## Political Institutions and Output Collapses

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### Executive summary — Key findings
- Major output collapses are costly and frequent in the developing world.  
- Five-year periods are classified jointly by growth regime (growth, stagnation, collapse) and political institutions using a finite state Markov chain.  
- Main empirical findings:
  - Growth is more likely to be sustained under democracy than under autocracy.  
  - Output collapses are more persistent under autocracy.  
  - Stagnation under autocracy is more likely to give way to outright collapse.  
  - Democratic countries appear to be more resilient.  
- Transition matrix estimated from the data is approximately block diagonal: transitions between growth regimes are common while transitions between institutional forms are not.  
- Extrapolating from data since 1971, countries will spend only a half to two-thirds of their time under democracy, implying long-run diversity in political outcomes.

### Methods and data — Classification and model
- State-space and timing:
  - Primary growth regimes: growth, stagnation, collapse.  
  - Political institutions: democracy and autocracy (baseline 3 × 2 = 6 states).  
  - Five-year periods begin in 1971 and end in 2016; each annual realization used once. Example growth observations: 1971–1976, 1976–1981, ...  
- Output and collapse definitions:
  - Output measured by GDP at constant national 2017 prices from Penn World Table version 10 (PWT 10); primary unit: output per head. Robustness: output per working-age adult (ages 15-64) from the World Development Indicators.  
  - Output collapse: within a five-year period, any fall of 5 percent or more among the six overlapping comparisons (five-year, two four-year subperiods, three three-year subperiods) classifies the period as a collapse.  
- Growth vs stagnation rule (when not collapse):
  - G(t) ≥ max (0.50, GR(t) − 0.75) where GR(t) is average OECD growth in period t. This imposes two requirements: annual growth must be at least GR(t) − 0.75 and at least 0.50.  
- Model:
  - Finite state Markov chain with transition matrix M; ψt+1 = ψtM and stationary distribution ψ∗ satisfies ψ∗ = ψ∗M.  
  - Main results draw on “almost 1000 transitions” and a balanced-panel preference; transition economies of Europe and central Asia excluded; OECD members by 1975 excluded.

### Three-state example (growth / stagnation / collapse) — Key statistics
- Panel: 155 countries, nine state observations each → 155×(9−1) = 1240 transitions.  
- Rounded transition matrix (rows sum to one after rounding):
  - Growth → Growth 0.68, Growth → Stagnation 0.12, Growth → Collapse 0.20  
  - Stagnation → Growth 0.50, Stagnation → Stagnation 0.24, Stagnation → Collapse 0.26  
  - Collapse → Growth 0.36, Collapse → Stagnation 0.18, Collapse → Collapse 0.46
- Dobrushin coefficient α(p) = 0.69.  
- Asymptotic half-life h = 2.71 years.  
- Transition counts:
  - Growth: 436 (to Growth), 83 (to Stagnation), 130 (to Collapse)  
  - Stagnation: 110, 51, 58  
  - Collapse: 134, 67, 171  
  - NT = 1240, N = 155, T = 8
- Mean first passage and recurrence times (years):
  - From Growth: to Stagnation 35.20, to Collapse 23.90  
  - From Stagnation: to Growth 11.00, to Collapse 22.10  
  - From Collapse: to Growth 12.90, to Stagnation 32.70  
  - Mean first recurrence (MFR): Growth 9.00, Stagnation 31.40, Collapse 17.60
- Stationary distribution: Growth 0.56, Stagnation 0.16, Collapse 0.28.

### Six-state analysis (V-Dem: DG, DS, DC, AG, AS, AC) — Transition matrix and implications
- Rounded transition matrix (rows sum to one after rounding):
  - DG → DG 0.72, DG → DS 0.11, DG → DC 0.11, DG → AG 0.05, DG → AC 0.01  
  - DS → DG 0.53, DS → DS 0.26, DS → DC 0.08, DS → AG 0.06, DS → AC 0.02  
  - DC → DG 0.42, DC → DS 0.21, DC → DC 0.25, DC → AG 0.06, DC → AC 0.06  
  - AG → AG 0.63, AG → AS 0.10, AG → AC 0.22, AG → DG 0.05  
  - AS → AG 0.42, AS → AS 0.21, AS → AC 0.31, AS → DG 0.03, AS → DS 0.03  
  - AC → AC 0.53, AC → AG 0.26, AC → AS 0.14, AC → DG 0.05, AC → DS 0.01, AC → DC 0.01
- Dobrushin coefficient α(p) = 0.14.  
- Asymptotic half-life h = 20.21 years.  
- Stationary distribution ψ*:
  - DG 0.34, DS 0.08, DC 0.07, AG 0.26, AS 0.06, AC 0.18  
  - Implies countries will spend around half the time under democracy and half under autocracy in the long run.
- Transition counts (NT = 992, N = 124, T = 8) and selected mean first passage / recurrence times:
  - DG row: 112 (DG), 19 (DS), 19 (DC), 9 (AG), 2 (AC)  
  - DG → AG mean first passage 71.80 years; DG → DS 67.50; DG → DC 78.00  
  - MFR: DG 14.50, DS 60.40, DC 71.40, AG 19.00, AS 77.30, AC 28.50
- Key substantive findings (V-Dem six-state):
  - Growth persistence: DG 0.72 vs AG 0.63.  
  - Collapse persistence: AC 0.53 vs DC 0.25.  
  - Stagnation to collapse: AS → AC 0.31 vs DS → DC 0.08.  
  - Direct democratic-growth to autocratic-collapse events are very rare: DG → AC = 0.01 (two events).

### Three political states (Polity: democracy / anocracy / autocracy) — Stationary implications
- Six-state setup with three political types × growth/collapse (stagnation merged into growth for this section). Rounded transition matrix reported in the source.  
- Dobrushin coefficient α(p) = 0.04.  
- Asymptotic half-life h = 22.74 years.  
- Stationary distribution ψ* (Polity-based):
  - DG 0.56, DC 0.10, NG 0.19, NC 0.06, AG 0.05, AC 0.03  
  - Implies long-run: 66 percent of time under democracy (DG + DC = 0.56 + 0.10), 25 percent under anocracy (NG + NC = 0.19 + 0.06), ~8 percent under full autocracy (AG + AC = 0.05 + 0.03).
- Interpretation: anocracy tends to be transitional; growth is more persistent under anocracy than under autocracy in this classification.

### Robustness checks — Aggregation, denominators, subgroups, and timing
- Aggregation: combining democratic stagnation and democratic collapse yields little change to stationary distributions or the Dobrushin coefficient.  
- Alternative denominator: replacing per-head with per working-age adult changes about 0.10 of period classifications; stationary distributions remain similar (per-head DG 0.34 vs per-working-age-adult DG 0.33). Full reported stationary distributions (per head):
  - DG 0.34, DS 0.08, DC 0.07, AG 0.26, AS 0.06, AC 0.18  
  - Per working-age adult: DG 0.33, DS 0.09, DC 0.08, AG 0.24, AS 0.07, AC 0.19
- Alternative democracy criterion: median V-Dem over five years changes only 3 percent of classifications; little impact on findings.  
- Subgroups:
  - SSA stationary: DG 0.32, DS 0.06, DC 0.03, AG 0.26, AS 0.09, AC 0.25  
  - Non-SSA stationary: DG 0.37, DS 0.10, DC 0.09, AG 0.26, AS 0.05, AC 0.13  
  - SSA shows more autocratic collapse but differences are smaller than might be expected; Dobrushin coefficient lower for Africa.  
- Time-split (1971-1996 vs 1996-2016): later span predicts more time growing and less time in collapse.  
- Different starting years (1970–1973): classifications can differ (up to %∆ = 0.30 when starting in 1973 vs 1971) but stationary distributions remain qualitatively similar.  
- Higher-order Markov processes not estimated due to panel size constraints; first-order five-year periods used as compromise.

### Inference, sampling variability, and limitations
- Transition matrix standard errors (Anderson-Goodman asymptotic SEs) reported in Table A.1.1; example row DG (probabilities with SEs):
  - 0.696 (0.036) 0.118 (0.025) 0.118 (0.025) 0.056 (0.018) 0.000 (0.000) 0.012 (0.009)
- Observations:
  - Standard errors largest for rare states (e.g., democratic collapse DC) due to few observations.  
  - For most rows, transition probabilities estimated quite precisely; for rare transitions, precise estimation is less critical than substantive interpretation.  
- Methodological limitations:
  - Approach generates stylized facts but is not causal.  
  - Some states (notably democratic collapse) are rare, so related probabilities draw on small numbers.  
  - Assumption of homogeneous transition probabilities over time and independence across countries is restrictive; results change with time variation or correlated transitions.  
  - Small sample size constrains richer state-space specifications and higher-order dynamics.

### Conclusions and policy-relevant implications
- Stylized facts:
  - Collapses are much longer-lasting under autocracy; growth is less likely to be sustained under autocracy.  
  - Under autocracy, stagnation is more likely to presage outright collapse.  
  - Democracies appear more resilient; democracy is not an absorbing state but can act as a safety net ruling out worst outcomes.  
  - Long-term institutional diversity is predicted: countries spend substantial time in both democracy and autocracy.
- Potential mechanisms:
  - Democratic accountability (e.g., the ability to remove failing leaders) may help prevent or manage crises and adapt to shocks.  
  - Autocracies may be structurally heterogeneous and expose countries to stochastic risk of protracted collapse, increasing cross-autocracy variance in long-run growth.
- Policy and research avenues:
  - Investigate whether autocratic regimes can adopt partial reforms (e.g., term limits or conflict-resolution mechanisms) that reduce collapse risk.  
  - Combine the Markov approach with studies of financial crises, macroeconomic management, and state capacity to probe causal mechanisms.  
  - Explore relaxing independence across countries to model correlated transitions (contagion) linked to global shocks.

*Source: IMF Working Paper — "Political Institutions and Output Collapses" (excerpts provided).*

### Executive Summary ......................................................................................................

### Executive Summary

### Key findings
- Major output collapses are costly and frequent in the developing world.
- Using cross-country data, five-year periods are classified in a two-dimensional state space based on growth regimes and political institutions.
- Three growth regimes are defined: phases of growth, stagnation, or collapse.
- Main empirical findings:
  - Growth is more likely to be sustained under democracy than under autocracy.
  - Output collapses are more persistent under autocracy.
  - Stagnation under autocracy is more likely to give way to outright collapse.
  - Democratic countries appear to be more resilient.
- Transition matrix estimated from the data is approximately block diagonal, reflecting that transitions between growth regimes are common while transitions between institutional forms are not.
- Extrapolating from data since 1971, countries will spend only a half to two-thirds of their time under democracy, implying long-run diversity in political outcomes.

### Methods and data
- Classification: five-year periods categorized jointly by growth regime (growth, stagnation, collapse) and political institutions.
- Modeling approach: finite state Markov chain for the joint evolution of output growth and political institutions.
- The approach allows computation of transition probabilities, persistence, and the stationary distribution implied by a given transition matrix.
- Two sets of empirical focus:
  - Persistence of growth, stagnation, and collapse across institutional forms (based on large numbers of observations and emphasized in results).
  - Institutional transitions (e.g., whether crises increase likelihood of democratization), which are less robust due to relatively few observed institutional transitions, especially democracy-to-autocracy shifts.

### Interpretation and implications
- Democracies can more readily remove failing leaders and may be better at resolving social conflict; this institutional mechanism is posited to underlie greater resilience to collapses.
- Autocracy is associated with a wider variety of long-run outcomes, including more frequent and more protracted collapses.
- Because transitions between institutional forms are relatively uncommon, countries often remain in the same institutional block even as they move between growth regimes; this amplifies the role of institutions in shaping the persistence of collapses.
- Once countries move into stagnation or collapse, recoveries may be unsteady and protracted.

### Longer-term projections and contextual analysis
- Stationary distribution analysis shows long-run political diversity rather than convergence to a single dominant regime.
- Historical split-sample analysis indicates growth has become more common and collapse less common over the sample, but recent shocks (Covid-19 pandemic, high inflation and debt, and higher interest rates) may lead to a new round of crises and unsteady recoveries.

### Limitations and robustness
- Results on persistence of growth regimes across institutional forms are based on large sample sizes and are more reliable.
- Results concerning the interplay between crisis episodes and institutional transitions are less robust due to limited instances of institutional change in the data.
- The Markov chain framework is transparent and extensible; some limitations will diminish as more data become available.

*Source: Executive Summary, “Political Institutions and Output Collapses,” IMF Working Paper (Executive Summary).*

### Section 3 introduces our approach. Section 4 describes the data, section 5 presents a simple example to fix

### wpiea2023036-print-pdf - Section 3 introduces our approach. Section 4 describes the data, section 5 presents a simple example to fix

### Background: motivation and context
- Prominent peacetime output collapses since 2000 include Zimbabwe in 2008, Venezuela in 2013, and more recently Lebanon and Sri Lanka.
- Polity project terminology: anocracies are hybrids of democracy and autocracy that do not meet the criteria for either.
- The paper adopts an “episodic growth” perspective (Easterly et al. 1993; Pritchett 2000, 2003), arguing that studying growth episodes (expansions, stagnation, collapses) can be more informative than focusing on average growth rates alone.
- Key prior findings and motivations cited:
  - Severe contractions often have a scarring effect, with growth afterwards remaining below trend (Aikman et al. 2022).
  - Cerra and Saxena (2008) cast doubt on output returning to pre-crisis trend.
  - Democratic lapses: the authors reference a roughly fifteen-year “democratic recession” and note that transitions to democracy outnumber transitions to autocracy over 1971-2016, but many transitions are reversible (‘bouncers’/‘cyclers’).
- Policy relevance: understanding pathways into and out of collapse can help governments and aid donors identify vulnerable countries and devise strategies to lessen risks.

### Basic ideas: model and state definitions
- Methodological framework: finite state Markov chain with discrete state space S and transition matrix M whose elements are non-negative and rows sum to one.
- Markov property maintained: transition probabilities depend only on the current state.
- Notation and dynamics:
  - ψt denotes the marginal/unconditional distribution over states at time t.
  - Evolution equation: ψt+1 = ψtM
  - Stationary distribution ψ∗ satisfies ψ∗ = ψ∗M; uniqueness implies long-run outcome.
- Rationale for observable states:
  - The paper treats growth outcomes and political institutions as observable states (following Quah and much of the political transitions literature) rather than unobservable-state approaches (Hamilton).
  - Using observable states and five-year periods emphasizes medium-run phenomena (sustained growth, major output collapses) rather than short-run cyclical fluctuations.
- State-space construction:
  - Primary growth regimes: growth, stagnation, collapse (three regimes).
  - Political institutions: democracy and autocracy (two observed types).
  - Combined state space in baseline: 3 growth regimes × 2 political institutions = 6 states.
- Advantages over income-class Markov analyses:
  - Transition matrices are less sparse when defined by growth regimes, leading to faster convergence to stationary distribution and lower sensitivity to small changes in transition probabilities (Dobrushin coefficient referenced).
- Data availability and sample size:
  - The paper’s main results draw on “almost 1000 transitions” to estimate transition probabilities.

### Methods and data: sample, measures, and state classification
- Sample scope and exclusions:
  - Focus on developing countries; exclude the 24 countries that were OECD members by 1975.
  - Main exception to inclusion: transition economies of Europe and central Asia (including successor states of the USSR) are excluded.
  - Five-year periods begin in 1971 and end in 2016.
- Justification for periodization:
  - Starting in 1971 places major events within five-year blocks: 1971-76 (first oil shock), 1981-86 (debt crisis begun 1982), 1996-2001 (East Asian financial crisis 1997-98), 2006-11 (global financial crisis 2007-9).
  - Five-year windows reduce the risk that a collapse straddles a boundary and remains undetected; alternative timing choices are examined in robustness checks.
- Output measurement:
  - Output measured by GDP at constant national 2017 prices from Penn World Table version 10 (PWT 10).
  - Primary unit: output per head using PWT 10 population series.
  - Robustness check: output per working-age adult (ages 15-64) from the World Development Indicators to approximate output per worker where informal sector is large.
- Definition of an output collapse:
  - A major decline in output that is sustained over time.
  - Within each five-year period, an output collapse is identified if output declines by 5 percent or more over:
    - five years, OR
    - either of the two subperiods of four consecutive years, OR
    - any of the three subperiods of three consecutive years.
  - Rationale: the 5 percent threshold avoids classifying milder business-cycle recessions as collapses; requiring at least three-year declines avoids picking up V-shaped recessions (e.g., Covid-19).
- Classification into growth or stagnation when not collapse:
  - Growth regime threshold defined using contemporaneous rich-country performance:
    - G(t) ≥ max (0.50, GR(t) − 0.75)
    - where GR(t) is the average rich country (OECD) growth rate in period t.
  - This rule imposes two requirements (explicit in the source):
    - annual growth must be at least equal to the average OECD growth rate in that five-year period minus 0.75, and
    - the threshold is bounded below by 0.50 (i.e., growth must meet or exceed 0.50 if GR(t) − 0.75 is below 0.50).
- Additional methodological points:
  - Use of five-year subperiods and multiple collapse criteria to capture diverse collapse dynamics and avoid sensitivity to start/end-year movements.
  - Balanced-panel preference and avoidance of pre-1970 data because many developing countries were still colonies during the 1960s.
  - The approach is explicitly aimed at generating stylized facts about interactions between political institutions and growth regimes rather than causal inference; complementary methods (panel regressions, duration analysis) may be more suitable for causal questions.

*Source: IMF Working Paper wpiea2023036, Sections II–IV.*

### 0.75 percentage points (we explain this adjustment shortly). Second, annual growth should also be at least 0.50

### Political Institutions and Output Collapses

### State definitions and classification
- Growth, stagnation, collapse: growth requires exceeding frontier growth less a shortfall of up to 0.75 percentage points and annual growth at least 0.50 percentage points. Stagnation is the residual category for countries neither collapsing nor meeting the growth requirements.  
- Political regimes (V-Dem, v2x_regime): ordinal values 0 = closed autocracy, 1 = electoral autocracy, 2 = electoral democracy, 3 = liberal democracy. A five-year period is classified as democratic if the minimum value over the five-year period is at least 2 (i.e., democratic for the full five years).  
- Alternative political classification: anocracy (hybrid/transitional regimes) using the Polity project (Polity 5). Polity coding: democratic if Polity score > 5 in each of five years; autocratic if Polity score < −5 in each of five years; otherwise anocracy. Special Polity codes −66 assigned adjusted score −7; −77 and −88 treated per Polity2 conventions.

### Three-state example (growth / stagnation / collapse)
- Panel: 155 countries, nine state observations each → 155×(9−1) = 1240 transitions.  
- Rounded transition matrix (rows sum to one after rounding adjustments):
  - Growth → Growth 0.68, Growth → Stagnation 0.12, Growth → Collapse 0.20
  - Stagnation → Growth 0.50, Stagnation → Stagnation 0.24, Stagnation → Collapse 0.26
  - Collapse → Growth 0.36, Collapse → Stagnation 0.18, Collapse → Collapse 0.46
- Dobrushin coefficient α(p) = 0.69.  
- Asymptotic half-life h = 2.71 years.  
- Transition counts:
  - Growth: 436 (to Growth), 83 (to Stagnation), 130 (to Collapse)
  - Stagnation: 110, 51, 58
  - Collapse: 134, 67, 171
  - NT = 1240, N = 155, T = 8
- Mean first passage and recurrence times (years):
  - From Growth: to Stagnation 35.20, to Collapse 23.90
  - From Stagnation: to Growth 11.00, to Collapse 22.10
  - From Collapse: to Growth 12.90, to Stagnation 32.70
  - Mean first recurrence (MFR): Growth 9.00, Stagnation 31.40, Collapse 17.60
- Stationary distribution: Growth 0.56, Stagnation 0.16, Collapse 0.28.

### Main findings on political institutions (V-Dem, six-state analysis)
- State labels: D/A = democratic/autocratic; G/S/C = growth/stagnation/collapse; six states DG, DS, DC, AG, AS, AC.  
- Rounded transition matrix (rows sum to one after rounding):
  - DG → DG 0.72, DG → DS 0.11, DG → DC 0.11, DG → AG 0.05, DG → AC 0.01
  - DS → DG 0.53, DS → DS 0.26, DS → DC 0.08, DS → AG 0.06, DS → AC 0.02
  - DC → DG 0.42, DC → DS 0.21, DC → DC 0.25, DC → AG 0.06, DC → AC 0.06
  - AG → AG 0.63, AG → AS 0.10, AG → AC 0.22, AG → DG 0.05
  - AS → AG 0.42, AS → AS 0.21, AS → AC 0.31, AS → DG 0.03, AS → DS 0.03
  - AC → AC 0.53, AC → AG 0.26, AC → AS 0.14, AC → DG 0.05, AC → DS 0.01, AC → DC 0.01
- Dobrushin coefficient α(p) = 0.14.  
- Asymptotic half-life h = 20.21 years.  
- Stationary distribution ψ*:
  - DG 0.34, DS 0.08, DC 0.07, AG 0.26, AS 0.06, AC 0.18
  - Implies countries will spend around half the time under democracy and half under autocracy in the long run.
- Transition counts:
  - DG row: 112 (DG), 19 (DS), 19 (DC), 9 (AG), 2 (AC)
  - DS row: 27, 11, 4, 3, 1
  - DC row: 14, 7, 8, 2, 2
  - AG row: 20, 3, 2, 218, 37, 79
  - AS row: 4, 4, 1, 51, 22, 37
  - AC row: 15, 5, 5, 73, 40, 136
  - NT = 992, N = 124, T = 8
- Mean first passage / mean first recurrence times (years) highlight long average times for political-institutional transitions (examples):
  - DG → AG mean first passage 71.80 years
  - DG → DS 67.50, DG → DC 78.00
  - MFR: DG 14.50, DS 60.40, DC 71.40, AG 19.00, AS 77.30, AC 28.50
- Key substantive findings:
  - Growth is more persistent under democracy than autocracy (DG persistence 0.72 vs AG persistence 0.63).  
  - Output collapses are far more persistent under autocracy than under democracy (AC persistence 0.53 vs DC persistence 0.25).  
  - Stagnation under autocracy is more likely to lead to collapse (AS → AC 0.31) than stagnation under democracy to collapse (DS → DC 0.08).  
  - Democratic countries appear more resilient; stagnating autocracies are especially vulnerable to deterioration.  
  - Direct transitions from democratic growth to autocratic collapse are very low (DG → AC = 0.01; only two such events).

### Three political states (Polity, introducing anocracy)
- Six-state setup with three political types (D/N/A) × growth/collapse (G/C). Stagnation merged into growth for this section.  
- Rounded transition matrix (rows sum to one after rounding):
  - DG → DG 0.86, DG → DC 0.11, DG → NG 0.03
  - DC → DG 0.52, DC → DC 0.33, DC → NG 0.13, DC → NC 0.02
  - NG → NG 0.70, NG → DG 0.12, NG → NC 0.11, NG → AG 0.03, NG → AC 0.01
  - NC → NG 0.35, NC → NC 0.36, NC → DG 0.13, NC → DC 0.02, NC → AG 0.10, NC → AC 0.04
  - AG → AG 0.55, AG → AC 0.25, AG → NG 0.09, AG → NC 0.11
  - AC → AC 0.50, AC → AG 0.26, AC → AC 0.50, AC → NC 0.15, AC → NG 0.09
- Dobrushin coefficient α(p) = 0.04.  
- Asymptotic half-life h = 22.74 years.  
- Stationary distribution ψ*:
  - DG 0.56, DC 0.10, NG 0.19, NC 0.06, AG 0.05, AC 0.03
  - Implies long-run: 66 percent of time under democracy (DG + DC = 0.56 + 0.10), 25 percent under anocracy (NG + NC = 0.19 + 0.06), ~8 percent under full autocracy (AG + AC = 0.05 + 0.03).
- Transition counts and mean passage times reported; anocracy tends to be transitional but growth is more persistent under anocracy than under autocracy.

### Robustness checks
- Aggregation: combining democratic stagnation and democratic collapse into one state (to address rarity of democratic collapses) yields little change to stationary distributions or Dobrushin coefficient.  
- Alternative denominator for growth: replacing GDP per head with GDP per working-age adult (ages 15-64) changes about 0.10 (10 percent) of period classifications; stationary distributions remain similar: per-head stationary DG 0.34 vs per-working-age-adult DG 0.33. Reported stationary distributions (per head):
  - DG 0.34, DS 0.08, DC 0.07, AG 0.26, AS 0.06, AC 0.18
  - Per working-age adult: DG 0.33, DS 0.09, DC 0.08, AG 0.24, AS 0.07, AC 0.19
- Alternative democracy criterion: median V-Dem value over five years classifies democracy; changes only 3 percent of state classifications and little impact on findings.  
- Subgroups (stationary distributions):
  - SSA (sub-Saharan Africa): DG 0.32, DS 0.06, DC 0.03, AG 0.26, AS 0.09, AC 0.25
  - Non-SSA: DG 0.37, DS 0.10, DC 0.09, AG 0.26, AS 0.05, AC 0.13
  - Differences exist (SSA more autocratic collapse), but smaller than might be expected. Dobrushin coefficient lower for Africa.  
- Time-split robustness (1971-1996 vs 1996-2016): later span predicts more time growing and less time in collapse. Example stationary patterns indicate increased DG and AG and reduced DC and AC in later period.  
- Different starting years (1970, 1971, 1972, 1973) alter classifications (%∆ up to 0.30 when starting in 1973 vs 1971), but stationary distributions remain qualitatively similar across start dates.  
- Higher-order Markov processes: not estimated due to panel size constraints; first-order five-year periods used as compromise.

### Conclusions and policy-relevant implications
- Stylized facts:
  - Collapses are much longer-lasting under autocracy; growth is less likely to be sustained under autocracy.  
  - Under autocracy, stagnation is more likely to presage outright collapse.  
  - Democracies appear more resilient; democracy can act as a safety net ruling out worst outcomes.  
  - Long-term institutional diversity is predicted: countries spend substantial time in both democracy and autocracy; democracy is not an absorbing state.
- Potential causal interpretations and mechanisms:
  - Democratic accountability (e.g., failing leaders can be voted out) may help prevent or manage crises and adapt to shocks.  
  - Autocracies may be structurally heterogeneous or expose countries to stochastic risk of protracted collapse, leading to greater cross-autocracy variance in long-run growth.
- Research and policy avenues:
  - Investigate whether autocratic regimes can adopt partial reforms (such as term limits or conflict-resolution mechanisms) that reduce collapse risk.  
  - Combine this Markov approach with studies of financial crises, macroeconomic mismanagement, and state capacity to probe causal mechanisms.  
  - Explore relaxing independence across countries to model correlated transitions (contagion) linked to global shocks (e.g., oil shock, debt crisis, financial crises).
- Limitations to bear in mind:
  - Method generates stylized facts but is not causal.  
  - Some states (notably democratic collapse) are rare, so related transition probabilities draw on small numbers.  
  - Assumption of homogeneous transition probabilities over time and independence across countries is restrictive; results change when allowing time variation.  
  - Small number of countries constrains state-space complexity.

*Source: IMF Working Paper — "Political Institutions and Output Collapses" (excerpts provided).*

### References

### wpiea2023036-print-pdf - References

### Timing assumptions and period construction
- Five-year periods are constructed so that each annual realization of growth or the political variables is used once and only once. Example sequence: 1971, 1976, 1981... First growth observation: (log(y1976) −log(y1971))/5; second: (log(y1981) −log(y1976))/5, and so on.
- Each year of growth influences only one period’s classification.
- OECD growth is measured similarly, taking an average across OECD members.
- Political variables for a period are based on the five-year block (e.g., the first period political variables are based on 1971-75; the next on 1976-80). For V-Dem, a country is considered democratic in the period only if it was democratic in each of the five years.

### Output-collapse classification rule
- To classify a five-year period as an output collapse, the authors examine output changes among the following year-pairs: 1971–1976, 1971–1975, 1972–1976, 1971–1974, 1972–1975, and 1973–1976 (i.e., the six overlapping comparisons within the five-year window).
- A period is labelled an output collapse if there is at least one fall of 5 percent or more among these output changes.
- Rationale: this approach aims to capture collapses that are substantial and protracted, rather than mild or V-shaped recessions.

### Transition matrix and sampling variability (Table A.1.1)
- Transition matrix labels: D/A refer to democratic/autocratic; G/S/C refer to growth/stagnation/collapse.
- Anderson-Goodman (1957) asymptotic standard errors are reported in parentheses below each transition probability.
- Reported transition matrix (probabilities) with standard errors:

  - Header states: DG DS DC AG AS AC

  - Row DG:
    - 0.696 0.118 0.118 0.056 0.000 0.012
    - (0.036) (0.025) (0.025) (0.018) (0.000) (0.009)

  - Row DS:
    - 0.587 0.239 0.087 0.065 0.000 0.022
    - (0.073) (0.063) (0.042) (0.036) (0.000) (0.022)

  - Row DC:
    - 0.424 0.212 0.242 0.061 0.000 0.061
    - (0.086) (0.071) (0.075) (0.042) (0.000) (0.042)

  - Row AG:
    - 0.056 0.008 0.006 0.607 0.103 0.220
    - (0.012) (0.005) (0.004) (0.026) (0.016) (0.022)

  - Row AS:
    - 0.034 0.034 0.008 0.429 0.185 0.311
    - (0.017) (0.017) (0.008) (0.045) (0.036) (0.042)

  - Row AC:
    - 0.055 0.018 0.018 0.266 0.146 0.496
    - (0.014) (0.008) (0.008) (0.027) (0.021) (0.030)

- Transition counts:

  - DG: 112 19 19 9 0 2
  - DS: 27 11 4 3 0 1
  - DC: 14 7 8 2 0 2
  - AG: 20 3 2 218 37 79
  - AS: 4 4 1 51 22 37
  - AC: 15 5 5 73 40 136

- Sample summary: NT = 992  N = 124  T = 8

### Inference and interpretation of standard errors
- The asymptotic result used (Anderson and Goodman, 1957) for estimated transition probabilities p̂ij:
  - √(n_i) (p̂ij − pij ) −→ N (0, pij (1 – pij ))
- ni is the number of observations of state i prior to the final period.
- Observations:
  - Standard errors are highest when the initial state is democratic collapse (DC) due to relatively few observations of that state.
  - For most rows, transition probabilities are estimated quite precisely.
  - For rare transitions, conventional statistical significance (discernible difference from zero) is less important for the authors’ purposes than whether the relevant probability is precisely estimated.
- The authors note a contrast with Kremer et al. (2001): Kremer et al. do not report standard errors; they carry out formal inference on the stationary distribution but require off-diagonal transition probabilities to be zero, which is not true here.

*IMF Working Papers — References and Annex I excerpt.*

### Annex II. Sequence of States by Country

### Annex II. Sequence of States by Country

### Table A2.1 — State classifications (simple three-state example)
- Coverage: Country-level sequences of states at five-year intervals with a 1971 start date: 1971, 1976, 1981, 1986, 1991, 1996, 2001, 2006, 2011.
- Format: Each row lists a 3-letter country code followed by nine state-classification integers (values 1, 2, or 3) corresponding to the nine dates above.
- Example rows (exact entries from the table):
  - ABW 1 1 1 1 2 2 2 3 1
  - AFG 3 3 1 3 3 3 1 1 3
  - AGO 3 3 2 3 3 2 1 1 3
- Scope note: The full table lists sequences for a large set of countries ending with ZWE 3 3 3 1 3 3 3 1 1.

### Table A2.2 — State Classification (V-Dem based)
- Coverage: Country-level sequences using V-Dem political-regime classifications for the same nine dates: 1971, 1976, 1981, 1986, 1991, 1996, 2001, 2006, 2011.
- Format: Each row lists a 3-letter country code followed by nine integer state-classification values (examples include values 1 through 6).
- Example rows (exact entries from the table):
  - AFG 6 6 4 6 6 6 4 4 6
  - AGO 6 6 5 6 6 5 4 4 6
  - ALB 5 4 5 6 4 4 4 1 1
- Scope note: Table ends with ZWE 6 6 6 4 6 6 6 4 4.

### Table A2.3 — State Classification (Polity based)
- Coverage: Country-level sequences using Polity data classifications for the same nine dates: 1971, 1976, 1981, 1986, 1991, 1996, 2001, 2006, 2011.
- Format: Each row lists a 3-letter country code followed by nine integer state-classification values (various integer codes appear).
- Example rows (exact entries from the table):
  - AFG 6 4 5 6 4 6 5 5 4
  - ALB 5 5 5 4 3 3 3 1 1
  - ARE 6 5 6 5 5 5 6 6 5
- Scope note: Table ends with ZMB 4 6 6 6 2 3 3 3 1.

*Annex II. Sequence of States by Country (tables provide country-coded sequences of state-classification integers at five-year intervals from 1971 to 2011).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023036-print-pdf.pdf_