nef Report on QE

There's a new report out from my friends at nef on alternative ways of doing QE in the UK.  I provided some comments on an earlier draft.  Although, I wouldn't agree with everything they say, it provides a good picture of what QE has and hasn't achieved in the UK and how it might be used more effectively.

The Short Rate, the Long Rate and the Exchange Rate

Reading about the market reaction to Bernanke's comments on a possible end to monetary stimulus, I was interested to note the appreciation of the dollar being generally attributed to associated expectations of a rise in dollar short rates.

Whilst this may indeed be the case in this instance, it's a good opportunity to highlight that there are two quite distinct reasons why we might expect an announcement on asset purchases to have this effect on the exchange rate.  It would be quite reasonable to expect an exchange rate impact, even if expectations of short term interest rates remained anchored.   The mechanics behind this are closely related to the way I have looked at Modelling QE.

For this type of analysis, it can be useful to think in terms of expected single period rates of return.  To simplify, we can think in terms of two asset classes: deposits, carrying a short rate of interest and bonds with a long rate.  For our single period, the return on deposits is known, but the return on bonds is not, because the latter depends on how the bond price changes in the period.  We therefore need to use an expected return, based on what the bond price is expected to be at the end of the period.

In the simplest models, the actual return on deposits and the expected return on bonds will be equal.  The assumption is that if they were not equal, investors would keep trying to switch their portfolios until the change in demand drove the expected returns into line.

This assumes that the two assets are perfect substitutes, but in reality there are plenty of reasons for believing they are not.  More sophisticated models will recognise that the two rates will typically be different.  The difference might be attributed to a liquidity premium or a term preference.  For convenience, I am going to call the excess of the expected single period return on bonds over the short rate the term preference (noting that this value could be positive or negative).

The important point here is that  the size of the term preference is a function of demand and supply.  For whatever reasons (often institutionally), there will be some investors that want exposure to long term rates and some that want exposure to short term rates. At the same time the relative supply of short term and long term assets may vary (through QE for example).  This is going to change the value of the term preference.

We can extend this analysis to the long term.  The expected long term return on bonds will be the compound of all the expected single period returns (that is, all the future returns expected now).  The expected long term return must equal the actual return (if a Treasury yields 2% to maturity and I expect it to yield 3% to maturity, I'm clearly mistaken).  In which case, the actual yield on bonds is equal to a compound of:

1. all the expected short term rates from now until the bond maturity; and

2. all the expected values of the term preference from now until the bond maturity.

where, in each case, expected means expected now.

So, when the bond yield changes, it may represent a change in expectations of future short rates, or it may represent a change in expectations of the term preference, or maybe a combination of both.  However, whilst it's possible that a change in asset purchases might not result in any changes to the actual short rate, it is highly unlikely that it will not lead to any changes in the term preference, as that would imply that investors were indifferent between long and short rate exposure.

Therefore, where the bond yield changes in response to an announcement on asset purchases, we know for sure that the expected value of the term preference has changed, but we don't necessarily know what it implies about the expected course of future short rates.

This has all been about changes in the domestic term structure.  How does this relate to the exchange rate?  The important point here is that what matters to the exchange rate is not just the short rate on deposits, but also the expected single period rate of return on bonds.  If investors with long-term rate preference invested exclusively in the domestic market, then this might not matter.  However, this does not appear to be the case; cross-border holdings of long-dated securities are substantial.  The demand and supply for these assets (which has immediate impact on the exchange rate) depends on the single period expected return on long assets, not on the short rate.

In conclusion, an announcement on asset purchases may do two things: it will definitely have an effect on the term preference; but it may also have an effect on expectations of short term interest rates.  These two effects are quite distinct, but both will have an impact on the exchange rate.

Modelling QE

This post outlines a theoretical model I've used for looking at the mechanical process by which QE impacts on the economy.  It is based on the UK economy and draws heavily on Tobin's portfolio approach to financial markets.*

The model is best understood by examining the balance sheet matrix on which it is based, a stylised version of the UK's financial balance sheet.  Although highly simplified, it still retains sufficient granularity to bring out the required mechanics.

	H'holds	PNFCs	MFIs	BoE	Gov't	RoW	Net
PNFC securities	Sh	-S				Sw	0
Gilts	Gh			Gcb	-G	Gw	0
RoW securities	F/x					-F/x	0
Deposits	Dh		-D			Dw	0
Loans	-Lh	-Lf	L				0
Reserves			R	-R			0

PNFC = private non-financial corporation

MFI = monetary financial institution (bank)

BoE = Bank of England

RoW = rest of world 

Asset prices and yields are driven by portfolio allocation functions for Households and RoW.  These are based on Tobin's, providing a demand for each asset based on the yields on all assets and an overall budget constraint.  The model then solves by bringing the market for each asset class into equilibrium, within the balancing constraints of the matrix. Three "price" variables need to be found: the price of private securities, the price of gilts and the exchange rate.  As each of these variables affects expected future returns, there is a high degree of inter-dependency.

The financial model sits within a simple Post-Keynsian style model of the real economy.  This is only intended to map out the long-run response path of the economy, which provides the feedback for expectation formation. Expectations place a crucial role in the model, and therefore issues such as whether the QE is expected to be temporary or permanent have a significant impact on the results.  Expectations are initially based on rule-of-thumb estimates, but the model includes an algorithm which enables yield expectations to be iteratively mapped to actual outcomes out to a distant future point.

Because the model is based on portfolio preferences, the spread between single period asset yields varies with the supply of those assets.  This means that traditional arbitrage model (whereby long term rates are a compound of expected short-term rates) does not in general hold, although there is a fair degree of correlation. Yields and prices can vary even in scenarios where the short-term rate is permanently fixed and even when the QE is only a temporary measure.

The structure of the model is explained in a little more detail below. 

Sectors

All sectors of the actual economy are represented.  Financial institutions that are not MFIs are treated as part of the household sector.  The BoE is treated separately from private MFIs.  Public corporations are treated as part of Government.

Assets

Marketable securities are grouped into three classes: PNFC securities (equity and debt securities of UK PNFCs), gilts and RoW (rest of world) securities.  The latter includes all foreign equity and bonds, whether private or issued by foreign governments.

The value of each of these asset classes depends on some measure of price.  For PNFC securities and gilts, value is the number of securities multiplied by a price index.  For RoW securities, the value is the (exogenous) foreign currency denominated value divided by the exchange rate.

The last three asset classes: deposits, loans and reserves do not have a variable price.  The return on each is based on an interest rate which is assumed to be determined exogenously by central bank policy.  Deposits from RoW is intended to represent a net figure, i.e. sterling deposits from abroad less sterling loans / deposits placed abroad.

In the real world, UK MFIs have substantial non-sterling assets and liabilities (greater than their sterling positions) but these are assumed to be matched and therefore ignored.  Likewise, non-sterling liabilities of PNFCs are ignored.  PNFC cash is netted off against loans.

Portfolio Allocation Functions

Household demand for each asset is based on a portfolio allocation function, using single period expected rates of return.  RoW has as demand functions for PNFC securities and gilts based on single period expected returns in the three marketable security classes and trend GDP.  Demand for sterling deposits is based on trend GDP and the relation between the (exogenous) foreign interest rate and the expected equivalent return on sterling deposits after expected exchange rate movements.

The functions require expected next period values for: the distribution on PNFC securities, the price of PNFC securities, the price of gilts and the exchange rate.  The same exchange rate expectations are used for expected deposits returns and for expected return on RoW securities.

Simulations

QE simulations involve an exogenous increase in gilts held by the BoE, matched by an increase in reserves. This increase in demand for gilts (or reduction in supply available to the rest of the market) increases the price and reduces the expected yield.  Portfolio re-balancing by households and RoW leads on to higher equity prices and a lower exchange rate.

Market prices respond immediately (even beforehand if expectations are allowed to reflect prior knowledge of the purchase).  The impact on the real economy is slower.  This involves (within the model) private sector spending response to increased wealth and reduced long-term rates, as well as exchange rate effects.  The increase in reserves is not modelled as having any direct impact on lending, as MFIs are not treated as reserve constrained.

* A General Equilibrium Approach to Monetary Theory, J. Tobin, Journal of Money, Credit and Banking (Feb, 1969)