The negative natural rate of interest in the modern theories of Liquidity Trap and Secular Stagnation: back to Böhm-Bawerk via Samuelson

Abstract

The negative natural rate of interest is since two decades eliciting theoretical and policy debates. It re-emerged, after a relatively long time, in Krugman’s Liquidity Trap model. Later, it was placed at the hearth of the Secular Stagnation theory by Summers. It is argued that Krugman’s negative natural rate of interest ensues from theoretical premises analogous to those present in Samuelson’s overlapping-generations model. In turn, Samuelson obtained a negative equilibrium interest rate by opportunely recasting Böhm-Bawerk’s three causes for a positive rate of interest. The present paper illustrates and analyses this line of thought until its recent developments.

Keywords:

• Secular Stagnation
• Liquidity Trap
• negative natural rate of interest
• Krugman
• Samuelson

JEL CODES:

• B13
• B20
• B30

Acknowledgments

Special thanks are due to Francesco Sergi and Massimo Di Matteo, who offered remarkably useful suggestions and paid a great deal of attention to a preliminary version of this work. I wish to thank Antonella Palumbo, Paolo Trabucchi, and one anonymous referee of a previous version for their useful suggestions and comments. I am also grateful to Luca Zamparelli and Fabio Petri for the initial encouragement to pursue this line of research. Special thanks to Federica Cappelli. The participants to the 2020 Young Scholars Seminars (ESHET), the 17th Annual STOREP conference, and the 2021 Annual ESHET Conference provided additional food for thought. Any errors are solely my own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 These considerations are however not meant to rehabilitate Böhm-Bawerk’s view to use it to explain current long-lasting stagnation. See Potuzak (2016) for the proposal to use Böhm-Bawerk’s framework to understand the current state of very low (or negative) real rates of interest throughout advanced capitalism, and Di Bucchianico (2021a) for a demand-led model of stagnation that, acknowledging the difficulties entailed by the NNRI, formulates an alternative that does not rely on it.

2 Krugman (1998, 150–151) then introduces investment in a stylised overlapping generations example. In it, the young cohort cultivates land and uses the proceeds to buy it from the old. The elder cohort consumes what it earns from selling the land. A sufficient population decline, causing the price of land to fall, can make the expected rate of return on buying land negative. This example is however only briefly mentioned and developed further.

3 Borrowing Blaug’s (1999) dichotomy, our enquiry is akin to a “rational” reconstruction.

4 His investigation on the nature and causes of interest obviously entailed many other facets besides the discussion of the three causes. For example, Böhm-Bawerk also needed to devise a measure of an economy’s endowment of capital independent of the rate of interest. This, among other things, led him to construct a measure of the “average period of production”, which however failed its aim (Gehrke and Kurz 2009).

5 We report the quote by altering the order in which Samuelson recalled the causes to keep it consistent throughout.

6 Wicksell’s attempt has been also interpreted as a case in which the focus on the production side led to ignore the consumption side, thereby leading to the underdetermination of his system due to an alleged “missing equation” (Kurz 2000).

7 Uhr (1960, 115–119) also reconstructs the evolution of Wicksell’s thinking concerning those Böhm-Bawerk’s insights. So, for instance, while in Value, Capital and Rent Wicksell denied the relevance of the first cause while accepting the second and the third, in the Lectures he also started questioning the emphasis put by Böhm-Bawerk on the third cause.

8 Without further additions, we single out the similarity between this structure and a recent overlapping generations model used to study Secular Stagnation (Eggertsson, Mehrotra, and Robbins 2019).

9 Böhm-Bawerk’s “first cause” could indeed in principle be of some interest to present day economies; this is due to the presence of a non-produced asset such as land (Feldstein 1977; Homburg 1991). Homburg’s point is that an economy with land cannot exhibit dynamic inefficiency, hence, the equilibrium rate of interest must exceed the rate of growth of the system. The Feldstein-Homburg argument could then be consider as a modernization Böhm-Bawerk’s “first cause”. However, von Weizsäcker (2014) and Hellwig (2020) show how the argument of Homburg does not seem to be robust to both theoretical and empirical counterarguments.  I owe this consideration to the useful comments of an anonymous referee. 

10 Samuelson’s result has been mentioned many times in the literature; see for example Boianovsky (2017).

11 Similar graphs meant to represent Böhm-Bawerk’s framework can also be found in Bernholz (1993, 24, 27), Negishi (1982, 165–167). In our representation, the resource constraint line represents the first cause, while the indifference curves contain the second cause. However, the graph can be easily used to represent all three, when the resource constraint describes the third cause and its outward shift depicts the first (Samuelson 1994, pp. 204–205). This last method is more in line with Fisher’s use of the graph. Further, we here ignore the fact that the curvature of the indifference curve, not only its steepness, contributes to determine the value of the rate of interest.

12 Samuelson later worked on refining the rationale of the “third cause” by means of his famous “surrogate” production function (Samuelson 1962) but, as Boianovsky (2020, 627) points out, while Diamond (1965) extended Samuelson’s (1958) framework, the 1970 Nobel Prize recipient did not pursue further the research on overlapping-generations modelling. As Lee (2019) recalls, Samuelson also engaged in a deeper treatment of the role of population dynamics. For a broader perspective on Samuelson’s theoretical enterprise, see Kurz (2010), Backhouse (2017), Cord, Anderson, and Barnett (2019).

13 The controversy did not end there, but it also experienced a second stage. On this point, see Fratini (2019b).

14 For other critiques of the use of a natural rate of interest in the Secular Stagnation theory, see Bertocco and Kalajzić (2018), Palley (2019), Hein (2020).

15 More specifically, the optimal interest rate r is bound, in the medium- to long-run, to converge towards values such that $r\ge n+x$ where n is the growth rate of the population.

16 On the connection between Keynes and Krugman, see also Harcourt (2008), Kregel (2003) and Taylor (2014). Fantacci and Sanfilippo (2020) illustrate also the role of Dennis Robertson in the birth and development of the Liquidity Trap concept in several exchanges entertained with Keynes.

17 Another limitation of the present work can be stressed: we almost exclusively rely on English language publications. However, not all Böhm-Bawerk’s relevant publications have been translated into English from German. For example, in the Third Edition of his book (published in 1909) Böhm-Bawerk replied to Bortkiewicz criticism (namely, that storage of goods, which is necessary to have more additional goods in the future, is costly) by pointing out that in an age with a well-functioning financial system of stable money storage costs are negligible and money hoarding would not be a problem. But, this kind of discussions has been only accessible to a German audience. I owe this part to the insightful comments of an anonymous referee. 

18 For a comparison between Pigou’s views on the topic of stagnation and the more recent theories, see Di Matteo (2020).