Chapter 22 — The Government Sector: Fiscal Policy and Public Debt

“We have always known that heedless self-interest was bad morals; we know now that it is bad economics.” — Franklin D. Roosevelt, Second Inaugural Address, 1937

The government is not merely one sector among many in the macroeconomic framework: it is the institution with the power to levy taxes, spend on goods and services, borrow, and — through its relationship with the central bank — ultimately print money. These powers make fiscal policy one of the two primary instruments of macroeconomic stabilization, alongside monetary policy. They also give rise to the discipline of public finance macroeconomics: the study of how government spending, taxation, and debt interact with private sector decisions, business cycles, and long-run growth.

This chapter develops the theory of fiscal policy in three steps. First, the arithmetic of the government budget constraint and debt dynamics — the accounting framework within which all fiscal policy operates. Second, the theory of Ricardian equivalence — the provocative proposition that, under certain conditions, it makes no difference whether the government finances spending through taxes or borrowing. Third, the theory of fiscal multipliers — the change in aggregate output generated by a unit change in government spending or taxes — and its dependence on the monetary policy regime and the state of the economy.

22.1 The Government Budget Constraint¶

The government finances its expenditure through three sources: current taxes, borrowing (issuing debt), and seigniorage (money creation). The flow government budget constraint states that the primary deficit (spending minus tax revenue) plus interest payments on existing debt must equal the sum of new borrowing and seigniorage:

where $G_t$ is government expenditure (excluding interest), $T_t$ is tax revenue, $B_t$ is the stock of nominal government bonds outstanding, $i_t$ is the nominal interest rate on existing debt, $\Delta B_t = B_{t+1} - B_t$ is new borrowing, and $\Delta M_t/P_t$ is real seigniorage. In most advanced economies, seigniorage is quantitatively small; the primary dynamic of interest is the evolution of the debt stock.

Definition (Primary Surplus and Deficit). The primary surplus $s_t = T_t - G_t$ is the difference between tax revenue and primary (non-interest) spending. A positive $s_t$ means the government is collecting more in taxes than it spends on goods and services (excluding interest payments); a negative $s_t$ is a primary deficit. The overall surplus also subtracts interest payments: $(T_t - G_t - i_t B_t)$.

Dividing the budget constraint by nominal GDP $P_t Y_t$ and expressing everything as shares of GDP, denoting lowercase letters as ratios (e.g., $b_t = B_t/(P_t Y_t)$):

where $r_t = i_t - \pi_t$ is the real interest rate, $g_t$ is the real GDP growth rate, $s_t = (T_t - G_t)/(P_t Y_t)$ is the primary surplus ratio, and $\dot{b}_t$ is the rate of change of the debt-to-GDP ratio.

This simple differential equation — the debt dynamics equation — is one of the most important in macroeconomics. It says the debt ratio rises when the real interest rate exceeds the growth rate ($r > g$, meaning interest payments outpace the economy’s expansion) and falls when the primary surplus $s_t$ is positive. The sign of $(r-g)$ is therefore crucial for debt sustainability.

Definition (Debt Sustainability). The debt ratio is sustainable if $b_t$ remains bounded over time. From the debt dynamics equation, the threshold condition is:

When $r > g$, the government must run a positive primary surplus large enough to service the excess of interest costs over growth. When $r < g$ — which held in many advanced economies during the 2010s and 2020s — the debt ratio can remain stable even with a primary deficit, because GDP growth automatically erodes the debt ratio.

The Intertemporal Government Budget Constraint¶

The flow constraint has an intertemporal counterpart: the present value of all future primary surpluses must equal the current debt stock:

This is the intertemporal government budget constraint (IGBC). It requires that the government not engage in a Ponzi scheme — borrowing forever to pay interest on existing debt without ever running a surplus. The IGBC provides the long-run solvency constraint that bounds fiscal policy: any fiscal expansion today (reduction in $s_t$) must be offset by a corresponding fiscal tightening at some future date, if the constraint is to be satisfied.

A key implication: the IGBC is a constraint on the entire path of fiscal policy, not on any single year’s budget. A government can run large deficits for years, provided it credibly commits to future surpluses sufficient to satisfy the IGBC. The question of whether such commitments are credible — and the political economy of fiscal rules that make them so — is a central issue in practical fiscal policy.

22.2 Ricardian Equivalence: The Neutrality of Debt Finance¶

The most provocative proposition in the theory of fiscal policy is Ricardian equivalence (Barro, 1974): under certain conditions, it makes no difference to the macroeconomic equilibrium whether the government finances a given path of spending through taxes today or through debt (taxes deferred to the future). The private sector fully offsets the fiscal expansion by increasing saving dollar-for-dollar.

The Two-Period Derivation¶

Consider a two-period economy. The government spends $G_1 + G_2/(1+r) = T_1 + T_2/(1+r)$ in present value (the IGBC). A household with income $y_1, y_2$ maximizes $u(c_1) + \beta u(c_2)$ subject to:

Now suppose the government reduces $T_1$ by $\Delta T$ and increases $T_2$ by $(1+r)\Delta T$ to satisfy its IGBC (debt-financed tax cut). Substituting into the household’s budget constraint:

The right-hand side is unchanged! The household’s intertemporal budget constraint is unaffected by the switch from tax to debt finance. Therefore, optimal consumption is unchanged: $\Delta c_1 = \Delta c_2 = 0$. Private saving rises by $\Delta T$ (the amount of the tax cut), exactly offsetting the government’s new deficit. The fiscal multiplier is zero.

Conditions for Equivalence and Its Failures¶

Ricardian equivalence requires four conditions, each of which fails to varying degrees in practice.

Condition 1: Infinite horizon or operative bequest motive. If households have finite horizons, a future tax increase may fall on a different generation than the one receiving the current tax cut. Future generations are not in the current household’s optimization, so current generations consume more. Barro’s (1974) argument was that altruistic bequest motives effectively extend horizons to infinity — if parents care about their children’s welfare and adjust bequests accordingly, then the household acts as an infinitely-lived dynasty. Whether bequests are sufficiently operative to justify this assumption is empirically contested.

Condition 2: Non-distortionary taxes. If future taxes are on labor income or capital, they distort economic decisions (labor supply, investment). The equivalence requires the intertemporal budget constraint to be purely a wealth effect with no substitution effect — possible only with lump-sum taxes.

Condition 3: Perfect capital markets. If households face borrowing constraints, they cannot smooth consumption optimally over time. A tax cut that loosens their current budget constraint will raise current consumption even if a future tax rise is anticipated. Empirically, a large fraction of households are liquidity-constrained (Chapter 11), making this condition fail importantly.

Condition 4: Equal government and household borrowing rates. If the government can borrow at a lower rate than households (because government debt is default-free while household borrowing carries a premium), a switch from debt to taxes relaxes the household’s effective budget constraint and raises consumption.

Empirical Evidence¶

The empirical literature on Ricardian equivalence finds consistent evidence against the null. Johnson, Parker, and Souleles (2006) study the 2001 U.S. tax rebate (a purely transitory transfer of $\$300$–600 per household) and find MPCs of approximately 0.25 in the first quarter and 0.6 over two quarters — substantially above zero, inconsistent with perfect Ricardian equivalence, though also substantially below one, inconsistent with the Keynesian extreme of no consumption smoothing. The most convincing interpretation is a world with partial liquidity constraints: constrained households (perhaps 30–40% of the population) have high MPCs, while unconstrained households behave approximately Ricardian.

22.3 Fiscal Multipliers: Theory and Evidence¶

Definition (Fiscal Multiplier). The fiscal multiplier is the change in equilibrium output per unit change in government spending:

An analogous tax multiplier $\mu_T = \partial Y^*/\partial T < 0$ gives the effect of taxation. The question of the size of fiscal multipliers is central to the debate about the effectiveness of fiscal stabilization policy.

The Multiplier in Various Models¶

In the Keynesian cross (Chapter 8), $\mu_G = 1/(1-b) > 1$ — the multiplier exceeds one because of induced consumption effects.

In the IS–LM model (Chapter 9), $\mu_G = h/(h+b_r k) < 1/(1-b)$ — less than the Keynesian cross value because the interest rate rises, crowding out investment.

In the New Keynesian model with Taylor rule, the central bank raises interest rates to offset inflationary pressure from fiscal expansion, further reducing the multiplier. Under standard Taylor rule parameters, the NK model predicts multipliers well below one.

At the effective lower bound (ELB), the Taylor rule is inactive (rates cannot fall further). Christiano, Eichenbaum, and Rebelo (2011) derive the ELB multiplier analytically for the NK model:

where $\varrho$ captures the persistence of the ELB spell, $\kappa$ is the NKPC slope, $\sigma$ is the IS slope, and $\delta_G$ is the fraction of spending on non-consumption goods. For plausible parameters, $\mu_G^{ELB}$ substantially exceeds one — potentially reaching 2–3 — because fiscal expansion generates inflation expectations that reduce the real interest rate, providing additional stimulus beyond the direct spending effect. This is the “forward guidance multiplier” working in reverse.

In open economies, the multiplier is reduced by import leakages: $\mu_G^{open} = 1/(1-b+m_Y) < 1/(1-b)$. For small open economies with high import propensities, multipliers can be close to zero.

Under Ricardian equivalence, the fiscal multiplier is zero for tax changes and equal to one for spending changes (the balanced budget theorem holds exactly). Under complete Ricardian equivalence, bond-financed tax cuts have no effect on output.

Empirical Estimation¶

Estimating fiscal multipliers empirically is challenging because government spending is endogenous: policymakers typically raise spending during recessions, creating a negative correlation between $G$ and $Y$ that biases naive OLS estimates.

Narrative identification (Ramey, 2011) constructs news variables measuring surprise defense spending increases from military buildups not driven by the business cycle (Korea, Vietnam, Cold War). The estimated government spending multiplier using this approach is approximately 0.6–0.9 — less than one.

Regional multipliers (Nakamura and Steinsson, 2014) exploit cross-state variation in defense spending to identify the fiscal multiplier. Because monetary policy cannot respond differentially to a state-level fiscal shock (the national interest rate is set for the whole country), the regional multiplier captures the direct demand effect without the monetary policy offset. The estimated regional multiplier is approximately 1.5–2.0, substantially higher than the aggregate multiplier.

State-dependence: Auerbach and Gorodnichenko (2012) find that fiscal multipliers are significantly higher during recessions (approximately 1.5–2.5) than during expansions (approximately 0–0.5), using a smooth-transition VAR that allows the multiplier to vary with the state of the business cycle. This state-dependence is consistent with the theoretical prediction: the ELB is more likely to bind during severe recessions, and households are more likely to be liquidity-constrained.

22.4 Debt Sustainability in Practice¶

The $r - g$ Differential¶

The sign of $r - g$ is critical for debt dynamics. Blanchard (2019) documented that in the United States, the average real interest rate on government debt has been below the average real GDP growth rate for most of the past 50 years — i.e., $r < g$ on average. This means that the government could maintain a stable debt ratio even with a permanent primary deficit: the GDP growth rate automatically erodes the debt ratio faster than interest costs accumulate it. The fiscal cost of public debt — in terms of required primary surpluses — has been historically modest.

However, this arithmetic does not imply that debt is costless or that any level of deficit is sustainable. Blanchard himself acknowledged several caveats: (i) $r - g$ could become positive in the future (as occurred in the 1980s); (ii) even with $r < g$, higher debt raises rollover risk; (iii) the distribution of outcomes matters — even if the expected value of $(r-g)$ is negative, there is a tail risk of debt spirals in adverse scenarios.

Fiscal Rules¶

Definition (Fiscal Rule). A fiscal rule is a statutory or constitutional constraint on the fiscal policy instrument — typically the deficit, debt, or expenditure growth. Examples include: Germany’s debt brake (constitutionally limits the structural deficit to 0.35% of GDP), the EU Stability and Growth Pact (requires member states to maintain deficits below 3% of GDP and debt below 60% of GDP), and various expenditure ceilings in Nordic countries.

Fiscal rules attempt to impose the precommitment discipline that Kydland and Prescott identified as necessary for time-consistent policy. Empirically, rules-based countries tend to have lower deficits and debt accumulation on average (Bova et al., 2015). But rules can be undermined by creative accounting (moving spending off-balance-sheet), waived during crises (the EU suspended SGP requirements repeatedly), or simply violated when the political cost of compliance exceeds the cost of breach. The effectiveness of fiscal rules depends critically on institutional enforcement mechanisms, political culture, and the credibility of the commitment.

Next: Chapter 23 — The Central Bank and Monetary Policy