Blogs review: Wallace Neutrality and Balance Sheet Monetary Policy

What’s at stake: The media has widely echoed that Michael Woodford – arguably the top monetary economist in the world – came out in support of Nominal GDP targeting in his speech at the Jackson Hole Economic Symposium. But Woodford’s 96 pages paper is much more than that as it provides certainly the best non-technical discussion of policy options available to central banks at the ZLB. The paper discusses forward guidance policies as well as balance-sheet policies, in which the central bank varies either the size or the composition of its balance sheet.  In this review, we focus on the latter as Woodford’s paper provides a useful complement to understand the ongoing blogosphere discussion about Wallace neutrality – an economics proposition due to Neil Wallace (1981) asserting that, in certain environments, alternative size and composition of the CB balance sheet have no effect.

Michael Woodford, Wallace Neutrality and Ricardian Neutrality

James Hamilton writes that Columbia University Professor Michael Woodford’s paper at the Fed’s Jackson Hole conference last week made the case that more large-scale asset purchases by the Fed would by themselves do nothing, and suggested that instead what really matters is the Fed’s communication of its future intentions.

Woodford’s case for the irrelevance of central-bank open-market operations is mostly based on Neil Wallace’s 1981 AER article, “A Modigliani-Miller theorem for open-market operations”.

Miles Kimball defines Wallace neutrality as follows:  a property of monetary economic models in which differences in the government’s overall balance sheet at moments in time when the nominal interest rate is zero have no general equilibrium effect on interest rates, prices, or non-financial economic activity. Richard Serlin (HT Mark Thoma) writes that in Wallace’s model, when the Fed prints money and buys up an asset with it, this affects no asset’s price, and doesn’t even change inflation!

Brad DeLong and Miles Kimball think that Wallace neutrality has baseline modeling status, in the same manner as Ricardian neutrality. Saying a model has baseline modeling status is saying that it should be the starting point for thinking about how the world works – as it reflects how the simplest economics models behave within the category of “optimizing models.”. The discussion is then about what might plausibly make things behave differently in the real world from that theoretical starting point.  Miles Kimball argues that the difference in the theoretical status of Wallace neutrality as compared to Ricardian neutrality is that we are earlier in the process of putting together good models of why the real world departs from Wallace neutrality. Studying theoretical reasons why the world might not obey Ricardian neutrality was frontier research 25 years ago.  Showing theoretical reasons why the world might not obey Wallace neutrality is frontier research now. 

The partial equilibrium logic of portfolio balance models

Miles Kimball writes that whenever the Fed buys an asset, you can think of it as the Fed adding to the demand for the asset or subtracting from the supply of the asset in private hands. Once the Fed buys these assets the values get written on a document called the Fed’s balance sheet.

Michael Woodford writes that it is often supposed that open-market purchases of securities by the central bank must inevitably affect the market prices of those securities (and hence other prices and quantities as well), through what is called a “portfolio-balance effect”: if the central bank holds less of certain assets and more of others, then the private sector is forced (as a requirement for equilibrium) to hold more of the former and less of the latter, and a change in the relative prices of the assets will almost always be required to induce the private parties to change the portfolios that they prefer. In order for such an effect to exist, it is thought to suffice that private parties not be perfectly indifferent between the two types of assets; and there are all sorts of reasons why differences in the risky payoffs associated with different assets should make them not perfect substitutes, even in a world with frictionless financial markets.

The general equilibrium logic of Wallace neutrality

Michael Woodford notes that it is important to note that such “portfolio-balance effects” do not exist in a modern, general-equilibrium theory of asset prices. Within this framework the market price of any asset should be determined by the present value of the random returns to which it is a claim, where the present value is calculated using an asset pricing kernel (stochastic discount factor) derived from the representative household’s marginal utility of income in different future states of the world. Insofar as a mere re-shuffling of assets between the central bank and the private sector should not change the real quantity of resources available for consumption in each state of the world, the representative household’s marginal utility of income in different states of the world should not change. Hence the pricing kernel should not change, and the market price of one unit of a given asset should not change, either, assuming that the risky returns to which the asset represents a claim have not changed.

How does 1950s-vintage “portfolio-balance” theory obtain a different result, even when the private sector is represented by a representative mean-variance investor? It assumes that if the private sector is forced to hold a portfolio that includes more exposure to a particular risk then private investors’ willingness to hold that particular risk will be reduced: investors will anticipate a higher marginal utility of income in the state in which the particular risk occurs, and so will pay less than before for securities that have especially low returns in that state. But the fact that the central bank takes the real-estate risk onto its own balance sheet, and allows the representative household to hold only securities that pay as much in the event of a crash as in other states, does not make the risk disappear from the economy. The central bank’s earnings on its portfolio will be lower in the crash state as a result of the asset exchange, and this will mean lower earnings distributed to the Treasury, which will in turn mean that higher taxes will have to be collected by the government from the private sector in that state; so the representative household’s after-tax income will be just as dependent on the real-estate risk as before. This is why the asset pricing kernel in a modern representative-household asset-pricing model does not change, and why asset prices are unaffected by the open-market operation.

So if the central bank buys more of asset x by selling shares of asset y, private investors should wish purchase more of asset y and divest themselves of asset x, by exactly the amounts that undo the effects of the central bank’s trades. The reason that they optimally choose to do this is in order to hedge the additional tax/transfer income risk that they take on as a result of the change in the central bank’s portfolio.

Richard Serlin (HT Mark Thoma) gives the bottom line intuition of Wallace neutrality. Consider that the government buys 100 million ounces of gold in a QE. The assumption is, of perfect foresight, perfect everything investors, that over the next several years, unemployment will go down and the Fed will reverse course, and then sell all of those 100 million ounces back again. Thus, the supply of gold in 10 years will be exactly the same as if the QE had never occurred. The gold just temporarily sits in government vaults (or with government ownership papers), rather than private ones, then goes back to the private vaults – No difference at all in 10 years. So, in 10 years the supply of gold is exactly the same, so the price of gold in 10 years will be exactly the same. If the price of gold in 10 years will be exactly the same, then its price today will be exactly the same, since with prefect foresight, perfect analysis, etc. investors, the today price is just the discounted 10 years from now price.

Wallace neutrality in the real world

Michael Woodford notes that the argument of Wallace neutrality applies also to standard open market operations. But it is easy to invalidate the neutrality result for open-market purchases of securities that increase the supply of reserves if one assumes that this particular asset is held for reasons beyond its pecuniary return alone – we may suppose that reserves at the Fed (and base money more generally) supply transactions services, by relaxing constraints that would otherwise restrict the transactions in which the holders of the asset can engage.

If assets other than “money” are valued only for their pecuniary returns, and all investors can purchase arbitrary quantities of any of these assets at the same (market) prices, then it can be shown that Wallace neutrality holds. It is possible, of course, that assets other than just the monetary liabilities of the central bank may be valued for their role in facilitating transactions, and not merely for their state-contingent pecuniary returns. Another reason for the irrelevance result stated above not to hold in practice can be the existence of binding constraints on participation in particular markets or on the positions that particular traders can take in those markets – or what Brad DeLong refers as hocus-pocus mumbo-jumbo in a storified Tweeter exchange with Miles Kimball. Examples of general-equilibrium analyses in which central-bank asset purchases are shown to affect both asset prices and the allocation of resources because of the existence of such constraints include Curdia and Woodford (2011) and Araujo et al. (2011).

The Wikipedia page for Wallace Neutrality – the result of a proposed public service provided by the readers of the Miles Kimball’s blog, Confessions of a Supply-Side Liberal – point to other recent works which invalidate Wallace neutrality based on different relaxed assumptions and novel mechanisms. For example, in Andrew Nowobilski‘s (2012) paper, open market operations powerfully influence economic outcomes due to the introduction of a financial sector engaging in liquidity transformation.

James Hamilton argues that the assumption underlying Woodford’s analysis – that changing the maturity structure would not change the real quantity of resources available for private consumption in any state of the world – is not correct. Take the maturity of debt the Treasury chooses to issue. The Treasury believes that if all of its debt were in the form of 3-month T-bills, then in some states of the world it would end up being exposed to a risk that it would rather not face. And what is the nature of that risk? I think again the obvious answer is that, with exclusive reliance on short-term debt, there would be some circumstances in which the government would be forced to raise taxes or cut spending at a time when it would rather not, and at a time that it would not be forced to act if it instead owed long-term debt with a known coupon payment due.

Richard Serlin will have a detailed post in the next few days detailing the problems when thinking Wallace neutrality actually occurs with QE in the real world. Stay tuned.

In a 1984 paper, Christophe Chamley and Herakles Polemarchakis addressed this issue in a general-equilibrium framework. They first derived Wallace’s result and then found conditions for which the neutrality does not hold. They manage to depart from Wallace’s result only because they considered non-contingent markets and the possibility of creation of other assets by the government. One condition for non-neutrality is when the central bank trades government’s assets that are nominally denominated. The second condition is when the supply of money is accompanied by transfers and subsidies to the banking sector. Few papers have pursued further these investigations. Today’s balance sheet policies – that keeps  blurring the lines between banking policy, monetary policy and fiscal policy – will certainly increase research in this area.

Thomas Sargent discussed, in his 2010 Phillips Lecture at the LSE, what is at stake in breaking Wallace neutrality and including different assets (and potential asset substitution) in contemporary dynamic models. The problem of assets substitution and non-neutrality of central bank’s operations was at the core of James Tobin‘s work in the 1950 and 1960s. It has been widely neglected since then and no microfoundations have been brought to Tobin’s intuitions and results. Tobin’s crucial insight was to focus attention on how outcomes of open market operations depend not only on the liabilities emitted by the central bank, but on the assets that ‘back’ those liabilities. The main political issue is that once these effects are recognized, banking policy becomes an integral part of monetary policy which, according to Sargent, is a step toward the rehabilitation of Adam Smith’s real bills doctrine, that is when central banks stand ready to purchase sound evidences of commercial indebtedness at a fixed interest rate set.