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We ask how fiscal deficits are financed in environments with two key features: (i) nominal rigidity, and (ii) a violation of Ricardian equivalence due to finite lives or liquidity constraints. In such environments, deficits can contribute to their own financing through two channels: a boom in real economic activity, which expands the tax base; and a surge in inflation, which erodes the real value of nominal government debt. Our main theoretical result establishes that this mechanism becomes more potent as fiscal adjustment is delayed, leading to full self‐financing in the limit: if the monetary authority does not lean too heavily against the fiscal stimulus, then the government can run a deficit today, refrain from tax hikes or spending cuts in the future, and still see its debt converge back to its initial level. We further demonstrate that a significant degree of self‐financing is achievable when the theory is disciplined by empirical evidence on marginal propensities to consume, nominal rigidities, the monetary policy reaction, and the speed of fiscal adjustment. 

We show that, in a general family of linearized structural macroeconomic models, knowledge of the empirically estimable causal effects of contemporaneous and news shocks to the prevailing policy rule is sufficient to construct counterfactuals under alternative policy rules. If the researcher is willing to postulate a loss function, our results furthermore allow her to recover an optimal policy rule for that loss. Under our assumptions, the derived counterfactuals and optimal policies are robust to the Lucas critique. We then discuss strategies for applying these insights when only a limited amount of empirical causal evidence on policy shock transmission is available. 

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations. We show that, in a general moving average model with external instruments, variance decompositions for the instrumented shock are interval-identified, with informative bounds. Various additional restrictions guarantee point identification of both variance and historical decompositions. Unlike SVAR analysis, our methods do not require invertibility. Applied to U.S. data, they give a tight upper bound on the importance of monetary shocks for inflation dynamics. 

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.