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
Imports & exports depend on income:
M = Md(E, Y)
= 𝑀 + mY
X = Xd(E, Y*)
=𝑋
assuming E & Y* fixed, for now.
=> TB = 𝑋 − (𝑀 +mY)
TB
…and rises in contractions
+
0
-
Y
TB falls in expansions…
where slope = -m ≡
- marginal propensity
to import
as does consumption:
Keynesian consumption function C = 𝐶 + cY .
ITF220 - Prof. J. Frankel, Harvard University
Trade
rises inimproved
recessions,
E.g.,
the balance
US trade balance
sharply
in expansions
in falls
the recession
of 2008-09
U.S. International Transactions
0
2004-2014
$ MILLIONS
PER QUARTER
Current
Account
-50000
-100000
-150000
Goods &
Services
-200000
-250000
I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III
2004
2005
2006
2007
2008
2009
Seasonally Adjusted
Balance on current account (line 1 less line 9) /4/
2010
2011
2012
2013
Balance on goods and services (line 2 less line 10)
ITF220 - Prof. J. Frankel, Harvard University
2014
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)
𝐶+𝐼+𝐺 + 𝑋 − 𝑀
𝑌=
1−𝑐+𝑚
𝐴+𝑋−𝑀
𝑌=
𝑠 + 𝑚
Prof. J. Frankel, Harvard University
where 𝐴 ≡ 𝐶+𝐼+𝐺
and s ≡ 1 – c.
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
NS ≡
S + BS ≡ I + TB
ITF220 - Prof. J. Frankel, Harvard University
National
Saving
Identity
US National Saving, Investment, & Current Account
as Shares of GDP, 1949-2009
Trend:
Gap widened,
as NS fell
relative to I
ITF220 - Prof. J. Frankel, Harvard University
Keynesian Consumption Function: C = 𝐶 + cYd .
or, expressed as a saving function: S = Yd - C = Yd - 𝐶 - cYd .
= - 𝐶 + sYd where s ≡ 1 – c.
}I
ITF220 - Prof. J. Frankel, Harvard University
Closed economy: NS – I = 0
Fiscal Expansion
1 < Closed-economy multiplier 1/s < ∞
ITF220 - Prof. J. Frankel, Harvard University
Open economy: NS – I = TB
=X–M
Imports: M = Md(E, Y), or = 𝑀+mY for simplicity
Exports: X = Xd(E), or = 𝑋 for simplicity.
=> TB = 𝑋 − (𝑀+mY )
Prof. J. Frankel, Harvard University
Open economy
Fiscal Expansion
slope = s
G
ΔY =
1
𝑠+𝑚
Δ𝐺 <
Prof. J. Frankel, Harvard University
1
Δ𝐺
𝑠
End of Lecture 4:
Introduction to the
Keynesian Model
ITF220 - Prof. J. Frankel, Harvard University
Appendix -- Puzzle:
Why did global trade collapse
in the 2008-09 global recession?
(more than usual)
2009
Bussière, Callegari, Ghironi, Sestieri & Yamano, 2013,
"Estimating Trade Elasticities:
Demand
Composition
and the Trade Collapse of 2008-2009."
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 2008-09.
Bussière, Callegari, Ghironi, Sestieri & Yamano, 2013,
"Estimating Trade Elasticities: Demand Composition and the Trade Collapse of 2008-2009."
ITF220 - Prof. J. Frankel, Harvard University