mathematical expression not reproducible].

For any [Z.sub.0], the independence of [e.sub.t+1] and [Z.sub.t] implies for states and controls (noting that [mathematical expression not reproducible] and similarly for [mathematical expression not reproducible] and [mathematical expression not reproducible]):

[mathematical expression not reproducible] (71)

[mathematical expression not reproducible] (72)

Let [Z.sub.0] be the fixed point of the law of motion for E[[Z.sub.t+1][Z.sub.0], u], conditional on t < 0, in other words, conditional on no unrest at time t or t + 1.

[mathematical expression not reproducible] (73)

From the elements of [Z.sub.0], we can calculate the ergodic means, variances, covariances, skewnesses, and sundry third moments of all elements of [z.sub.t] conditional on no unrest. This is the starting point of our GIRF. For t = 1, 2, 3..., use the laws of motion for [X.sub.t] and [Z.sub.t] to iterate forward, conditional on both the path u and the counterfactual path [mathematical expression not reproducible], and use those paths to calculate the GIRF for [X.sub.t]:

[mathematical expression not reproducible] (74)

This notation is very condensed. For example, [mathematical expression not reproducible] is a very large matrix, with very large polynomials containing terms with order as high as [[epsilon].sup.9.sub.t+1]. There are a large number of terms in every element of these matrices, even if expressed as Kronecker products; that is why we rely on the symbolic manipulation of Mathematica to expand these polynomials. Even after exploiting the very high degree of symmetry and redundant terms in [Z.sub.t], there are over 20,000 unique elements in that vector. Mathematica can handle these calculations very quickly, calculating the GIRFs for both states and controls in under two minutes.

1. C. ONLINE DATA APPENDIX: LIST OF NAVCO UNREST EPISODES

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Lance Kent and Toan Phan

Amazon, lanckent@amazon.com (work completed while the author was affiliated with the College of William & Mary); Federal Reserve Bank of Richmond, toanvphan@gmail.com. This paper supersedes an earlier working paper entitled "Business Cycles and Revolutions." The authors are grateful for helpful discussions with Daron Acemoglu, Filipe Campante, Matthias Doepke, B.R. Gabriel, Elias Papaioannou, and Romain Wacziarg. The authors would also like to thank seminar participants at the Atlanta Fed, Midwest Macro, the National University of Singapore, the 2014 ASSA Meetings, Duke University, the 2014 ISNIE meetings, the 2014 ESEM meetings in Toulouse, Queen's University Belfast, Utrecht University, and Maastricht University for their suggestions and feedback. The views expressed herein are those of the authors and not those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

(1) See the related literature section for a discussion of existing studies.

(2) The calculation of skewness and other higher-order moments is sensitive to the tails of the distribution of interest. Since realizations on the tails are rare, many Monte Carlo draws are needed to ensure that the tails are sufficiently sampled. Therefore, for a given simulation length, the influence of Monte Carlo simulation error is going to be much more pernicious for higher-order moments, such as skewness, than for lower-order moments, such as the mean.

(3) See, e.g., Kuran (1989), Chenoweth and Stephan (2011), and Edmond (2013). We also verify this in our probit analysis to predict the onset of unrest in Appendix A.2.

(4) E.g., Nakamura et al. (2013) allow disasters to be correlated across countries but suppose that the probability of a given country entering into a disaster "on its own" is fixed over time.

(5) It is important to note that we do not identify unrest episodes themselves as disasters.

(6) More recent versions of the dataset include more recent years.

(7) If p is the continuation probability and x is the annual loss, then the cumulative loss is estimated to be [mathematical expression not reproducible].

(8) While there is also a visibly larger left tail for the distribution of investment growth, the bootstrapped difference in the skewness in investment growth between unrest and no unrest is not significantly different from zero, with a p-value of 0.83. This is because there are a few observations of investment growth that are very large in absolute value on both sides of the distribution (consistent with sharp falls in investment and subsequent rebounds), and the bootstrapped estimate of the difference in skewness is sensitive to these outliers.

(9) The unrest shock in each period t affects the distribution of the TFP in period t, and because TFP is autocorrelated, the unrest shock will affect the distribution of future TFP terms too. This is different from a "news shock" that does not affect current TFP, only future TFP.

(10) The sensitivity parameter of interest rate to debt is simply set to a small value to avoid a unit root, as in Garcia-Cicco et al. (2010) and Schmitt-Grohe and Uribe (2003).

(11) In Vissing-Jorgensen and Attanasio (2003), the estimated risk-aversion parameter can take a wide range of values, as large as thirty. To be conservative, we only set the maximum risk-aversion to be twenty.

(12) We do not attempt to match kurtoses exactly, since we approximate equilibrium only to third order. We choose the kurtosis of the TFP processes high enough to permit existence of the Normal Inverse Gaussian distribution for the calibrated second-order and third-order moments. The calibrated kurtosis of TFP is approximately equal to that of the empirical distribution of output growth.

(13) For example, if sectors of the economy differ not only with respect to average productivity, but also exposure to political uncertainty under unrest, we might see a reallocation of capital to relatively inefficient sectors, driving up the share of output growth loss explained. Recent work by Acemoglu et al. (2014) provides evidence that, during the Egyptian experience of the Arab Spring, firms that had closer ties to the threatened regime suffered greater losses on the Egyptian stock market than firms that did not. Exploring the macroeconomic significance of this and other micro risks associated with political unrest would be complementary to our analysis and is outside of the scope of this paper.

(14) Remember, we are using a calibration where [zeta] < 1, so [micro] > 0 and [micro](1-[zeta]) > 0.

(15) The regions, as classified by the World Bank, are: East Asia and Pacific, Europe and Central Asia, Latin America and Caribbean, Middle East and North Africa, South Asia, and sub-Saharan Africa.

(16) Data for coups come from Marshall and Marshall (2011) and data for Polity come from Marshall and Jaggers (2002).

(17) We include the perturbation parameter in the definition of the state vector to simplify notation. Andreasen et al. (2017) include a brief discussion of this notation in the extensive appendix to their paper.

Table 1 Empirical Moments In and Out of Unrest No unrest Unrest Difference Ratio (c.i.) (c.i.) [p-value] [p-value] Output growth Mean 0.17 -1.75 -1.92 (0.03,0.32) (-2.46,-1.04) [0.00] Standard Dev. 5.62 8.63 1.53 (5.30,5.95) (7.05,10.20) [0.00] Skewness -0.69 -2.26 -1.57 (-1.68,0.30) (-4.16,-0.35) [0.15] Kurtosis 23.61 23.38 -0.23 (15.95,31.27) (13.86,32.91) [0.97] Consumption grth Mean 0.12 -1.10 -1.22 (-0.11,0.36) (-1.90,-0.31) [0.00] Standard Dev. 8.34 9.80 1.17 (7.69,8.99) (7.30,12.29) [0.00] Skewness 0.40 -2.96 -3.36 (-1.38,2.17) (-6.52,0.60) [0.10] Kurtosis 33.46 39.88 6.42 (17.34,49.57) (6.66,73.10) [0.73] Investment grth Mean 0.40 -3.56 -3.96 (-0.19,1.00) (-6.00,-1.12) [0.00] Standard Dev. 20.29 27.45 1.35 (18.69,21.89) (22.93,31.96) [0.00] Skewness -0.94 -0.71 0.24 (-2.52,0.64) (-2.14,0.73) [0.83] Kurtosis 31.78 15.11 -16.66 (17.77,45.80) (11.21,19.00) [0.03] K-S test [p-value] Output growth [0.00] Mean Standard Dev. Skewness Kurtosis Consumption grth [0.00] Mean Standard Dev. Skewness Kurtosis Investment grth [0.00] Mean Standard Dev. Skewness Kurtosis Notes: Empirical moments in and out of unrest with bootstrapped 95 percent confidence intervals (in brackets) and p-values (in square brackets) on hypothesis tests that there is no difference between the two distributions. The first two columns report the estimated moments. The third column reports the difference in the estimated moments, along with the p-value for a test of the null hypothesis that there is no difference between the corresponding moments. The fourth column reports the ratio of the estimated standard deviations, along with the p-value for the Levene test of the equality of variances. The fifth column reports the p-value for the Kolmogorov-Smirnov test of whether the two distributions of shocks (under unrest and no unrest) are the same. Table 2 Calibrated Parameters Parameter From literature [alpha] Capital share in production [beta] Discount factor [delta] Depreciation [phi] Adjustment costs to capital g Trend growth rate [theta] Disutility from labor [omega] Disutility from labor d Steady-state debt level [psi] Interest rate sensitivity to debt [zeta] Inverse intertemporal elasticity of substitution [gamma] Risk aversion Estimates from data [p.sub.onset] Probability of unrest onset [p.sub.cont.] Probability of unrest continuation Chosen to match target [[sigma].sub.q] Std. of TFP shock [[epsilon].sub.t] in quiet times [s.sub.q] Skewness of TFP shock [[epsilon].sub.t] in quiet times [k.sub.q] Kurtosis of TFP shock [[epsilon].sub.t] in quiet times [[sigma].sub.u] Std. of TFP shock [[epsilon].sub.t] during unrest [s.sub.u] Skewness of TFP shock [[epsilon].sub.t] during unrest [k.sub.u] Kurtosis of TFP shock [[epsilon].sub.t] during unrest Value Source/Target From literature [alpha] 0.32 Garcia-Cicco et al. (2010) [beta] 0.922 - [delta] 0.126 - [phi] 3.3 - g 1.005 - [theta] 0.224 - [omega] 1.6 - d 0.007 - [psi] [10.sup.-5] - [zeta] 0.9 to 5 Table 3 [gamma] 5 to 20 Table 3 Estimates from data [p.sub.onset] 0.014 Appendix A.2 [p.sub.cont.] 0.833 Appendix A.2 Chosen to match target [[sigma].sub.q] 2.75 Table 1 [s.sub.q] -1.10 Table 1 [k.sub.q] 22 (*) [[sigma].sub.u] 4.66 Table 1 [s.sub.u] -2.83 Table 1 [k.sub.u] 22 (*) Notes: (*) means chosen sufficiently high to permit existence of Normal Inverse Gaussian distribution. Table 3 Epstein-Zin Parameter Calibrations in the Literature [zeta] [gamma] Fernandez-Villaverde et al. (2011) 5 5 Colacito et al. (2013) 0.9 10 Vissing-Jorgensen and Attanasio (2003) 0.9 20 Table 4 Numerical Results Numerical Results Baseline High risk av. No EZ, low risk av. [zeta]-0.9, [zeta]-0.9, [zeta]-5, [gamma]-10 [gamma]-20 [gamma]-5 Output growth First order 0 0 0 Second order 11 21 6 Third order 21 62 9 Consumption growth First order 0 0 0 Second order 22 742 7 Third order 45 128 11 Investment growth First order 0 0 0 Second order 27 51 16 Third order 51 148 23 Notes: Numerical results for the percentages of the empirically observed average losses in the growth rates of output, consumption, and investment that are explained by the model. The rows show the percentage explained by using first-order, second-order, and third-order approximations of the solution to the model. Table 5 Estimated Onset Probability Onset Baseline (2) [mathematical expression not reproducible] -0.003 (0.01) Ethnic Frac Language Frac Religion Frac Gini Europe, Central Asia Latin America, Caribbean Middle East, North Africa North America South Asia Sub-Saharan Africa constant -2.209 (***) -2.147 (***) (0.03) (0.04) Pr([U.sub.i,t]|[U.sub.i,t-1] = 0) 0.014 0.016 (0.00) (0.00) N 9272 5910 Onset (3) (4) [mathematical expression not reproducible] -0.004 -0.005 (0.01) (0.02) Ethnic Frac 0.500 (**) (0.24) Language Frac -0.050 (0.21) Religion Frac -0.227 (0.18) Gini -0.014 (0.01) Europe, Central Asia Latin America, Caribbean Middle East, North Africa North America South Asia Sub-Saharan Africa constant -2.240 (***) -1.386 (***) (0.11) (0.46) Pr([U.sub.i,t]|[U.sub.i,t-1] = 0) 0.013 0.083 (0.00) (0.07) N 5357 599 Onset (5) [mathematical expression not reproducible] -0.001 (0.01) Ethnic Frac Language Frac Religion Frac Gini Europe, Central Asia -0.095 (0.15) Latin America, Caribbean 0.021 (0.15) Middle East, North Africa -0.005 (0.18) North America no obs. South Asia 0.432 (**) (0.19) Sub-Saharan Africa 0.125 (0.14) constant -2.182 (***) (0.11) Pr([U.sub.i,t]|[U.sub.i,t-1] = 0) 0.01 (0.00) N 5771 Notes: Probit coefficient estimates to predict onset of unrest, [U.sub.it], and derived probabilities. [DELTA][Y.sub.it] denotes real GDP growth (= 100 x (ln [Y.sub.t] - ln [Y.sub.t-1])). Standard errors in parentheses. East Asia is the baseline region for the specification with region FE. (*): p < 0:10. (**): p < 0:05. (***): p < 0:01. Table 6 Estimated Continuation Probability Continuation Baseline [mathematical expression not reproducible] Ethnic Frac'n Language Frac'n Religion Frac'n Gini Europe, Central Asia Latin America, Caribbean Middle East, North Africa North America South Asia Sub-Saharan Africa constant 0.967 (***) (0.06) Pr([U.sub.i,t]|[U.sub.i,t-1] = 1) 0.833 (0.01) N 732 Continuation (2) (3) [mathematical expression not reproducible] 0.011 (*) 0.009 (0.01) (0.01) Ethnic Frac'n 0.423 (0.34) Language Frac'n 0.406 (0.27) Religion Frac'n -1.022 (**) (0.32) Gini Europe, Central Asia Latin America, Caribbean Middle East, North Africa North America South Asia Sub-Saharan Africa constant 0.995 (***) 0.974 (***) (0.06) (0.18) Pr([U.sub.i,t]|[U.sub.i,t-1] = 1) 0.840 0.835 (0.02) (0.04) N 590 558 Continuation (4) (5) [mathematical expression not reproducible] -0.016 0.010 (0.03) (0.01) Ethnic Frac'n Language Frac'n Religion Frac'n Gini 0.006 (0.02) Europe, Central Asia -0.800 (***) (0.26) Latin America, Caribbean 0.317 (0.22) Middle East, North Africa -0.044 (0.28) North America no obs. South Asia -0.199 (0.30) Sub-Saharan Africa 0.007 (0.20) constant 0.694 1.001 (***) (0.75) (0.18) Pr([U.sub.i,t]|[U.sub.i,t-1] = 1) 0.756 0.842 (0.24) (0.04) N 74 590 Notes: Probit coefficient estimates to predict onset of unrest, [U.sub.it], and derived probabilities. [DELTA][Y.sub.it] denotes real GDP growth (= 100 x (ln [Y.sub.t] - ln [Y.sub.t-1])). Standard errors in parentheses. East Asia is the baseline region for the specification with region FE. (*): p < 0:10. (**): p < 0:05. (***): p < 0:01. Table 7 Estimated Probability of Political Events [Coup.sub.it] [DELTA][Pol.sub.it] > 0 [U.sub.i,t] 0.494 (***) 0.802 (***) (0.07) (0.07) Lagged output -0.005 -0.017 (***) growth[dagger] (0.00) (0.00) [U.sub.i,t*]Lagged -0.002 0.004 output growth[dagger] (0.01) (0.01) constant -1.585 (***) -1.696 (***) N 6500 6500 [DELTA][Pol.sub.it] < 0 [U.sub.i,t] 0.431 (***) (0.09) Lagged output -0.005 growth[dagger] (0.01) [U.sub.i,t*]Lagged 0.002 output growth[dagger] (0.01) constant -1.937 (***) N 6500 [DELTA][Pol.sub.it] > 5 [U.sub.i,t] 0.849 (***) (0.10) Lagged output -0.019 (**) growth[dagger] (0.01) [U.sub.i,t*]Lagged 0.003 output growth[dagger] (0.01) constant -2.397 (***) N 6500 [DELTA][Pol.sub.it] < -5 [U.sub.i,t] 0.420 (**) (0.13) Lagged output -0.007 growth[dagger] (0.01) [U.sub.i,t*]Lagged 0.003 output growth[dagger] (0.02) constant -2.437 (***) N 6500 Notes: Probit coefficient estimates to predict other political upheavals as functions of current unrest and derived probabilities. [dagger] relative to country-specific average output growth: [mathematical expression not reproducible]. Probabilities evaluated at lagged real output growth equal to country-specific average. Standard errors in parentheses. (*): p < 0:10. (**): p < 0:05. (***): p < 0:01. Table 8 List of Episodes of Mass Political Campaigns Country Begin End Campaign year year 1 Afghanistan 1978 1978 Afghans 2 Afghanistan 1992 1996 Taliban/Anti-Government Forces 3 Afghanistan 2001 2006 Taliban Resistance 4 Albania 1989 1991 Albania Anti-Communist 5 Algeria 1962 1963 Former Rebel Leaders 6 Algeria 1992 2006 Islamic Salvation Front 7 Angola 1975 2002 UNITA 8 Argentina 1973 1977 ERP/Monteneros 9 Argentina 1977 1983 Argentina pro-democracy movement 10 Argentina 1987 1987 Argentiana coup plot 11 Bangladesh 1987 1990 Bangladesh Anti-Ershad 12 Belarus 1988 1991 Belarus Anti-Communist 13 Belarus 2006 2006 Belarus Regime Opposition 14 Benin 1989 1990 Benin Anti-Communist 15 Bolivia 1952 1952 Bolivian Leftists 16 Bolivia 1977 1982 Bolivian Anti-Junta 17 Brazil 1984 1985 Diretas ja 18 Bulgaria 1989 1989 Bulgaria Anti-Communist 19 Burma 1988 2006 Karens 20 Burma 1988 1990 Burma pro-democracy movement 21 Burundi 1972 1973 First Hutu Rebellion 22 Burundi 1988 1988 Second Hutu Rebellion 23 Burundi 1991 1992 Tutsi supremacists 24 Burundi 1993 2002 Third Hutu Rebellion 25 Cambodia 1970 1975 Khmer Rouge 26 Cambodia 1978 1979 Anti-Khmer Rouge 27 Cambodia 1989 1997 Second Khmer Rouge 28 Chad 1968 1990 Frolinat 29 Chad 1994 1998 Chad rebels 30 Chile 1973 1973 Pinochet-led rebels 31 Chile 1983 1989 Anti-Pinochet Movement 32 China 1956 1957 Hundred Flowers Movement 33 China 1966 1968 Cultural Revolution Red Guards 34 China 1976 1979 Democracy Movement 35 China 1989 1989 Tiananmen 36 Colombia 1946 1953 Liberals of 1949 37 Colombia 1964 2006 Revolutionary Armed Forces of Colombia and National Liberation Army 38 Costa Rica 1948 1948 National Union Party 39 Croatia 1999 2000 Croatian Institutional Reform 40 Cuba 1956 1959 Cuban Revolution 41 Czechoslovakia 1989 1990 Velvet Revolution 42 Djibouti 1991 1994 Afar insurgency 43 Dominican Republic 1965 1965 Dominican leftists 44 Egypt 2000 2005 Kifaya 45 El Salvador 1977 1991 Salvadoran Civil Conflict 46 Ethiopia 1981 1991 Tigrean People's Liberation Front 47 France 1960 1962 Pro-French Nationalists 48 Georgia 2003 2003 Rose Revolution 49 Ghana 1949 1950 Convention People's Party movement 50 Ghana 2000 2000 Anti-Rawlings 51 Greece 1963 1963 Anti-Karamanlis 52 Greece 1973 1974 Greece Anti-Military 53 Guatemala 1954 1954 Conservative movement 54 Guatemala 1961 1996 Marxist rebels (URNG) Country Target 1 Afghanistan Afghan government 2 Afghanistan Afghan regime 3 Afghanistan Afghan government 4 Albania Communist regime 5 Algeria Ben Bella regime 6 Algeria Algerian government 7 Angola Angolan government 8 Argentina Argentina regime 9 Argentina Military junta 10 Argentina Attempted coup 11 Bangladesh Military rule 12 Belarus Communist regime 13 Belarus Belarus government 14 Benin Communist regime 15 Bolivia Military junta 16 Bolivia Military juntas 17 Brazil Military rule 18 Bulgaria Communist regime 19 Burma Burmese government 20 Burma Military junta 21 Burundi Tutsi influence in government 22 Burundi Tutsi influence in government 23 Burundi Buyoya regime 24 Burundi Power-sharing/Tutsi-dominated government 25 Cambodia Cambodian government 26 Cambodia Cambodian government 27 Cambodia Cambodian government 28 Chad Chadian government 29 Chad Chadian regime 30 Chile Allende regime 31 Chile Augusto Pinochet 32 China Communist regime 33 China Anti-Maoists 34 China Communist regime 35 China Communist regime 36 Colombia Conservative govt 37 Colombia Colombia govt and US influence 38 Costa Rica Calderon regime 39 Croatia Semi-presidential system 40 Cuba Batista regime 41 Czechoslovakia Communist regime 42 Djibouti Djibouti regime 43 Dominican Republic Loyalist regime 44 Egypt Mubarak regime 45 El Salvador El Salvador government 46 Ethiopia Ethiopian government 47 France French withdrawal from Algeria 48 Georgia Shevardnadze regime 49 Ghana British Rule 50 Ghana Rawlings govt 51 Greece Karamanlis regime 52 Greece Military rule 53 Guatemala Arbenz leftist regime 54 Guatemala government of Guatemala Table 9 List of Episodes of Mass Political Campaigns Country Begin End Campaign year year 55 Guyana 1990 1990 Anti-Burnham / Hoyte 56 Haiti 1985 1985 Anti-Duvalier 57 Hungary 1956 1956 Hungary Anti-Communist 58 Hungary 1989 1989 Hungary pro-dem movement 59 India 1967 1971 Naxalite rebellion 60 Indonesia 1949 1962 Darul Islam 61 Indonesia 1956 1960 Indonesian leftists/Anti Sukarno 62 Indonesia 1997 1998 Anti-Suharto 63 Iran 1977 1978 Iranian Revolution 64 Iran 1981 1982 Iranian Mujahideen 65 Iran 1982 1983 KDPI 66 Iraq 1959 1959 Shammar Tribe and pro-Western officers 67 Iraq 1991 1991 Shiite rebellion 68 Ivory Coast 2002 2005 PMIC 69 Kenya 1990 1991 Anti-Arap Moi 70 Kyrgyzstan 1990 1991 Kyrgyzstan Democratic Movement 71 Kyrgyzstan 2005 2005 Tulip Revolution 72 Laos 1960 1975 Pathet Lao 73 Lebanon 1958 1958 Anti-Shamun 74 Lebanon 1975 1975 Lebanon leftists 75 Lebanon 2005 2005 Cedar Revolution 76 Liberia 1989 1990 Anti-Doe rebels 77 Liberia 1992 1995 NPFL & ULIMO 78 Liberia 1996 1996 National patriotic forces 79 Liberia 2003 2003 LURD 80 Madagascar 1991 1993 Active Forces 81 Madagascar 2002 2002 Madagasar pro-democracy movement 82 Malawi 1959 1959 Nyasaland African Congress 83 Malawi 1992 1993 Anti-Banda 84 Maldives 2003 2006 Anti-Gayoom 85 Mali 1990 1992 Mali Anti-Military 86 Mexico 1987 2000 Anti-PRI 87 Mexico 2006 2006 Anti-Calderon 88 Mongolia 1989 1990 Mongolian Anti-communist 89 Mozambique 1979 1992 Renamo 90 Nepal 1990 1990 The Stir 91 Nepal 1996 2006 CPN-M/UPF 92 Nicaragua 1978 1979 FSLN 93 Nicaragua 1980 1990 Contras 94 Niger 1991 1992 Niger Anti-Military 95 Nigeria 1993 1998 Nigeria Anti-Military 96 Oman 1964 1976 Popular Front for the Liberation of Oman and the Arab Gulf (PFLOAG) 97 Pakistan 1968 1969 Anti-Khan 98 Pakistan 1983 1983 Pakistan pro-dem movement 99 Pakistan 1994 1995 Mohajir 100 Panama 1987 1989 Anti-Noriega 101 Papua New Guinea 1988 1988 Bougainville Revolt 102 Paraguay 1947 1947 Paraguay leftist rebellion 103 Peru 1980 1995 Sendero Luminoso (The Shining Path) Senderista Insurgency 104 Peru 1996 1997 Tupac Amaru Revolutionary Movement (MRTA) - Senderista Insurgency 105 Peru 2000 2000 Anti-Fujimori 106 Philippines 1946 1954 Hukbalahap Rebellion 107 Philippines 1972 2006 New People's Army 108 Philippines 1983 1986 People Power 109 Philippines 2001 2001 Second People Power Movement 110 Poland 1956 1956 Poznan Protests Country Target 55 Guyana Burnham/Hoyte autocratic regime 56 Haiti Jean Claude Duvalier 57 Hungary Communist regime 58 Hungary Communist regime 59 India Indian regime 60 Indonesia Indonesian government 61 Indonesia Sukarno regime 62 Indonesia Suharto rule 63 Iran Shah Reza Pahlavi 64 Iran Khomenei regime 65 Iran Iranian regime 66 Iraq Qassim regime 67 Iraq Hussein regime 68 Ivory Coast Incumbent regime 69 Kenya Daniel Arap Moi 70 Kyrgyzstan Communist regime 71 Kyrgyzstan Akayev regime 72 Laos Laotian government 73 Lebanon Shamun regime 74 Lebanon Lebanese government 75 Lebanon Syrian forces 76 Liberia Doe regime 77 Liberia Johnson regime 78 Liberia Liberian govt 79 Liberia Taylor regime 80 Madagascar Didier Radsiraka 81 Madagascar Radsiraka regime 82 Malawi British rule 83 Malawi Banda regime 84 Maldives Maumoon Abudul Gayoom's regime 85 Mali Military rule 86 Mexico Corrupt govt 87 Mexico Calderon regime 88 Mongolia Communist regime 89 Mozambique Mozambique government 90 Nepal Monarchy/Panchayat regime 91 Nepal Nepalese government 92 Nicaragua Nicaraguan regime 93 Nicaragua Sandinista regime 94 Niger Military rule 95 Nigeria Military rule 96 Oman Oman government 97 Pakistan Khan regime 98 Pakistan Zia al-Huq 99 Pakistan Pakistani government 100 Panama Noriega regime 101 Papua New Guinea Papuan regime 102 Paraguay Morinigo regime 103 Peru Peruvian government 104 Peru Peruvian government 105 Peru Fujimori govt 106 Philippines Filipino government 107 Philippines Filipino government 108 Philippines Ferdinand Marcos 109 Philippines Estrada regime 110 Poland Communist regime Table 10 List of Episodes of Mass Political Campaigns Country Begin End Campaign year year 111 Poland 1968 1968 Poland Anti-Communist I 112 Poland 1970 1970 Poland Anti-Communist II 113 Poland 1976 1976 Poland Warsaw worker uprising 114 Poland 1980 1989 Solidarity 115 Portugal 1973 1974 Carnation Revolution 116 Romania 1987 1989 Anti-Ceaucescu rebels 117 Russia 1990 1961 Russia pro-dem movement 118 Rwanda 1961 1964 Watusi 119 Rwanda 1990 1994 Tutsi rebels 120 Rwanda 1994 1994 Patriotic Front 121 Senegal 2000 2000 Anti-Diouf 122 Serbia 1996 2000 Anti-Milosevic 123 Sierra Leone 1991 1996 RUF 124 Slovenia 1989 1990 Slovenia Anti-Communist 125 Somalia 1982 1991 Somalia clan factions; SNM 127 South Africa 1952 1961 South Atrica First Defiance Campaign 128 South Africa 1984 1964 South Atrica Second Defiance Campaign 129 South Korea 1960 1960 South Korea Student Revolution 130 South Korea 1979 1980 South Korea Anti-Junta 131 South Korea 1987 1987 South Korea Anti-Military 132 Sri Lanka 1971 1971 JVP 133 Sri Lanka 1972 1672 LTTE 134 Sudan 1985 1985 Anti-Jaafar 135 Sudan 1985 2005 SPLA-Garang faction 136 Sudan 2003 2006 JEM/SLA 137 Syria 1980 1982 Muslim Brotherhood 138 Taiwan 1976 1985 Taiwan pro-democracy movement 139 Tajikistan 1992 1997 Popular Democratic Army (UTO) 140 Tanzania 1992 1992 Tanzania pro-democracy movement 141 Thailand 1966 1981 Thai communist rebels 142 Thailand 1973 1973 Thai student protests 143 Thailand 1992 1962 Thai pro-dem movement 144 Thailand 2005 2006 Anti-Thaksin 145 Uganda 1980 1986 National Resistance Army 146 Uganda 1986 2006 LRA 147 Ukraine 2001 2004 Orange Revolution 148 Uruguay 1963 1672 Tupamaros 149 Uruguay 1984 1985 Uruguay Anti-Military 150 Venezuela 1958 1958 Anti-Jimenez 151 Venezuela 1958 1963 Armed Forces for National Liberation (FALN) 152 Yugoslavia 1968 1968 Yugoslavia student protests 153 Yugoslavia 1970 1971 Croatian nationalists 154 Zambia 1990 1991 Zambia Anti-Single Party 155 Zambia 2001 2001 Anti-Chiluba 156 Zimbabwe 1974 1979 Zimbabwe African People's Union 157 Zimbabwe 1982 1987 PF-ZAPU guerillas Country Target 111 Poland Communist regime 112 Poland Communist regime 113 Poland Communist regime 114 Poland Communist regime 115 Portugal Military rule 116 Romania Ceacescu regime 117 Russia Anti-coup 118 Rwanda Hutuy regime 119 Rwanda Hutu regime 120 Rwanda Hutu regime and genocide 121 Senegal Diouf govt 122 Serbia Milosevic regime 123 Sierra Leone Republican government 124 Slovenia Communist regime 125 Somalia Siad Barre regime 127 South Africa Apartheid 128 South Africa Apartheid 129 South Korea Rhee regime 130 South Korea Military junta 131 South Korea Military government 132 Sri Lanka Sri Lankan government 133 Sri Lanka Sri Lankan occupation 134 Sudan Jaafar Nimiery 135 Sudan Sudanese government 136 Sudan Janjaweed militia 137 Syria Syrian regime 138 Taiwan Autocratic regime 139 Tajikistan Rakhmanov regime 140 Tanzania Mwinyi regime 141 Thailand Thai government 142 Thailand Military dictatorship 143 Thailand Suchinda regime 144 Thailand Thaksin regime 145 Uganda Okello regime 146 Uganda Museveni government 147 Ukraine Kuchma regime 148 Uruguay Uruguay government 149 Uruguay Military rule 150 Venezuela Jimenez dictatorship 151 Venezuela Betancourt regime 152 Yugoslavia Communist regime 153 Yugoslavia Yugoslav government 154 Zambia One-party rule 155 Zambia Chiluba regime 156 Zimbabwe Smith/Muzorena regime 157 Zimbabwe Mugabe regime

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Author: | Kent, Lance; Phan, Toan |
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Publication: | Economic Quarterly |

Date: | Mar 22, 2019 |

Words: | 15437 |

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