## _wp06158

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---

### I. Introduction — observed facts, hypothesis, and contribution
- Observed correlations and empirical facts:
  - Countries with more unequal income distribution tend to have higher inflation (references: Albanesi, 2002; Easterly and Fischer, 2001; Dolmas et al., 2000; Bulir, 1998; Beetsma and Van Der Ploeg, 1996).
  - Correlation between the inflation transformation ρ/(1+ρ) and income inequality for a cross-section of 90 countries is 0.22 (both variables averaged over 1990-2004); statistically significant at the 5 percent level.
  - Income inequality measured by the Gini coefficient (lies between 0 and 1). The inflation transformation ρ/(1+ρ) gives the inflation tax paid on money balances.
- Core hypothesis and mechanism:
  - Political influence depends on income (elite bias). Greater income inequality magnifies disparities in political power, biasing policy toward elites.
  - Inflation can be regressive because the wealthy avoid the inflation tax more easily than others (fixed cost of adopting inflation-proof financial assets).
  - Prediction: reductions in elite bias should reduce inflation more in more unequal societies (interaction effect between inequality and changes in elite bias).
- Contributions:
  - Theoretical: tractable endogenous policy-formation model for general income distributions; captures distributional impacts of inflation and role of elite bias.
  - Empirical: identification strategy using interaction between initial inequality and changes in elite bias, exploiting a quasi-exogenous democratization shock in the late 1980s–early 1990s (the “third wave”).
- Empirical approach and initial evidence:
  - Focus on percentage change in the inflation tax rate between 1975–89 and 1990–2004 for a cross-section of countries.
  - Interaction term: initial income inequality interacted with the change in elite bias (democratization).
  - Instrumental strategy: use Cold War relationships as instruments for democratization.
  - Summary cell estimates from Table 1 (Mean Percentage Change in the Average Inflation Tax Rate, 1975-89 to 1990-2004), sample: 83 countries; categorical variables defined as above/below mean; robust standard errors in parentheses; numbers of countries by cell (reading left to right, top to bottom): 31, 24, 9, 19:
    - Low Inequality, No Fall in Bias [A]: -4.8** (1.9)
    - High Inequality, No Fall in Bias: -3.6* (2.1)
    - Difference [2] - [1]: 1.2 (2.8)
    - Low Inequality, Fall in Bias [B]: 2.6 (3.5)
    - High Inequality, Fall in Bias: -9.0*** (2.4)
    - Difference [2] - [1]: -11.6** (4.2)
    - Difference [B] - [A] in Low Inequality: 7.4* (3.9)
    - Difference [B] - [A] in High Inequality: -5.4* (3.2)
    - Interaction (comparison across cells): -12.7** (5.1)
- Relation to literature:
  - Complements work linking inequality and inflation via regressive inflation mechanisms (Albanesi, 2002; Bhattacharya et al., 2003; Dolmas et al., 2000; Beetsma and Van DerPloeg, 1996).
  - Contrasts with accounts where greater democracy raises inflation in high-inequality countries (Desai et al., 2003; 2005).
  - Discusses empirical evidence on inflation aversion across income groups and on elite political influence.

### II. Household optimization — model structure and key equations
- Framework and setup:
  - Overlapping generations (OLG) model. Time discrete. Cohort of households i in each period t, unit mass. Each household lives two periods. Endowments y_i^t drawn from time-invariant distribution F(y_i) over [y_min, y_max], continuous and differentiable, with E[y_i] = 1.
  - Households consume only in the second period of life; two valueless assets: cash m (supply controlled by government) and a second asset d in fixed nominal supply (an inflation shelter). No uncertainty.
  - Fixed real cost of operating in the market for the second asset denoted ϕ ∈ [0,1], payable if D_i^t = 1 (indicator that household holds any of the second asset).
  - Utility specification: U_i = ln c_i^t + β ln g_t.
- Budget constraint and definitions:
  - Budget constraint (as in source):
    - c_i^t + ϕ_t - y_i^t - D_i^t = m_i^t p_{t+1} + d_i^t q_{t+1}
  - Rewritten (equation (3)):
    - c_i^t = y_i^t - (1 - z_i^t)(1 - τ_t - b^m_t) y_i^t + (z_i^t - D_i^t)(1 - τ_t - b^q_t) y_i^t
  - Definitions:
    - z_i^t denotes share of saving via the inflation shelter; D_i^t = 1 if z_i^t > 0.
    - b^m_t and b^q_t are “tax rates” due to changes in asset prices (b^m_t is the inflation tax).
  - Optimal asset choice (corner solutions due to fixed cost):
    - z_i^t = 1 if y_i^t > b_y^t; 0 otherwise. (Equation (4))
  - Aggregate real balances and government budget constraint:
    - b m_t ≡ m_t / p_t = ∫_i y_i^t (1 - z_i^t) di = ∫_i j y_i^t [1_{y_i^t < b_y^t}] di. (Equation (5))
    - g_t = τ_t [1 - θ/(1 - b^F_t)] + b m_{t+1} - b m_t + b^m_t b m_t. (Equation (6))
    - b^F_t ≡ ∫_i (1 - D_i^t) di (measure of cash-holders).
  - Government seigniorage revenues arise from increases in demand for money (b m_{t+1} - b m_t) and from taxing real balances (b^m_t b m_t). Households anticipate relative tax rates on consumption via each asset (policy parameter ω_t); ∂ b m_t / ∂ ω_t ≤ 0.

### III. Political optimization — voting, objectives, and implications
- Political environment and timing:
  - Probabilistic voting model (Lindbeck and Weibull, 1987; Persson and Tabellini, 2000).
  - Policymakers elected for one period choose (g_t, τ_t, b^m_t) subject to budget constraint. Two candidates A and B; majority voting rule.
  - Timing: cohort t trades at period t prices; asset choice based on anticipated policy G_t; in period t+1 cohort t votes on platforms G_t^A and G_t^B; asset markets clear; government implements policy; cohort t consumes and dies.
- Politician objectives and representation:
  - Candidates maximize probability of election, equivalent to maximizing a weighted social welfare function subject to budget constraint.
  - Reduced-form assumption: agents differ in political weight w_i^t, assumed non-decreasing in income (captures elite bias and unequal political influence).
- Model implications (conceptual):
  - Without elite bias, policymaker uses progressive income tax and all households hold cash (no positive seigniorage).
  - With sufficient elite bias, policymaker favors policies beneficial to richer groups, potentially leading to positive seigniorage in equilibrium.
  - Model delivers a positive relationship between inequality and inflation for sufficiently high elite bias.
- Empirical identification strategy (reiterated):
  - Use the late 1980s–early 1990s democratization wave as a quasi-exogenous reduction in elite bias.
  - IV strategy: use Cold War relationships as instruments for democratization.

### IV. Analytical results — FOCs, equilibria, and comparative statics
- Probabilistic voting first-order characterization:
  - Policymaker choice probability (equation (7)):
    - p_A_t = 1/2 + ∫_i w_i_t [U_i(G_A_t) - U_i(G_B_t)] di
  - Define total political weight of cash- and non-cash-holding agents as W_0 and W_1; cash-holders fraction b_F_t:
    - W_0 ≡ ∫_{i: y_i_t ≤ b_y_t} w_i_t di ; W_1 ≡ ∫_{i: y_i_t > b_y_t} w_i_t di
  - Political weights derived from endogenous faction grouping; faction weight non-decreasing in faction average income:
    - w_j = (e y)^{ζ}; ζ ≥ 0
  - Agent weight by cash-holding status (equation (13)):
    - w_i = ( (e y)^{ζ} for y_i ≤ b_y ; (e (y-τ))^{ζ} for y_i > b_y )
- First-order conditions for policymaker (equations (9)-(11)):
  - [b'_t] 1/(1-ξ_t - b'_t W_0) - ε_{0t} bm_t = 0
  - [ξ_t] 1/(1-ξ_t - b'_t W_0) + 1/(1-ξ_t - b_q_t W_1) - ε_{0t} (1 - (1 - b_F_t)) = 0
  - [g_t] β (W_0 + W_1) - ε_{0t} = 0
- Political-economy interior solution (Proposition 1, equation (8)):
  - γ_t(by_t) = (W_1 bm_t) / (W_0 [1 - bm_t - (1 - b_F_t)])
- Ramsey (first-best) case (Proposition 2):
  - Ramsey equilibrium with equal household weights w_i_t = w̄_i has non-positive inflation tax rate and all agents hold cash:
    - Result: all agents hold cash in every period ⇒ b_q = 0 and b' ≤ 0
- Special functional form and equilibrium conditions:
  - Asset-holding condition (equation (14)):
    - D_t = b_y_t / (b_y_t - τ)
  - Political-economy interior solution under specific weighting (equation (15)):
    - γ_t = [ (1 - b_F_t) (y - τ)^{ζ} / (b_F_t y^{ζ}) ] [ bm_t / (1 - bm_t - (1 - b_F_t)) ] = [ ((y - τ)/y)^{ζ} ]^{ζ^{-1}}
  - Stationary solution (equation (17)): γ_t = γ = (1 - ξ)/(1 - ξ - b')_t
  - Assume ζ > 1 going forward for interior solution existence.
- Existence and uniqueness (Proposition 3):
  - Assume (y_max - τ) > 1. Then an equilibrium with γ > 1 exists if ζ > 1.
- Comparative statics and inequality link (Propositions 4–6):
  - Proposition 4: For F_0 and F_1 where F_1 is Lorenz dominated by F_0, γ(b_y; F_1) > γ(b_y; F_0).
  - Proposition 5: Optimal policy γ is increasing in ζ:
    - ∂γ/∂ζ = ∂/∂ζ [ ((y - τ)/y)^{ζ} ]^{ζ^{-1}} = b^{ζ^{-1}} ln b ≥ 0
  - Proposition 6: Greater income inequality increases responsiveness of inflation to political bias:
    - For F_1 Lorenz-dominated by F_0 and appropriate assumptions, ∂(∂γ/∂ζ)/∂F (F_1) > ∂(∂γ/∂ζ)/∂F (F_0)
  - Intuition: political bias and income inequality interact multiplicatively to affect the inflation tax.
- Fiscal outcome invariance (Proposition 7):
  - Changes in income distribution and in ζ have no effect on government spending g as a fraction of output net of asset market participation costs:
    - g / [1 - (1 - b_F)^{...}] = β / (1 + β)

### V. Empirical analysis — identification, data, and estimation
- Identification:
  - Difference-in-differences (DD) and Instrumental Variables (IV) exploiting late 1980s/early 1990s democratization wave associated with end of Cold War.
- DD specification (equation (23)):
  - Δb' = α_0 + α_1 Ineq + α_2 ΔBias + α_3 (Ineq × ΔBias) + α_4 X + u ; prediction: α_3 > 0
- IV first-stage (equation (24)):
  - ΔBias instrumented using Cold War alignment measures (S_SOV), indicator D_B≥0.5, quadratic terms and interactions as excluded instruments.
- Data and sample:
  - Time periods: 1975-1989 and 1990-2004
  - Inequality: UNU/WIDER WIID (Gini); quality-coded and adjusted for survey method
  - Political bias proxy: 1 - Polity IV democracy score (scaled 0–1)
  - Dependent variable: change in average inflation tax rate Δb' (IMF IFS)
  - Cold War alliance measures from Tucker (1999) and Signorino & Ritter (1999)
  - Sample: 83 countries
- Selected descriptive statistics (Table 3):
  - Δb' (N=83): mean = -0.0462 ; SD = 2.107 ; min = -0.526 ; max = 2.296
  - Inequality (N=83): mean = 42.29 ; SD = 9.22 ; min = 2.964 ; max = 62
  - ΔBias (N=83): mean = -0.193 ; SD = 0.271 ; min = -0.985 ; max = 0.167
  - S_SOV (N=83): mean = 3.718 ; SD = 1.116 ; min = -6.403 ; max = 5.919
  - D_B≥0.5 (N=83): mean = 0.566 ; SD = 0.499 ; min = 0 ; max = 1

### VI. Empirical results — DD and IV estimates, diagnostics
- Difference-in-Differences (Table 4) — coefficient on interaction Ineq × ΔBias (α_3):
  - Column I (no controls): α_3 = 0.00860 ( :00337 ) ; statistically significant at 5 percent
  - Column II (with controls): α_3 = 0.0112 ( :00460 ) ; statistically significant at 5 percent
  - Column III (dropping country dummies): α_3 = 0.00644 ( :00172 ) ; statistically significant at 0.1 percent
  - Column IV (alternative periods/specification): α_3 = 0.00790 ( :00193 ) ; statistically significant at 0.1 percent
  - Columns V–VI (excluding Eastern Europe or industrialized countries): α_3 = 0.00925 ( :00389 ) and α_3 = 0.00872 ( :00280 ), respectively; statistically significant
- Coefficient on ΔBias (α_2) in DD is negative in all specifications (example Column I: α_2 = -0.389 ( :145 ), significant).
- Sample sizes for DD specifications vary: 83, 81, 134, 79, 61 (see Table 4). R^2 reported per column (example Column I: R^2 = 0.109).
- Instrumental Variables (Table 5) — interaction coefficient Ineq × ΔBias:
  - 2SLS Column I: α_3 = 0.0130 ( :00529 ) ; statistically significant at 5 percent
  - 2SLS Column II: α_3 = 0.0102 ( :00703 ) ; not statistically significant
  - 2SLS Column III (with controls): α_3 = 0.00918 ( :00336 ) ; statistically significant at 0.1 percent
  - LIML Columns (IV–VI) similar (example Column IV: α_3 = 0.0141 ( :00602 ))
- Coefficient on ΔBias (α_2) in IV estimates often negative and sometimes statistically significant (example 2SLS Column I: α_2 = -0.513 ( :190 ), significant).
- Diagnostics:
  - First-stage F statistics reported: 24.6 ; 15.3 ; 3.65 ; 4.02 ; 9.51 ; 6.75 (indicating relevance concerns in some specifications).
  - Over-identification p-values: 0.429; 0.503; 0.529 (suggest instruments pass overidentification tests).
  - Stock and Yogo weak-instrument tests flag potential weak instruments under 2SLS in some specifications; LIML used as robustness.

### VII. Robustness checks and quantitative interpretation
- Robustness to WIID data quality thresholds (Table 6):
  - Interaction coefficient α_3 remains positive across quality thresholds (quality ≤ 3, ≤ 2, ≤ 1).
  - Under strictest quality threshold sample reduced and statistical significance falls.
- Quantitative interpretation examples:
  - Comparing low-inequality countries where one experiences a significant fall in political bias and one does not: differential change in Δb' ≈ 7 percent.
  - Net differential effect between high and low inequality countries ≈ 13 percent; in extreme cases differential in inflation up to about 15 percentage points depending on initial inflation.

### VIII. Key interpretations, puzzles, and policy implications
- Primary empirical finding:
  - Interaction term (Ineq × ΔBias) positive and generally statistically significant — consistent with Proposition 6: inequality amplifies responsiveness of inflation to political bias.
- Puzzles:
  - Negative coefficient on ΔBias alone (α_2 < 0) implies democratization sometimes associated with higher inflation in low-inequality countries — not predicted by baseline model; possible omitted mechanisms (e.g., simultaneous economic reforms, transitional fiscal pressures).
- Policy implication (model-driven):
  - Democratic reforms reduce inflation particularly in unequal societies because they shift political weight away from elites who benefit from regressive seigniorage finance.
- Methodological notes:
  - DD and IV strategies both exploit end of Cold War as source of exogenous democratization.
  - Instruments (Cold War alliance measures) pass over-identification tests; weak-instrument concerns addressed with LIML.

### IX. Conclusions — synthesis of theoretical and empirical results
- Theoretical contribution:
  - Model links distribution of income (inequality) and political bias (elite influence) to inflation via seigniorage choice; political bias and inequality interact multiplicatively to raise inflation (Propositions 4–6).
- Empirical conclusion:
  - Using the late-1980s/early-1990s democratization wave as a quasi-experiment, evidence supports the model’s prediction that greater initial inequality leads democratizing countries to experience larger declines in the inflation tax.
- Caveat:
  - Some empirical patterns (ΔBias negative effect in low-inequality countries) contradict simple model predictions and point to omitted mechanisms meriting further research.

*Source: _wp06158 - introduction. Later I assume a speciÖc functional form for the relationship between agentsí income and their political weight in order to arrive at analytical results. (PDF content unit supplied).*

### References .............................................................................................................

### _wp06158 - References .............................................................................................................

### I. Introduction
- Observed correlations and empirical facts:
  - Countries with more unequal income distribution tend to have higher inflation (references: Albanesi, 2002; Easterly and Fischer, 2001; Dolmas et al., 2000; Bulir, 1998; Beetsma and Van Der Ploeg, 1996).
  - The correlation between a scaled measure of inflation (the “inflation tax rate” ρ/(1+ρ)) and income inequality for a cross-section of 90 countries is 0.22. Both variables are averaged over 1990-2004. The estimated correlation is statistically significant at the 5 percent level.
  - Income inequality is measured by the Gini coefficient (lies between 0 and 1). The inflation transformation ρ/(1+ρ) gives the inflation tax paid on money balances.
- Core hypothesis and mechanism:
  - Political influence depends on income (elite bias). Greater income inequality magnifies disparities in political power, biasing policy toward elites.
  - Inflation can be regressive because the wealthy avoid the inflation tax more easily than others (fixed cost of adopting inflation-proof financial assets).
  - Prediction: reductions in elite bias should reduce inflation more in more unequal societies (interaction effect between inequality and changes in elite bias).
- Contributions:
  - Theoretical: explains the inflation-inequality relationship via a tractable endogenous policy-formation model for general income distributions; captures distributional impacts of inflation and role of elite bias.
  - Empirical: proposes an identification strategy using interaction between initial inequality and changes in elite bias, exploiting a quasi-exogenous democratization shock in the late 1980s–early 1990s (the “third wave” of democratization).
- Empirical approach and initial evidence:
  - Analysis focuses on percentage change in the inflation tax rate between 1975–89 and 1990–2004 for a cross-section of countries.
  - Interaction term: initial income inequality interacted with the change in elite bias (democratization).
  - Instrumental strategy: use Cold War relationships as instruments for democratization (motivated by the end of the Cold War as a likely exogenous contributor to democratization).
  - Table 1 (Mean Percentage Change in the Average Inflation Tax Rate, 1975-89 to 1990-2004) summary:
    - Sample: 83 countries grouped by initial inequality (Low/High) and whether they experienced democratization (No Fall in Bias / Fall in Bias).
    - Cell values (mean percentage change; robust standard errors in parentheses):
      - Low Inequality, No Fall in Bias [A]: -4.8** (1.9)
      - High Inequality, No Fall in Bias: -3.6* (2.1)
      - Difference [2] - [1]: 1.2 (2.8)
      - Low Inequality, Fall in Bias [B]: 2.6 (3.5)
      - High Inequality, Fall in Bias: -9.0*** (2.4)
      - Difference [2] - [1]: -11.6** (4.2)
      - Difference [B] - [A] in Low Inequality: 7.4* (3.9)
      - Difference [B] - [A] in High Inequality: -5.4* (3.2)
      - Interaction (comparison across cells): -12.7** (5.1)
    - Notes: categorical variables defined as above/below mean; numbers of countries in categories (reading left to right, top to bottom): 31, 24, 9, 19. Robust standard errors in parentheses.
  - Empirical methods employed: difference-in-differences (DD) treating democratization as an exogenous treatment whose impact can differ by inequality level; instrumental-variables (IV) approach using Cold War alliances to isolate exogenous democratization.
  - Main empirical finding preview: robust support for the predicted interaction effect using both DD and IV techniques (details in Section IV).

- Relation to existing literature:
  - Complements work showing inflation tends to increase with income inequality through regressive inflation mechanisms (Albanesi, 2002; Bhattacharya et al., 2003; Dolmas et al., 2000; Beetsma and Van DerPloeg, 1996).
  - Cites empirical and theoretical literature on distributional impacts of inflation and fixed costs of access to inflation-hedging assets (Kane and Morisett, 1993; Ferreira and Litchfield, 1999; Cardoso, 1992; Erosa and Ventura, 2002; Luttmer, 1999; Mulligan and Sala-i-Martin, 1996).
  - Contrasts with accounts where greater democracy raises inflation in high-inequality countries (Desai et al., 2003; 2005).
  - Discusses empirical evidence on inflation aversion across income groups (Easterly and Fischer, 2001; Fischer and Huizinga, 1982; Scheve, 2003; 2004) and on elite political influence (Benabou, 2000; 2005; Besley et al., 2005; Crowe, 2005).

### II. Household Optimization (Model Structure and Key Equations)
- Framework and setup:
  - Overlapping generations (OLG) model. Time is discrete. Cohort of households i in each period t, unit mass. Each household lives two periods. Endowments y_i^t drawn from time-invariant distribution F(y_i) over [y_min, y_max], continuous and differentiable, with E[y_i] = 1.
  - Households consume only in the second period of life; endowments are perishable, requiring a transactions technology.
  - Two inherently valueless assets: cash m (supply controlled by government) and a second asset d in fixed nominal supply (an inflation shelter). No uncertainty.
  - Fixed real cost of operating in the market for the second asset denoted ϕ ∈ [0,1], payable if D_i^t = 1 (indicator that household holds any of the second asset).
  - Utility specification (log utility for tractability): U_i = ln c_i^t + β ln g_t.
- Budget constraint and definitions:
  - Budget constraint (as written in source):
    - c_i^t + ϕ_t - y_i^t - D_i^t = m_i^t p_{t+1} + d_i^t q_{t+1}
    - Rewritten (equation (3) in source):
      c_i^t = y_i^t - (1 - z_i^t)(1 - τ_t - b^m_t) y_i^t + (z_i^t - D_i^t)(1 - τ_t - b^q_t) y_i^t
    - Definitions: z_i^t denotes share of saving via the inflation shelter; D_i^t = 1 if z_i^t > 0; b^m_t and b^q_t are “tax rates” due to changes in asset prices (b^m_t is the inflation tax).
  - Optimal asset choice (corner solutions due to fixed cost):
    - z_i^t = 1 if y_i^t > b_y^t; 0 otherwise. (Equation (4) in source)
    - The threshold b_y^t depends on policy parameters.
  - Aggregate real balances and government budget constraint:
    - b m_t ≡ m_t / p_t = ∫_i y_i^t (1 - z_i^t) di = ∫_i j y_i^t [1_{y_i^t < b_y^t}] di. (Equation (5))
    - g_t = τ_t [1 - θ/(1 - b^F_t)] + b m_{t+1} - b m_t + b^m_t b m_t. (Equation (6))
    - b^F_t ≡ ∫_i (1 - D_i^t) di (measure of cash-holders).
  - Government seigniorage revenues arise from increases in demand for money (b m_{t+1} - b m_t) and from taxing real balances (b^m_t b m_t). Households anticipate relative tax rates on consumption via each asset (policy parameter ω_t); ∂ b m_t / ∂ ω_t ≤ 0.

### III. Political Optimization
- Political environment and timing:
  - Probabilistic voting model (Lindbeck and Weibull, 1987; Persson and Tabellini, 2000).
  - Policymakers elected for one period choose (g_t, τ_t, b^m_t) subject to budget constraint. Two candidates A and B; majority voting rule.
  - Timing: cohort t born in period t trades at period t prices; asset choice based on anticipated policy G_t; in period t+1 cohort t votes on platforms G_t^A and G_t^B; asset markets clear; government implements policy; cohort t consumes and dies.
- Politician objectives and representation:
  - Candidates maximize probability of election, equivalent to maximizing a weighted social welfare function subject to budget constraint.
  - Critical reduced-form assumption: agents differ in political weight w_i^t, assumed non-decreasing in income (captures elite bias and unequal political influence).
- Model implications (conceptual):
  - Without elite bias, policymaker uses progressive income tax and all households hold cash (no positive seigniorage).
  - With elite bias sufficiently high, policymaker favors policies beneficial to richer groups, potentially leading to positive seigniorage in equilibrium.
  - The model delivers a positive relationship between inequality and inflation for sufficiently high elite bias.

- Empirical identification strategy (reiterated):
  - Use the late 1980s–early 1990s democratization wave as a quasi-exogenous reduction in elite bias.
  - IV strategy: use Cold War relationships as instruments for democratization to isolate exogenous political change.

*Source: _wp06158 - References (excerpts from pages 3–9 of the supplied PDF).*

### introduction. Later I assume a speciÖc functional form for the relationship between agentsí

### _wp06158 - introduction. Later I assume a speciÖc functional form for the relationship between agentsí income and their political weight in order to arrive at analytical results.

### Model overview and setup
- Policymaker chooses Gt to maximize candidate Aís probability of winning given probabilistic voting with iid uniform noise (equation (7)):
  - p_A_t = 1/2 + ∫_i w_i_t [U_i(G_A_t) - U_i(G_B_t)] di  (equation (7))
- Government balanced-budget constraint and perfect foresight; D_i_t and bm_t predetermined, bm_{t+1} determined by expected policies.
- Define total political weight of cash- and non-cash-holding agents as W_0 and W_1; cash-holders fraction b_F_t:
  - W_0 ≡ ∫_{i: y_i_t ≤ b_y_t} w_i_t di ; W_1 ≡ ∫_{i: y_i_t > b_y_t} w_i_t di
- Political weights derived from endogenous faction grouping; faction weight non-decreasing in faction average income:
  - w_j = (e y_j)^{ζ}; ζ ≥ 0
- Agent weight by cash-holding status (equation (13)):
  - w_i = ( (e y)^{ζ} for y_i ≤ b_y ; (e (y-τ))^{ζ} for y_i > b_y )  (equation (13))

### Analytical results (first-order conditions, equilibrium characterizations)
- First-order conditions for policymaker (FOCs) for variables b'_t, ξ_t and g_t (equations (9)-(11)):
  - 1/(1-ξ_t - b'_t W_0) - ε_{0t} bm_t = 0  [b'_t]  (9)
  - 1/(1-ξ_t - b'_t W_0) + 1/(1-ξ_t - b_q_t W_1) - ε_{0t} (1 - (1 - b_F_t)) = 0  [ξ_t]  (10)
  - β (W_0 + W_1) - ε_{0t} = 0  [g_t]  (11)
- Combining (9)–(10) yields political-economy interior solution (Proposition 1, equation (8)):
  - γ_t(by_t) = (W_1 bm_t) / (W_0 [1 - bm_t - (1 - b_F_t)])  (equation (8))
- Corner solution: f_t = 1; z_i_t = 0 for all i is always an equilibrium but not plausible if internal solution (8) exists.

### Ramsey (first-best) case (Proposition 2)
- Ramsey equilibrium (equal household weights w_i_t = w̄_i) has non-positive inflation tax rate and all agents hold cash:
  - Result: all agents hold cash in every period ⇒ b_q = 0 and b' ≤ 0 (Proposition 2; equation (12) shows inconsistency of γ > 1)
  - Intuition: seigniorage is regressive; absent political economy, policymaker avoids seigniorage.

### Special functional form and equilibrium conditions
- Asset-holding condition (households) (equation (14)):
  - D_t = b_y_t / (b_y_t - τ)  (equation (14))
- Political-economy interior solution under the specific weighting function (equation (15)):
  - γ_t = [ (1 - b_F_t) (y - τ)^{ζ} / (b_F_t y^{ζ}) ] [ bm_t / (1 - bm_t - (1 - b_F_t)) ] = [ ((y - τ)/y)^{ζ} ]^{ζ^{-1}}  (equation (15))
- Stationary solution: γ_t = γ = (1 - ξ)/(1 - ξ - b')_t  (equation (17)); since ζ > 1 sufficient for interior solution, assume ζ > 1 going forward.

### Existence and uniqueness (Proposition 3)
- Assume (y_max - τ) > 1. Then an equilibrium with γ > 1 exists if ζ > 1 (Proposition 3).
- Marginal cost (MC) and marginal benefit (MB) comparison yields an intermediate γ with MC = MB (equation (16)).

### Comparative statics and inequality link (Propositions 4–6)
- Political-economy solution can be represented as iso-γ lines in (F, L) Lorenz parameter space; increases in γ correspond to downward shifts in iso-γ lines analogous to Lorenz dominance.
- Proposition 4: For two income distributions F_0 and F_1 where F_1 is Lorenz dominated by F_0 (and both satisfy Appendix assumptions), γ(b_y; F_1) > γ(b_y; F_0).
- Proposition 5: Optimal policy γ is increasing in ζ:
  - ∂γ/∂ζ = ∂/∂ζ [ ((y - τ)/y)^{ζ} ]^{ζ^{-1}} = b^{ζ^{-1}} ln b ≥ 0  (equation (20))
- Proposition 6: Greater income inequality increases responsiveness of inflation to political bias:
  - For F_1 Lorenz-dominated by F_0 and appropriate assumptions, ∂(∂γ/∂ζ)/∂F (F_1) > ∂(∂γ/∂ζ)/∂F (F_0) (equation (21))
  - Intuition: political bias and income inequality interact multiplicatively to affect inflation tax.

### Fiscal outcome invariance (Proposition 7)
- Changes in income distribution and in ζ have no effect on government spending g as a fraction of output net of asset market participation costs:
  - g / [1 - (1 - b_F)^{...}] = β / (1 + β)  (equation (22))
  - Government spending depends only on parameter β (importance of public good in utility).

### Empirical analysis — identification strategy and data
- Identification: Difference-in-differences (DD) and Instrumental Variables (IV) exploiting the late 1980s/early 1990s wave of democratization (treated as exogenous shock associated with end of Cold War).
- DD regression (equation (23)):
  - Δb' = α_0 + α_1 Ineq + α_2 ΔBias + α_3 (Ineq × ΔBias) + α_4 X + u ; prediction: α_3 > 0
- IV first-stage specification for ΔBias (equation (24)) uses Cold War alignment measures (S_SOV), indicator D_B≥0.5, and quadratic terms and interactions as excluded instruments.
- Data:
  - Time periods: 1975-1989 and 1990-2004
  - Inequality: UNU/WIDER WIID (Gini); quality-coded and adjusted for survey method
  - Political bias proxy: 1 - Polity IV democracy score (scaled 0–1)
  - Dependent variable: change in average inflation tax rate Δb' (IMF IFS)
  - Cold War alliance measures from Tucker (1999) and Signorino & Ritter (1999)
  - Sample: 83 countries; Table 3 descriptive statistics include:
    - Δb' (N=83): mean = -0.0462 ; SD = 2.107 ; min = -0.526 ; max = 2.296
    - Inequality (N=83): mean = 42.29 ; SD = 9.22 ; min = 2.964 ; max = 62
    - ΔBias (N=83): mean = -0.193 ; SD = 0.271 ; min = -0.985 ; max = 0.167
    - S_SOV (N=83): mean = 3.718 ; SD = 1.116 ; min = -6.403 ; max = 5.919
    - D_B≥0.5 (N=83): mean = 0.566 ; SD = 0.499 ; min = 0 ; max = 1

### Empirical results — Difference-in-Differences (selected estimates)
- DD regressions (Table 4) — coefficient on interaction Ineq × ΔBias (α_3):
  - Column I (no controls): α_3 = 0.00860 ( :00337 ) ; statistically significant at 5 percent
  - Column II (with controls): α_3 = 0.0112 ( :00460 ) ; statistically significant at 5 percent
  - Column III (dropping country dummies): α_3 = 0.00644 ( :00172 ) ; statistically significant at 0.1 percent
  - Column IV (alternative periods/specification): α_3 = 0.00790 ( :00193 ) ; statistically significant at 0.1 percent
  - Columns V–VI (excluding Eastern Europe or industrialized countries): α_3 = 0.00925 ( :00389 ) and α_3 = 0.00872 ( :00280 ), respectively; statistically significant
- Coefficient on ΔBias (α_2) is negative in all DD specifications (e.g., Column I: α_2 = -0.389 ( :145 ), significant).

- Sample sizes and statistics:
  - Observations vary by specification: 83, 81, 134, 79, 61 (see Table 4)
  - R^2 reported per column (e.g., Column I: R^2 = 0.109)

### Empirical results — Instrumental Variables (selected estimates)
- IV (2SLS and LIML) results (Table 5) — interaction coefficient on Ineq × ΔBias:
  - 2SLS Column I: α_3 = 0.0130 ( :00529 ) ; statistically significant at 5 percent
  - 2SLS Column II: α_3 = 0.0102 ( :00703 ) ; not statistically significant
  - 2SLS Column III (with controls): α_3 = 0.00918 ( :00336 ) ; statistically significant at 0.1 percent
  - LIML Columns (IV–VI) produce similar estimates (e.g., Column IV: α_3 = 0.0141 ( :00602 ))
- Coefficient on ΔBias (α_2) in IV estimates often negative and sometimes statistically significant (e.g., 2SLS Column I: α_2 = -0.513 ( :190 ), significant).
- Diagnostics:
  - First-stage F statistics reported (e.g., 24.6 ; 15.3 ; 3.65 ; 4.02 ; 9.51 ; 6.75) indicating relevance concerns in some specs
  - Over-identification p-values (e.g., 0.429; 0.503; 0.529) suggest instruments pass overidentification tests
  - Stock and Yogo weak-instrument tests flag potential weak instruments under 2SLS in some specifications; LIML used as robustness.

### Robustness and additional checks
- Robustness to WIID data quality thresholds (Table 6):
  - Interaction coefficient α_3 remains positive across quality thresholds (quality ≤ 3, ≤ 2, ≤ 1)
  - Under strictest quality threshold sample reduced and statistical significance falls (likely due to smaller N)
- Quantitative interpretation:
  - Comparing low-inequality countries where one experiences a significant fall in political bias and one does not: differential change in Δb' ≈ 7 percent
  - Net differential effect between high and low inequality countries ≈ 13 percent; in extreme cases differential in inflation up to about 15 percentage points depending on initial inflation

### Key empirical interpretation and discussion
- Primary empirical finding: interaction term (Ineq × ΔBias) positive and generally statistically significant — consistent with Proposition 6 that inequality amplifies responsiveness of inflation to political bias.
- Unexpected finding: negative coefficient on ΔBias alone (α_2 < 0) implies democratization sometimes associated with higher inflation in low-inequality countries — a result not predicted by the baseline model and suggested as area for further research.
- Methodological points:
  - DD and IV identification strategies both exploit end of Cold War as source of exogenous democratization
  - Instruments (Cold War alliance measures) pass over-identification tests; weak-instrument concerns exist but LIML robustness checks support findings.

### Conclusions (empirical and theoretical synthesis)
- Theoretical contribution: model links distribution of income (inequality) and political bias (elite influence) to inflation via seigniorage choice; political bias and inequality interact multiplicatively to raise inflation (Propositions 4–6).
- Empirical conclusion: using the late-1980s/early-1990s democratization wave as a quasi-experiment, evidence supports the modelís prediction that greater initial inequality leads democratizing countries to experience larger declines in the inflation tax (i.e., inequality amplifies the effect of political change on inflation).
- Policy implication (model-driven): democratic reforms reduce inflation particularly in unequal societies because they shift political weight away from elites who benefit from regressive seigniorage finance.
- Caveat: some empirical patterns (ΔBias negative effect in low-inequality countries) contradict simple model predictions and point to omitted mechanisms (e.g., simultaneous economic reforms, transitional fiscal pressures) meriting further research.

*Italic: Source — _wp06158 - introduction. Later I assume a speciÖc functional form for the relationship between agentsí income and their political weight in order to arrive at analytical results. (PDF content unit supplied).*

### REFERENCES

### REFERENCES

### Inflation, Inequality, and Poverty
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- Cardoso, Eliana, 1992, “Inflation and Poverty,” NBER Working Paper No. 4006 (Cambridge, Massachusetts: National Bureau of Economic Research).  
- Datt, Gaurav, and Martin Ravallion, 2002, “Why has Economic Growth been more Pro-Poor   in some States of India than in Others?” Journal of Development Economics, Vol. 57,   pp. 259–87.  
- Easterly, William and Stanley Fischer, 2001, “Inflation and the Poor,” Journal of Money, Credit and Banking, Vol. 33, pp. 160–78.  
- Erosa, Andres, and Gustavo Ventura, 2002, “On Inflation as a Regressive Consumption Tax,” Journal of Monetary Economics, Vol. 49, pp. 761–95.  
- Ferreira, Francisco, and Julie Litchfield, 1999,  “Education or Inflation? The Roles of Structural Factors and Macroeconomic Instability in Explaining Brazilian Inequality in the 1980s,” Distributional Analysis Research Programme Discussion Paper No. 41, STICERD, London School of Economics.  
- Romer, C., and D. Romer, 1998, “Monetary Policy and the Well-Being of the Poor,” NBER Working Paper No. 6793 (Cambridge, Massachusetts: National Bureau of Economic Research).  
- Shiller, Robert, 1996, “Why Do People Dislike Inflation? NBER Working Paper No. 5539 (Cambridge, Massachusetts: National Bureau of Economic Research).  
- Beetsma, Roel, and Frederick Van Der Ploeg, 1996, “Does Inequality Cause Inflation? The Political Economy of Inflation, Taxation and Government Debt,” Public Choice, Vol. 87, pp. 143–62.  
- Bhattacharya, Joydeep, Helle Bunzel, and Joseph Haslag, 2003, “Inflationary Finance in a Simple Voting Model,” Working Paper 03012 (Ames, Iowa: Iowa State University).  
- Epaulard, Anne, 2003, “Macroeconomic Performance and Poverty Reduction,” IMF Working Paper 03/72 (Washignton: International Monetary Fund).  
- Bulir, Ales, 1998, “Income Inequality: Does Inflation Matter?” IMF Working Paper 98/7  (Washington: International Monetary Fund).   

### Political Economy, Democracy, and Public Choice
- Alesina, Alberto, and Dani Rodrik, 1994, “Distributive Politics and Economic Growth,”  Quarterly Journal of Economics, Vol. 109, No. 2, pp. 465–90.  
- Benabou, Roland, 2005, “Inequality, Technology and the Social Contract,” in Handbook of Economic Growth, Vol. 1, No.2, pp. 1595–1638, ed. by Philippe Aghion and Steven Durlauf (North-Holland).  
- ———, 2000, “Unequal Societies: Income Distribution and the Social Contract,” American Economic Review, Vol. 90, No. 1, pp. 96–129.  
- Besley, Timothy, and Anne Case, 2000, “Unnatural Experiments? Estimating the Incidence of Endogenous Policies,” Economic Journal, Vol. 110, No. 467, pp. F672-F694.  
- Besley, Timothy, Torston Persson, and Daniel Sturm, 2005, Political Competition and Economic Performance:  Theory and Evidence from the United States, (unpublished; London: London School of Economics).  
- Downs, Anthony, 1957, An Economic Theory of Democracy (New York: Harper and Row).  
- Desai, Raj M., Anders Olofsgard, and Tarik M. Yousef, 2003, “Democracy, Inequality and Inflation,” American Political Science Review, Vol. 97, No. 3, pp. 391–406.  
- ———, 2005, “Inflation and Inequality: Does Political Structure Matter?” Economics Letters, Vol. 87, No. 1, pp. 41–6.  
- Lindbeck, Assar, and Jorgen Weibull, 1987, “Balanced-Budget Redistribution as the Outcome of Political Eompetition,” Public Choice, 52, pp. 273–97.  
- Mulligan, Casey B., Ricard Gil, and Xavier Sala-i-Martin, 2004, “Do Democracies have Different Public Policies than Nondemocracies?” Journal of Economic Perspectives   Vol. 18 (1), pp. 51–74.  
- Persson, Torsten, and Guido Tabellini, 2000, Political Economics:  Explaining Economic Policy (Cambridge, Massachusetts: MIT Press).  
- Huntington, Samuel, 1991, The Third Wave: Democratization in the Late Twentieth Century (Norman: University of Oklahoma Press).  
- Jaggers, Keith, and Ted Robert Guff, 1995, “Tracking Democracy’s Third Wave with the Polity III Data,” Journal of Peace Research  32 (4), pp. 469–82.  
- Marshall, Monty G., and Keith Jaggers, 2001, Polity IV Project:  Political Regime Characteristics and Transitions, 1800–1999 (Maryland: University of Maryland Center for International Development and Conflict Management.  Available from <http://www.cidcm.umd.edu/inscr/polity/>  
- Simensen, Jarle, 1999, “Democracy and Globalization:  Nineteen Eighty-Nine and the ‘Third Wave’” Journal of World History 10 (2), pp. 391–411.  
- Mulligan, Casey B., and Xavier Sala-i-Martin, 1996, “Adoption of Financial Technologies:  Implications for Money Demand and Monetary Policy,” NBER Working Paper No. 5504 (Cambridge, Massachusetts: National Bureau of Economic Research).  

### Monetary Policy, Central Banking, and Public Preferences
- Fischer, Stanley, and John Huizinga, 1982, “Inflation, Unemployment, and Public Opinion Polls,” Journal of Money, Credit and Banking, Vol. 14 (1), pp. 1-19.  
- Dolmas, Jim, Gregory W. Huffman, and Mark A. Wynne, 2000, “Inequality, Inflation and Central Bank Independence,” Canadian Journal of Economics, Vol. 33, No. 1,              pp. 271–87.  
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- Kane, Cheikh, and Jacques Morisett, 1993, “Who Would Vote for Infation in Brazil?” World Bank Policy Research Working Paper WPS 1183 (Washington: The World Bank).  
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- ———, 2004, “Public Inflation Aversion and the Political Economy of Macroeconomic Policymaking,” Industrial Organisation 58, pp. 1–34.  
- Bhattacharya, Joydeep, Helle Bunzel, and Joseph Haslag, 2003, “Inflationary Finance in a Simple Voting Model,” Working Paper 03012 (Ames, Iowa: Iowa State University).  

### Econometric Methods, Identification, and Measurement
- Aitchison, J., and J. A. C. Brown, 1957,  The Lognormal Distribution (Cambridge, Massachusetts: Cambridge University Press).  
- Baltagi, Badi H., 2001, Econometric Analysis of Panel Data (Chichester, U.K.: John Wiley & Sons, Ltd., 2nd ed.).  
- Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan, 2004, “How Much Should We Trust Differences-in-Differences Estimates?” Quarterly Journal of Economics, Vol. 119,  No. 1, pp. 249–75.  
- Signorino, Curtis S., and Jeffrey M. Ritter, 1999, “Tau-b or Not Tau-b: Measuring the Similarity of Foreign Policy Positions,” International Studies Quarterly Vol. 43 (1),     pp. 115–44.  
- Stock, James H., Jonathan H. Wright, and Motohiro Yogo, 2002, “A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments,” Journal of Business and Economic Statistics 20 (4), pp. 518–29.  
- Stock, James H., and Motohiro Yogo, 2002, “Testing for Weak Instruments in Linear IV Regression,” Technical Working Paper 284 (Cambridge, Massachusetts: National Bureau of Economic Research).  

### Data Sources, Tables, and Databases
- GNU/WIDER-UNDP, 2005, UNU/WIDER-UNDP World Income Inequality Database, Version 2.0, June 2005.  
- Heston, Alan, Robert Summers, and Bettina Aten, 2002, Penn World Table Version 6.1 (Philadelphia, Pennsylvania: Center for International Comparisons at the University of Pennsylvania (CICUP).  
- Click, Reid, 1998, “Seigniorage in a Cross-Section of Countries,” Journal of Money, Credit and Banking, Vol. 30, No. 2, pp. 154–71.  
- Tucker, Richard, 1999, Similarity of Alliance Portfolios, 1816–1984. Version 2.50. Available from <http://www.vanderbilt.edu/ ̃rtucker/data/affinity/alliance/similar>  

### Other Relevant Studies and Books
- Blum, William, 2003, Killing Hope: UW Military and CIA Interventions since World War II, (London: Zed Books).  
- Crowe, Christopher, 2005, “The Political Economy of Macroeconomic Policy” (Ph.D. Thesis;  London: University of London).  
- Luttmer, Erzo G., 1999, “What Level of Fixed Costs Can Reconcile Consumption and Stock Returns,” Journal of Political Economy, Vol. 107 (5), pp. 969–97.  
- Romer, C., and D. Romer, 1998, “Monetary Policy and the Well-Being of the Poor,” NBER Working Paper No. 6793 (Cambridge, Massachusetts: National Bureau of Economic Research).  
- Milesi-Ferretti, Gian Maria, 1994, “Wage Indexation and Time Inconsistency,” Journal of Money, Credit and Banking, Vol. 26, pp. 941–50.  

*Source: _wp06158 - REFERENCES*

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