1. THE KEYNESIAN MODEL Lecture 4: Introduction to Keynesian Model:
Derivation; National Saving Identity.
Lecture 5: Multipliers for spending & exports;
the transfer problem.
Lecture 6: Large-country model; International transmission under fixed vs. floating exchange rates
Lecture 7: Adjustment of a CA deficit via expenditure-reducing vs. expenditure-switching policies
Lecture 8: Monetary factors

2. - Prof. J. Frankel, Harvard University
Imports & exports depend on income:
M = Md(E, Y)
X = Xd(E, Y*)
= 𝑀 + m Y
= 𝑋
assuming E & Y* fixed, for now.
=> TB = 𝑋 −( 𝑀 + mY) Y TB + -
…and rises in contractions
where slope = -m ≡
- marginal propensity
to import
TB falls in expansions…
as does consumption: Keynesian consumption function
C = 𝐶 + c Y
- Prof. J. Frankel, Harvard University

3. Prof. J. Frankel, Harvard University
E.g., the US trade & current account balances improved sharply in the recession of
PER QUARTER
PER QUARTER
Prof. J. Frankel, Harvard University

4. Prof. J. Frankel, Harvard University
Determination of equilibrium income in open-economy Keynesian model
Y ≡ A + TB
≡ (C + I + G) + (X – M)
= ( 𝐶 +cY + 𝐼 + 𝐺 ) + ( 𝑋 - 𝑀 - mY).
Now solve:
Y - cY + mY = 𝐶 + 𝐼 + 𝐺 + ( 𝑋 - 𝑀 )
𝑌= 𝐶 + 𝐼 + 𝐺 + 𝑋 − 𝑀 1−𝑐+𝑚
𝑌= 𝐴 + 𝑋 − 𝑀 𝑠 + 𝑚
where 𝐴 ≡ 𝐶 + 𝐼 + 𝐺
and s ≡ 1 – c.
Prof. J. Frankel, Harvard University

5. - Prof. J. Frankel, Harvard University
Derivation of National Saving Identity
Income ≡ Output (assuming no transfers)
Y ≡ GDP
/ /
C + S + T ≡ C + I + G + X -M
S + (T-G) ≡ I + X – M
National
Saving
Identity
NS ≡ S + BS ≡ I + TB
- Prof. J. Frankel, Harvard University

6. Trend: Gap widened, as NS fell relative to I
When national saving falls relative to investment, the trade balance falls.
Trend: Gap widened, as NS fell relative to I
CFR, Oct. 12, 2016

7. ITF220 - Prof. J. Frankel, Harvard University
Keynesian Consumption Function: C = 𝐶 + cYd , where Yd ≡ disposable income .
or, expressed as a saving function: S = Yd - C
= Yd - 𝐶 - cYd .
= - 𝐶 + sYd where s ≡ 1 – c. }
ITF220 - Prof. J. Frankel, Harvard University

8. Prof. J. Frankel, Harvard University
Closed economy: NS – I = 0 Fiscal Expansion .
1 < Closed-economy multiplier 1/s < ∞
Prof. J. Frankel, Harvard University

9. Prof. J. Frankel, Harvard University
Open economy: NS – I = TB = X – M
Imports: M = 𝑀 +mY.
Exports: X = 𝑋 .
(keeping exchange rate fixed for now)
=> TB = 𝑋 −( 𝑀 +mY )
Prof. J. Frankel, Harvard University

10. Prof. J. Frankel, Harvard University
Open economy
Fiscal Expansion
slope = s ●
ΔY = 1 𝑠+𝑚 Δ 𝐺
< 1 𝑠 Δ 𝐺
Prof. J. Frankel, Harvard University

11. ITF220 - Prof. J. Frankel, Harvard University
End of Lecture 4:
Introduction to the Keynesian Model
ITF220 - Prof. J. Frankel, Harvard University

12. ITF220 - Prof. J. Frankel, Harvard University
Appendix Puzzle: Why did global trade collapse in the global recession?
(more than usual)
2009
Bussière, Callegari, Ghironi, Sestieri & Yamano, 2013, "Estimating Trade Elasticities: Demand Composition and the Trade Collapse of "
ITF220 - Prof. J. Frankel, Harvard University

13. ITF220 - Prof. J. Frankel, Harvard University
One answer: There is a marginal propensity to import out of investment, greater than the marginal propensity to import by consumers. And investment fell much more than consumption in
Bussière, Callegari, Ghironi, Sestieri & Yamano, 2013, "Estimating Trade Elasticities: Demand Composition and the Trade Collapse of "
ITF220 - Prof. J. Frankel, Harvard University