From the NBER working paper series — essential reading if you want to follow what the mainstream of the profession is up to — here are a couple interesting recent papers on fiscal policy. They offer some genuinely valuable insights, while also demonstrating the limits of orthodoxy.
Geographic Cross-Sectional Fiscal Spending Multipliers: What Have We Learned?
NBER Working Paper No. 23577
Gabriel Chodorow-Reich has a useful new entry in the burgeoning literature on the empirics of fiscal multipliers — a review of the now-substantial work on state-level multipliers. Most of these papers are based on spending under the 2009 stimulus (the ARRA) — since many components of its spending were set by formulas not responsive to local economic conditions, cross-state variation can reasonably be considered exogenous. (Another reason the ARRA features so heavily in these papers is, of course, that the revival of mainstream interest in fiscal multipliers is mostly a post-crisis phenomenon.) Other studies estimate local multipliers based on other public spending with plausibly exogenous regional variation, such as that involved in a military buildup or response to a natural disaster.
How do these local multipliers translate into the national multiplier we are usually more interested in? There are two main differences, pointing in opposite directions. On the one hand, states are more open than the US as a whole (or than other large countries, though perhaps not more than small European countries). This means more spillover of demand across borders, meaning a smaller multiplier. On the other hand, since states don’t conduct their own monetary policy (and since the US banking system is no longer partitioned by state) the usual channels of crowding out don’t operate at the state level. This implies a bigger multiplier. It’s hard to say which of these effects is bigger in general, but when interest rates are constrained, by the zero lower bound for example, crowding out doesn’t happen by that channel at the national level either. So at the zero lower bound, Chodorow-Reich argues, the national multiplier should be unambiguously greater than the average state multiplier.
Based on the various studies he discusses (including a couple of his own), he estimates a state-level multiplier of 1.8. He subtracts an arbitrary tenth of a point to allow for financial crowding out even at the ZLB, giving a value of 1.7 as a lower bound for the national multiplier. This is toward the high end of existing estimates. For whatever reason, Chodorow-Reich makes no effort to even guess at the impact of the greater openness of state-level economies. But if we suppose that the typical import share at the state level is double the national import share, then a back-of-the-envelope calculation suggests that a state-level multiplier of 1.7 implies a national multiplier somewhere above 2.0. 
It’s a helpful paper, offering some more empirical support for the new view of fiscal policy that seems to be gradually displacing the balanced-budget orthodoxy of the past generation. But it must be said that it is one of those papers that presents some very interesting empirical results and is evidently attempting to deal with a concrete, policy-relevant question about economic reality — but that seems to devote a disproportionate amount of energy to making its results intelligible within mainstream theory. We’ll really have made progress when this kind of work can be published without a lot of apologies for the use of “non-Ricardian agents.”
The Dire Effects of the Lack of Monetary and Fiscal Coordination
Francesco Bianchi, Leonardo Melosi
NBER Working Paper No. 23605
The subordination of real-world insight to theoretical toy-train sets is much worse in this paper. But there is a genuine insight in it — that when you have a fiscal authority targeting the debt-GDP ratio and a monetary authority targeting inflation (or equivalently, unemployment or the output gap), then when they are independent their actions can create destabilizing feedback loops. In the simple case, suppose the monetary authority responds to higher inflation by raising interest rates. This raises debt service costs, forcing the fiscal authority to reduce spending or raise taxes to meet its debt target. The contractionary effect of this fiscal shift will have to be offset by the central bank lowering rates. This process may converge toward the unique combination of fiscal balance and interest rate at which both inflation and debt ratio are at their desired levels. But as Arjun Jayadev and I have shown, it can also diverge, with the interactions the actions of each authority provoking more and more violent responses from the other.
I’m glad to see some mainstream people recognizing this problem. As the authors note, the basic point was made by Michael Woodford. (Unsurprisingly, they don’t cite this recent paper by Peter Skott and Soon Ryoo, which carefully works through the possible dynamics between the two policy rules. ) The implications, as the NBER authors correctly state, are, first, that fiscal policy and monetary policy have to be seen as jointly affecting both the output gap and the public debt; and that if preventing a rising debt ratio is an important goal of policy, holding down interest rates and/or allowing a higher inflation rate are useful tools for achieving it. Unfortunately, the paper doesn’t really develop these ideas — the meat of it is a mathematical exercise showing how these results can occur in the world of a representative agent maximizing its utility over infinite time, if you set up the frictions just right. For the simplest case, suppose the multiplier is equal to (1-m)[1/(1-mpc)], where m is the marginal propensity to import and mpc is the marginal propensity to consume. Then if the state level import propensity is 0.4 and the state level multiplier is 1.7, that implies an mpc of 0.65. Combine that with a national import propensity of 0.2 and you get a national multiplier of 2.3.  The paper was published in Metroeconomica in 2016, but I’m linking to the unpaywalled 2015 working paper version.