BUSINESS CYCLES WITH REVOLUTIONS

BUSINESS CYCLES WITH REVOLUTIONS LANCE KENT &TOANPHAN Preliminary and incomplete. We welcome comments. Abstract. This paper attempts to address one question, both empirically and theoretically: What are the impacts of political revolutions on the business cycles of developing countries? Empirically, we find that the emergence from a revolution amounts to a shock that results in permanent increases in the level of real output, real investment and capital inflows. Taken together, our estimated VAR shows that following the first protests to overthrow the government, the average economy gets worse before it gets better. Wethen build a simple DSGE model with equilibrium revolutions. We embed a political economy game between two players (the people and the ruling elites) in a real business cycle model of a small open economy. Our model can replicate business cycles that are qualitatively consistent with our empirical finding that the economy gets worse before it gets better. 1. Introduction This paper attempts to address one question, both empirically and theoretically: What are the impacts of political revolutions on the business cycles of developing countries? This is an important question, especially following the recent uprisings of the people in the Arab World that overthrew several long-standing autocratic regimes. We would like to be able to make some (at least qualitative) predictions about the economies of these countries in the Middle East and North Africa during and after these radical political transitions. This is also a non-trivial question. Empirically, there is an endogenous relationship between political revolutions and the business cycles. Economic recessions could reduce the opportunity cost of revolting, and thus could make revolutions more likely. On the other hand, a revolution could worsen an economic recession by introducing political instability that hurts investment. But a successful revolution that overthrows akleptocraticregimecouldpossiblyimprovetheeconomyinthelongrun,byreducingcorruptionandexpropriation. Theoretically, there has not been a dynamic stochastic general equilibrium (DSGE) model of a nation s business cycles with equilibrium revolutions. It is possibly because embedding a political economy game in a DSGE framework requires many simultaneously moving parts. Contributions. Surprisingly, according to our knowledge, very little in the literature that have addressed this question, either empirically or theoretically. Our paper attempts to provide one answer. In doing so, we bring two potential contributions. Lance Kent, College of William and Mary, lckent@wm.edu and http://lancekent.org. Toan Phan, UNC Chapel Hill, phan@unc.edu and http://toanphan.org. 1

BUSINESS CYCLES WITH REVOLUTIONS 2 First, in a flexible macroeconomic time-series framework, we explore the incidence and propagation of shocks arising from successful revolutions. We estimate a panel vector autoregression (VAR) over 157 countries and 6 macroeconomic time series, where revolution occurs when an estimated index of discontent breaches an estimated threshold. We use data compiled from several sources to restrict attention to events that are sharp persistent changes in the polity score that are preceded by protests and not associated with military coups or civil wars. While we are able to identify the emergence of countries from revolutions, identifying their starting dates is a somewhat more subtle task. Because of this, our evidence on the index of discontent is weak; we are only able to document that real output growth, averaged over all countries undergoing revolutions in our sample, is markedly lower in the two years preceding the events we identify as revolutions than in years preceding or following the events. However, our evidence on what happens after revolutions is stronger: we find that the emergence from a revolution amounts to a shock that results in permanent increases in the level of real output, real investment and capital inflows. Taken together, our estimated VAR shows that following the first protests to overthrow the government, the average economy gets worse before it gets better. This is our first contribution. Our second contribution is a simple DSGE model with equilibrium revolutions. We embed a political economy game between two players (the people and the ruling elites) in a real business cycle model of a small open economy. Our model can replicate business cycles that are qualitatively consistent with our empirical finding that it gets worse before it gets better, i.e. revolution worsens the economy in the short run, but asuccessfulrevolutionthatestablishesademocracyimprovestheeconomyinthelongrunbyremovingthe kleptocratic elites. Literature. As mentioned, to our knowledge, the economic and political science literature so far has little to say about the impact of political revolutions on the business cycles. Empirically, there has been an extensive literature on the relationship between democratizations and growth (see Rodrik and Wacziarg (2005), Papaioannou and Siourounis (2008) and references therein). However, this literature is usually mute about the relationship between revolutions (democratizations where incumbent autocrats are overthrown by popular protests) and the business cycles (which includes not only output, but also investment, capital inflows/outflows, imports/exports and real exchange rates). Some recent papers (Freund and Jaud (2013) and Khandelwal and Roitman (2013)) provide some event studies of this relationship in recent revolutions. However, we believe our paper is the first to provide a preliminary VAR analysis of revolutions. Theoretically, there has been a relatively large political economy literature on democratizations, especially following Acemoglu and Robinson (2000b) and their book Acemoglu and Robinson (2005). However, this literature usually models revolutions as a threat off the equilibrium path. Thus there is usually no equilibrium revolutions. To answer our original question (what are the macroeconomic impacts of revolutions), we need a

BUSINESS CYCLES WITH REVOLUTIONS 3 model with equilibrium revolutions. Our paper attempts to fill this need, building on insights from Acemoglu and Robinson (2000b). Finally, this paper builds on our own work on the Arab Spring. In Kent and Phan (2013b), we take a careful look into why the Arab Spring revolutions happened, and how short- and long-run macroeconomic conditions might have influenced the different outcomes: relatively peaceful abdications in Tunisia and Egypt, but civil wars in Syria and Libya. Then in Kent and Phan (2013a), we build a neoclassical growth model with endogenous revolutions. The plan of the paper is the following. We provide our preliminary empirical analysis in section 2. We then provide our theoretical framework in section 3. Section 4 provides our theoretical results and compares them to stylized features in data. Section 5 concludes. 2. Evidence We want to know what happens after revolutions. The first step is to establish some stylized facts that will be suggestive for building a dynamic structural macro model. Data. We estimate a panel VAR over 157 countries and using annual data over the interval 1960-2011. The vector of variables Y that evolve in the VAR are real output, real investment, inflation, the nominal exchange rate against the US dollar, real imports and real exports. All variables are taken from the World Development Indicators database, and all except inflation are in first differences in logs. We draw data on timing of political events from the NAVCO (Nonviolent and Violent Campaigns and Outcomes) dataset. For each episode, the NAVCO dataset gives (among other information) the country, the beginning year, the ending year, the main participating groups, the stated purpose of the movement, the presence of violence, and the degree to which the movement was successful. While the dataset contains a wide spectrum of political mass events including civil wars and terrorist activity, we restrict attention to campaigns that are nonviolent, pro-democracy mass movements whose stated goal is to remove a dictatorship or junta. We do this because we do not want to conflate the effects of emerging from a nonviolent revolution with the effects of a military coup or a civil war, which will undoubtedly have very different macroeconomic consequences. Ongoing work will estimate the impacts of each type of disturbance in a unified specification. Under these restrictive criteria, we observe 44 episodes for which we have sufficient data on real economic variables during the year of the revolution and afterwards. If a single observation of any of our economic series is missing from a given year and country, we drop both that year and the following year for that country from the sample. What is left is a sample with 3664 observations of (country, year) pairs, but with a small number of revolutions. These revolutions have an average duration of 2.5 years. Of them, 26 are successes (meaning that the movement deposes the targeted regime), 10 are limited successes (meaning that the regime retains power but makes some concessions to the movement), and 8 are failures (meaning that the movement

BUSINESS CYCLES WITH REVOLUTIONS 4 does not change the status quo. Future work will empirically explore the difference in long-run outcomes between successful and failed movements, but in this version we do not distinguish between them. The full list of episodes, with timing and outcomes, is the in the Appendix. Specification. Wemodelunrestasanendogenous threshold process. Unrest is a state that countries enter into and exit from stochastically. In our empirical specification, a country is in a state of unrest during NAVCO episodes. We also track the aftereffects of unrest, by coding a country as being in a post-unrest state for all years following the first NAVCO episode. The probability of entering into a unrest is endogenous: we posit that there is a stochastic index of discontent Z it that, when negative, is necessary and sufficient for a country to transition into a state of unrest. The index of discontent is a linear function of an exogenous shock it and a set of variables X it, which include a constant, lagged Y it 1,thepresenceofconflictinfour or more neighboring countries, and other indicators that have been shown to predict the onset of conflict in the political science literature. Under this specification, periods of unrest are endogenous rare events. Our empirical goal to measure the effects of unrest, both during the episodes themselves and afterwards. We do this with a panel VAR with country fixed effects and regime changes. The drift coefficient D it and autoregressive coefficients A it of the VAR governing Y it have three additive terms: first, a time-invariant country fixed effect; second, a term that is only present during the state of unrest; third, a term that is present if the country is in the post-unrest state. The country fixed effect allows us to identify variation within countries over time as they enter and exit the unrest state. The coefficients on the unrest state and the post-unrest state capture the disruption due to the event itself and the strength of the following recovery, potentially inclusive of prolonged institution-building. Y it =D it + Y it 1 A it + it D it =D i + D rev 1 rev,it + D post 1 post,it A it =A i + A rev 1 rev,it + A post 1 post,it Z it =X it B + it Pr(rev it norm it 1 or post it 1 )=Pr(Z it < 0) = ( X it B) Pr(post it rev it ): exogenous Results. We estimate the model with maximum likelihood. Since we observe the episodes of unrest, this amounts to OLS for the VAR coefficients and MLE for the unobserved index of discontent. Each country that experiences unrest in our sample effectively experiences three regimes governing its VAR: pre-unrest, during unrest, and post-unrest. Both the drift and the autoregressive coefficients differ in

BUSINESS CYCLES WITH REVOLUTIONS 5 these three regimes. We report coefficient estimates in a web appendix, but more economically meaningful are the ergodic means and the impulse responses implied by these coefficients. 1: It gets worse before it gets better. Table 1 reports implied ergodic means of output growth under the estimated coefficients for the three regimes, evaluated at the average country fixed effect. Note that the ergodic mean under a given state is also the growth rate of output that would prevail if a country stayed in that state for a very long time without additional shocks. That is, these represent the steady state growth rates under each regime. Switching between regimes is also switching between steady state growth rates. Pre-Unrest During Unrest Post-Unrest Specification ( D i )(I Ā i ) 1 ( D i + D rev )(I Ā i A rev ) 1 ( D i + D post )(I Ā i A post ) 1 Point estimate for output growth 4.65% 2.18% 5.39% 90% confidence interval (2.73%, 6.43%) (-0.8%, 4.8) (3.64%, 7.08%) Table 1. Ergodic means of output growth under three regimes The point estimate for the ergodic mean output growth rate during unrest is lower than that before unrest, and the ergodic mean output growth rate after unrest is greater than that before. This is the sense in which it gets worse before it gets better. However, the 90% confidence intervals all overlap. Formally, we can only reject the one-sided null hypothesis that the pre-unrest ergodic mean output growth rate is less than that during unrest (that is, the null that output growth improves during unrest) at =0.1 and we can only reject the one-sided null hypothesis that the post-unrest ergodic mean output growth rate is less than that before unrest (that is, the null that output growth is worse after unrest than before it) at =0.2. It is our hope to be able to draw tighter inference about these ergodic means once we distinguish between unrest episodes involving differing numbers of protestors and once we distinguish between the success or failure of the mass movements. 2: Entering and exiting the state of unrest. The ergodic means do not tell the whole story of what happens in the short run as a country falls into and recovers from unrest. Even if a country starts at the pre-unrest ergodic mean, the dynamics following the shift into a period of unrest depend on both the new ergodic mean and the change in the autoregressive coefficients. Since the average duration of unrest episodes is only 2.5 years, the speed of transition between ergodic means is crucial for estimating the expected severity of the downturn during the episode. In the following figures, we suppose that a hypothetical country (again at the average country fixed effect) starts at the pre-unrest ergodic mean in period 1, is in the unrest state in periods 2 through 4 (shaded), and emerges into the post-unrest state from period 5 onward. We plot responses of output growth, investment growth, growth in net exports, and the depreciation rate of the real exchange rate in response to these regime changes, relative to a country that stays at the pre-unrest ergodic mean throughout. The shocks are held constant at 0 in these responses.

BUSINESS CYCLES WITH REVOLUTIONS 6 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 0.05 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Unrest!t=2,3,4!! Figure 1. Growth rate of real output relative to pre-unrest ergodic mean, unrest in periods 2-4 wth!of!real!investment!vs!counterfactual!of!no!unrest 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Unrest!t=2,3,4!! Figure 2. Growth rate of real investment relative to pre-unrest ergodic mean, unrest in periods 2-4 Again, it gets worse before it gets better. Further, we see that it gets worse fairly quickly. Output growth falls 2.5% below the pre-unrest level after only the second year of the episode. The response of investment is similar to that of output but more exaggerated. In fact, we can (just barely) reject the one-sided null that the post-unrest ergodic mean investment growth rate is less than that pre-unrest at =0.1. Growth in net exports is significantly greater during the period of unrest. A plausible hypothesis is that this is capturing

BUSINESS CYCLES WITH REVOLUTIONS 7 0.12 0.1 0.08 0.06 0.04 0.02 0 0.02 0.04 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Unrest!t=2,3,4!! Figure 3. Growth rate of real net exports relative to pre-unrest ergodic mean, unrest in periods 2-4 0.15 Growth Rate of Real Exchange Rate. Unrest in t=2..4. 80% confidence interval 0.1 0.05 0 0.05 0.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Unrest!t=2,3,4!! Figure 4. Growth rate of the real exchange rate relative to pre-unrest ergodic mean, unrest in periods 2-4 capital outflows in the wake of the onset of unrest. We are unable to say anything about the real exchange rate, since the confidence interval is so wide. 3: Propagation in times of unrest. The shift of regime is not the only shock that economies are subject to. Once a country enters a state of unrest, the propagation of other shocks changes as well. In the specification we estimate, this shows up in the coefficients A rev,orthetermintheautoregressivematrix that is active when a country is experiencing unrest. With this estimate in hand we can discuss changes in

BUSINESS CYCLES WITH REVOLUTIONS 8 propagation without having to identify specific shocks or give them a structural interpretation. What we find is that being in the unrest state amplifies at least a few impulse responses. The figures below each show the difference between two impulse responses, both in response to the same shock, but under different regimes. The shock in the first graph is a one percent fall in the growth rate of output. The response is to the growth rate of investment. What s plotted is the difference between the impulse response during unrest and the impulse response before unrest. In other words, the negative spike of investment in period 2 represents the additional fall in investment the same shock to output had under unrest as opposed to before unrest. This graph shows that unrest has amplified investment s sensitivity to shocks to output. onse!of!investment!is!more!exaggerated!under!unre 1 0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Figure 5. Impulse response of real investment growth to a fall in real output growth of one percent, difference between impulse during revolt and impulse pre-revolt. The following figure performs the same exercise for net exports. The effect is largely the same: a one percent fall in output growth causes an additional one percent increase in net exports under unrest as compared with the period before unrest. The presence of social unrest has amplified the effects of output shocks on net exports as well.

BUSINESS CYCLES WITH REVOLUTIONS 9 2 Difference between response during unrest and prior. 80% CI 1.5 1 0.5 0 0.5 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Figure 6. Impulse response of real net export growth to a fall in real output growth of one percent, difference between impulse during revolt and impulse pre-revolt. 4: Revolutions need sparks. Mass unrest is a rare event. Preliminary estimates of B, theweights on the covariates X in the estimated index of discontent, yield implied time-varying ex-ante probabilities ˆPr(rev X t ) that are only weakly correlated with the actual incidence of NAVCO episodes. In other words X, which includes many aggregate quantities observable to the econometrician, cannot fully account for the incidence of unrest. We conclude that another factor is at play: an shock, unseen to the econometrician, that enables the mass of protestors to overcome the coordination problem and effectively mount a movement. 5: Anticipating unrest: the spectre of turmoil or the promise of change? Mass unrest is a rare event. Even if the episodes lead to large swings in output and investment when they arrive, they do not account for much of the total volatility of the time series because they are so rare. Indeed, effects arising from the time-variation of the probability of unrest might be able to explain far more of the higher moments of the time series than the events themselves. We are still exploring specifications to identify this effect. 3. Theory 3.1. Environment. Time is discrete and infinite. The small open economy is populated by a unit population of citizens. In the initial period t =0, the country is ruled by an autocratic elite group. Throughout we will refer to these two groups as the people and the elite. Everybody has an infinite life. And there is a single good.

BUSINESS CYCLES WITH REVOLUTIONS 10 Besides the people and the elites, there is a continuum of measure one of competitive firms and there is acontinuumofforeigninvestors. Weassumeforeigninvestorssupplyallthefirms capitalstock(asina standard foreign direct investment model). 1 Firms profit maximization problem in each period is standard: where the production function is: max K t,l t Y t w t L t r t K t Y t = A t 1 K t L 1 t, with A t being the effective productivity term, K t being capital rental, and L t is domestic labor. Firms take wage rate w t and rental rate r t as given. The productivity term has two components: A t =(1 X t ) a t, where a t is the usual exogenous technological term, and X t 2 [0, 1) is the endogenous political term of our model (to be defined shortly). The log of a t follows an AR(1) process: log a t = log a t 1 +(1 ) log a + t, where < 1 is persistence, a is a constant term, and t are identically and independently distributed across time according to a normal distribution N(0, ). The steady state of this process is a. Wenormalizea =1. Foreign investors are risk neutral. They maximize their total expected profit: X max {K t+j} j 0 j 0 j f t+j subject to f t+j = r tk t K t+1 +(1 )K t, where is the capital depreciation rate and is their discount rate. Citizens are also risk-neutral and also discount the future at rate.each citizen supplies one unit of labor inelastically in each period. Her total expected utility from consumption is: E t X j 0 j c t+j, and her budget constraint is simply: c t apple w t, 1 This assumption is for simplicity. Foreign direct investment is a very simple way to model capital inflows and outflows. The model can be easily rewritten for a closed economy.

BUSINESS CYCLES WITH REVOLUTIONS 11 where w t is her wage income. In period t, iftheeliteiscurrentlyinpower,thenthereisanexogenous coordination shock (a spark ) s t, which is either 0 or 1. If s t =1,thenthepeoplehasanopportunityto coordinate a revolution. The people then collectively choose to revolt (rev t =1)ornot(rev t =0). But if s t =0,thenthereisnocoordinationamongthepeopleandtheycannotstageanyrevolution.Forsimplicity, we assume s t shocks are independently and identically distributed across time, and Pr(s t = 1) = p s 2 (0, 1). 2 There are three possible political states: x t 2 {E,U,D}. If x t = E, thentheeliteautocraticallyrulesthe country in period t. If x t = U, thenthecountryisinthemiddleofpoliticalunrest.andifx t = D, thenthe country is democratic. If x t = E, i.e.,theeliteisinpower,theyseeksrentfromthepeople. Wemodelrent-seekinginthesimplest possible way: the elite sets an expropriation rate t 0. The most the elite can expropriate is at rate < 1. If there is no revolution, the elite stays in power and consumes C t = t Y t,andtheeffective productivity for firms is: A t =(1 t ) a t apple a t. However, if people stage a revolution in period t, thentheelitecannotextractrent(thisassumptionisfor simplicity), and their utility is < 0. Furthermore, revolution causes political unrest that reduces the productivity for firms by a factor 2 (0, 1): A t =(1 ) a t <a t. For now, we assume is an exogenous constant (it is straightforward to consider stochastic ). This term captures productivity loss from weaker economic institutions (such as protection of properties). If x t = U, i.e.,thecountryisthemiddleofpoliticalunrest. Wecontinuetoweassumetheelitecannot extract rent in period t, andtheeffective productivity of firms is again: A t =(1 ) a t <a t, and the elite continues to get utility under political unrest. If x t = D, i.e.,thecountryisdemocraticandtheeliteisoutofpower,thenweassumethatrentseeking is D <. Forsimplicity,weset D =0. 3 Hence: A t = a t. For simplicity, also assume that the elite derives utility under democracy. 4 2 It is sufficient to assume that st follows an AR(1) process where the persistence is sufficiently small. 3 Alternatively, we can assume the median voter (i.e., a citizen) sets expropriation tax, and it is optimal for the median voter to set zero expropriation tax. 4 More generally, we can assume the elite derives utility D < 0.

BUSINESS CYCLES WITH REVOLUTIONS 12 The effective productivity can be summarized by: A t =(1 rev t t 1 revt )a t. {z } political loss term X t We assume the elite is also risk neutral and discounts the future at the same rate. Their total expected utility is: where E t X j 0 j C t+j 8 t a t Kt L 1 t if x t = E and rev t =0 >< C t = >: if x t = E and rev t =1 if x t = U if x t = D. We assume is sufficiently large that the elite always wants to avoid a revolution (if possible). The timing of the game is the following: If x t = E (the country is under elite rule) Technological shock a t and coordination shock s t realize, The ruling elite chooses rent-seeking (expropriation) rate t 2 [0, ], Foreign investors decide new capital stock K t+1, If s t =1,thepeoplecollectivelydecidetostagearevolutionornot,rev t 2 {0, 1}. Evolution of political state: If rev t =0,thenx t+1 = E (the elite continues to rule next period) If rev t =1,thentheoutcomeoftherevolutionisdeterminedbyan(exogenous)stochastic process: With probability p D, x t+1 = D (the country becomes democratic next period), With probability p E, x t+1 = E (the revolution fails and the elite remains in power next period), With probability p U =1 p D p E, x t+1 = U (unrest continues to next period). If x t = U (the country is under unrest) Technological shock a t realizes, Foreign investors decide new capital stock K t+1, Evolution of political state: With probability p D, x t+1 = D, With probability p E, x t+1 = E,

BUSINESS CYCLES WITH REVOLUTIONS 13 With probability 1 p D p E, x t+1 = U. If x t = D (the country is in democracy) Technological shock a t realizes, Foreign investors decide new capital stock K t+1. Remark 1. After a revolution, we can add another possibility: with probability p W,arevolutionleadstoa civil war (and p D + p E + p U + p W =1). Once in a civil war, the country escapes from the war back into elite rule with probability p W!E >p E, and into democracy with probability p W!D <p D. Remark 2. We can add a possibility of a coup. After the country becomes democratic, with an exogenous probability p coup in each period, the country can fall back into elite rule. Once back in autocracy, the game repeats. 3.2. Recursive reformulation. In equilibrium, labor market must clear: L t =1. Thus the first order conditions of firms are: (1) (2) r t = A t 1 K1 t w t = A t K t. The first order condition of foreign investors is: (3) 1= E t [r t+1 +1 ]. If s t =1(citizens can coordinate), then the payoff for citizens from staging a revolution is: (4) V R (K t,a t,k t+1 )= c R t + p D E[V D (K t+1,a t+1 ) a t ] + p E E[V E (K t+1,a t+1 ) a t ] + p U E[V U (K t+1,a t+1 ) a t ] where c R t =(1 The payoff for citizens from not revolting is: {z} )a t Kt. loss from unrest onset (5) V NR (K t,a t, t,k t+1 )= c NR t + E[V E (K t+1,a t+1 ) a t ] where c NR t =(1 {z} t )a t Kt. expropriation by elite

BUSINESS CYCLES WITH REVOLUTIONS 14 The payoff for citizens under democracy is: (6) V D (K t,a t )=c D t + E[V D (K t+1,a t+1 ) a t ] where c D t = a t K t. If x t = E and s t =1, the citizens decide whether to revolt or not. Their maximization problem is: (7) V E (K t,a t ) = max{v NR (K t,a t, t,k t+1 ),V R (K t,a t,k t+1 )} where K t+1 solves K t+1 = E[A t+1 Kt+1 +1 a t,k t,s t = 1] and t = E (K t,a t,s t = 1), where e is the elite s rent-seeking strategy (which the citizens take as given). If indifferent between revolting or not, we assume citizens choose to not revolt. Let rev(k t,a t, t ) be the solution to the maximization problem above given t. If x t = E and s t =0,then (8) V E (K t,a t )=V NR (K t,a t, t,k t+1 ) where t = E (K t,a t,s t = 0). and K t+1 solves K t+1 = E[A t+1 Kt+1 +1 a t,k t,s t = 0] where the expectation of A t+1 takes as given the elite s rent-seeking policy and the people s revolt decision in t +1. The payoff for citizens in the middle of political unrest is: (9) V U (K t,a t )= c U t + p D E[V D (K t+1,a t+1 ) a t ] + p E E[V E (K t+1,a t+1 ) a t ] + p U E[V U (K t+1,a t+1 ) a t ] where c U t =(1 )a t K t.

BUSINESS CYCLES WITH REVOLUTIONS 15 If x t = E, theoptimalrent-seekingproblemfortherulingeliteis: W (K t,a t,s t ) (10) = max t2[0, ] Pr[rev t = 0] Ct NR + E[W (K t+1,a t+1,s t+1 ) a t ] 1 Pr[rev t = 1] 1 where C NR t = a t K t /(1 ) Pr[rev t = 0] = 1 s t rev t (K t,a t, t )) Pr[rev t = 1] = s t rev t (K t,a t, t ). Let E (K t,a t,s t ) be the solution to this maximization problem. Remark 3. It is easy to see that if s t =0,thereisnothreatofrevolt,soelitessetmaximumrent-seekingtax E (K t,a t,s t = 0) =. But if s t =1,sinceelitesalwayswantstoavoidrevolt(recallweassume is sufficiently large), elites will set rent-seeking tax so that citizens are indifferent between revolting or not. Formally, E (K t,a t,s t = 1) solves: V NR (K t,a t, t,k t+1 )=V R (K t,a t,k t+1 ) where K t+1 solves K t+1 = E[A t+1 Kt+1 +1 a t,k t,s t = 1]. Definition. Arecursiveequilibriumconsistsofrent-seekingpolicy E (K, a, s), foreigninvestmentstrategy K 0 (K, a, s), revoltstrategyrev(k, a, K 0 ),valuefunctionsv x (K, a) for x 2 {E,U,D} and value functions V R (K, a, K 0 ) and V NR (K, a, K 0 ) such that: Rent-seeking policy solves the elite s maximization problem (10), Foreign investment strategy satisfies first order conditions (1), (2), (3), and Revolt strategy solves the people s maximization problem (7) (to revolt or not when s =1), Value functions satisfy equations (4), (5), (6), (7), (8), (9) and (10).

BUSINESS CYCLES WITH REVOLUTIONS 16 The key trade-off in this model is whether people should revolt or not. The difference in payoffs is: V R (K, a, K 0 ) V NR (K, a,,k 0 ) = (w NR w R ) {z } opportunity cost of revolting + p D E[V D (K 0,a 0 ) V E (K 0,a 0 ) a] + p U E[V U (K 0,a 0 ) V E (K 0,a 0 ) a]. where the first term captures the opportunity cost of revolting in period t: w NR w R =( )ak. We assume: >, so that there is a positive opportunity cost of revolting (otherwise people always revolt should there be a spark, and the problem is not interesting). Also, if the people are indifferent between revolting or not, we assume that they choose to revolt (this is not an essential assumption). 3.3. Results. Lemma 4. Assume a t = a =1for all t. Then there is an equilibrium revolution if and only if : (11) 1+ p U ( ) (K 1 p ss) E U {z } total expected cost of revolting pd < 1 [(K D ss) (K E ss) ] + p U p D 1 p D {z } total expected gain from revolting where K D ss is the steady state capital stock under permanent democracy, i.e.: 1/(1 ) Kss D =. (1 )(1 + ) and K E ss is the steady state capital stock under elite rule before any spark, i.e.: Kss E =[1 (p s +(1 p s ) ) ] K {z } ss. D expected "political distortion" Intuitively, this lemma states that there is equilibrium revolution if and only if people is not too impatient ( is not too small), the probability of unrest leading to democracy p D is not too small, and/or the productivity loss from revolting is not too large compared to (i.e., is not too large). From now on, we will assume that inequality (11) holds. Lemma 5. Assume a t = a =1for all t. Let t be the first period with a spark, i.e., s 0 = = s t period t. 1 =0and s t =1. Then people revolt in

BUSINESS CYCLES WITH REVOLUTIONS 17 Suppose the unrest resolves into a democracy in period t>t. Before the revolution, the capital stock is at the lower steady state K E ss, i.e.,k 0 = = K = K E ss. After unrest resolves into democracy, the capital stock increases to the higher steady state K D ss, i.e.,k +1 = K +2 = = K D ss >K E ss. Proposition 6. [Equilibrium revolution] There exists a threshold a(k t 1 ) > 0 such that: revolution breaks out in period t>0 if and only if (i) there is a spark in period t, s t =1, and (ii) the economic shock is sufficiently bad, a t apple a(k t 1 ). This proposition implies that a recession (in the sense that the exogenous technology shock is smaller than a certain threshold) necessary but not sufficient for revolution. It also implies that recession increases probability of revolution. Amplification and propagation. Consider two identical countries A and B, bothatkleptocraticsteadystate. In period t, theyexperiencethesameeconomicshock: a A t = a B t = a t,butonlycountryb receives a spark shock: s A t =0,s B t =1. If a t >a(k ss ), then same impulse response. If a t apple a(k ss ),thenverydifferent impulse responses and different propagation. See figure 1, 2 and 3. Figure 7. Response to technology shock in period t with and without a spark shock in period t. 3.4. Precautionary saving and asset pricing. 3.4.1. Precautionary saving (for a stormy day). So far we have abstained from the elite s inter-temporal problem. Now, we give the elite an opportunity to save. 3.4.2. Asset pricing with rare regime changes.

BUSINESS CYCLES WITH REVOLUTIONS 18 Figure 8. Response to spark shock in period t and exit to democracy in period T Figure 9. Response to spark shock in period t and exit back to elite rule in period T 4. Conclusion This paper strives for two contributions. First, it provides preliminary findings of the impacts of revolutions on the macroeconomy of developing countries. Second, it provides a simple dynamic stochastic general equilibrium of a small open economy with revolutions on the equilibrium path. This model allows us to analyze business cycles with revolutions and unrest. It reproduces stylized features of our empirical findings on the business cycles of developing countries under political transitions. As this paper is being written, we are working on improving our empirical analysis. We are extending our sample of revolutions by going back further in time. We are working on refining the timing of the beginning of each revolution. This is critical to estimating the endogeneity of revolutions in our VAR analysis. On the theoretical side, we are working on finding a numerical solution to the recursive equilibrium. The next

BUSINESS CYCLES WITH REVOLUTIONS 19 natural step would be to estimate the model s parameters from data. We would like to replicate the impulse responses to revolutions that our empirical analysis yields. We believe that exploring the sophisticated two-way relationship between political transitions (revolutions and democratizations, revolutionary civil wars and coups) and business cycles is an exciting avenue for future research, especially in light of the recent uprisings across the Arab World. This short paper attempts to be a building block in that wider project. References Acemoglu, D. and Robinson, J. (2000b). Why did the west extend the franchise? democracy, inequality, and growth in historical perspective. The Quarterly Journal of Economics, 115(4):1167 1199. Acemoglu, D. and Robinson, J. (2005). Economic origins of dictatorship and democracy. Cambridge University Press. Freund, C. and Jaud, M. (2013). Regime change, democracy and growth. Kent, L. and Phan, T. (2013a). Growth and arab spring revolutions. Technical report. Kent, L. and Phan, T. (2013b). Protest and repression: a model of the arab spring. Technical report. Khandelwal, P. and Roitman, A. (2013). The economics of political transitions: Implications for the arab spring. Papaioannou, E. and Siourounis, G. (2008). Democratisation and growth. The Economic Journal, 118(532):1520 1551. Rodrik, D. and Wacziarg, R. (2005). Do democratic transitions produce bad economic outcomes? The American economic review, 95(2):50 55. Appendix Proofs. Will be available in the next version of the working paper.