Theory of Fiscal Responsibility and Irresponsibility: Halac & Yared (2024)

What this is. The paper’s core propositions, the equilibrium model, and the factorization method with the defining equations: enough to know what it found and how, without reading all 47 pages. To replicate or extend it, read the full source at the original.

TL;DR

The paper presents a political economy model of fiscal policy in which successive deficit-biased governments, each privately observing an i.i.d. shock to the social value of deficit-financed spending, interact dynamically. When the parameters and interior-debt conditions support them, the best equilibrium has a fiscally responsible regime (a maximally enforced deficit limit that restrains overborrowing) and a fiscally irresponsible regime (a maximally enforced surplus limit that induces further overborrowing as punishment). Transitions are triggered by sufficiently high fiscal shocks, so policy depends on history even though shocks are i.i.d. In the log-utility example, regimes require a sufficiently high discount factor and sufficiently large deficit bias; this offers a theoretical account of why fiscal consolidations may cluster at crisis periods. Related dynamic models by Battaglini and Coate (2008) and Yared (2010) study publicly observable shocks; Yared (2010) also features more persistence than Markov outcomes. Private information combined with limited commitment generates the history-dependent regime dynamics here.

Core results

#	Result	Locator	Magnitude as reported
R1	Two-Regime Bang-Bang: under the paper’s interior-debt and regularity conditions, on-path continuation values in the best equilibrium take only the highest or lowest feasible value	Proposition 1, p. 1588	If debt is interior on path and $Q'(\theta) \neq 0$ almost everywhere, $V_{t+1}(h^{t-1}, b_t) \in \{\underline{V}(b_t),\bar{V}(b_t)\}$ at every on-path history
R2	Fiscally Responsible Regime = Deficit Limit: under the proposition’s interior-debt condition, the welfare-maximizing regime is a maximally enforced deficit limit; low-shock governments borrow flexibly, mid-shock governments are constrained at the limit, and sufficiently high-shock governments break it	Proposition 2, p. 1590; Figure 2 (left panel), p. 1591	Three-threshold structure parameterized by $\theta^*$ and $\theta^{**}$: borrowing is at the limit $b^r(\omega,\theta^*)$ for $\theta \in [\theta^*,\theta^{**}]$ and breaks the limit for $\theta > \theta^{**}$
R3	Fiscally Irresponsible Regime = Surplus Limit: the welfare-minimizing punishment regime is a maximally enforced surplus limit; all types borrow weakly above their own preferred level, and some strictly above it. High-shock governments borrow flexibly, mid-shock governments are constrained, and sufficiently low-shock governments break the limit and remain irresponsible; the regime is always temporary	Proposition 3, p. 1592; Figure 2 (right panel), p. 1591	Surplus limit threshold satisfies $\theta_n^{**} < \bar{\theta}$, ensuring that types $\theta \in [\theta_n^{**}, \bar{\theta}]$ respect the limit with positive probability and return the economy to responsibility, so the irresponsible regime is never absorbing
R4	Regime Transitions at Crises: transitions from fiscal responsibility to irresponsibility occur when a shock exceeds $\theta^{**}$; transitions from irresponsibility to responsibility occur when a shock is at least $\theta_n^{**}$; fiscal policy depends on history, not just current conditions	Section IV.E, pp. 1594-1595	Starting in the responsible regime: $\theta_t \leq \theta^{**}$ keeps the economy responsible at $t+1$; $\theta_t > \theta^{**}$ triggers irresponsibility. Starting in the irresponsible regime: $\theta_t \geq \theta_n^{**}$ triggers return to responsibility
R5	Deficit Bias Threshold for Fiscal Regimes (analytical example, log utility): regimes arise if and only if the discount factor $\delta$ exceeds a cutoff $\tilde{\delta}$ and deficit bias $\alpha$ exceeds a cutoff $\tilde{\alpha}$; the Markov equilibrium is unique when the bias is too small	Proposition 4, p. 1597; Corollary 1, p. 1598	For $\delta > \tilde{\delta}$, regimes exist iff $T'(0) > 1$, equivalent to $\alpha > \tilde{\alpha}$; $\tilde{\alpha}$ decreases with $\delta$. On-path transitions occur over a distinct range $\alpha \in (\tilde{\alpha},\tilde{\tilde{\alpha}})$ for some $\tilde{\tilde{\alpha}} > \tilde{\alpha}$
R6	Numerical Simulation (calibrated to US data, 1970-2020): the simulated fiscal path shows two extended shaded periods of irresponsibility; responsible-regime spending is sometimes constrained below the flexible Markov rate, while both rates exceed the first-best at all dates	Figure 4, p. 1602	Parameters: $\alpha = 1.151$, $\delta = 0.943$, lognormal shocks with mean 0 and variance $\xi = 0.175$, $R = 1.05$. Deficit-limit threshold = 0.0736 (flexible spending rate of $\theta^*$); surplus-limit threshold = 0.0867 (flexible spending rate of $\theta_n^*$)
R7	Fiscal consolidations cluster around recessions in the motivating evidence: the introduction documents prolonged consolidation waves for the United States and European Union, with consolidations tending to begin and end during recessions	Figure 1 and discussion, pp. 1575-1576	Alesina, Favero, and Giavazzi (2019) data cover the United States and European Union from 1980 to 2014; the figure reports a descriptive pattern, not an estimated coefficient
R8	Either missing friction removes regime history dependence: without deficit bias or with observable fiscal shocks, the best equilibrium restarts each period at the highest feasible continuation value	Lemma 1, p. 1586	$V_{t+1}(h^{t-1}, b_t) = \bar{V}(b_t)$ at every on-path history if $\alpha=1$ or the shock is observable; regimes do not arise
R9	Transitions occur on path for a nonempty range of deficit biases: for a sufficiently patient society and bias above the regime-existence cutoff, the deficit limit is tight enough to be broken after some high shocks	Corollary 1, p. 1598	For $\delta>\tilde{\delta}$ there is $\tilde{\tilde{\alpha}}>\tilde{\alpha}$ such that transitions occur on path when $\alpha\in(\tilde{\alpha},\tilde{\tilde{\alpha}})$

Overall (paper’s conclusion). The same deficit bias that can lead governments to overaccumulate debt is also a key factor behind the emergence of fiscal regimes: when bias is large enough and the discount factor is high enough, the threat of fiscal irresponsibility in the future makes fiscal responsibility in the present sustainable. Regime transitions are punctuated by crises, and fiscal policy depends on the history of past decisions, consistent with econometric evidence of two-regime fiscal dynamics documented for the United States and the European Union.

Theory / model

The model is an infinite-horizon small open economy with periods $t = \{0, 1, \ldots\}$ in which a new government takes power each period (§II.A, p. 1581). At the beginning of period t, an i.i.d. shock to the social value of spending is drawn from:

$\theta_t \in \Theta \equiv [\underline{\theta}, \bar{\theta}], \quad f(\theta) > 0, \quad F(\cdot) \text{ its CDF}$

The shock is privately observed by the government in power at date t (its “type”). The government budget constraint (eq. 1, p. 1581) is:

g_t = \tau - Rb_{t-1} + b_t \tag{1}

where $\tau > 0$ is exogenous tax revenue, $R > 1$ is the exogenous gross interest rate on government bonds, $b_t$ is the government’s debt choice within exogenous bounds, and $g_t \geq 0$ is government spending. The debt choice is not restricted to be nonnegative. Letting $\omega(h^{t-1}) \equiv \tau - Rb_{t-1}(h^{t-1})$ denote available resources given inherited debt, spending satisfies $g_t = \omega + b_t$.

Social welfare at date t (p. 1581):

$V_t = \mathbb{E}_t\!\left[\sum_{k=0}^{\infty} \delta^k \theta_{t+k} U(g_{t+k})\right] = \mathbb{E}_t\!\left[\theta_t U(g_t) + \delta V_{t+1}\right]$

where $\delta \in (0,1)$ is the social discount factor and $U(\cdot)$ is strictly increasing and strictly concave. A large shock $\theta_t$ represents a high social value of deficit-financed spending, as in an economic crisis.

Government welfare at date t (eq. 2, p. 1582):

W_t = \alpha \theta_t U(g_t) + \delta V_{t+1} \tag{2}

where $\alpha > 1$ is the deficit bias: the government overvalues current utility of spending relative to society by a factor $\alpha$, capturing private benefits from directing resources to preferred spending categories or constituencies (Aguiar and Amador 2011). Crucially, the government at date t shares society’s preferences from date $t+1$ onward.

There are three frictions: (i) deficit bias ($\alpha > 1$), (ii) private information ($\theta_t$ observed only by the period-t government), and (iii) limited commitment (no external enforcement; only future equilibrium behavior can reward or punish). Lemma 1 (p. 1586) shows that either deficit bias or private information alone is insufficient to generate history dependence: both frictions together are necessary.

Equilibrium (§II.B, p. 1582-1583). A strategy for the period-t government is $\sigma_t(h^{t-1}, \theta_t)$: a feasible debt level for each public history $h^{t-1} = \{b_{-1}, b_0, \ldots, b_{t-1}\}$ and type $\theta_t$. Two incentive constraints must hold for all histories:

Private information constraint (eq. 3, p. 1583): for all $\theta, \theta' \in \Theta$,

\alpha\theta U(\omega + b(\theta)) + \delta V(b(\theta)) \geq \alpha\theta U(\omega + b(\theta')) + \delta V(b(\theta')) \tag{3}

Limited commitment constraint (eq. 4, p. 1583): for all $\theta \in \Theta$ and all $b'_t$ not prescribed for any type,

\alpha\theta U(\omega + b(\theta)) + \delta V(b(\theta)) \geq \alpha\theta U(\omega + b'_t) + \delta V(b'_t) \tag{4}

Given debt is bounded and shocks i.i.d., there exist highest and lowest continuation values $\bar{V}(b)$ and $\underline{V}(b)$ achievable in equilibrium from debt level b. The government’s flexible borrowing conditional on the worst punishment is (eq. 5, p. 1584):

b^p(\omega,\theta) \in \arg\max_{b \in [\underline{b}(b_{t-1}),\bar{b}(b_{t-1})]} \{\alpha\theta U(\omega + b) + \delta \underline{V}(b)\} \tag{5}

A necessary condition for the limited commitment constraint (4) to hold is (eq. 6, p. 1584):

\alpha\theta U(\omega + b(\theta)) + \delta V(b(\theta)) \geq \alpha\theta U(\omega + b^p(\omega,\theta)) + \delta \underline{V}(b^p(\omega,\theta)) \tag{6}

Constraints (3) and (6) are necessary and sufficient for a debt sequence to be supported by equilibrium strategies.

Best equilibrium recursive program ($\mathcal{P}_{\max}$, §II.C, p. 1584-1585):

\bar{V}(b_{-1}) = \max_{b(\theta),\, V(b(\theta))} \mathbb{E}[\theta U(\omega + b(\theta)) + \delta V(b(\theta))] \tag{$\mathcal{P}_{\max}$}

The recursive program is subject to the three conditions printed as eqs. 7-9 (§II.C, pp. 1584-1585):

\alpha\theta U(\omega + b(\theta)) + \delta V(b(\theta)) \geq \alpha\theta U(\omega + b(\theta')) + \delta V(b(\theta')) \quad \forall\theta,\theta' \in \Theta \tag{7}

\alpha\theta U(\omega + b(\theta)) + \delta V(b(\theta)) \geq \alpha\theta U(\omega + b^p(\omega,\theta)) + \delta \underline{V}(b^p(\omega,\theta)) \quad \forall\theta \in \Theta \tag{8}

b(\theta) \in [\underline{b}(b_{-1}),\bar{b}(b_{-1})], \quad V(b(\theta)) \in [\underline{V}(b(\theta)),\bar{V}(b(\theta))] \quad \forall\theta \in \Theta \tag{9}

The worst-case program $\mathcal{P}_{\min}$ minimizes the same objective subject to (7)-(9), yielding $\underline{V}(b_{-1})$. Assumption 1 (p. 1585) ensures these value functions are continuously differentiable and concave with $\bar{V}(b) > \underline{V}(b)$; this holds for CARA and CRRA preferences.

Virtual welfare rewrite (§IV.A, p. 1587). Following Amador, Werning, and Angeletos (2006), substituting the envelope condition of the private-information constraint into the objective of $\mathcal{P}_{\max}$ yields the virtual welfare representation (eq. 11, p. 1587):

The associated envelope representation of government welfare is eq. 10 (p. 1587):

\alpha\theta U(\omega+b(\theta)) + \delta V(b(\theta)) = \alpha\underline{\theta}U(\omega+b(\underline{\theta})) + \delta V(b(\underline{\theta})) + \alpha\int_{\underline{\theta}}^{\theta} U(\omega+b(\tilde{\theta}))\,d\tilde{\theta} \tag{10}

\alpha\underline{\theta} U(\omega + b(\underline{\theta})) + \delta V(b(\underline{\theta})) + \alpha \int_{\underline{\theta}}^{\bar{\theta}} U(\omega + b(\theta)) Q(\theta)\, d\theta \tag{11}

where the virtual welfare weight is:

$Q(\theta) \equiv 1 - F(\theta) - \theta f(\theta)\!\left(1 - \tfrac{1}{\alpha}\right)$

The first term $1 - F(\theta)$ is the standard virtual surplus from mechanism design (Myerson 1981); the second term $-\theta f(\theta)(1 - 1/\alpha)$ captures society’s cost of prescribing higher borrowing when governments are biased. Assumption 2 (p. 1589) requires $Q'(\theta) < 0$ for $\theta < \hat{\theta}$ and $Q'(\theta) > 0$ for $\theta > \hat{\theta}$, which holds for uniform, exponential, lognormal, gamma, and beta distributions over a range of parameters.

Method

Recursive representation (§II.C, p. 1584). Because shocks are i.i.d. and debt is bounded, the best equilibrium can be characterized via a static per-period optimization ($\mathcal{P}_{\max}$ above) by assigning each type $\theta$ a debt level $b(\theta)$ and a continuation value $V(b(\theta))$ drawn from the feasible set $[\underline{V}(b),\bar{V}(b)]$. The per-period problem embeds the infinite-horizon structure entirely through the continuation value set. This recursive representation uses the promised-utility-recursion technique generalized to the Markovian adverse-selection setting.

Bang-bang structure (Proposition 1, p. 1588). Under the proposition’s assumptions (interior debt on path and $Q'(\theta) \neq 0$ almost everywhere), perturbation arguments on $\mathcal{P}_{\max}$ show that interior continuation values are suboptimal: for any solution with interior $V(b(\theta))$, there is a perturbation that either compresses borrowing (when $Q'(\theta) < 0$) or steepens it (when $Q'(\theta) > 0$), strictly increasing social welfare. Hence the optimal continuation values take only the two extreme values $\{\underline{V}(b),\bar{V}(b)\}$. The proof uses the mechanism-design and principal-agent perturbation technique from Halac and Yared (2022), extended to the dynamic limited-commitment setting.

Maximally enforced limits (Propositions 2-3, pp. 1590, 1592). Given the bang-bang property, the best equilibrium prescribes a threshold structure. For the fiscally responsible regime ($\mathcal{P}_{\max}$), the solution satisfies (eq. 12, p. 1590):

\bigl(b(\theta), V(b(\theta))\bigr) = \begin{cases} \bigl(b^r(\omega,\theta),\, \bar{V}(b^r(\omega,\theta))\bigr) & \text{if } \theta < \theta^*, \\ \bigl(b^r(\omega,\theta^*),\, \bar{V}(b^r(\omega,\theta^*))\bigr) & \text{if } \theta \in [\theta^*,\theta^{**}], \\ \bigl(b^p(\omega,\theta),\, \underline{V}(b^p(\omega,\theta))\bigr) & \text{if } \theta > \theta^{**}, \end{cases} \tag{12}

where $b^r(\omega,\theta) \equiv \arg\max_{b} \{\alpha\theta U(\omega+b) + \delta\bar{V}(b)\}$ is the flexible borrowing conditional on the highest continuation value. The limited commitment constraint binds with equality at the threshold type $\theta^{**}$ (eq. 13, p. 1590):

\alpha\theta^{**} U(\omega + b^r(\omega,\theta^*)) + \delta\bar{V}(b^r(\omega,\theta^*)) = \alpha\theta^{**} U(\omega + b^p(\omega,\theta^{**})) + \delta\underline{V}(b^p(\omega,\theta^{**})) \tag{13}

The fiscally irresponsible regime ($\mathcal{P}_{\min}$, Proposition 3) takes the mirror form: a maximally enforced surplus limit at $b^r(\omega,\theta_n^*)$, with high types $\theta > \theta_n^*$ borrowing at their flexible level, mid-types constrained at the surplus limit, and low types $\theta < \theta_n^{**}$ breaking the limit and remaining in the irresponsible regime.

For the worst-equilibrium program, Proposition 3 gives the mirror policy and the binding limited-commitment threshold condition (eqs. 14-15, p. 1592):

\bigl(b(\theta),V(b(\theta))\bigr)=\begin{cases}\bigl(b^r(\omega,\theta),\bar{V}(b^r(\omega,\theta))\bigr)&\text{if }\theta>\theta_n^*,\\\bigl(b^r(\omega,\theta_n^*),\bar{V}(b^r(\omega,\theta_n^*))\bigr)&\text{if }\theta\in[\theta_n^{**},\theta_n^*],\\\bigl(b^p(\omega,\theta),\underline{V}(b^p(\omega,\theta))\bigr)&\text{if }\theta<\theta_n^{**},\end{cases} \tag{14}

\alpha\theta_n^{**}U(\omega+b^r(\omega,\theta_n^*)) + \delta\bar{V}(b^r(\omega,\theta_n^*)) = \alpha\theta_n^{**}U(\omega+b^p(\omega,\theta_n^{**})) + \delta\underline{V}(b^p(\omega,\theta_n^{**})) \tag{15}

Factorization algorithm (§V.C, p. 1599-1600). In the analytical example with $U(\cdot) = \log(\cdot)$, the gap between highest and lowest value functions is constant in debt: $\bar{V}(b) - \underline{V}(b) = P^*$ for some $P^* \geq 0$ (eq. 17, p. 1596). The equilibrium with fiscal regimes corresponds to the largest fixed point of the operator $T(P)$, which computes the largest self-enforceable punishment today given a punishment of size P available tomorrow (eq. 21, p. 1599):

The log-utility example rewrites spending in terms of a saving rate and expresses social welfare as (eq. 16, p. 1595):

g_t=(1-s_t)R\left(\frac{\tau}{R-1}-b_{t-1}\right), \quad V_t=\mathbb{E}_t\left[\sum_{k=0}^{\infty}\delta^k\left(\theta_{t+k}U(1-s_{t+k})+\frac{\delta}{1-\delta}\theta_{t+k}U(s_{t+k})\right)\right]+\chi(b_{t-1}) \tag{16}

The difference between the highest and lowest continuation values is constant in inherited debt (eq. 17, p. 1596):

\bar{V}(b)-\underline{V}(b)=P^* \tag{17}

Integrating the two binding limited-commitment conditions and subtracting the continuation values gives the factorization system (eqs. 18-20, p. 1599):

\delta P^*=\alpha\int_{\theta^*}^{\theta^{**}}\left[U(g^f(\theta))-U(g^f(\theta^*))\right]d\theta \tag{18}

\delta P^*=\alpha\int_{\theta_n^{**}}^{\theta_n^*}\left[U(g^f(\theta))-U(g^f(\theta_n^*))\right]d\theta \tag{19}

P^*=\delta P^*+\alpha\left[\int_{\theta^*}^{\theta^{**}}\left(U(g^f(\theta^*))-U(g^f(\theta))\right)Q(\theta)d\theta-\int_{\theta_n^{**}}^{\theta_n^*}\left(U(g^f(\theta_n^*))-U(g^f(\theta))\right)Q(\theta)d\theta\right] \tag{20}

T(P) = \max_{\theta^*, \theta^{**}, \theta_n^*, \theta_n^{**}} \left\{ \delta P + \alpha \!\left[ \int_{\theta^*}^{\theta^{**}} \!\bigl(U(g^f(\theta^*)) - U(g^f(\theta))\bigr) Q(\theta)\, d\theta - \int_{\theta_n^{**}}^{\theta_n^*} \!\bigl(U(g^f(\theta_n^*)) - U(g^f(\theta))\bigr) Q(\theta)\, d\theta \right] \right\} \tag{21}

subject to limited commitment binding at the deficit and surplus thresholds (eqs. 22-23, p. 1599):

\delta P \geq \alpha \int_{\theta^*}^{\theta^{**}} \bigl[U(g^f(\theta)) - U(g^f(\theta^*))\bigr]\, d\theta \tag{22}

\delta P \geq \alpha \int_{\theta_n^{**}}^{\theta_n^*} \bigl[U(g^f(\theta_n^*)) - U(g^f(\theta))\bigr]\, d\theta \tag{23}

where $g^f(\theta) \equiv b^r(\omega,\theta) + \omega$ is the flexible spending level. The operator $T$ is increasing and concave with $T(0) = 0$ and $\lim_{P\to\infty} T'(P) < 1$. A positive fixed point $P^* > 0$ with $T(P^*) = P^*$ exists if and only if $T'(0) > 1$, which is the condition for fiscal regimes. This algorithm is analogous to Abreu, Pearce, and Stacchetti (1990) but applies from below (starting at the Markov outcome $P = 0$) rather than from above; this difference is key for finding a condition for the fixed point to exceed the Markov outcome (p. 1600-1601).

Empirical specifications

The paper’s main results are theoretical (no empirical estimation). Section V.D (p. 1601-1603) presents a numerical simulation to illustrate regime dynamics.

Parameter calibration. Parameters are chosen so that the mean and variance of the flexible spending rate match the mean and variance of US government spending over 1970-2020, using data on federal debt, receipts, and outlays from the Federal Reserve Bank of St. Louis (FRED, cited p. 1601):

• Lognormal shock distribution: mean 0, variance $\xi = 0.175$, truncated to support $[\underline{\theta}, \bar{\theta}] = [0.01, 100.01]$
• Social discount factor: $\delta = 0.943$
• Gross interest rate: $R = 1.05$
• Deficit bias: $\alpha = 1.151$, calibrated so that $1/\alpha \approx 0.87$ corresponds to a reelection probability implying average government duration of 7.6 years, matching the average time the same party held the US presidency from 1944 to 2020 (footnote 26, p. 1601)

Simulation results. The factorization algorithm, applied to these parameters, yields a unique best equilibrium with fiscal regimes. The implied thresholds are:

• Deficit limit threshold: flexible spending rate of type $\theta^* = 0.0736$
• Surplus limit threshold: flexible spending rate of type $\theta_n^* = 0.0867$

Figure 4 (p. 1602) plots the simulated best-equilibrium spending rate alongside the first-best and flexible (Markov) rates. Two extended shaded periods (fiscal irresponsibility) are visible. During fiscally responsible periods, the best-equilibrium rate coincides with the flexible rate when the latter is below the deficit limit, and is constrained at the threshold when the flexible rate slightly exceeds it; for high enough shocks the government breaks the limit and the shaded irresponsible period begins. During irresponsible periods, the best-equilibrium rate coincides with the flexible rate when above the surplus limit. If the flexible rate is just below the limit, governments raise spending to the threshold and return to responsibility; for low enough shocks they break the surplus limit and remain irresponsible.

Datasets used

Dataset	Role in paper	Wiki page
FRED (Federal Reserve Bank of St. Louis): US federal debt, receipts, outlays	Calibration targets for flexible spending rate mean and variance (1970-2020, annual)	FRED

Sample: United States, 1970-2020, annual frequency, for calibration only. The paper’s main propositions are theoretical and hold for any economy satisfying Assumptions 1 and 2.

When to read the full paper

Use the original if you are: working on dynamic mechanism design with adverse selection and limited commitment (Appendices A-C contain the formal perturbation proofs for Propositions 1-3); applying or extending the factorization algorithm to other games with one-dimensional state and adverse-selection incentive constraints (§V.C); studying the theoretical foundations for observed fiscal consolidation patterns and the role of political biases in driving debt accumulation; or connecting the model to quantitative fiscal analysis (the paper’s conclusion §VI identifies key extensions: persistent shocks, richer fiscal instruments, and multiple-period government bias).

Attribution and rights

Source: peer-reviewed, Journal of Political Economy 133(5), May 2025, pp. 1574-1620. Copyright 2025 The University of Chicago. All rights reserved. This distillation includes LLM extraction dated 2026-06-26 and 2026-10-04, and was re-verified by an LLM on 2026-10-04; it is not human-verified or independently reproduced. The paper is paywalled; the PDF is not hosted here. Extract only.

Halac, Marina, and Pierre Yared. “A Theory of Fiscal Responsibility and Irresponsibility.” Journal of Political Economy 133, no. 5 (May 2025): 1574-1620. DOI: 10.1086/734131.