Sticky Prices versus Sticky Information: Does It Matter For Policy Paradoxes?

This paper shows that government spending multiplier at the zero lower bound (ZLB) is larger under sticky information than under sticky prices. Similarly, well known paradoxes, e.g., the paradox of toil and the paradox of flexibility become more severe under sticky information. These results depend crucially on the duration of the fiscal policy stimulus relative to the fundamental shock in the economy. Such policy coordination is all the more important in the sticky information framework. In the aftermath of the Great Recession, a number of papers documented that fiscal policy is extremely effective to increase demand at the ZLB. In particular, the classic government spending multiplier is greater than one, while under normal circumstances it is not for then monetary policy can do the job via interest rate cuts. Examples include Eggertsson (2011), Christiano, Eichenbaum and Rebelo (2009), Woodford (2011). The literature also uncovered peculiar paradoxes, such as the paradox of toil (Eggertsson (2010)) and the paradox of flexibility (Bhattarai, Eggertsson and Schoenle (2014)). These results could be interpreted either as a serious challenge to the conventional wisdom or reflect some fundamental flaws of the New Keynesian framework. These results were, however, derived under the assumption that prices are sticky, as in Calvo (1983). It has long been recognized that the Calvo model of price setting has many peculiar features. This led researchers to explore alternatives, such as information frictions. One of the most prominent proposal to replace the New Keynesian Phillips curve based upon Calvo prices is the assumption of sticky information, proposed by Mankiw and Reis (2001). According to their hypothesis, firms adjust their prices slowly because they do not continuously update their information set. Mankiw and Reis argued that this alternative assumption helps explain the data better along certain dimensions. A very natural question, in the light of the radical findings documented in the Calvo model at the ZLB, is if these results carry over to a setting where information rigidities are assumed instead of sticky prices. The main conclusion of this paper is that the answer is yes. In an important and intriguing recent paper, Kiley (2016), documents experiments in which the fiscal policy results of the Calvo model are overturned upon assuming informational frictions as in Mankiw and Reis. The thought experiment Kiley conducts is as follows: Suppose the Central Bank follows an interest rate peg for 100 periods. What happens if the government increases spending for 1, 2, . . . upto 25 periods? What happens if taxes are increased for 1 to 25 periods? Kiley documents that while under Calvo prices the predictions are in line with the existing literature at the ZLB, the predictions are different under informational frictions. In particular, the government spending multiplier is small, tax multiplier is negative and the paradox of flexibility disappears. Kiley’s experiment is referred to in this paper as an interest rate peg experiment (PEG-EX). Kiley interprets these findings as suggesting that the sticky-information model is free from policy paradoxes, and thus to be favored over the Calvo model. Here, instead, we argue that these findings are an artifact of the thought experiment considered. The paradoxes in the sticky information framework in fact get even stronger in policy experiments that correspond more closely to those considered in the existing literature. This paper compares sticky prices and sticky information doing a different experiment. This experiment is identical to the one conducted in Eggertsson (2011), Christiano, Eichenbaum and Rebelo (2009), Eggertsson (2010), Woodford (2011). The ZLB is binding due to exogenous fundamental shocks. Once the shocks are over, the policy is given by a simple inflation target (which is missed for the duration of the shocks, due to the ZLB). This experiment is referred to as ZLB experiment (ZLB-EX). This paper documents that the results derived in the literature under sticky prices in the ZLB-EX are even more extreme if sticky prices are replaced with sticky information. The government spending multiplier becomes larger, and the paradox of toil and flexibility become more pronounced. This is because in the purely forward looking sticky-price model, current policy leaves expectations of future variables unchanged. Hence, there is only a "direct" effect of current policy on current output. In the backward looking sticky-information model, however, current policy has an additional "indirect" effect on current output, which comes from its effect on the expectations of future variables. While this may seem to contradict Kiley’s findings, it does not. Instead it clarifies that Kiley’s PEG-EX is a fundamentally different experiment than done in the existing literature. What is particularly subtle – and interesting – about the comparison, and likely to trigger confusion, is that under sticky prices the ZLB-EX and PEG-EX lead to exactly the same result. It is only when assuming sticky information that the results of the ZLB-EX and the PEG-EX are different. This does not have anything to do with the nature of the nominal frictions. Instead, it is a consequence of the fact that the sticky-information model has infinite number of endogenous state variables. Meanwhile the Calvo model is purely forward looking. The presence of endogenous state variables in the sticky-information model implies that comparing the reaction of an economy assuming an exogenous interest rate peg, versus the reaction of the economy if the central bank’s policy is bounded by zero due to fundamental shocks, leads to very different results. The same does not apply for perfectly forward looking systems like the Calvo model of price stickiness. This paper first shows analytical examples that clarify the intuition behind these findings. It then moves to numerical examples that replicate Kiley’s results. These examples confirm that Kiley’s results are driven by the difference in experiments being conducted rather than anything fundamental about the assumption of price stickiness. Arguably, the ZLB-EX is more economically relevant than PEG-EX. It seems of more limited economic interest – at least in the context of the crisis that started in 2008 – to explore the behavior of New Keynesian models if the short-term interest rate is temporarily pegged for no apparent reasons. Instead, the most economically interesting experiment appears to be when the interest rate is pegged due to the fact that the ZLB is binding on account of a fundamental recessionary shock that prevents the central bank from achieving its objective of stabilizing inflation and output. In a numerical exercise, the two models are calibrated to produce a 10% drop in output and 2% annual deflation on impact. It clearly demonstrates that in the ZLB-EX, government spending is more expansionary at zero interest rate than at positive interest rate and that tax cuts are contractionary at the ZLB, in both the models of nominal stickiness. Moreover, these paradoxes are starker under sticky information. Specifically, the government spending multiplier is three times larger, and the tax multiplier is four times larger in the sticky information model relative to the sticky price model. Finally, this paper also illustrates numerically that the paradox of flexibility is starker under sticky-information. This result is harder to intuit from an analytical example, because the response of output to increased flexibility in the sticky information model depends on the persistence of the underlying fundamental rate shock. Overall, the paradoxical results for fiscal policy multiplier at the ZLB could be interpreted as reflecting a weakness of the Calvo model. This paper, however, clarifies that these paradoxes are not a product of the Calvo assumption, but rather are a fundamental feature of models with nominal rigidities, irrespective of its source, be it sticky prices or sticky information.