Kobayashi-sensei's Economic Research Picks

Part 13: A Model of Secular Stagnation

Faculty Fellow

Econo-kun is in his second year of the master's program at a private university, studying hard to become an economist.

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: This time, I would like to focus on "A Model of Secular Stagnation" (NBER Working Paper 20574) by Gauti B. Eggertsson and Neil R. Mehrotra. The secular stagnation hypothesis has been gaining significant attention in the community of economists in the United States, prompted by Lawrence Summers' remarks in 2013 in which he argued that secular stagnation might become the "new normal." The secular stagnation hypothesis posits that economic stagnation continues over a prolonged period of time because of tighter borrowing constraints, population aging, and widening income inequality.

Econo-kun's photoEcono-kun: Against the backdrop of the long-lasting economic stagnation in Japan since the 1990s and the growing concern that the ongoing stagnation of the U.S. and European economies from 2009 onward may become chronic, the secular stagnation hypothesis has been discussed in many newspaper articles and online blogs.

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: Yes. However, all of those prior arguments are economic commentaries, not formal theories. In contrast, Eggertsson et al. explained the idea of secular stagnation in the form of a coherent theoretical model.

If the world economies—Japan, the United States, Europe, and more—are bound for long-lasting stagnation, a correct understanding of the secular stagnation hypothesis is indispensable in designing future economic policies. The paper is a very significant step forward in promoting such understanding.

Econo-kun's photoEcono-kun: What is the purpose of this paper?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: Summers put forward the proposition that the economic stagnation in the United States and Europe is likely to persist as the natural rate of interest is permanently negative. The paper proposes a theoretical model to explain his idea. However, the paper makes no reference to any empirical studies showing that the natural rate of interest is permanently negative. Thus, the purpose of this paper is to construct a preliminary theoretical model for the secular stagnation hypothesis, setting aside for now the question of whether there exists supporting empirical evidence.

Econo-kun's photoEcono-kun: Could you explain the model proposed in the paper?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: Let me give a brief summary of the paper.

1. Endowment Economy
The basic model is an overlapping generation (OLG) model in which each generation lives through the three stages of life, namely, young, middle age, and elderly. The young borrow and the middle-aged save. As both loan demand and loan supply are subject to the influence of borrowing constraints and the rate of population growth, the natural rate of interest can be negative depending on their impact. The key finding of this section is that the natural rate of interest turns negative when borrowing limits are tightened and/or the rate of population growth falls permanently as shown analytically.

2. Price Level Determination
This section considers a model with flexible prices. Where the natural rate of interest is positive, market clearing occurs under full employment provided that the inflation target is set at either a positive or zero rate of inflation. However, when the natural rate of interest is negative, inflation needs to be fairly high in order for an equilibrium to exist (i.e., there exists no equilibrium in an endowment economy if the inflation target is low).

3. Endogenous Output
This section considers a model in which the middle-aged work to produce consumption goods. The supply of labor is constant and wages are downwardly rigid (real rigidity). Now, suppose that such downwardly rigid wages are not rigid upwardly. In this setting, wages do not fall quickly enough to maintain employment, resulting in unemployment (i.e., an equilibrium occurs at the level of wages that is too high to maintain employment).

Aggregate supply (AS) and aggregate demand (AD) curves drawn with the vertical axis representing the rate of inflation are both upward sloping when the nominal interest rate i is zero (the slope of the AD curve is steeper than that of the AS curve). In this case, a deflationary equilibrium accompanied by unemployment can be the only possible equilibrium in the event of a tightening of borrowing limits and/or a fall in the rate of population growth (as is the case with the finding in Section 2 of the paper) (Note 1).

4. Keynesian Paradoxes
Paradox of thrift: When productivity improves, the AS curve shifts toward the lower right, resulting in a decrease in output at the equilibrium (i.e., an increase in productivity operates to suppress price increases and thus results in deeper deflation, which causes the real interest rates to rise and output to contract because the nominal rate of interest is bound to zero).

Paradox of flexibility: When wages become less rigid (i.e., greater flexibility in wages), the slope of the AS curve becomes steeper and the equilibrium output decreases (i.e., the expected rate of inflation falls, which causes the real interest rate to rise because the nominal interest rate is bound to zero).

5. Monetary Policy
As the inflation target is raised, the kink (i.e., the point at which the nominal interest rate takes the value of zero at full employment) shifts toward the upper right to generate a full employment equilibrium. At the same time, however, there remains a deflation equilibrium (resulting in multiple equilibria). This means that raising the inflation target does not guarantee an exit from the deflation equilibrium. We cannot rule out the possibility that the deflation equilibrium may continue even after raising the inflation target.

6. Fiscal Policy
Fiscal policy (i.e., intergenerational income redistribution by means of taxation and government bond issues) eliminates a secular stagnation equilibrium, enabling a shift to the full employment equilibrium (i.e., government bond issues increase the natural rate of interest and the kink shifts toward the lower right).

In a zero interest rate environment, fiscal policy has a significant multiplier effect. This is because Ricardian equivalence breaks down in this model (i.e., the AD curve shifts toward the right if the middle-aged expect that they will not be the ones to be taxed to pay down the government debt in the future).

7. Determinacy
Among the three steady states or equilibria, a deflation equilibrium (underemployment and deflation) is determinate, whereas another deflation equilibrium (full employment and deflation) is indeterminate and conforms to the typical deflation steady state in the model proposed by Benhabib et al. The inflation equilibrium at full employment is a normal equilibrium. Equilibrium determinacy can be examined by linearizing the model around the steady states concerned.

8. Introducing Capital
Suppose that wages are flexible and the relative price of capital p_t is determined exogenously. Here, if the propensity for saving increases due to a preference shock, the AD curve shifts toward the left. Furthermore, as the deflation equilibrium with a zero interest rate is in the upward-sloping segment for both the AD and AS curves, the deflation equilibrium shifts toward the left, resulting in output contractions and deeper deflation.

Econo-kun's photoEcono-kun: What are the policy implications of this paper?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: In this model, the effectiveness of monetary policy is somewhat limited in the secular stagnation equilibrium. Raising the inflation target does not necessarily enable an exit from deflation (i.e., the model has two equilibria, one with deflation and another with inflation, but is not predictive of which one would occur). Rather, the model presents fiscal policy as an effective policy that would definitely achieve an exit from deflation.

The paper poses a challenge to those advocating for a reflationary policy in that it suggests the possibility that Japan, Europe, and the United States may not be able to exit from their persistent stagnation with their current stimulus policies that are heavily reliant on monetary easing. Also, the model proposed in this paper provides a theoretical foundation for the United States and the United Kingdom in arguing against austerity policies implemented in the eurozone countries as it effectively calls for expansionary fiscal measures.

Econo-kun's photoEcono-kun: Are there any holes in the theory presented in the paper?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: I see the following three problems with the paper:

1. Why do permanent shocks occur?
In the model proposed in the paper, a permanent shock (e.g., tighter borrowing limits, slower population growth) causes the natural rate of interest to drop into negative territory. However, the paper does not provide any explanation, for instance, as to how and why borrowing constraints change permanently. If the mechanism of changes in borrowing constraints is known, we should be able to think of economic policy measures to change that mechanism. But the paper is silent on that point and confined to considering only monetary and fiscal policies. Identifying the mechanism of changes in borrowing constraints and considering measures to ease the constraints would generate more useful and effective measures to address secular stagnation.

2. Is the model coherent when it is not cashless?
The model underlying the paper is assumes a cashless economy. Where cash is non-existent, the secular stagnation equilibrium, a steady state in which deflation persists permanently, can be defined coherently.

However, when cash is introduced into the model, the transversality condition for cash cannot be satisfied in the deflation equilibrium unless the Friedman rule—i.e., a monetary policy that calls for gradually reducing the quantity of money supply to zero—is adopted. And if the transversality condition is not satisfied, the equilibrium cannot be considered as theoretically coherent.

Typically, the assumption of a cashless economy is used in New Keynesian models for the purpose of simplification. However, when we try to consider a steady state with permanent deflation, this assumption becomes crucial. This means that the deflation equilibrium cannot exist in an economy with cash when we assume monetary easing, i.e., a monetary policy that does not reduce money supply. This raises a fundamental question regarding the practical relevance of the model.

Eggertsson et al. do not discuss this problem of the transversatility condition arising from the introduction of cash into the model. I believe this poses a significant problem to the credibility of the model.

3. Is it relevant to assume a negative natural rate of interest?
The primary objective Eggertsson et al. sought to achieve in this paper is to show that it is theoretically possible for the natural rate of interest—the real interest rate at which the economy would stay at full employment—to be negative over a long period of time. In real life episodes of secular stagnation, is the negative rate of interest negative? We do not have sufficient evidence to prove that. Since the natural rate of interest is a variable that cannot be observed directly, empirical studies have been conducted to measure the natural rate of interest in various methods. Very few studies show that the natural rate of interest has dropped into negative territory in the United States and Europe. There are some studies showing that the natural rate of interest turned negative in Japan in the 1990s and onward. However, such situation did not necessarily last long (although certain models showed that the natural rate of interest stayed in negative territory for three years, the length of such period vary when the models are modified).

More empirical studies need to be carried out to measure the natural rate of interest, particularly with respect to the U.S. and European economies after the 2009 financial crisis.

November 7, 2014
  1. ^ Given the structure of this model, it could be possible for the secular stagnation equilibrium to exist even when the natural rate of interest is positive. This is because it is believed that a negative natural rate of interest is not a necessary condition for the existence of the secular stagnation equilibrium (i.e., if the inflation target denoted as Π* is large enough, the kink occurs when Π > 1). Thus, the conditions for the occurrence of the secular stagnation in Section 4 could be present even in the absence of the conditions specified in Section 2.

November 7, 2014

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