A SUNSPOT-BASED THEORY OF UNCONVENTIONAL MONETARY POLICY ROGER E.A. FARMER University of Warwick and NIESR PAWEL ZABCZYK CCBS, Bank of England and Centre for Macroeconomics

This paper is about the effectiveness of qualitative easing, a form of unconventional monetary policy that changes the risk composition of the central bank balance sheet with the goal of stabilizing economic activity. We construct a general equilibrium model where agents have rational expectations and there is a complete set of financial securities, but where some agents are unable to participate in financial markets. We show that a change in the risk composition of the central bank’s balance sheet will change equilibrium asset prices and we prove that, in our model, a policy in which the central bank stabilizes non-fundamental fluctuations in the stock market is Pareto improving and self-financing. Central banks throughout the world have recently engaged in two kinds of unconventional monetary policies: quantitative easing (QE), which is “an increase in the size of the balance sheet of the central bank through an increase in its monetary liabilities”, and qualitative easing (QualE) which is “a shift in the composition of the assets of the central bank towards less liquid and riskier assets, holding constant the size of the balance sheet. ” Date: March 28, 2018. An earlier incarnation of this paper with the title “Qualitative Easing: How it Works and Why it Matters” (Farmer, 2012d) appeared as an NBER and a CEPR working paper. The current version was written after extensive discussions with Pawel Zabczyk during, and following, Farmer’s visit, as Senior HoublonNorman Fellow at the Bank of England in 2013. In contrast to the earlier paper, here we introduce money. Farmer thanks the Center for Central Bank Studies at the Bank of England for their hospitality. We thank participants of seminars at the National Institute for Economic and Social Research, Warwick University, The Swiss National Bank and the Bank of Italy. Bernard Winkler, Francesco Lippi and Christian Hepenstrick have all contributed thoughtful dicussions of our work and we thank them for their comments. We have also benefited from discussions with Andy Haldane, Minouche Shafik and Martin Weale. The views expressed in this paper are those of the authors, and not necessarily those of the Bank of England. The quote is from Willem Buiter (2008) who proposed this very useful taxonomy in a piece on his ‘Maverecon’ Financial Times blog. Farmer (2013) used this distinction to argue that the Bank should actively stabilize the asset markets. This paper provides the theory that explains why Qualitative Easing is effective. Earlier working papers that explain why financial markets may be Pareto Inefficient include Farmer (2002b,a, 2012c, 2014, 2015) and Farmer et al. (2012). 1 Because qualitative easing is conducted by the central bank, it is often classified as a monetary policy. But because it adds risk to the public balance sheet that is ultimately borne by the taxpayer, QualE is better thought of as a fiscal or quasi-fiscal policy (Buiter, 2010). This distinction is important because, in order to be effective, QualE necessarily redistributes resources from one group of agents to another. In theoretical papers that study the effectiveness of QualE, researchers often assume that financial markets are complete and that there is complete participation in these markets. When these two conditions hold, a change in the risk composition of the central bank’s balance sheet has no effect on asset prices. For example, in an influential paper that was presented at the 2012 Jackson Hole Conference, Michael Woodford (2012) made the claim that QualE is unlikely to be effective and, to the extent that it does stimulate economic activity, that stimulus must come through the impact of QualE on the expectations of financial market participants of future Fed policy actions. In contrast, Joseph Gagnon (2012) has argued that qualitative easing works through the portfolio balance effect, a term attributed to James Tobin (1963; 1969) who assumed that private agents’ asset demands are functions of relative asset prices, much as the demands for commodities depend on relative goods prices. QualE is ineffective when participation in assets markets is complete because market participants are able to undo the effects of a portfolio shift by the central bank through private trades in securities. As a consequence, QualE has no effect on the distribution of resources, either between borrowers and lenders in the current financial markets, or between current market participants and those yet to be born. We will argue here, that the assumption of complete participation is not a good characterization of real world financial markets and that QualE is effective because it redistributes resources across states of nature for people who are unable to participate in financial markets that open before they are born. We make the case for the effectiveness of qualitative easing by constructing an analytically tractable general equilibrium model where agents are rational and have rational expectations and where the financial markets are complete. Our setup has two important features. First, some people in our model do not trade in the financial markets. This means that, while our results have a flavour similar to those in Arajo et al. (2015), which studies the efficacy of unconventional monetary policy under endogenous collateral constraints, they naturally generalize to setups such as the overlapping generations model (OLG). There, despite the dynamic-completeness of asset markets and the absence of any Citing papers by Krugman (1998) and Eggertsson and Woodford (2002) where the case is made explicitly, Woodford (2012) argues that this so-called portfolio balance view is invalid, and, if central bank asset purchases are to be effective, their effectiveness must rely on their ability to alter the public’s expectations of future central bank policies. Examples of recent empirical papers that find a significant effect of Fed asset purchases on asset prices include Vissing Jorgensen and Krishnamurthy (2011); Gagnon et al. (2011); D’Amico and King (2010); Neely (2010); Li and Wei (2012), and Hamilton and Wu (2012). 2 collateral constraints, incomplete participation follows from the fact that people have finite lives. Second, people in our model use money as a medium of exchange. This result ensures that, in the absence of uncertainty, the model possesses multiple equilibria. It also implies that the underlying mechanism is different from that in Arajo et al. (2015), and can be seen as an application of the insights of Cass and Shell (1983) to the study of QualE effectiveness in a monetary economy. In this environment, we show that 1) a central bank that takes risk onto its balance sheet can increase welfare and 2) the optimal intervention restores efficiency and is selffinancing. When all uncertainty is non-fundamental, the optimal policy is for the central bank to stabilize the stock market so that the return to the stock market is equal in every state to the return on a one-period real government bond. In the presence of fundamental shocks, the government intervention eliminates non-fundamental volatility. 1. How our Model is Related to Previous Literature Our model is related to the work of Cass and Shell (1983). These authors construct a two-period, purely real, pure-exchange general-equilibrium model. In the first period, of their model, households trade financial assets. In the second period they trade goods. In the Cass-Shell example there are multiple equilibria in the second period. They show that, if some households are not present in period 1, purely non-fundamental uncertainty can influence the equilibrium allocation of goods across households. We adapt the Cass-Shell example in two ways. First, we introduce money as a medium of exchange. Second, we build a model with production, rather than pure exchange. Adding money allows us to explain the distinction between conventional monetary policy, which alters the size of the central bank’s balance sheet, and unconventional monetary policy, which alters its composition between safe and risky assets. Adding production, allows us to explain how unconventional monetary policy can alter output and employment. To model money, we include the real value of money balances as an argument of utility functions. This approach originated with Don Patinkin (1956) and we think of it as a short-cut that explains why people choose to hold an asset that is dominated in rate-of-return. For convenience, and to simplify algebra, we use the money wage as our numeraire and we assume that money, measured relative to the money wage, yields utility. Frank Hahn (1965) pointed out that monetary general equilibrium models always contain at least two equilibria; one in which money has value and one in which it does not. In these models, money is not essential for exchange, and there is always an equilibrium in which the price level is infinite and exchange is accomplished by barter. It is common in general equilibrium models of money, to divide cash-balances by the price level. We divide instead by the money wage to simplify some of the algebra. Nothing of substance in our argument hinges on this modeling choice. 3 In addition to these two equilibria, one with barter and one where money has value, infinite horizon general equilibrium monetary models typically also contain a continuum of non-stationary equilibria. Sometimes, as shown by Brock (1974), most of these equilibria are unrealistic as a description of reality: They converge to a steady state where money has no value. But in other examples, as shown by Benhabib et al. (2001), there is a continuum of equilibria that converge to a steady state where money has positive value but the money interest rate is low. These equilibria provide a possible description of the current situation where interest rates in many western economies have been equal to zero, or even negative, for several years. It is possible to construct dynamic ex