theory of Macroeconomics

ECON5002 – Macroeconomic Theory

Week 8: Expectations Reading: Blanchard chapters 14 and 17

Dr Kim Hawtrey

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› definitions ! all financial assets in the economy that allow participants to own/lend or

borrow/owe parcels of funds* can be summed up in three types: - M (‘money’) represents all non-yield-bearing financial securities - B (‘bonds’) represents all interest-bearing financial securities - Q (‘shares’) represents all dividing-bearing financial securities

these three each have distinct characteristics and macroeconomic role

! bonds are loan-type contracts involving a principal amount being loaned (at time=0), contractually defined interest payments by the borrower to the lender, and the return of the original principal upon maturity (time=n)

! examples of B include government bonds, corporate bonds, commercial bills, promissory notes, bank loans, etc

! if you borrow (lend) Pt dollars this year, you will repay (receive) (1+it)Pt dollars next year, where it is the (non-zero, pre-set) rate of interest

* financial markets perform two basic functions: trading parcels of funds (using M,B or Q) and trading parcels of risk (using derivatives like forwards, futures, options or swaps)

Expectations and the interest rate

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› definitions ! recall the interest rate measures the reward-for-illiquidity/cost-of-liquidity

that underpins the money demand decision (versus holding bonds)

! the interest rate also measures the time value of money = the penalty paid by the borrower for the privilege of spending early,

before they receive future income = the compensation charged by the lender for the inconvenience of

delaying their spending, of income already received

! by nature, bonds are intertemporal contracts, agreed today but with promised payments occurring over future time periods

! the future, by definition, is uncertain " the further into the future a bond’s payments will occur (the longer the maturity), the greater the uncertainty

! the economy’s interest rate therefore depends on expectations

Expectations and the interest rate

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› definitions ! one way that expectations get reflected is the term structure of rates,

shown by the yield curve, which gives the relationship between term to maturity and yield to maturity, for bonds of various lengths

! the yield curve normally will slope upwards to the right, because the further into the future a bond extends, the greater the uncertainty premium required by lenders

the yield curve will i the yield curve i rotate (counter) shifts (up) down clockwise when people when the central (raise) lower their bank (raises) expectation of future lowers the current interest rates, relative interest rate policy to the current rate setting

maturity

Expectations and the interest rate

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› real rate of interest ! another way expectations affect interest rates is via Pe

! so far in our macro model, we have used the nominal interest rate i nominal interest rates are quoted rates, expressed in today’s dollars, explicitly stated in the loan/bond contract, unadjusted for inflation

! we now need to work in terms of the real interest rate r real interest rates are inflation-adjusted rates, expressed in terms of a basket of goods, implicit and revealed only after computation

! when we borrow (lend) we ultimately care about the amount of goods we will sacrifice (earn), rather than the amount of dollars

! by working with the real rate, we can account for the effect of price expectations Pe on the interest rate that best affects spending decisions

! by using r we align our interest rate variable with other model variables that have already been defined in real terms

Expectations and the interest rate

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› real rate of interest ! the one-year real rate of interest is given by:

1 + rt = (1+ it) [Pt/Pet+1] which adjusts the nominal return on $1 loaned for any loss in value (of principal + interest) incurred due to increases in the price level

! recall that pet+1 = (Pet+1 – Pt)/Pt " (Pt/Pet+1) = 1/(1+pet+1) and so 1 + rt = (1+ it)/(1+pet+1) (1)

or, since r and p are both small, rt » it - pet+1 (approximately) (1’) ! the real interest rate (closely) equals the nominal rate minus inflation

- when expected inflation equals zero, i and r are equal - because pe is usually positive, r is normally less than i - for a given i, the higher is pe, then the lower the real rate

ie. as well as incorporating the time value of money (= r), the nominal rate (i) also compensates the lender when inflation erodes their principal

Expectations and the interest rate

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› real rate of interest

it = nominal interest rate for year t

rt = real interest rate for year t

Lending one dollar this year yields (1+ it) dollars next year. Alternatively, borrowing one dollar this year implies paying back (1+ it) dollars next year.

Pt = price this year.

Pet+1= expected price next year.

Expectations and the interest rate

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› real interest rate and ISLM model ! C and I decisions are based on the real interest rate - eg. when deciding

how much investment to undertake, firms care about real funding costs ! we now use an amended IS relation:

Y = C(Y-T) + I(Y,r) + G ie. Y = C(Y-T) + I(Y, i - pe) + G

where r has replaced i and we are using r = i - pe

! we also now use an amended monetary policy rule: i = (rn + pe) + a(p - pT)

where in = rn + pT and using r = i - pe, ! the interest rate directly affected by monetary policy is still the nominal

interest rate, so we continue to use the original LM relation: M/P = YL(i)

Expectations and the interest rate

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› real interest rate and ISLM model

Expectations and the interest rate

Equilibrium output and interest rates The equilibrium level of output and the equilibrium nominal interest rate are given by the intersection of the IS curve and the LM curve. The real interest rate equals the nominal interest rate minus expected inflation (=pT).

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› real interest rate and ISLM model ! the revised IS and LM curves look the same, but now the equilibrium has

a shadow outcome in terms of the real interest rate ! monetary policy (and LM curve) depend on the nominal rate i .. BUT

spending (and IS curve) depend on the real rate r " the effects of monetary policy on output now depend on

how movements in i translate into movements in r ! consider a monetary policy easing (pT´ > pT) - suppose the central bank

raises its inflation target from pT to pT’ in the short run: - the central bank lowers the nominal rate i and the LM curve shifts down - with the nominal rate lowered from iA to iB, the real rate is also lowered (by the same amount) from rA to rB

- in the short run, the economy moves from A to B - output rises temporarily to YB

Expectations and the interest rate

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› real interest rate and ISLM model

Expectations and the interest rate

short-run effect of an expansionary monetary policy

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› real interest rate and ISLM model ! in the medium run: › - output returns to its natural level (Y®YA= Yn ) in the medium run › (recall from week 5)

- therefore r returns to rn in the medium run (r ® rn = rA) why? from the amended IS curve with Y=Yn we must have r = rn (unchanged) because at natural output, Yn = C(Yn-T) + I(Yn,rn) + G

› Þ in the medium run, the real interest rate returns to its natural rate rn Þ rn is independent of inflation or money growth (it is determined entirely by

real factors) › - from the interest rate rule i must be higher in the medium run

why? iA´ = rA + pT’ (pT’> pT) " so central bank must allow i to rise › (to iA´ >iA ) and LM curve must (in net terms) shift upwards › Þ in the medium run, an increase in the inflation target leads to an equal › increase in the nominal interest rate (= the natural rate rn plus pT´) ›

Expectations and the interest rate

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› real interest rate and ISLM model

Expectations and the interest rate

medium run effect of an expansionary monetary policy

IS curve shifts right to accommodate higher i for any given Y LM curve shifts up as i goes to higher iA´ Y and i go from A (to B) then to A′ i goes to iA’ (= rn+pT’) r returns to rn (= rA)

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› real interest rate and ISLM model

Expectations and the interest rate

The medium run adjustment of real and nominal interest rates to expansionary monetary policy

An increase in the inflation target leads initially to a decrease in both the real and nominal interest rates. Over time, the real rate returns to its initial value. The nominal rate converges to a new higher value, equal to the initial value plus the increase in the inflation target.

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› modelling C and I decisions ! we posit a consumption function that has the following components:

Ct = C[(YLt – Tt), Wt] where Ct is current consumption, (YLt – Tt) is after-tax labour income, and Wt is total wealth (= material wealth* + human wealth*). This says consumption is an increasing function of current after-tax labour income and wealth (which includes future expectations)

! we posit an investment function that has the following components: It = I[Wt,V(Wet)]

where It is current investment, Wt is current profit per unit of capital, and V(Wet) is the net present value (NPV) of expected future unit profits. This says investment is an increasing function of current and future expected real profits.

* sum of current net financial assets + net housing assets * the net present value (NPV) of expected future after-tax labour income

Expectations and C, I

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› modelling C and I decisions ! expectations affect consumption and investment decisions, both directly

and indirectly (through changes to asset prices): - an increase in expected future after-tax real labour income and/or a decrease in expected future real interest rates* Þ ­(human)W Þ ­C

- an increase in expected future dividends and/or a decrease in expected future real interest rates* Þ ­(financial)W Þ ­C

- a decrease in expected future nominal interest rates leads to a rise in bond prices Þ ­(financial)W Þ ­C

- an increase in expected future real after-tax profits and/or a decrease in expected future real interest rates* Þ ­I

And vice versa. * interest rate effect operates via lowering the discount factor and therefore

raising the calculated NPV of (a given stream of) future income

Expectations and C, I

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› modelling C and I decisions ! the chart shows the channels from expectations to C, I

Expectations and C, I

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› augmented IS curve ! recall our amended IS equation (slide 8):

Y = C(Y-T) + I(Y,r) + G .. however this had no role for future expectations .. it assumed that consumption depended only on current income and that investment depended only on current output and the current interest rate

! to take into account the effect of expectations, we need a revised expectations-augmented IS curve:

- first, rewrite the IS equation as Y = A(Y, T, r) + G

where A(Y, T, r) = private spending = C(Y-T) + I(Y,r) - next, extend this IS equation to incorporate expectations by making spending depend on both current and expected future (’) values

Y = A(Y, T, r, Y’e, T’e, r’e) + G (+ - - + - - )

Expectations-augmented ISLM

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› augmented IS curve

Expectations-augmented ISLM

The new IS curve Given expectations, a decrease in the current real interest rate leads to only a small increase in output: the new IS curve is steeply downward sloping. Changes in expected variables shift the new curve: - increases in government

spending, or in expected future output, shift the IS curve to the right - increases in taxes, in

expected future taxes, or in the expected future real interest rate shift the IS curve to the left

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› augmented IS curve ! the revised IS curve is still downward sloping ! however, the new curve is very steep, which means that a large

decrease in only the current interest rate is likely to have only a small effect on equilibrium income, for two reasons: - a decrease in only the current real interest rate has little effect on spending, given unchanged future expected interest rates

- the multiplier is likely to be small, because if changes in current income are not accompanied by changes in future income, they will have only a limited effect on consumption and investment

for instance, firms are unlikely to change their investment plans greatly if future real funding costs are not expected to be any lower than before

! on the chart (slide 19), a large decrease in the current real interest rate – from rA to rB – results in only a small increase in output (YA to YB)

Expectations-augmented ISLM

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› LM curve in the augmented setting ! recall that the interest rate that enters the original LM relation is the

current interest rate . . . the RHS of LM equation gives the demand for money as

M/P = YL(i) this says the opportunity cost of holding money today depends on the current nominal interest rate only, not on the expected nominal interest rate (say) one year from now [in reality, people’s money holdings depend on expectations of future interest rates too: if the bond yield is expected to rise (fall) then the bond price is expected to fall (rise) " agents will exit bonds now and switch to holding money to avoid capital loss, until after the price fall is over]

! for simplicity, however, we will assume that the LM curve is not modified by expectations and retain the original LM relation

Expectations-augmented ISLM

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› equilibrium in revised ISLM

assuming r = i then we can interpret the i axis directly in terms of r

Expectations-augmented ISLM

The expectations-augmented IS–LM model

The new IS curve is steeply downward sloping: other things equal, a change in the current interest rate has a small effect on output. The unchanged LM curve has the original (upward) slope. The equilibrium is at the intersection of the new IS curve and original LM curve.

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› expectations and fiscal policy ! recall (week 5) the impact of reducing the budget deficit:

- in the short run, deficit reduction leads to a decrease in output - in the medium run, deficit reduction has no effect on output, but leads to a lower interest rate and higher investment

- in the long run, higher investment leads to a higher capital stock, and thus a higher level of output

that is, deficit reduction – while good for the economy in the long run – has an adverse effect in the short run (this often deters governments from tackling budget deficits - why take the risk of a recession now for benefits that will accrue only in the future?)

! however, when people take into account the expected future beneficial effects of deficit reduction, deficit reduction may actually increase spending and output, even in the short run

Expectations and policy actions

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› expectations and fiscal policy

when account is taken of its effect on expectations, a ¯G need not lead to a short run fall in output

Expectations and policy actions

The effects of a deficit reduction on current output In response to the announcement of deficit reduction by ¯G: - current spending goes down and the IS curve shifts left - expected future output goes up and the interest rate down, so IS shifts to the right again

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› expectations and fiscal policy ! net result: the opposing shifts in IS can potentially cancel out, and even

result in ­Y Q: by how much? A: to measure the exact size of the net effect on output, we would

require the precise details of the IS and LM equations generally, if deficit reduction improves expectations, the short-run effect will be less painful

! small cuts in government spending now and large expected cuts in the future will cause output to increase more in the current period—a concept known as backloading .. backloading, however, may lead to a problem with the credibility of

the deficit reduction program—leaving most of the reduction for the future, not the present, making them vulnerable to future default

Expectations and policy actions

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› expectations and fiscal policy ! to summarise: the change in output as a result of deficit reduction

depends on: ! the credibility of the program ! the timing of the program ! the composition of the program ! the state of government finances in the first place

! case study: Ireland recorded a positive output effect of deficit reduction

Expectations and policy actions

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› expectations and monetary policy ! consider a (conventional) monetary policy expansion, ie. suppose the

central bank decides to reduce the policy (ie. nominal) interest rate

! the effect of a decrease in the current nominal rate on the current and expected future real interest rates depends on two factors: 1. whether the easier monetary policy now leads financial markets to

revise their expectations of the future nominal interest rate i’e

2. how financial markets revise their expectations of both current inflation pe, and future inflation p’e

! assume for simplicity:

since r = i, we can write LM as M/P = YL(r) and conveniently (for this particular policy experiment) interpret the i axis directly in terms of r, and focus solely on expectations of the future nominal rate, when i falls

Expectations and policy actions

p e and p'e = 0 Û r = i and r'e = i'e

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› expectations and monetary policy

when the RBA ¯ current interest rate, people anticipate ¯ future interest rates as well Þ ­ spending Þ IS shifts right to IS’’

Expectations and policy actions

RBA lowers interest rate to rB If future expectations of r and Y are unchanged, equilibrium is B If future expectations of r also fall and of Y also increase, equilibrium is C

Effects of conventional expansionary monetary policy

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› expectations and monetary policy ! next, consider an unconventional monetary policy expansion

In 2008-09, during the GFC, options for traditional monetary policy in in the US had been exhausted —the nominal short-term interest rate had already be reduced to almost zero, leaving no room for further rate cuts

Exploring unchartered territory, unconventional policies were adopted by the US FED (and also by Bank of England and European Central bank): # ‘quantitative easing’ (QE): open market operations to buy longer term

government bonds # ‘credit easing’ (CE): central bank purchases of other (private sector)

financial assets, like mortgage-backed securities, stocks, etc. The idea is that, by injecting cash to support liquidity in the economy (which had frozen during the GFC, to the alarm of financial markets), the FED would support confidence by stoking expectations that future money policy would remain easy, interest rates low, and inflation positive*

* this cast central banks in the unfamiliar role of actually encouraging inflation

Expectations and policy actions

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Expectations and policy actions

Did the US FED’s unconventional policy work? Most research shows that these policies reduced actual interest rates only very modestly (perhaps, by 0.5% for long-term bonds). And yet post-GFC, the US managed to avoid a catastrophic Japan-style deflation. The explanation is that while QE has only a minor impact on actual interest rates, it has a major impact the market’s (and public’s) confidence.

QEI began in Nov2008: was really a credit easing (CE) as the FED bought mortgage-based securities (to a peak of $2.1trillion in Jun2010) QEII from Aug2010: Fed bought long-term government bonds ($600billion) QEIII from Sep2012: continued buying mortgage-based bonds ($40billion per month)

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› implications ! from our discussion (slides 23-30), it is clear the effects of monetary

policy – as well as fiscal policy – depend crucially on expectations: - policy announcements+actions affect not only today’s interest rate, but

also the private sectors’ rate expectations and future planning - consequently the impact of monetary policy is magnified (ie. while the

direct spot effect of a monetary action may be limited, the indirect forward impact, taking expectations into account, is much larger)

" expectations have an ‘intertemporal policy multiplier’ effect ! this suggests that information (availability, accuracy) matters greatly

- when current market prices/quantities fully reflect all true information about the economy, we say markets are efficient

- when policy settings and official intentions are fully announced and acted upon, we say policy is time consistent

these are necessary pre-conditions for optimal allocative decision-making

Expectations and policy actions

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› implications ! if available information (about data or policy) is incomplete/inaccurate,

the resulting inefficiency/inconsistency creates damaging expectation risk - consumers and firms may delay/shelve spending plans as uncertainty

reduces the risk-adjusted benefit, and confidence is undermined - the heightened risk around decision-making will harm macro outcomes

! our discussion reinforces the analytic significance of rational expectations - it is essential we recognize that people’s expectations are formed using

a systematic (not illogical), forward-looking (not inertial) perspective - economists are not suggesting that people always have perfectly

correct expectations—sometimes economic agents are excessively pessimistic or optimistic—simply that errors will be a random walk

! in the progress of macroeconomic science the recognition of information effects and the adoption of rational expectations is a key development in the last 50 years

Expectations and policy actions