Blogs review: Empirical and theoretical multiplier uncertainty

by Jérémie Cohen-Setton on 12th November 2012

What’s at stake: A recent “box” in the first chapter of the WEO, co-authored by IMF Chief Economist Olivier Blanchard and his colleague Daniel Leigh, have reinvigorated the debate over whether austerity measures imposed on struggling eurozone countries has contributed to a deepening recession. On Wednesday, the European Commission responded with its own “box” pointing to the importance of distinguishing permanent from temporary fiscal adjustments. Contrary to what the battle of the boxes suggests, if there is multiplier uncertainty, it is very unlikely to come from the empirical front. Rather, it may come from recent challenges to previously accepted theoretical results.

The battle of the boxes

Dominic Wilson, Julian Richers and Jari Stehn have the most comprehensive discussion of the IMF box. Blanchard and Leigh show that the forecast errors from their April 2010 GDP growth forecasts for 2010 and 2011 are systematically related to their forecasts of planned fiscal consolidation. The authors argue that the overall direction of their conclusions is sensible, based on what we know of the empirical literature. But the strength of these particular relationships between GDP forecast errors and planned fiscal consolidations is sensitive to choices over time periods and the inclusion of other controls – like the 2009 structural government balance for instance.

The European Commission’s box (on page 41) argues if multipliers were underestimated, the underestimation concerned the multipliers of temporary expansions in 2010, not permanent consolidation in 2011. The 2010 stimulus measures are associated with large positive forecast errors for the countries that have implemented them. But as the impact multiplier associated with temporary fiscal contractions/expansions is substantially larger than the multiplier of permanent fiscal consolidations, bundling together countries that SR stimulus measures in 2010 with those that have undertaken measures to permanently reduce debt levels biases the estimate of the permanent consolidation multiplier in an upward direction.

How did policymakers end-up using such low multipliers?

The European Commission’s box reports the size of the multipliers used in its models. The multipliers of the Commission’s structural macroeconomic model QUEST for temporary fiscal shocks are between 0.1-0.4 for tax changes, but in the range of 0.7-1.5 for spending changes when credit constraints are high and interest rates are at the zero-lower bound. However, it is generally accepted that the impact multiplier associated with permanent fiscal consolidations is substantially smaller because of more positive crowding in effects. The QUEST has that the multiplier for such a consolidation is on average for a balanced-composition consolidation around 0.4. To account for the specificities of the current environment – ZLB, global fiscal retrenchment – the average multiplier can rise to 0.5-0.7.

Antonio Fatas writes that about eleven years ago there was a series of academic papers that estimated fiscal policy multipliers. The conclusion of the earlier papers is that multipliers were somewhere in the range 1-1.5. The academic literature on this issue grew very fast with a large number of papers confirming the earlier estimates but also with a set of other papers that challenge the size of fiscal multipliers. In particular, papers that used events such as wars tended to find smaller multipliers. As soon as the 2008 crisis started the debate went from a simple academic discussion to an urgent policy issue. Since then the debate has become much more ideological than academic. We have had a series of additional academic papers that, if any, suggest that multipliers are even larger than the initial estimates because of the special circumstances we are in. But these new (and old) academic results have simply be displaced by the ideological debate that followed the fiscal policy stimulus of the 2008-2009 period.

Paul Krugman writes that policy makers basically threw out everything we’ve learned about business cycles these past 80 years in favor of doctrines that made them feel comfortable. But to which extent should academics be rude to policymakers? This is basically an operational question; as Mark Thoma says, the goal is to change minds — although the big question there is whether you’re trying to change the minds of the policy makers themselves, or the minds of other people, so we can get a new and better set of policy makers. It wasn’t nice to characterize the doctrine of expansionary austerity as belief in the confidence fairy (or to make fun of policymakers that are “shocked shocked” to find out what we already knew), but I do believe that it focused the discussion in a way that a less caustic approach would not have achieved.

Are large fiscal multipliers at the ZLB an artifact of log-linearization?

Interestingly, the biggest challenge to large multipliers does not seem to come from the empirical front, but rather from the theoretical front.

Mark Thoma writes that one thing that doesn't get enough attention in DSGE models is the constraints, implicit assumptions, etc. imposed when the theoretical model is log-linearized. The paper below helps fill this gap by comparing a theoretical true economy to its log-linearized counterpart, and showing that the results of the two models can be quite different when the economy is at the zero bound.

Anton Braun, Lena Mareen Korber and Yuichiro Waki (HT Mark Thoma) write that using the log-linearized equilibrium conditions gives incorrect results about existence and uniqueness of equilibrium and provides an incorrect classification of the types of zero-bound equilibria that can arise in the true economy. These problems are severe. For instance, while the government purchase multiplier is above two in the log-linearized economy it is about one in the true economy. The authors make these points using a stochastic NK model that is similar to specifications considered in Eggertsson (2011) and Woodford (2011).

Lawrence J. Christiano and Martin Eichenbaum write that working with the actual nonlinear equilibrium conditions, they find the existence of equilibriums that are not visible to analyses based on linearization, as well as sunspot equilibriums. These findings challenge the findings about the properties of the ZLB so far reported. The authors find, however, that the equilibriums that are invisible to analyses using linearization are not E-learnable and so those equilibriums may perhaps be treated as mathematical curiosities. In addition, evidence that the quality of linear approximations is poor rests on examples where output deviates by more than 20 percent from its steady state, cases where no one would expect linear approximations to work well. For perturbations of reasonable size, the conclusions arrived at in the zlb analysis that use linear approximations appear to be robust.

Are fiscal multipliers smaller in a currency union?

Emmanuel Fahri and Ivan Werming (HT Simon Wren-Lewis and Marginal Revolution) have what may become the ultimate paper on fiscal policy at the ZLB and in a Monetary Union. Simon Wren-Lewis notes that the authors focus on the ‘consumption multiplier’, which is the impact of government spending on consumption. So in a closed economy a consumption multiplier of zero is a government spending multiplier of one (there is no capital).

Emmanuel Fahri and Ivan Werming find the surprising result that fiscal multipliers are necessarily lower whenever the exchange rate is fixed. The crucial difference is in monetary policy: although a fixed exchange rate implies a fixed nominal interest rate, the converse is not true. Indeed, the authors prove that the liquidity trap analysis implicitly combines a shock to government spending with a one-off devaluation. The positive response of consumption relies entirely on this devaluation. A currency union rules out such devaluations, explaining the negative response of consumption. The authors also explore non-Ricardian effects from fiscal policy by introducing hand-to- mouth consumers – a tractable way of modeling liquidity constraints. In a liquidity trap as well as in a currency union, government spending now has an additional stimulative effect as it increases the income and consumption of hand-to-mouth agents. But although there is an additional effect, the comparison of fiscal multipliers in a liquidity trap and a currency union, are unaffected.

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