Evolution of Risk and Political Regimes

Transcription

1 Centre for Economic and Financial Research at New Economic School February 2010 Evolution of Risk and Political Regimes Maria Petrova Robert Bates Working Paper o 137 CEFIR / ES Working Paper series

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26 Besley, Timothy Principled Agents? The Political Economy of Good Government. Oxford: Oxford University Press. Besley, Timothy & Masayuki Kudamatsu Institutions and Economic Performance. Princeton University Press chapter Making Autocracy Work, pp Blundell, Richard W. & Stephen R. Bond Initial Conditions and Moment Restrictions in Dynamic Panel Models. Journal of Econometrics 87: Boix, Carles & Milan Svolik The Foundations of Limited Authoritarian Government: Institutions and Power-Sharing in Dictatorships. Papers Princeton University, Research Program in Political Economy. Collier, David & Steven Levitsky Democracy with Adjectives. World Politics 49: Cox, Gary Authoritarian Elections and Leadership Succession, Paper Presented to the 2009 Annual Meeting of he American Political Science Association. Easterly, William, Michael Kremer, Lant Pritchet & Lawrence Summers Good Policy or Good Luck? Country Growth Performance and Temporary Shocks. Journal of Monetary Economincs 32(3): EM-DAT The OFDA/CRED International Disaster Database.. URL: Epstein, David L.;, Robert H.; Bates, Jack; Goldstone, Ira; Kristensen & Sharyn O Halloran Democratic Transitions. American Journal of Political Science 59: Fearon, James & David Laitin Ethnicity, Insurgency, and Civil War. American Political Science Review 97(1):75 90.

27 Ferejohn, John Democracy, Accountability, and Representation. Cambridge University Press chapter Accountability and Authority: Toward a Theory of Political Accountability. Gandhi, Jennifer Political Instituions under Dictatorship. New York: Cambridge University Press. Gandhi, Jennifer & Adam Przeworski Authoritarian Institutions and the Survival of Autocrats. Comparative Political Studies 40(11): Gandhi, Jennifer & Przeworski Cooperation, Cooptation, and Rebellion under Dictaorships. Economics and Politics 18(1):1 26. Gates, Scott;, Nils Petter Gleditsch & Håvard Hegre Democratization in Eastern and Central Europe. Boulder, CO: East European Monographs chapter Democracy and Civil Con ict after the Cold War, pp Geddes, Barbara Paradigms and Sand Castles. Ann Arbor: University of Michigan Press. Gehlbach, Scott & Philip Keefer Investment without Democracy: Ruling Party Institutuonalization and Credible Commitment in Autocracies. Working Paper. Gehlbach, Scott & Philip Keefer Private Investment and the Institutionalization of Collective Action in Autocracies: Ruling Parties, Militaries and Bureacracies. Paper Presented to the 2009 Annual Meeting of he American Political Science Association. Glaeser, Edward L., Rafael La Porta, Florencio Lopez de Silanes & Andrei Shleifer Do Institutions Cause Growth? Journal of Economic Growth 9(3): Goldstone, Jack, Monty Marshall, Robert Bates & David Epstein State failure task force project, phase iii report. McLean, VA: Science Applications International Corporation. Haber, Stephen The Oxford Handbook of Political Economy. Oxford University Press chapter Authoritarian Government.

28 Haber, Stephen, Armando Razo & Noel Maurer he Politics of Property Rights: Political Instability, Credible Commitments, and Economic Growth in Mexico, New York: Cambridge University Press. Hausman, Ricardo, Lant Pritchett & Dani Rodrik Growth accelerations. Journal of Economic Growth 10: Hegre, Håvard The Duration and Termination of Civil War. Journal of Peace Research 41(3): Holmstrom, Bengt Moral hazard and observability. Bell Journal of Economics 10(1): Humphreys, Macartan & Robert H. Bates Political Institutions and Economic Policies. British Journal of Political Science 35(3): Huntington, Samuel P The Third Wave. Norman, OK: Oklahoma University Press. ICRG Dataset on country risks.. Jerzmanowski, Michal Empirics of hills, plateaus, mountains and plains: A Markov-switching approach to growth. Journal of Development Economics 81(2): Johnson, Simon, Peter Boone, Alasdair Breach & Eric Friedman Corporate governance in the Asian nancial crisis. Journal of Financial Economics 58(1-2): Jones, Benjamin F. & Benjamin A. Olken Do Leaders Matter? National Leadership and Growth Since World War II. The Quarterly Journal of Economics 120(3): Keefer, Philip & Steven Knack. N.d. The political dimension of economic growth. chapter Political stability and economic stagnation.

29 Kenyon, Thomas & Megumi Naoi Policy Uncertainty in Hybrid Regimes - Evidence from Firm Level Surveys. Comparative Political Studies 43(6). Kiewiet, D. Roderick & Douglas Rivers A Retrospective on Retrospective Voting. Political Behavior 6: Knack, Stephen & Philip Keefer Institutions and Economic Performance: Cross-Country Tests Using Institutional Measures. Economics and Politics 7(3): Knack, Stephen & Philip Keefer IRIS-3: File on International Country Risk Guide (ICRG) Data. 3rd Edition.. Levitsjy, Steven & Lucan Way The Rise of Competitive Authoritarianism. Journal of Democracy 13(2): Lipset, Seymour Martin Political Man. Garden City NY: Doubleday. Magaloni, Beatriz Voting for Autocracy. New York: Cambridge University Press. Marshall, Monty G. & Keith Jaggers Polity IV Project: Political Regime Characteristics and Transitions, URL: Nickel, Stephen Biases in Dynamic Models with Fixed E ects. Econometrica 49:1417½U1426. North, Douglas C. & Barry R. Weingast Constitutions and Commitment: The Evolutions of Institutions Governing Public Choice in Seventeenth-Century England. Journal of Economic History 69: Paltseva, Elena Autocracy, Devolution and Growth. Working Paper. Persson, Torsten & Guido Tabellini Political Economics. Cambridge, MA: MIT Press.

30 Pop-Eleches, Grigore & Graeme Robertson Elections, Information, and Liberalization in the Post-Cold War Era. Paper presented at the 2009 Annual Meeting of American Political Science Association. Pritchett, Lant Understanding Patterns of Economic Growth: Searching for Hills among Plateaus, Mountains, and Plains. World Bank Economic Review 14(2): Przeworski, Adam, Michael Alvarez, Jose Antonio Chiebub & Fernando Limongi Democracy and Development. New York: Cambridge University Press. Rodrik, Dani Policy Uncertainty and Private Investment in Developing Countries. Journal of Development Economics 36(2): Wolfers, Justin Are Voters Rational? Evidence from Gubernatorial Elections. Research papers Stanford University, Graduate School of Business.

31 Figure 1. World Democratization Trends, Reproduced from Epstein, Bates, et al. (2006) Log GDP per capita, PPP, in ZAR HTI SDN MLI LUX USA SGP CHE HKG BEL DNK CAN AUT JPN FRA NOR AUSITA ISL ARE SWE FIN GBR NLD KWT ISR NZL IRL QAT BHR ESP PRT MLT GRC KOR BHS CHL OMN SAU CZE ARG URY VEN MEX CRI COL BWA GAB PAN ZAF MYS TTOTHA HUN BRA IRN TUR POL TUN ECU BGR PER DOM DZA ROM RUS GTM JORPRYJAM PHL SUR SYR MAR IDN SLV BOL GUY EGY CHN AGO HND ZWE LKA NIC CMR GIN COG SEN CIV PAK GHA VNM MNG GMB IND TGO KEN UGA MDG BFA BGD NGA ZMB NER YEM MOZ MWI SLE ETH Avg. Protection Against Risk of Expropriation, Figure 2. Reproduced from Acemoglu, Daron, Simon Johnson and James A. Robinson (2001) The Colonial Origins of Comparative Development: An Empirical Investigation American Economic Review, 91, TZA

32 θ= θ H Do not predate, y=1 Government Predate yy=1 Nature yy=0 People People People Nature Overthrow Do not overthrow success failure Next period, new government Nature θ= θ L Government Nature Do not predate Predate, y=0 yy=1 yy=0 People Expropriate People People People attempt to overthrow the government Do not overthrow Overthrow Nature failure success Next period, the same government Next period, new government Figure 3. Timing of the first period of stage game. The part of the tree with a short-horizon government is not depicted. Density Polity Density Democracy Figure 4. Histogram of Polity variable, Figure 5. Histogram of Democracy variable, (Polity=Democracy-Autocracy) Source: Polity IV Project Source: Polity IV Project Density Autocracy Figure 6. Histogram of Autocracy variable, Source: Polity IV Project

33 Variance of expropriation risk Intermediate regimes Autocracies Democracies Figure 7. Variance of expropriation risk, by regime type, Source: IRIS-3, Polity IV Project, authors calculations Intermediate regimes 40 Autocracies Democracies 10 0 Figure 8. Variance of growth rate, by regime type. Source: WDI 2005, Polity IV Project, authors calculations.

34 Expropriation risk Autocracy Intermediate Regime Democracy -2 Economic Risk Autocracy Intermediate Regime Democracy -10 Risk of repudiation of contracts Autocracy Intermediate Regime Democracy Financial Risk Autocracy Intermediate Regime Democracy -10 Figure 9. Regression coefficients for collapse effect on risk variables as a function of political regime. Based on the regression from table 6.

35 Table 1. Negative economic shocks, by region, World Bank region Number of collapses Unconditional probability of having collapse Australia and Oceania Center, South and East Asia Eastern Europe/Former USSR Latin America North Africa/Middle East Sub-Saharian Africa Western Europe/North America Total Source: WDI 2005, authors calculations Table 2. Average growth variables for economic shocks, by region, WB Region Average growth before Average growth after Average growth change Australia and Oceania Center, South and East Asia Eastern Europe/Former USSR Latin America North Africa/Middle East Sub-Saharian Africa Western Europe/North America Total Source: WDI 2005, authors calculations Table 3. Natural disasters counted for disaster variable Disaster type Occurrence, Earthquake 590 Drought 496 Extreme Temperature 223 Flood 1978 Slides 343 Volcano 104 Wave / Surge 15 Wind Storm 1685 Source: Emergency Disasters Database, EM-DAT 2006

36 Table 4. Summary statistics and sources of data Variable Source Observations Mean Std. Dev. Min Max Expropriation risk IRIS Risk of repudiation of IRIS contracts Economic risk ICRG Financial risk ICRG Government stability ICRG Polity Polity IV Autocracy dummy Polity IV, calculations Intermediate regime dummy Polity IV, calculations Democracy dummy Polity IV, calculations Collapse dummy WDI 2005, calculations Collapse in previous 3 years WDI 2005, calculations Natural disasters EM-DAT, calculations Natural disasters in previous EM-DAT, years calculations Negative term of trade shock Rodrik (1999), dummy calculations Negative term of trade shocks Rodrik (1999), in previous 3 years calculations Log (GDP per capita) WDI Openness WDI Log (Population) WDI Vulnerability to natural EM-DAT, disasters calculations Government change dummy Leadership duration database, PITF

37 Table 5. Risk variables and economic shocks, FE. Economic shocks are instrumented by natural disasters and terms of trade shocks Expropriation risk, t+1 Risk of repudiation of ICRG Economic ICRG Financial Risk, t+1 contracts, t+1 Risk, t+1 Economic shock in years t, t-1, or t-2 [2.56]** [2.23]** [2.92]*** [2.51]** Log GDP pc, lagged 3 years [5.40]*** [7.89]*** [8.78]*** [7.04]*** Openness, lagged 3 years [0.62] [0.89] [2.38]** [1.72]* Year [10.11]*** [9.38]*** [2.25]** [0.14] Log (Population) lagged 3 years [0.54] [0.20] [0.46] [0.22] Expropriation Risk, lagged 3 years [2.73]*** Risk of repudiation of contracts, l. 3years [1.34] ICRG Economic Risk, lagged 3 years [11.89]*** ICRG Financial Risk, lagged 3 years [2.84]*** Observations Number of countries Absolute value of z statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

38 Table 6. Risk variables and economic shocks, with interactions, FE Economic shocks are instrumented by natural disasters and terms of trade shocks Expropriation risk, t+1 Risk of repudiation of ICRG Economic ICRG Financial Risk, t+1 contracts, t+1 Risk, t+1 Shock*Autocracy [1.20] [1.47] [0.52] [0.92] Shock*Intermediate Regime [2.69]*** [1.87]* [3.20]*** [2.88]*** Shock*Democracy [0.75] [0.07] [1.21] [0.40] Autocracy [0.28] [0.53] [0.84] [0.28] Intermediate Regime [2.02]** [0.84] [0.77] [0.74] Log GDP pc, lagged 3 years [3.13]*** [2.37]** [1.41] [3.02]*** Openness, lagged 3 years [0.60] [0.76] [1.41] [1.59] Year [1.68]* [2.17]** [1.20] [0.72] Log (Population) lagged 3 years [3.89]*** [4.51]*** [1.28] [7.39]*** Expropriation Risk, lagged 3 years [2.18]** Risk of repudiation of contracts, l. 3years [2.30]** ICRG Economic Risk, lagged 3 years [0.99] ICRG Financial Risk, lagged 3 years [2.88]*** Observations Number of countries Absolute value of z statistics in brackets * significant at 10%; ** significant at 5%; *** significant at 1%

39 APPENDIX Lemma 3 (Full version of lemma 2) At t = 2, in a continuation game with the old government, the set of equilibria is the following: 1. For R > (B + R)(1 p H ) : If y 1 = 0, equilibrium strategies are x H2 = 1, x L2 = 1, and sj1 = not overthrow; sj0 = overthrow; If x H1 = 1, x L1 = 0, and y 1 = 1 then x H2 = 1, x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if 2. If (B + R)p L < R < (B + R)(1 p H ) : p L p H (1 p H ) > 1. If y 1 = 0, equilibrium strategies are x H2 = 1, x L2 = 1, and sj1 = not overthrow; sj0 = overthrow; If y 1 = 1, x H1 = 1, and x L1 = 0 then x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L ph (1 )p L +p H (1 )p H (1 p H ) > 1. If y 1 = 1, x H1 = 0, and x L1 = 0 then x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if 1 3. If (B + R)p L > R : (1 c 1)(1 p H ) p L (+(1 )p H ) > 1. If y 1 = 0 and x H1 = 1, equilibrium strategies are x H2 = 0, x L2 = 0, and sj1 = not overthrow; sj0 = overthrow; If y 1 = 0, x H1 = 0, and x L1 = 1, strategies x H2 = 0, x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute equilibrium in a continuation game only if = 1 (1 )(1 p H)+1 ; p L ( c 1+(1 c 1)p H)(1 )(1 p H ) < 1, here If y 1 = 0, x H1 = 0, and x L1 = 0, strategies x H2 = 0, x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute equilibrium in a continuation game only if = + (1 p H )(1 ) (1 )(1 p L ) ; 1 p L (1 )(1 p H ) p L +(1 c 1)p H < 1; here If y 1 = 0, x H1 = 1, and x L1 = 0, strategies x H2 = 0, x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute equilibrium in a continuation game only if p +(1 ) H ; p H +(1 )p L (1 c 1p L )p L (1 c 1)(1 p H )p H < 1; here c 1 =

40 If y 1 = 0, x H1 = 0, and x L1 = 0, strategies x H2 = 0, x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute equilibrium in a continuation game only if 1 = p +(1 ) H ; +(1 )p L p L (1 )(1 p H ) (+(1 )p H ) > 1; here 4. For any, if x H1 = 1, x L1 = 0 or 1, and y 1 = 1, then s 1 j1 = s 1 j0 = not overthrow, x H2 = 1, and x L2 = 1 constitute equilibrium in a continuation game; 5. For any, if x H1 = 0, x L1 = 0, and y 1 = 1, then x H2 = 1, and x L2 = 1, and sj1 = sj0 = not overthrow constitute equilibrium in a continuation game. 6. For any, if x H1 = 0, x L1 = 0, and y 1 = 1; then x H2 = 1, x L2 = 1, and sj1 = sj0 = not overthrow constitute equilibrium in a continuation game if Proof of Lemma 1. p L p H (1 p H ) > 1. Consider a subgame at t = 2 if a new government comes to power. For any government from the pool of possible governments, the prior probability that a government has high competence is, while the prior probability that a government has a long time horizon is. As we are looking for the equilibrium in pure strategies, the government s strategy P r(xj; t = 2) can be written as x 2 2 f0; 1g, where is the type of the government. This notation refers only to the government with a long time horizon, as all governments with a short time horizon predate in all states of the world. The outcome y = 1 is possible if: (1) competence = H, discount =, and predation x = 1, (2) competence = H, discount =, and predation x = 0, (3) competence = H, discount = 0, and predation x = 1, (4) competence = L, discount =, and predation x = 0. The outcome y = 0 is possible in the following cases: (1) competence = H, discount =, and predation x = 1, (2) competence = H, discount = 0, and predation x = 1, (3) competence = L, discount =, and predation x = 0, (4) competence = L, discount =, and predation x = 1, and (5) competence = L, discount = 0, and predation x = 1. Probabilities of these outcomes depend on people s prior beliefs about the types of a government and on the government s strategy. People s posterior beliefs about the government s competence are computed by Bayesian formula: c 2 j y=1 = x H2 p H +(1 x H2 )+(1 )p H x H2 p H +(1 x H2 )+(1 )p H +(1 )(1 x L2 )p L c 2 j y=0 = x H2 (1 p H )+(1 )(1 p H ) x H2 (1 p H )+(1 )(1 p H )+(1 )(1 x L2 )(1 p L )+(1 )x L2 +(1 )(1 )

41 Now consider four possible pure strategy pro les of a government at t = 2: x H2 = 1; x L2 = 1; x H2 = 1; x L2 = 0; x H2 = 0; x L2 = 1; x H2 = 0; x L2 = 0. The rest of the proof is organized as follows. First, for each strategy of a government, we nd people s best response to this strategy. Second, we check if the original strategy pro le of a government is still a best response to people s strategy, i.e. if a proposed pair of strategies constitute an equilibrium in this game. Note that everywhere it is optimal for people to change the government if their posterior that the government has high competence is lower than. Similar, it is optimal to keep the government if people s posterior that the government has high competence is higher than. (1) Assume that x H2 = 1; x L2 = 1. People s posteriors about the government s competence are c 2 j y=1 = p H (1 p p H = 1 >, c 2 j y=0 = H ) (1 p H )+(1 ) = (1 p H) p H +1 <. Therefore, the optimal response of people to the assumed government s strategy is sj1 = not overthrow; sj0 = overthrow. The payo s of di erent types of the government given the people s strategy are following. For = H, the payo from predation is U( H jx = 1) = B +R+ (p H (B + R) + (1 p H )(1 )(B + R)), and the payo from restraint is U( H jx = 0) = B+(B+R). So, for a high-competent government, predation is pro table if R > (1 Similarly, for = L, the payo from predation is U( L jx = 1) = B + R + (1 p H )(B+R). )(B + R), and the payo from restraint is U( L jx = 0) = B + (p L (B + R) + (1 p L )(1 )(B + R)). Therefore, a low-competent government predates if R > p L (B + R): As 1 sj0 = overthrow constitute equilibrium if R > (1 p H > p L, strategy pro les x H2 = 1; x L2 = 1; and sj1 = not overthrow; p H )(B + R). (2) Assume that x H2 = 1; x L2 = 0. People s posteriors about the government s competence are c 2 j y=1 = p H (1 p p H +(1 )p L = +(1 ) p L >, c 2 j y=0 = H ) ph (1 p H )+(1 )(1 p L )+(1 )(1 ) = <. Therefore, the optimal response of people to the assumed government s strategy is sj1 = not overthrow; sj0 = +(1 ) 1 p L 1 p H overthrow. For a high-competent government, predation is pro table if R > (1 p H )(B +R). Similarly, a low-competent government predates if R > p L (B + R): As 1 p H > p L, strategy x L2 = 0 is not optimal for a low-type government, and for any parameter values x H2 = 1; x L2 = 0 is not the part of an equilibrium. (3) Assume that x H2 = 0; x L2 = 1. People s posteriors about the government s competence are c 2 j y=1 = +(1 )p H +(1 )p H = 1 >, c 2 j y=0 = (1 )(1 p H ) (1 )(1 p H )+1 = +(1 ) 1 (1 )(1 p H ) <. Therefore, the optimal response of people to the assumed government s strategy is sj1 = not overthrow; sj0 = overthrow. As before, for a high-competent government, predation is pro table if R > (1 = L, predation is optimal if R > p L (B +R): As 1 p H )(B + R). Similarly, for p H > p L, strategy pro les x H2 = 0; x L2 = 1; and sj1 = not

42 overthrow; sj0 = overthrow constitute equilibrium if p L (B + R) < R < (1 p H )(B + R). (4) Assume that x H2 = 0; x L2 = 0. People s posteriors about the government s competence are c 2 j y=1 = +(1 )p H +(1 )p H +(1 )p L = + (1 )p L c 2 j y=0 = +(1 )p H > (as p L <, and, therefore, p L < + (1 ) p H ), (1 )(1 p H ) (1 )(1 p H )+(1 )(1 p L ) = 1 p +(1 ) L (1 )(1 p H ) < (as 1 > 1 p H, and 1 p L > 1 ). Therefore, the optimal response of people to the assumed government s strategy is sj1 = not overthrow; sj0 = overthrow. As before, for a high-competent government, predation is pro table if R > (1 p H )(B + R), and for a low-competent government, the predation is pro table if R > p L (B + R): As a result, the strategy pro les x H2 = 0; x L2 = 0; and sj1 = not overthrow; sj0 = overthrow constitute equilibrium if p L (B + R) > R. Proof of Lemma 2. After the rst period, the people s posterior beliefs that the government has high competence depend on the government strategy in the rst period. Similar to the case of a new government in the second period, these beliefs can be computed by Bayesian updating: j y1=1 = x H1 p H +(1 x H1 )+(1 )p H x H1 p H +(1 x H1 )+(1 )p H +(1 )(1 x L1 )p L j y1=0 = x H1 (1 p H )+(1 )(1 p H ) x H1 (1 p H )+(1 )(1 p H )+(1 )(1 x L1 )(1 p L )+(1 )x L1 +(1 )(1 ) For x H1 = 1, x L1 = 1, these beliefs are j y1=1 = 1 and j y1=0 = p H p H +(1 )p L = (1 p H ) (1 p H )+(1 ) <. +(1 ) p L For x H1 = 1, x L1 = 0, these beliefs are j y1=1 = > and j y1=0 = ph (1 p H ) (1 p H )+(1 )(1 p L )+(1 )(1 ) = <. +(1 ) 1 p L 1 p H For x H1 = 0, x L1 = 1, these beliefs are j y1=1 = 1 > and j y1=0 = (1 )(1 p H) (1 )(1 p H )+1 = 1 +(1 ) (1 )(1 p H ). For x H1 = 0, x L1 = 0, these beliefs are j y1=1 = < + (1 ) p H ), and j y1=0 = 1 p L > 1 ). +(1 )p H +(1 )p H +(1 )p L = (1 )(1 p H ) (1 )(1 p H )+(1 )(1 p L ) = 1 p +(1 ) L (1 )(1 p H ) > (as p + (1 )p L L +(1 )p H < (as 1 > 1 p H, and Now, we look separately at the cases of y = 0 and y = 1 and analyze which equilibria might be supported for di erent strategies of the government in the rst period. 1. Assume that y = 0, x H1 = 1, and x L1 = 1. Here j y1=0 = (1 p H) 1 p H <, c 1 j y1=0 =. If x H2 = 1, and x L2 = 1, the posterior beliefs of people about the government s competence are c 2 j y2=1 = 1 and c 2 j y2=0 = (1 p H) p H +1 < <. Then the optimal strategy of people is sj1 = not <

43 overthrow; sj0 = overthrow. Therefore, as calculations in the proof of Lemma 1 show, strategies x H2 = 1, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if R > (1 p H )(B + R). If x H2 = 1, and x L2 = 0, the posterior beliefs of people about the government s competence are c 2 j y2=1 = +(1 ) c = 1 p L ph +(1 c 2 j y2=1 is smaller than if p ) L p H (1 p H ) p L < and c 2 j y2=0 = p H (1 p H ) > 1, and higher than if p L p H (1 strategy of people is sj1 = not overthrow; sj0 = overthrow if if +(1 ) 1 c 1 p L 1 p H < j y1=0 <. Note that p H ) > 1 < 1. Then the optimal p L p H (1 p H ) < 1 and s 1j1 = s 1 j0 = overthrow p L p H (1 p H ) > 1. In both cases, strategy x L2 = 0 is not optimal for a low-type government, and for any parameter values x H2 = 1; x L2 = 0 is not the part of an equilibrium. If x H2 = 0, and x L2 = 1, the posterior beliefs of people about the government s competence are c 2 j y2=1 = 1 and c 2 j y2=0 = +(1 ) 1 (1 c 1 )(1 p H ) < j y1=0 <. Then the optimal strategy of people is sj1 = not overthrow; sj0 = overthrow. Therefore, as calculations in the proof of Lemma 1 show, strategies x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) < R < (1 p H )(B + R). If x H2 = 0, and x L2 = 0, the posterior beliefs of people about the government s competence are c 2 j y2=1 = and c 2 j y2=0 = + (1 ) p L = (1 ) +(1 c + p L 1 )p H ( +(1 )p H )(1 p H ) 1 +(1 ) p L (1 )(1 p H ) > (as p L < 1 p H and c 1 < c 1 + (1 ) p H ) < j y1=0 <. Then the optimal strategy of people is sj1 = not overthrow; sj0 = overthrow:therefore, strategies x H2 = 0, and x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) > R. 2. Assume that y = 0, x H1 = 1, and x L1 = 0. Here j y1=0 = 1 p +(1 ) H (1 p H )+(1 )(1 p L ) <. +(1 ) 1 p L 1 p H <, and c 1 j y1=0 = If x H2 = 1, and x L2 = 1, the posterior beliefs of people about the government s competence are c 2 j y2=1 = 1 and c 2 j y2=0 = (1 p H) p H +1 < <. The optimal strategy of people is sj1 = not overthrow; sj0 = overthrow. Therefore, strategies x H2 = 1, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if R > (1 p H )(B + R). If x H2 = 1, and x L2 = 0, the posterior beliefs of people about the government s competence are c 2 j y2=1 = +(1 ) c = 1 p L ph +(1 ) c 1 p L (1 p L ) p H (1 p H ) and c 2 j y2=0 = +(1 ) 1 c 1 p L 1 p H < j y1=0 <.

44 Note that c 2 j y2=1 is higher than if p L(1 p L ) p H (1 p H ) > 1, and lower than if p L(1 p L ) p H (1 p H ) < 1. Then the optimal strategy of people is sj1 = not overthrow; sj0 = overthrow if c 1 p L(1 p L ) p H (1 p H ) > 1 and s 1 j1 = s 1 j0 = overthrow if c 1 p L(1 p L ) p H (1 p H ) < 1. In both cases, strategy x L2 = 0 is not optimal for a low-type government, and for any parameter values x H2 = 1; x L2 = 0 is not the part of an equilibrium. If x H2 = 0, and x L2 = 1, the posterior beliefs of people about the government s competence are c 2 j y2=1 = 1 and c 2 j y2=0 = +(1 ) 1 (1 c 1 )(1 p H ) < j y1=0 <. Then optimal strategy of people is sj1 = not overthrow; sj0 = overthrow. Therefore, strategies x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) < R < (1 p H )(B + R). If x H2 = 0, and x L2 = 0, the posterior beliefs of people about the government s competence are c 2 j y2=1 = + (1 ) p L = +(1 c + (1 ) p L (1 p L ) 1 )p H ( +(1 )p H )(1 p H ) c c 2 j y2=0 = 1 1 +(1 ) p L (1 )(1 p H ) > (as p L (1 p L ) < 1 p H and c 1 < c 1 +(1 )p H ) and < j y1=0 < (as 1 p L > 1 ). The optimal strategy of people is sj1 = not overthrow; sj0 = overthrow Therefore, strategies x H2 = 0, and x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) > R. 3. Assume that y = 0, x H1 = 0, and x L1 = 1. Here j y1=0 = 1 (1 )(1 p H)+1 <. +(1 ) 1 (1 )(1 p H ) <, j y1=0 = If x H2 = 1 and x L2 = 1 then c 2 j y2=1 = 1 and c 2 j y2=0 = (1 p H) p H +1 <. Then strategies x H2 = 1, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if R > (1 p H )(B + R). If x H2 = 1 and x L2 = 0, then c 2 j y2=1 = +(1 ) c = 1 p L ph (1 ) + (1 p H )(1 ) c 1 p L ph and c 2 j y2=0 = +(1 ) 1 c 1 p L 1 p H < j y1=0 <. If c 2 j y2=1 >, the optimal strategy of people is sj1 = not overthrow; sj0 = overthrow and if c 2 j y2=1 <, the strategy of people is s 1 j1 = s 1 j0 = overthrow. In both cases, x H2 = 1; x L2 = 0 is not the part of an equilibrium. If x H2 = 0 and x L2 = 1, then c 2 j y2=1 = 1 and c 2 j y2=0 = +(1 ) 1 (1 c 1 )(1 p H ) < j y1=0 <. Then strategies x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) < R < (1 p H )(B + R).

45 If x H2 = 0 and x L2 = 0, then c 2 j y2=1 = 1 +(1 ) p L (1 )(1 p H ) p L + (1 ) p L = (1 ) +(1 c + p L 1 )p H ( +(1 )p H )(1 )(1 p H ) and c 2 j y2=0 = < j y1=0 < (as 1 p L > 1 ). Note that c 2 j y2=1 is higher than if ( +(1 c < 1, and lower than if 1p c L 1)p H)(1 )(1 p H ) strategy of people is sj1 = not overthrow; sj0 = overthrow if ( c 1+(1 c 1)p H)(1 )(1 p H ) p L ( c 1+(1 c 1)p H)(1 )(1 p H ) < 1 > 1. Then the optimal c and s 1 j1 = s 1 j0 = overthrow if 1p L ( +(1 c > 1. Note that x H2 = 0, and x L2 = 0 are not 1)p H)(1 )(1 p H ) best responses to s 1 j1 = s 1 j0 = overthrow. As a result, strategies x H2 = 0, and x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game only if p L (B + R) > R and p L ( c 1+(1 c 1)p H)(1 )(1 p H ) < 1: 4. Assume that y = 0, x H1 = 0, and x L1 = 0. Here j y1=0 = + (1 p H) (1 ) (1 )(1 p L ) <. +(1 1 p ) L (1 )(1 p H ) <, j y1=0 = If x H2 = 1 and x L2 = 1 then c 2 j y2=1 = 1 and c 2 j y2=0 = (1 p H) p H +1 <. Then strategies x H2 = 1, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if R > (1 p H )(B + R). If x H2 = 1 and x L2 = 0, then c 2 j y2=1 = +(1 ) c = 1 p L ph (1 ) 1 p + L (1 p H ) (1 ) c 1 p L ph and c 2 j y2=0 = +(1 ) 1 c 1 p L 1 p H < j y1=0 <. If c 2 j y2=1 >, the optimal strategy of people is sj1 = not overthrow; sj0 = overthrow and if c 2 j y2=1 <, the strategy of people is s 1 j1 = s 1 j0 = overthrow. In both cases, x H2 = 1; x L2 = 0 is not the part of an equilibrium. If x H2 = 0 and x L2 = 1, then c 2 j y2=1 = 1 and c 2 j y2=0 = +(1 ) 1 (1 c 1 )(1 p H ) < j y1=0 <. Then strategies x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) < R < (1 If x H2 = 0 and x L2 = 0, then c 2 j y2=1 = 1 +(1 ) p L (1 )(1 p H ) p H )(B + R). + (1 ) p L = +(1 )p H + (1 ) p L (1 p L ) ( +(1 )p H )(1 )(1 p H ) and c 2 j y2=0 = < j y1=0 < (as 1 p L > 1 ). Note that c 2 j y2=1 is higher than if p L + (1 ) p H 1 p L (1 ) (1 p H ) < 1

46 and lower than if p L +(1 c 1)p H 1 p L not overthrow; sj0 = overthrow if 1 p L (1 )(1 p H ) (1 )(1 p H ) > 1. Then the optimal strategy of people is sj1 = p L 1 p L +(1 )p H (1 )(1 p H ) < 1 and s 1 j1 = s 1 j0 = overthrow if p L +(1 c 1)p H > 1. Note that x H2 = 0, and x L2 = 0 are not best responses to s 1 j1 = s 1 j0 = overthrow. As a result, strategies x H2 = 0, and x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game only if p L (B+R) > R and 1 p L (1 )(1 p H ) p L +(1 c 1)p H < Assume that y = 1, x H1 = 1, and x L1 = 1. Here j y1=1 = 1 >, c 1 j y1=1 =. For any strategy of the government in the second period, posterior beliefs about the government s competence are c 2 j y2=1 = 1 and c 2 j y2=0 = 1. Therefore, the optimal strategy for people is s 1 j1 = s 1 j0 = not overthrow, and x H2 = 1, and x L2 = 1 is the government s optimal response to that. So, the strategies s 1 j1 = s 1 j0 = not overthrow, x H2 = 1, and x L2 = 1 constitute equilibrium in a continuation game. 6. Assume that y = 1, x H1 = 1, and x L1 = 0. Here j y1=1 =. +(1 ) p L >, c 1 j y1=0 = ph +(1 ) p H > p H +(1 )p L If x H2 = 1, and x L2 = 1, then c 2 j y2=1 = 1 and c 2 j y2=0 = (1 p H) 1 p H = c 2 j y2=0 is higher than if p L p H (1 p H ) < 1, and lower than if p L p H (1 of people is sj1 = not overthrow; sj0 = overthrow if if p H ) p +(1 ) L p H (1 p H ). Note that > 1. Then the optimal strategy p L p H (1 p H ) < 1 and s 1j1 = s 1 j0 = not overthrow p L p H (1 p H ) > 1. Therefore, strategies x H2 = 1, x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if R > (1 p H )(B + R) and strategies x H2 = 1, x L2 = 1, and s 1 j1 = s 1 j0 = not overthrow constitute equilibrium if If x H2 = 1, and x L2 = 0, then c 2 j y2=1 = p L p H (1 p H ) > 1, while p L p H (1 p H ) < 1. c +(1 ) c > c 1 p L 1 > and c 2 j y2=0 = 1 ph +(1 ) 1 p L = 1 p H +(1 ) p L ph 1 p L. If c 2 j y2=0 >, the optimal strategy of people is sj1 = sj0 = not overthrow 1 p H and if c 2 j y2=0 <, the strategy of people is sj1 = not overthrow; sj0 = overthrow. In both cases, x H2 = 1; x L2 = 0 is not the part of an equilibrium. If x H2 = 0, and x L2 = 1, then c 2 j y2=1 = 1 and c 2 j y2=0 = + (1 ) 1 (1 c 1)(1 p H ) = + (1 ) p L ph (1 )p L +p H (1 )p H (1 p H ) If c 2 j y2=0 >, the optimal strategy of people is sj1 = sj0 = not overthrow and if c 2 j y2=0 <, the strategy of people is sj1 = not overthrow; sj0 = overthrow. If sj1 = sj0 = not overthrow, the strategy

47 x H2 = 0 and x L2 = 1 is not a best response. Therefore, strategies x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) < R < (1 p H )(B + R) and p L ph (1 )p L +p H (1 )p H (1 p H ) > 1. If x H2 = 0, and x L2 = 0, then c 2 j y2=1 = + (1 ) p L +(1 c 1 )p H > > and c 2 j y2=0 = + (1 ) 1 c 1p L (1 c 1)(1 p H ) = + (1 ) (1 p L )p L (1 )(1 p H )p H Note that c 2 j y2=0 is higher than if (1 c 1p L )p L (1 c 1)(1 p H )p H < 1, and lower than if (1 c 1p L )p L (1 c 1)(1 p H )p H.Then the (1 optimal strategy of people is sj1 = not overthrow; sj0 = overthrow if p L )p L (1 c < 1 and s 1 j1 = 1)(1 p H )p H (1 s 1 j0 = not overthrow if p L )p L (1 c > 1. Therefore, strategies x H2 = 0, and x L2 = 0, and sj1 = not 1)(1 p H )p H overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) > R and (1 c 1p L )p L (1 c 1)(1 p H )p H < Assume that y = 1, x H1 = 0, and x L1 = 1. Here j y1=1 = 1 >, c 1 j y1=1 = +(1 )p H <. For any strategy of the government in the second period, posterior beliefs about the government s competence are c 2 j y2=1 = 1 and c 2 j y2=0 = 1. Therefore, the optimal strategy for people is s 1 j1 = s 1 j0 = not overthrow, and x H2 = 1, and x L2 = 1 is the government s optimal response to that. So, the strategies s 1 j1 = s 1 j0 = not overthrow, x H2 = 1, and x L2 = 1 constitute equilibrium in a continuation game. 8. Assume that y = 1, x H1 = 0, and x L1 = 0. Here j y1=1 =. >, c 1 j y1=1 = +(1 ) +(1 )p H + (1 )p L If x H2 = 1 and x L2 = 1 then c 2 j y2=1 = 1 and c 2 j y2=0 = (1 p H) p H +1 = (1 )p + L (+(1 )p H )(1 p H ) p H > +(1 )p L Then strategies x H2 = 1, and x L2 = 1, and sj1 = sj0 = not overthrow constitute an equilibrium in a continuation game. ) p L If x H2 = 1 and x L2 = 0, then c 2 j y2=1 = > c +(1 1 > and c 2 j y2=0 = ph If c 2 j y2=1 >, the optimal strategy of people is sj1 = sj0 = not overthrow and if c 2 j y2=1 <, the >. +(1 ) 1 p L. 1 p H strategy of people is sj1 = not overthrow; sj0 = overthrow. In both cases, x H2 = 1; x L2 = 0 is not the part of an equilibrium.

48 If x H2 = 0 and x L2 = 1, then c 2 j y2=1 = 1 and c 2 j y2=0 = +(1 ) 1 (1 c 1 )(1 p H ) = 1 p +(1 ) L (1 )(1 p H ) (+(1 )p H ) If c 2 j y2=0 <, the optimal strategy of people is sj1 = not overthrow; sj0 = overthrow and if c 2 j y2=1 >, the strategy of people is s 1 j1 = s 1 j0 = not overthrow. Then strategies x H2 = 0, and x L2 = 1, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B+R) < R < (1 p H )(B + R) and 1 (1 c 1)(1 p H ) If x H2 = 0 and x L2 = 0, then c 2 j y2=1 = (1 ) p L ) p L (1 )(1 p H ) +(1 p L (+(1 )p H ) > 1. + (1 ) p L +(1 c 1 )p H > j y1=1 > and c 2 j y2=0 = 1 +(1 ) p L (1 )(1 p H ). If c 2 j y2=0 <, the optimal strategy of people is sj1 = not overthrow; +(1 )p H sj0 = overthrow and if c 2 j y2=1 >, the strategy of people is s 1 j1 = s 1 j0 = not overthrow. Therefore, strategies x H2 = 0, and x L2 = 0, and sj1 = not overthrow; sj0 = overthrow constitute an equilibrium in a continuation game if p L (B + R) > R and (1 p L ) (1 )(1 p H ) p L +(1 )p H > 1. = Proof of Proposition 1. We consider the case of the following equilibrium in a continuation game: after observing y 1 = 0, citizens play s 1 j1 = not overthrow; s 1 j0 = overthrow for any government s strategy in the rst period, while after observing y 1 = 1, citizens play s 1 j1 = s 1 j0 = not overthrow for any government s strategy in the rst period. Equilibrium strategies of the government in the second period after y 1 = 0 are computed conditional on. Continuation payo s of the government after the rst period depend on its strategy in the rst period and the realization of policy outcome in the rst period. Denote V type;w;y1 a continuation payo for type type after observing y 1 following strategy pro le w 2 f00; 01; 10; 11g of governments in the rst period. We are looking for Perfect Bayesian equilibrium. To nd all pure strategy equilibrium, the strategy of each type of the government should be a best response to the strategy of the other type of the government given beliefs. Payo s of the government are the following: U H (x H1 = 1; x L1 = 1) = B + R + (p H V H;11;1 + (1 p H )(1 )V H;11;0 ) U L (x H1 = 1; x L1 = 1) = B + R + (1 ) V L;11;0 U H (x H1 = 1; x L1 = 0) = B + R + (p H V H;10;1 + (1 p H )(1 )V H;10;0 ) U L (x H1 = 1; x L1 = 0) = B + (p L V L;10;1 + (1 p L )(1 )V L;10;0

49 U H (x H1 = 0; x L1 = 1) = B + V H;01;1 U L (x H1 = 0; x L1 = 1) = B + R + (1 ) V L;01;0 U H (x H1 = 0; x L1 = 0) = B + V H;00;1 U L (x H1 = 0; x L1 = 0) = B + (p L V L;00;1 + (1 p L )(1 )V L;00;0 Continuation payo s are the following: V H;11;1 = V H;01;1 = V H;00;1 = (1 + ) [B + R] 8 B + R + (p >< H + (1 p H )(1 )) [B + R] if R > (1 p H )(B + R) V H;11;0 = V H;10;1 = V H;10;0 = B + [B + R] if p L (B + R) < R < (1 p H )(B + R) >: B + [B + R] if R < p L (B + R) V L;11;0 = V L;10;0 = V L;10;1 = V L;01;0 = V L;00;1 = 8 B + R + (1 ) [B + R] if R > (1 p >< H )(B + R) =V L;00;0 = B + R + (1 ) [B + R] if p L (B + R) < R < (1 p H )(B + R) >: B + (p L + (1 p L )(1 )) [B + R] if R < p L (B + R) The best response of a high-competent government to x L1 = 1 is x H1 = 1 if B + R + (p H V H;11;1 + (1 p H )(1 )V H;11;0 ) > B + V H;01;1 i.e. if R + (1 p H )(1 )V H;11;0 > (1 p H )V H;11;1. For R < (1 p H )(B + R), this condition is equivalent to R (1 p H ) + (1 ) (B + [B + R]) > (1 + ) [B + R] ; i.e. < 1 + R (1+)[B+R] (1 p H ) (B+[B+R]) = h (1 ph )(B+R) R ; R(1 (1 p H )) (B+[B+R])(1 p H ). In other words, the best response to x L1 = 1 is x H1 = 1 if 2 R R (1 p H ) (B+[B+R]) = R(1 (1 p H )) (B+[B+R])(1 p H ) For R > (1 p H )(B + R), condition R + (1 p H )(1 )V H;11;0 > (1 p H )V H;11;1 is equivalent to R + (1 p H )(1 ) (B + R + (p H + (1 p H )(1 )) [B + R]) > (1 p H )(1+) [B + R], i.e. (1 ) 2 2 (1 p H ) 2 [B + R]+ (1 )(1 p H )(B + R)(1 + p H ) + R (1 p H )(1 + ) [B + R] > 0. Taking into account that is probability and belongs to [0; 1] interval, the latest condition is equivalent to > 1 2, where 2 is a positive solution of equation (1 ) 2 (1 p H ) + (1 )(1 + p H ) + R=(B + R)(1 p H ) (1 + ) = 0. So, the best response to x L1 = 1 h n oi is x H1 = 1 if 2 2 ; max R(1 (1 ph )) (B+[B+R])(1 p H ) ; (1 p H)(B+R) R. p H )(1 Similarly, the best response of a high-competent government to x L1 = 0 is x H1 = 1 if B + R + (p H + (1 ))V H;10;0 > B + V H;00;1, i.e. if the same conditions as before are satis ed. The best response of a low-competent government to x H1 = 1 is x L1 = 1 if B + R + (1 ) V L;11;0 > B + (p L V L;10;1 + (1 p L )(1 )V L;10;0, i.e. if R > p L V L;11;0. If R > p L (B + R), this inequality is equivalent to R > p L (1 + (1 )) [B + R], which can be rewritten as 2 p L 2 p L (1 + ) + R B+R > 0: If R is su ciently i.

50 large, p 2 L 2 (1 + ) 2 4 R B+R p L 2 < 0; and, as a result, the best response to x H1 = 1 is x L1 = 1. Alternatively, if R < p L (B + R), x L1 = 1 is a best response if R > p L (B + (p L + (1 p L )(1 )) [B + R]) : The latter inequality is equivalent to 2 (1 p L ) ( B B+R + ) + large, i.e. if ( B B+R + )2 4 R p L (B+R) (1 R p L (B+R) > 0, which is always satis ed if R is su ciently p L) < 0. Therefore, for a low-competent government, if R is su ciently large, the best response to x H1 = 1 is x L1 = 1: In contrast, if R is su ciently small, the best response to x H1 = 1 might be x L1 = 0 for su ciently large : Similarly, the best response of a low competent government to x H1 = 0 is x L1 = 1 if R is su ciently large, and.x L1 = 0 if R is su ciently small and is su ciently large. For people, for all strategy pro les except x H1 = 1, x L1 = 0, s 1 j1 = not overthrow; s 1 j0 = overthrow is a best response as a positive outcome increases the ex-post probability of a high-competent government, while a negative outcome decreases this probability. As a result, possible equilibria in the rst stage are the following. If R is su ciently large, the equilibrium set of strategies is x L1 = 1, x H1 = 1; sj1 = not overthrow; sj0 = overthrow if is su ciently large (i.e. > 2 ) and x L1 = 1, x H1 = 0; s 1 j1 = not overthrow; s 1 j0 = overthrow if is su ciently small. If R is su ciently small, the equilibrium set of strategies is x L1 = 1, x H1 = 1; s 1 j1 = not overthrow; s 1 j0 = overthrow if is su ciently large (i.e. > 2 ), x L1 = 1, x H1 = 0; s 1 j1 = not overthrow; s 1 j0 = overthrow if is in intermediate range, and x L1 = 0, x H1 = 0; s 1 j1 = not overthrow; s 1 j0 = overthrow if is su ciently small. Equilibria in continuation games are described above in lemma2. Proof of Proposition 2. From the proof of lemma 2, j y1=0;x H1 =1;x L1 =1 = (1 p H) 1 p H <, j y1=0;x H1 =0;x L1 =1 = +(1 ) 1 (1 )(1 p H ) <, and j y1=0;x H1 =0;x L1 =0 = goes up, as low-competent government predate more often. Proof of Proposition 3. 1 p +(1 ) L (1 )(1 p H ) <. In any case, the risk of predation For intermediate values of, a low-competent government predates, while a highcompetent government refrains from predation in the second period. The risk of predation, therefore, varies with, the posterior belief about. For high or low values of, both types of government behave in the same way, both in the rst and in the second period. So, the estimated risk of predation does not change in these cases.

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