1

Open Economy Macroeconomics MJRI.10.038

Advanced macroeconomics MJRI.10.042

D. Romer “Advanced macroeconomics”

Chapter 5. TRADITIONAL KEYNESIAN THEORIES OF

FLUCTUATIONS

Introduction

Chapters 5 and 6 develop fluctuation models based on the assumption that there

are barriers to the instantaneous adjustments of nominal prices and wages

→ so-called “nominal stickiness”

Implications of this assumption:

- Sluggish nominal adjustment causes changes in AD at given price level, to affect

the amount that firms produce.

- As a result, it causes only monetary disturbances which affect only demand.

- Also many real shocks (e.g. changes in G, I or A) affect AD at given price level ->

sluggish price adjustment creates new channel1 through which these shocks

affect employment and output.

Two main goals of this chapter:

1) To investigate aggregate demand

a. Determinants of AD at given price level

b. The effects of changes in the price level

2) Alternative assumptions about the form of nominal rigidity, which influence

firms’ willingness to change output in response to changes in AD, real wages,

markups and inflation.

Chapter 6 turns to the reasons why nominal prices and wages might not adjust

immediately to disturbances.

Traditional Keynesian models; analysis focuses on the effects of one-time changes.

1 I.e. other than the intertemporal-substitution and capital-accumulation mechanisms of basic real-business-cycle models.

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5.1 Review of the Keynesian Model of Aggregate Demand

In output-price (or output-inflation) space:

- Downward-sloping AD (aggregate demand) curve summarizes the demand side of

the economy

o AD is derived from IS-LM curves, considering different price levels

- Upward-sloping AS (aggregate supply) curve shows the supply side

o If AS in vertical (in the long-run), then changes in AD affect only prices

o If AS is upward-sloping, changes in AD affect both prices and output

In output-interest rate space:

- Downward-sloping IS curve (investments I = savings S)

- Upward-sloping LM curve (money demand L = money supply M)

AD analysis in (closed economy (5.1) and open economy (5.2):

- sticky nominal prices and wages

- firms change output in response to changes in demand

AS analysis (5.3 and 5.4):

- how different combinations of wage and price rigidity, and non-Walrasian

features of the labor and goods market yield different implications about

the effect of shifts in AD on output, real wages, unemployment and

markups

- Short-run and long-run output-inflation tradeoffs.

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The IS Curve – shows the combinations of output and the interest rate such

that planned and actual expenditures on output are equal.

Alternative (but not accurate) explanation: AD shows alternative equilibrium

points in the goods market.

Planned real expenditure function (general formulation) (eq. 5.1):

𝐸 = 𝐸(𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇), 0 < 𝐸𝑦 < 1, 𝐸𝑖−𝜋𝑒 < 0, 𝐸𝐺 > 0, 𝐸𝑇 < 0

E in terms of its components (standard formulation) (eq. 5.2):

𝐸 = 𝐶(𝑌 − 𝑇) + 𝐼(𝑖 − 𝜋𝑒) + 𝐺

NB! Restrictions in this specification may be highly unrealistic! -> EXAMPLES?

Equilibrium requires (eq. 5.3):

𝐸 = 𝑌

Explanation: real actual expenditure equals real actual output. For example, if

actual expenditure is less than planned expenditure, then firms are

accumulating unwanted inventories and respond by cutting their output.

Substituting (5.3) into (5.1) yields (eq. 5.4):

𝑌 = 𝐸(𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇)

Differentiating both sides of (5.4) with respect to i gives the slope of IS-

curve (eq. 5.5 or 5.6):

𝑑𝑌

𝑑𝑖|

𝐼𝑆= 𝐸𝑦 (

𝑑𝑌

𝑑𝑖|

𝐼𝑆) + 𝐸𝑖−𝜋𝑒 →

𝑑𝑌

𝑑𝑖|

𝐼𝑆=

𝐸𝑖−𝜋𝑒

1−𝐸𝑦

Implication: IS curve is flatter when either 𝐸𝑖−𝜋𝑒 or 𝐸𝑦 is larger.

Intuition: the larger the effect of interest rate on E, the larger the downward

shift of E → the larger the required fall in output in order to balance Y=E.

→ Keynesian Multiplier effect!

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The LM Curve – shows the combinations of output and the interest rate that

lead to equilibrium in the money market for a given price level.

The condition for supply and demand of real balance to be equal at a give

price level (eq. 5.7):

𝑀

𝑃= 𝐿(𝑖, 𝑌), 𝐿𝑖 < 0, 𝐿𝑌 > 0

- We consider money as high-powered money (currency + reserves) which

pays no nominal interest -> i.e 𝑖 is the opportunity cost of holding money

- M/P denotes real balances

- Volume of transactions is higher greater when output is higher -> demand

for real balances is increasing in output

Differentiating both sides of (5.7) with respect to Y and rearranging gives

the slope of LM-curve (eq. 5.8):

𝑑𝑖

𝑑𝑌|

𝐿𝑀= −

𝐿𝑌

𝐿𝑖> 0

- LM is upward-sloping

- LM is steeper if income elasticity of money demand (𝐿𝑌) is higher and/or

interest elasticity (𝐿𝑖) is lower

Additional remarks about the IS-LM model:

- All assets other than money are treated as perfect substitutes

- Total wealth in the economy equals to the total value of all assets

- Total value of any individual’s asset holdings must equal his or her total

wealth

- If the market for every asset but one clears, the market for the remaining

asset must also clear

- As in the IS-LM model are only two assets (money and everything else), only

one asset-market equilibrium is needed → we look only at money market!

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The AD Curve

The intersection of the IS and LM curves shows the values of i and Y such that

money market clears and actual and planned expenditures are equal (for any

given levels of 𝑀, 𝑃, 𝜋𝑒 , 𝐺, 𝑇).

Next we derive the relationship between P and Y. Consider the effect in

increase in P (i.e. inflation):

- Since P does not enter in 𝐸(●), the IS curve is unaffected

- M/P decreases → higher interest rate is needed to clear the money market

for a given level of Y → LM curve shifts up

- As a result, i raises and Y falls (see Fig. 5.4) → the level of output at the

intersection of IS and LM curves is a decreasing function of P.

To find the slope of the AD curve, differentiate (5.4) and (5.7) with respect

to P . This yields two equations in two unknowns (eq. 5.9 and 5.10):

𝑑𝑌

𝑑𝑃|

𝐴𝐷= 𝐸𝑌

𝑑𝑌

𝑑𝑃|

𝐴𝐷+ 𝐸𝑖−𝜋𝑒

𝑑𝑖

𝑑𝑃|

𝐴𝐷

−𝑀

𝑃2= 𝐿𝑖

𝑑𝑖

𝑑𝑃|

𝐴𝐷+ 𝐿𝑌

𝑑𝑌

𝑑𝑃|

𝐴𝐷

Solving these equations gives (eq. 5.11), which shows the determinants of

the slope of AD curve:

𝑑𝑌

𝑑𝑃|

𝐴𝐷=

−𝑀 𝑃2⁄

[(1 − 𝐸𝑌) 𝐿𝑖 𝐸𝑖−𝜋𝑒⁄ ] + 𝐿𝑌< 0

Example: The Effects of an Increase in Government Purchases

(pp. 224-225, Figure 5.5)

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5.2 The Open Economy

Now we take into account the importance of the exchange rate and

international trade to short-run fluctuation.

The Real Exchange Rate and Planned Expenditure

Define nominal exchange rate 𝜀 as the price of one unit of foreign currency in

terms of domestic currency.

- Rise in 𝜀 means that foreign currency becomes more expensive,

corresponding to a weakening (depreciation) of domestic currency

- Fall in 𝜀 corresponds to appreciation of the domestic currency.

Definition of real exchange rate: 𝜀𝑃∗

𝑃 (the price of foreign goods in units of

domestic goods).

Higher real exchange rate implies that foreign goods are now more expensive

relative to domestic goods, so everyone (both domestically and abroad) wants

to by domestic goods → planned expenditure rises.

Real exchange rate and planned expenditures move in the same direction!

Eq. (5.4) becomes (5.12):

𝑌 = 𝐸 (𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇,𝜀𝑃∗

𝑃)

- 𝐸(●) is increasing in 𝜀𝑃∗

𝑃

- We assume that money demand is unaffected by exchange rate, so the LM

curve is also not affected by the openness of the economy.

- We focus on the small country case (i.e. any individual country is small

relative to the entire rest of the world) → take 𝑃∗ as given.

BUT: it is not reasonable to take exchange rate as given.

Additional assumptions are needed regarding:

- Exchange rate regime (floating or fixed)

- Capital mobility (perfect or imperfect)

- Exchange-rate expectations (static or rational)

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The Mundell (1968) – Fleming (1962) Model

Assumptions:

1) static exchange-rate expectations

2) perfect capital mobility

In case of differences in expected real interest rate between domestic and

foreign assets, investors put all their wealth into assets with higher yield →

the expected rates of return should become equal (eq. 5.13): 𝑖 = 𝑖∗

In case of floating exchange rate, AD is determined by equations (5.7), (5.12)

and (5.13) with three unknowns 𝑖, 𝑌, 𝜀. This system reduces to:

Vertical LM* curve (eq. 5.14):

𝑀

𝑃= 𝐿(𝑖∗, 𝑌)

Upward-sloping IS* curve (eq. 5.15):

𝑌 = 𝐸 (𝑌, 𝑖∗ − 𝜋𝑒 , 𝐺, 𝑇,𝜀𝑃∗

𝑃)

Vertical LM means that output for a given price level (i.e. the position of AD

curve) is determined entirely in the money market.

Example: if 𝑮 ↑, then IS* shifts right → appreciation of domestic currency (𝜀 ↓),

but no effect on output → AD curve is unaffected (see Figure5.7).

In case of fixed exchange rate there are 2 changes in the model:

1) the exchange rate is pegged at some level (eq. 5.16): 𝜀 = 𝜀 ̅

2) money supply becomes endogenous

3) AD is now determined by equations (5.7), (5.12), (5.13) and (5.16).

LM* equation can be neglected (determines only the M), so the model is

reduced to (i) upward-sloping IS* curve and (ii) horizontal line for 𝜀 = 𝜀 ̅ (Fig.5.8)

Changes in E now affect AD. If 𝑮 ↑, then IS* shifts right and output increases

(for any P). Disturbances in the money market have no effect on Y.

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Rational Exchange-Rate Expectations and Overshooting

Static exchange-rate expectations assumed so far would lead to systematic

errors in exchange-rate forecasts. Next we assume rational expectations which

enable investors earn higher rate of return.

Implications: domestic and foreign interest rates should not equal. Instead,

investing domestically and investing abroad must have the same expected

payoff (eq. 5.17):

𝑒𝑖∆𝑡 =𝐸[𝜀(𝑡 + ∆𝑡)]

𝜀(𝑡)𝑒𝑖∗∆𝑡

Derivatives of both sides with respect to ∆𝑡 are equal (eq. 5.18):

𝑒𝑖∆𝑡𝑖 =𝐸[𝜀(𝑡 + ∆𝑡)]

𝜀(𝑡)𝑒𝑖∗∆𝑡𝑖∗ + 𝑒𝑖∗∆𝑡

𝐸[𝜀̇(𝑡 + ∆𝑡)]

𝜀(𝑡)

When the expression is evaluated at ∆𝑡 = 0, it simplifies to (eq. 5.19), which is called uncovered2 interest-rate parity:

𝑖 = 𝑖∗ +𝐸[𝜀̇(𝑡)]

𝜀(𝑡)

Implication: Under perfect capital mobility, interest-rate differences must be

offset by expectations of exchange-rate movements.

“Exchange-rate overshooting” (Dornbusch 1976) refers to situations where

the initial reaction of a variable to a shock is greater than its long-run response.

EXAMPLE: Suppose increase in money supply M↑, while 𝑖 = 𝑖∗ and exchange

rate is not expected to change. What happens? (see also graphical explanation)

- According to Keynesian model, monetary disturbances have no real effect

in the long run (price level and exchange rate rise proportionally with the

increase in money).

- In the short run, monetary expansion reduces interest rate and according to

(5.19) 𝐸[𝜀̇(𝑡)] must be negative (i.e. investors expect domestic currency

appreciation) → this means that domestic currency is worth less now than

in the longer future → Question: whether the monetary expansion reduces

domestic interest rate at all? (the answer is YES; see p. 231)

2 i.e. risks are not covered, but investors are assumed to be risk-neutral.

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Imperfect Capital Mobility and floating exchange rate

Relaxing the assumption of free capital movement: transaction costs

argument, risks, desire for diversity etc. Assume again static exchange-rate

expectations. Then capital flows depend on the difference between domestic

and foreign interest rate.

Define capital flow 𝐶𝐹 as foreigners’ purchases of domestic assets minus

domestic residents’ purchases of foreign assets (eq. 5.20):

𝐶𝐹 = 𝐶𝐹(𝑖 − 𝑖∗), 𝐶𝐹′(●) > 0

The capital flow CF must be equal and opposite to NX (eq. 5.21) –

balance-of-payments equation:

𝐶𝐹(𝑖 − 𝑖∗) + 𝑁𝑋 (𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇,𝜀𝑃∗

𝑃) = 0

In open economy where only NX is affected by 𝜀 , we can rewrite planned

expenditure as the sum of domestic residents’ planned expenditure and net

exports (eq. 5.22):

𝑌 = 𝐸𝐷(𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇) + 𝑁𝑋 (𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇,𝜀𝑃∗

𝑃)

0 < 𝐸𝑌𝐷 < 1, 𝐸𝑖−𝜋𝑒

𝐷 < 0, 𝐸𝐺𝐷 > 0, 𝐸𝑇

𝐷 < 0

We can use (5.21) to substitute for net exports and thereby eliminate the

exchange rate from the model (eq. 5.23 and fig. 5.9):

𝑌 = 𝐸𝐷(𝑌, 𝑖 − 𝜋𝑒 , 𝐺, 𝑇) − 𝐶𝐹(𝑖 − 𝑖∗)

Note: exchange rate is implicitly changing as we move along the IS** curve.

Interest rate has double effect on Y and IS** is therefore flatter:

a) Direct effect on domestic demand 𝐸𝐷

b) Indirect effect through the change in exchange rate and NX

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5.3 Alternative Assumptions about Wage and Price Rigidity

Assumption: incomplete nominal adjustment → explaining factors?

General purpose of this subchapter is to explore different combinations of nominal wage and price rigidity together with characteristics of labor and goods markets that result in non-vertical AS.

Different sets of assumptions have different implications for unemployment, real wage and markup in response to AD fluctuations; and also to firms, pricing behaviour. Case 1: Keynes’s Model

Nominal wage is rigid (eq. 5.24): 𝑊 = �̅�

Output is produced by competitive firms. Labor is the only factor of

production that is variable in the short run, and is subject to decreasing

returns (eq. 5.25):

𝑌 = 𝐹(𝐿), 𝐹′(●) > 0, 𝐹′′(●) < 0

Firms are competitive. They hire labor up to the point where the marginal

product of labor equals the real wage (eq. 5.26):

𝐹′(𝐿) =𝑊

𝑃

Eq-s (5.24)-(5.26) imply an upward-sloping AS curve. If nominal wages are

fixed, higher price level implies lower real wage. Firms respond by rising

employment, which increases output → so there is positive relationship

between P and Y (see Fig. 5.11). Implications:

- Fluctuations in AD lead to movements of employment and real wage along

the downward-sloping 𝐿𝐷 curve. As a result, both prices and output are

affected

- For example, decline in AD leads to fall in P, a rise in W/P, and fall in output.

- This model implies a countercyclical real wage in response to AD shocks.

NB! This result is not supported by empirics, which suggests rather moderately

procyclical real wages…

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Case 2: Sticky Prices, Flexible Wages, and a Competitive Labor Market

Prices rather than wages are rigid (eq. 5.27):

𝑃 = �̅�

Wages are flexible; workers are on their labor supply curve, which is

assumed to be upward-sloping (eq. 5.28):

𝐿 = 𝐿𝑆 (𝑊

𝑃), 𝐿𝑆′(●) > 0

Implications:

- Horisontal AS; fluctuations in AD cause firms to change E and Y until 𝑌𝑀𝐴𝑋.

- Until 𝑃 ≥ 𝑀𝐶 and 𝑊/𝑃 ≤ 𝐹′(𝐿), labor demand curve is vertical (respective

E is called effective labor demand). Workers are on their 𝐿𝑆 curve and there

is no unemployment (see Fig. 5.13, point E).

- This model implies procyclical real wage and countercyclical markup (ratio

of price to marginal cost)

Case 3: Sticky Prices, Flexible Wages, and Real Labor Market Imperfections

Assume that firms have some real-wage function (eq. 5.29):

𝑊

𝑃= 𝑤(𝐿), 𝑤′(●) ≥ 0

Examples: efficiency wages, trade union’s wage policy etc.

Implications:

- Fluctuations in AD and respectively in 𝐿𝐷 lead to movements along the real-

wage function → there would be involuntary unemployment.

- If function 𝑤(𝐿) is flatter than 𝐿𝑆, unemployment rises when AD falls.

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Case 4: Sticky Wages, Flexible Prices, and Imperfect Competition

Price function, where 𝑊

𝐹′(𝐿) is marginal cost and 𝜇 is the markup (eq.

5.30):

𝑃 = 𝜇(𝐿)𝑊

𝐹′(𝐿)

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5.4 Output-Inflation Tradeoffs

A Permanent Output-Inflation Tradeoff?

Appears, if:

- Nominal wages or nominal prices are completely fixed in the short run

- These fixed levels are determined by previous period’s wages and prices.

Consider the AS model with fixed wages, flexible prices and competitive goods

market. Suppose that wages are adjusted to previous period’s inflation. Then

the aggregate supply side of the economy is described as following:

𝑊𝑡 = 𝐴𝑃𝑡−1, 𝐴 > 0 (eq. 5.31)

𝑌𝑡 = 𝐹(𝐿𝑡), 𝐹′(●) > 0, 𝐹′′(●) < 0 (eq. 5.32)

𝐹′(𝐿𝑡) =𝑊𝑡

𝑃𝑡 (eq. 5.33)

AS0 and AS0 are initially steady, but then policymakers use fiscal or monetary

policy in period 1 to shift AD0 curve out to AD1. As a result, price level rises to

P1 and output rises to Y1 (see Figure 5.16, p. 244). The wage is adjusted to

previous period’s inflation, by factor 𝑃1 𝑃0⁄ (eq. 5.34):

𝑊2

𝑊1=

𝐴𝑃1

𝐴𝑃0=

𝑃1

𝑃0

If there is no further inflation, i.e. 𝑃2 = 𝑃1 , then the real wage is 𝐴 𝑃1 𝑃1 = 𝐴⁄ ,

which is equal to the real wage in period 0. Thus AS2 goes through the point

(Y0, P1) -> employment and output would be the same as in period 0.

This process can continue indefinitely: if policymakers follow expansionary

policies, they can keep output (and employment) at higher level at the cost of

inflation.

Phillips curve (Phillips 1958)

But this pattern started to disappear in the late 1960s and early 1970s

(see Figure 5.17)

WHY?

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Figure 5.17 p. 246 (Romer ed 2)

The Natural Rate hypothesis (Friedman 1968, Phelps 1968)

- Nominal variables (like money supply or inflation) could not permanently

affect real variables (such as output or unemployment)

- In the long run the behaviour of real variables is determined by real forces

- Permanently expansionary policy would change the way how prices or wages

are set

- There is some “normal” or “natural” rate of unemployment (which is

determined by real rather than nominal forces)

Other explanations of the empirical failure of Phillips curve:

- Aggregate supply shocks (e.g. oil price increases in 1970s of sharp increase in

labor supply)

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The Expectations-Augmented Phillips Curve

Assume fully flexible prices and wages in the long run -> vertical LRAS curve ->

demand shocks do not affect output -> 𝑌 = �̅� (potential output).

What about short-run AS modelling?

i) Wages and prices are not assumed to be completely unresponsive to the

current state of the economy

ii) The possibility of supply shocks is allowed

iii) Adjustment to past and expected future inflation is assumed to be more

complicated

A typical modern Keynesian formulation of aggregate supply is (eq. 5.35):

ln 𝑃𝑡 = ln 𝑃𝑡−1 + 𝜋𝑡∗ + 𝜆(ln 𝑌𝑡 − ln �̅�𝑡) + 𝜀𝑡

𝑆, 𝜆 > 0

or (eq. 5.36):

𝜋𝑡 = 𝜋𝑡∗ + 𝜆(ln 𝑌𝑡 − ln �̅�𝑡) + 𝜀𝑡

𝑆

“Core” or “underlying” inflation, equals the previous period’s actual inflation

(eq. 5.37):

𝜋𝑡∗ = 𝜋𝑡−1

Replacing core inflation in (5.36) with expected inflation (eq. 5.38):

𝜋𝑡 = 𝜋𝑡𝑒 + 𝜆(ln 𝑌𝑡 − ln �̅�𝑡) + 𝜀𝑡

𝑆

We get the short-run aggregate supply curve in inflation-output space (eq.

5.39):

𝜋𝑡 = 𝜙𝜋𝑡𝑒 + (1 − 𝜙)𝜋𝑡−1 + 𝜆(ln 𝑌𝑡 − ln �̅�𝑡) + 𝜀𝑡

𝑆, 0 ≤ 𝜙 ≤ 1

Implications:

- The core inflation is a weighted average of past inflation and expected future

inflation

- Core inflation is not just mechanical function of past inflation, but still there is

some link between these two

- No general model of aggregate supply …