University of Massachusetts Amherst ScholarWorks@UMass Amherst Economics Department Working Paper Series Economics 2018 A Note on Krugman's Liquidity Trap Stefano Di Bucchianico Department of Economics, Roma Tre University (Italy) Follow this and additional works at: https://scholarworks.umass.edu/econ_workingpaper Part of the Economics Commons Recommended Citation Di Bucchianico, Stefano, "A Note on Krugman's Liquidity Trap" (2018). UMass Amherst Economics Working Papers. 254. https://doi.org/10.7275/13358827 This Article is brought to you for free and open access by the Economics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Economics Department Working Paper Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. A NOTE ON KRUGMAN’S LIQUIDITY TRAP Stefano Di Bucchianico* November 2018 Abstract: The 1998 stylized model of Krugman constituted a ground-breaking contribution explaining the long lasting Japanese stagnation as the consequence of a ‘liquidity trap’ situation featuring a negative natural interest rate. Our critique to such a proposal will focus on three aspects. First, we will question the logical structure of the model, providing an alternative interpretation of its closure. Second, we will argue that aggregate demand has no role in the explanation, as the cause for the persistent excess of savings over desired investment is the result of a supply side shock plus a financial rigidity on the nominal interest rate. Finally, we will discuss the restrictive assumptions needed to get a negative natural interest rate, the concept that lies at the foundation of the entire theoretical apparatus. Our conclusion is that the explanation offered within the 1998 contribution does not provide a satisfying rationale for the Japanese stagnation. Keywords: Liquidity trap, Japanese stagnation, natural interest rate JEL Codes: E31, E40, E52, E58 *Department of Economics, Roma Tre University, [email protected] 1. Introduction Krugman (1998) discusses extensively the Japanese prolonged stagnation of the late eighties – nineties, many times referred to as the Japanese ‘lost decade’, trying to trace back its ultimate causes. His aim was to provide a possible explanation for that situation by means of a new analytical concept. Later on such contribution has been often cited by the author himself as one of his best pieces, and has gained widespread acceptance in the academy as a path-breaking article. Its importance rests also in the fact that the analytical germ of what, after the Great Recession, will be called the ‘demand side Secular Stagnation’ strand of thought (Summers 2014, 2015) can be found in this contribution. In particular, in this stylized model we find a formal treatment of how a negative natural real interest rate can appear in an economy; when the latter is coupled with the zero lower bound on the nominal interest rate, an underemployment equilibrium emerges. The analysis carried out in this paper has a twofold goal: on the one hand, we want to ascertain whether the novelty constituted by an equilibrium position featuring a negative natural real interest rate is analytically justified, on the other hand, we analyse what is the role of aggregate demand in the explanation for the long term economic stagnation of the Japanese economy. In our discussion we will highlight how the conclusions that Krugman drew from the model appear unwarranted from both a theoretical and an empirical viewpoint. In particular, we will see that the steps for the convergence to an equilibrium can be read differently from what the author proposed, and that the negative natural interest rate appearance is tied to a series of overtly restrictive assumption. Moreover, on the empirical side there is no confirm for the fundamental hypothesis of a decreasing potential output, which lies at the basis of his explanation. We further complement these arguments by maintaining that aggregate demand does not play any role in this theoretical apparatus, which basically relies on a supply side shock and a rigidity on the nominal interest rate to interpret the Japanese stagnation. Given that Summers has recently described the issue of Secular Stagnation for the US economy using a close analogy to the reasoning of Krugman, this work can also serve to recognize what are the roots of the demand side Secular Stagnation theory. In section 2 we are going to reconstruct the model of Krugman, which starts from an endowment economy and is then refined with the price rigidity case and an example to study investment, in section 3 we discuss the questionable assumptions needed to get the underemployment equilibrium and the irrelevant role that aggregate demand plays in such a model, while section 4 concludes. 2 2. The 1998 seminal contribution of Paul Krugman about Japan Krugman, in the writing of the model, was mainly interested in retrieving the Keynesian ‘liquidity trap’ category from the old – fashioned IS – LM analysis.1 This is the objective of the first half of the paper, while the second is devoted to applying the conclusions of the model to the Japanese case. In working out such task however, Krugman aimed also at updating that tool with three features: i) an intertemporal structure based on rational expectations, ii) an open economy treatment with foreign trade and capital mobility, iii) the role of financial intermediaries. In what follows, we are going to deal with the basic formulation of the model. Our interest points mostly to the general formulation, since in that framework the natural real interest rate is shown to be negative given some specific condition, and the zero lower bound on the nominal interest rate prevents the economy from attaining full employment. As Krugman formulates it, a ‘liquidity trap’ is “a situation in which conventional monetary policy has become impotent, because nominal interest rates are at or near zero: injecting monetary base into the economy has no effect, because base and bonds are viewed by the private sector as perfect substitutes”. (Krugman 1998, p. 141) Let us notice that by coupling this description with the negativity of the natural interest rate, we get the same picture described by the intuition of Summers (2014, 2015) about the US stagnation. Summers handles the US case proposing a reasoning in which the real natural interest rate turns negative when the demand for investment is peculiarly weak while the supply of savings is high. This causes the emergence of an underemployment situation since the zero lower bound on the nominal interest rate and the low inflations prospects prevent the Central Bank from being able to hit the equilibrium real interest rate. Therefore, it is in our opinion interesting to discuss the 1998 model as the first in which a negative real natural interest rate is presented as an impediment to full employment output realization, and to single out its relevance also in light of the recent discussion about Secular Stagnation. Given the very stylized nature of the model we are going to review, it is in our opinion useful starting with a narrative description of the most important messages that Krugman wants to convey to the reader. Then, we are going to follow Krugman in putting those clues in a simple model. The American economist aimed at recreating in a modern intertemporal two periods model a situation of Keynesian flavour in which, given a rigidity on the nominal interest rate determined on 1 Whose first proposer in a formalized model had been Hicks (1937). 3 the financial market, the real natural interest rate is not attainable by monetary policy.2 The initial version of the model is built upon these hypothesis: agents in the model are described by a single representative agent with a given utility function; there are two time periods, today and tomorrow. Once tomorrow comes about, the economy remains in the state described by the second period situation. Only the transition between the two periods is described; there is no production, as only endowments of a single consumption good are given to the representative agent today and tomorrow; the Quantity Theory of Money holds, as the Central Bank can raise the price level by injecting money into the economy; there is price flexibility for what concerns the price of the single consumption good available, but there is also a rigidity on the nominal interest rate, which cannot go below zero; the price level of tomorrow is given. Krugman, in the first place, wants to reproduce analytically a situation in which a liquidity trap emerges. As we will see, by supposing that the endowments of the consumption good are given for the two periods, and given the utility function of the representative agent, he can arrive at the real natural interest rate. When a specific assumption upon the amount of endowments available is made (namely, that the endowment tomorrow is adequately lower than the one of today), such a natural interest rate becomes negative. Given the zero lower bound on the nominal interest rate, the Central Bank can push the nominal interest rate at most down to zero, but no further; yet the attainment of the equilibrium real rate could be brought about by stimulating inflation. Indeed, even if the nominal interest rate is stuck at zero, raising inflation expectations can succeed in appropriately lowering the real interest rate down to the level of the natural rate, thus achieving equilibrium. It is here that the hypothesis about the given price level of tomorrow acquires an important role. Such an hypothesis in fact represents a way to formalize the idea that agents are so convinced about the reliability and willingness of the monetary authority to preserve price stability that they will not believe that the price level tomorrow will be considerably higher than today.