Rational Bubbles and Beneficial Public Debt

Rational Bubbles and Beneficial Public Debt: Arbitrage Limits in Dynastic Economies∗ David Domeij†and Tore Ellingsen‡ March 18, 2016 Abstract We develop a dynastic general equilibrium model that admits bubbles and Ponzi schemes under rational expectations. Because current rents on average grow more slowly than aggregate output, while future rents are stochastic and imperfectly pledgeable, all agents are eventually liquidity constrained. Hence, although short-selling is costless, arbitrage does not eliminate non-fundamental asset values. In the most comprehensive version of our framework, precautionary saving is caused by imperfectly insurable labor income and entrepreneurial rents. Agents can save in physical capital, claims on intangible capital, and government bonds as well as in private bubbles. Calibrating the model to US data, we argue that public debt is a backed Ponzi scheme; it could be settled in finite time, but it could also constitute a considerable share of output indefinitely. However, paying down public debt would entail large welfare losses. For reasons of social insurance, it is better to harbor non-fundamental asset values in the form of public debt than in the form of private bubbles. Governments that can sustain more public debt should therefore tax private assets that are otherwise prone to bubbles. JEL classification: E21, E31 Keywords: Bubbles, Incomplete Markets, Fiscal Policy ∗We thank Klaus Adam, Tobias Broer, Ferre de Graeve, Denis Gromb, John Hassler, Paul Klein, Per Krusell, Espen Moen, John Moore, Lars Ljungqvist, Jose-V´ ´ıctor R´ıos-Rull, Asbjørn Rødseth, Jose´ Scheinkman, Per Stromberg,¨ Lars E.O. Svensson, Jean Tirole, Jaume Ventura, and Michael Woodford for valuable discussions, several anonymous referees for objecting to earlier versions, and the Ragnar Soderberg¨ Foundation (Ellingsen) and the Jan Wallander and Tom Hedelius Foundation (Domeij) for financial support. †Stockholm School of Economics, [email protected] ‡Stockholm School of Economics, Norwegian School of Economics, [email protected]. 1 Introduction If people have rational expectations, can asset prices have bubbles? In a growing economy, will it be possible for governments to earn a recurrent “free lunch” by raising their debts in tandem with output? A literature on public debt and asset prices in incomplete markets demonstrates that there are conditions under which the answers to both questions are affirmative; see in particular Allais (1947), Samuelson (1958), Dia- mond (1965), Bewley (1980,1983), and Tirole (1985).1 Bubbles and Ponzi-schemes are logically compatible with rational behavior and beliefs. However, for the last couple of decades – after the objections of, among others, Barro (1974), Abel et al. (1989), and Santos and Woodford (1997) – mainstream profes- sional opinion has been that the necessary conditions for rational bubbles and Ponzi- schemes are unlikely to be fulfilled in practice. Thus, the theory of asset prices in general and fiscal and monetary theory in particular must rest on other foundations. Santos and Woodford (1997, page 48) summarize their insights as follows: These results suggest that known examples of pricing bubbles depend upon rather special circumstances. In consequence, familiar examples (such as the overlapping generations model of Samuelson (1958) or the Bewley (1980) model) seem to be quite fragile as potential foundations for monetary theory. For when these models are extended to allow for trading in additional assets that are sufficiently productive (in particular, capital earning returns satisfying the criterion of Abel et al.), or to include an infinitely lived house- hold (or Barro “dynasty”) that is able to borrow against its future endow- ment and that owns a fraction of aggregate wealth, pricing bubbles – and hence monetary equilibria – can be excluded under quite general assumptions. Likewise, LeRoy (2004, page 801) reluctantly concludes: Within the neoclassical paradigm there is no obvious way to derail the chain of reasoning that excludes bubbles. It seems we must accept either that bubbles do not exist or, like LeRoy, continue to believe that bubbles exist in reality, but suspend our faith in models that rest on purely neoclassical assumptions. 1Other notable early contributions to this literature include Wallace (1980), Blanchard and Watson (1982), and Weil (1987); for further references, see Blanchard and Fischer (1989, Chapter 5) and Farhi and Tirole (2012). 2 We argue that this judgment is premature. Barro (1974) demonstrates that altruism can rectify the market incompleteness in Diamond (1965), but does not preclude the possibility that asset markets in such dynastic economies could be incomplete for other reasons. The empirical finding of Abel et al. (1989) that the economy is dynamically efficient – i.e., average dividend and interest payments exceed average investment – only implies that there cannot be bubbles on assets whose return is as high as the average return on capital.2 While this finding technically rejects all models of rational bubbles that only admit a single interest rate, such as Samuelson (1958), Diamond (1965), and Tirole (1985), there are closely similar models with multiple interest rates in which there can be bubbles on low-yielding assets as well as Ponzi public debt. This was noted in various contexts already by Woodford (1990), Bertocchi (1991), and Blanchard and Weil (2001),3 and is a crucial justification for more recent theories of rational bubbles, such as Farhi and Tirole (2012). However, the theoretical arguments of Santos and Woodford (1997) (henceforth SW) are apparently stronger. They say that dynastically oriented agents will be able to arbitrage away all bubbles in economies with a plausibly rich asset structure. The goal of this paper is to dispute the relevance of SW’s assumptions. In a nutshell, we claim that incomplete markets create natural limits to arbitrage; any dynasty that tries to make an arbitrage profit from a rational bubble is bound to go broke and be forced to close the position before any profit can be harvested.4 Specifically, we present a quan- titative model that admits bubbles and Ponzi-schemes without unrealistic restrictions on the set of tradable assets. We pay particular attention to calibrations in which non- fundamental asset values are large. In these calibrations, public debt corresponding to current US levels is both sustainable and costless. The debt is also backed, in the sense that it could be entirely repaid in finite time. Yet, along a balanced growth path public debt constitutes a constant and large fraction of output, and debt service never requires primary surpluses. If debt were to be further increased until the equilibrium real interest rate on government bonds exceeded the economy’s rate of growth, ratio- 2Geerolf (2013) argues that aggregate data do not admit Abel et al’s (1989) conclusion that US or the other advanced economies are dynamically efficient. However, if we confine attention to the business sector, it seems quite clear that weighted average returns to stocks and bonds exceed the economy’s growth rate by a wide margin over long stretches of time. 3Blanchard and Weil (2001) was originally written around 1990. For other contributions along similar lines, see Gale (1990), Manuelli (1990), Zilcha (1990), Bertocchi (1994) and Barbie, Hagedorn, and Kaul (2004, 2007). 4Limits to arbitrage are crucial also in the literature on irrational bubbles, as emphasized by Shleifer and Vishny (1997). But where we focus on the limits imposed by the nature of the income processes of individuals, that literature has focused more on agency problems in fund management; see Gromb and Vayanos (2010) for a survey. Of course, the two perspectives are complementary. For a recent broader survey of the literature on irrational bubbles, see Scheinkman (2014). 3 nal bubbles and Ponzi-values would disappear. In the model, public debt is always socially preferable to bubbles on private assets, yet eliminating bubbles through high interest rates may not be desirable due to negative effects on capital accumulation. Three natural conditions combine to limit arbitrage in our model: 1. All immortal assets have dividend growth rates below the economy’s growth rate. 2. All mortal assets’ expected unconditional dividend growth rates are below the economy’s growth rate (but could be higher conditional on survival). 3. At any time there are unborn assets, for example future projects that nobody knows about yet, whose rents cannot currently be contracted on. Condition 1 is well known to be necessary.5 Inasmuch as productivity growth is bi- ased towards physical or human capital rather than land, it is also realistic. Condition 2, or rather the notion of stochastically dying alienable rents, is probably the single most novel component of our model. Despite the fact that in reality (almost) all firms die eventually, we are not aware of any previous work in the bubble literature that considers mortal alienable rents.6 Condition 3, whose relevance to the theory of rational bubbles has previously been discussed by Tirole (1985, p1508), is the second key dif- ference between our model and SW. In SW’s setting, ownership of securities that are currently traded entails ownership of any future securities; it is as if entitlements to all future innovations are effectively owned by existing firms. While Condition 2 is new to the bubble literature, we note that Garleanu,ˆ Kogan, and Panageas (2012) recently invoke both Conditions 2 and 3 in their (bubble-free) analysis of asset price puzzles. Their purpose is to understand the level of risk-premia and the heterogeneity in returns across firms based on the competition from new en- trants – the replacement risk – that the firms face. In our model, on the other hand, the role of replacement risk is to make existing assets sufficiently poor stores of value as to prevent arbitrage over an infinite horizon. To what extent is Condition 3 empirically accurate? As a case in point, consider Facebook, an internet company started by novices in 2003.

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