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Econ 191: Background material for Prof. Eichengreen’sLecture on International Currencies

Owen Zidar

University of California, Berkeley

owenzidargsi@gmail.com

September 11, 2012

Owen Zidar (Econ 191) Background for Eichengreen September 11, 2012 1 / 33

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Next Week: Professor Eichengreen lecturing on internationalcurrencies

Owen Zidar (Econ 191) Background for Eichengreen September 11, 2012 2 / 33

Overview of Today’s Lecture

1 Historical Context: Brief History of the Evolution of theInternational Monetary System

2 Tools: Referesher on Multivariate Regression

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1. Big Picture - History of International Monetary System1

Gold Standard 1821-1914

Interwar period

Bretton Woods Fixed Exchange Rates: 1946-1973

After Bretton Woods

1Sources: ritholtz.com/blog/ for exchange rate images and InternationalEconomics by Krugman and Obstfeld

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I. Gold Standard: 1821-1914

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I. Gold Standard

You can “cash in” your paper notes for predetermined amount of goldSome Issues:

Limits monetary growth to gold stock, which can’t be adjusted inresponse to economic conditions

Global shortage of gold put downward pressure on prices

E.g. In 1896, the U.S. price level was roughly 40% below its 1869 level

Farmers were squeezed between declining prices for crops and thefixed dollar payments for their mortgages and other debts.

William Jennings Bryan, Cross of Gold, and Wizard of Oz

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II. WWI ‘Dirty Float’ 1915-1925

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II. Interwar Period

War is Expensive: Many countries suspended gold standard, US dida few year later when it entered WWI

Inflation Taxes

Strength in US: US returned to Gold in 1919

Genoa: 1922 conference establishing gold exchange standard2

Restricted Monetary Flexibility: 1925 Britain returned to the goldstandard. Contractionary policy to get back to prewar price level.

2Countries could hold securities convertible into gold issued by othercountries as reserves

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II. Interwar Gold-Exchange Standard: 1926-1931

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II. Pre-Bretton Woods Floats: 1932-1944

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III. Bretton Woods: 1945-1971

Fixed exchange rates against the dollar

Unvarying dollar price of gold: $35 an ounce

Member countries held international reserves in dollars

They had the right to sell dollars for gold at the official price3

They also had the right to adjust their peg to the dollar (pending IMFagreement)

3Bretton Woods differed from interwar gold exchange standard in that theright to sell dollars to the Treasury for gold was limited to official foreigncreditors (governments and central banks

Owen Zidar (Econ 191) Background for Eichengreen September 11, 2012 11 / 33

III. Bretton Woods: 1945-1971

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IV. Smithsonian Agreement: 1972-1973

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III. Floats and Pegs: 1974-1979

US macro policies in the late 1960s helped cause the breakdown ofBretton Woods by early 1973

Most advanced countries abandoned stated pegs, while manydeveloping countries stayed pegged

1974-1975: Stagflation4 led most gov’ts to use monetary and fiscalpolicy

Many attempts to coordinate pseudo-fixed exchange rates withinEurope

4Stagnant growth, high inflation. Higher commodity prices increasedinflation & depressed output. Expectations of future inflation fed into wages &prices

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IV. Floats and Pegs: 1974-1979

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IV. ERM, Euro, ... : 1980-

Dollar Fluctuates: 1976-1979 Weak Dollar, Paul Volker & Deficits,Joint Intervention to depreciate in 1985

ERM semi-pegged system: member banks would intervene tomaintain 2.25% band. UK joined in 1990 and exited 2 years after.

German Reunification: 1990 reunification set off inflationarypressures, divergent needs in Europe and speculative attacks (leadingto 15% bands in 1993).

Inflation Convergence: European countries peg to deutche markwithin Europe’s fixed exchange rate mechanism EMS5

Euro: Maastrict Treaty and a common currency in 1999

Asian Crisis of 1997: Many stopped adhering to dollar pegs after

5European Monetary SystemOwen Zidar (Econ 191) Background for Eichengreen September 11, 2012 16 / 33

IV. ERM, Euro, ... : 1980-

Owen Zidar (Econ 191) Background for Eichengreen September 11, 2012 17 / 33

Part 2: Multivariate Regression Refresher6

Contents

1 Preliminaries

2 Big picture idea: summarize data

3 Linear model4 Multivariate

Frisch Waugh interpretationOmitted Variable BiasReading reg output

5 Methods: D-D and IV

6 Probit

6Some of these notes are based on Mostly Harmless Econometrics andCharlie Gibbon’s 140 notes

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1. Preliminaries

1 Expectations

E(Y ) = Y1 × Prob1 + Y2 × Prob2 + ...+ Yj × Probj (1)

2 VarianceVar(Y ) = E[Y − µy ]2 (2)

3 CovarianceCov(X ,Y ) = E[X − µx ][Y − µy ] (3)

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2. Big picture

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3. Linear model

Decomposition

yi = E[yi |xi ] + (yi − E[yi |xi ])︸ ︷︷ ︸≡εi

(4)

= β0 + β1xi + εi (5)

Example: Height by gender

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3. Linear model Continued

What is β1? β1 = Cov(x ,y)Var(x)

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4. Multivariate model

yi = β0 + β1x1i + β2x2i + ...+ +βkxki + εi

(6)

βk =Cov(y , x̃k)

Var(x̃k)(7)

where x̃k is the residual regression of xk on all the other covariates.

Takeaway: βk is the relationship between y and the part of xk thatisn’t related to other x’s

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4. Multivariate model: Omitted Variable Bias

Suppose that the true model is

yi = γ0 + γ1Schoolingi + γ2Abilityi + ε̃i (8)

Also suppose that Abilityi can be written:

Abilityi = α0 + α1Schoolingi + ηi (9)

What happens if we omit ability and run a “short” regression?

yi = β0 + β1Schoolingi + εi (10)

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4. Multivariate model: Omitted Variable Bias cont.

What happens if we omit ability and run a “short” regression?Plug in ability expression from (10) into true model to see

yi = γ0 + γ1Schoolingi + γ2(α0 + α1Schoolingi + ηi ) + ε̃i

yi = (γ0 + γ2)︸ ︷︷ ︸β1

+ (γ1 + γ2α1)︸ ︷︷ ︸β2

Schoolingi + (ηi + ε̃i )︸ ︷︷ ︸εi

Takeaways

β2 = γ1 + γ2α1

Short equals long plus the effect of omitted times the regression ofomitted on included.

Does γ2α1 = 0?

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4. Reading regression output

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5. Methods: Difference in Difference

Effect = [After-Before]Treatment − [After − Before]Control

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5. Methods: Instrumental Variables

Setupyi = γ0 + γ1Schoolingi + γ2Abilityi + ε̃i︸ ︷︷ ︸

≡vi

(11)

Exclusion Restriction:7 An instrument, zi , is correlated with Schoolingibut uncorrelated with other determinants of dependent variables

Cov(vi , zi ) = 0

Cov(yi − γ0 − γ1Schooling,zi ) = 0

Cov(yi , zi )− γ1Cov(Schooling,zi ) = 0

Cov(yi , zi )

Cov(Schooling,zi )= γ1

7because zi can be “excluded” from the causal modelOwen Zidar (Econ 191) Background for Eichengreen September 11, 2012 28 / 33

5. Methods: Instrumental Variables continued

Implementing this: First stage and reduced form

Schoolingi = θ0 + θ1zi + ηi (12)

yi = π0 + π1zi + ui (13)

γ1 =Cov(yi , zi )

Cov(Schooling,zi )

γ1 =Cov(yi , zi )/Var(zi )

Cov(Schooling,zi )/Var(zi )

γ1 =π1θ1

Caution: Important that first stage is strong (rule of thumb is F > 10)

Owen Zidar (Econ 191) Background for Eichengreen September 11, 2012 29 / 33

6. Probit8

What if limited dependent variable? Yi = 0 or Yi = 1

8Graph from Ashenfelter et al’s Statistics and Econometrics BookOwen Zidar (Econ 191) Background for Eichengreen September 11, 2012 30 / 33

6. Probit (continued)

Setup:

E(Yi ) = Pr(Yi = 0)0︸ ︷︷ ︸=0

+Pr(Yi = 1)1

= Pr(Yi = 1)

≡ Φ(xiβ)︸ ︷︷ ︸probit

Marginal Effects:

∂Pi

∂xi=∂Φ(xiβ)

∂xi= βφ(xiβ)

where Φ is the c.d.f. and φ is the p.d.f. of the normal distribution9

9Φ is prob(z < xiβ), z ∼ N(0, 1), so need to standardize if actually using thisOwen Zidar (Econ 191) Background for Eichengreen September 11, 2012 31 / 33

6. Probit continued

What does this look like in a graph?

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Next Time

Professor Eichengreen on International Currencies

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