1. EC6012 Lecture 7
Stephen Kinsella
Notation
Review
Equation System
EC6012 Lecture 7 Steady State
Solutions
Government Money with Portfolio Choice II Portfolio Choice
with Expectations
Puzzling Results from
the model
Real World
Applications
Stephen Kinsella
January 24, 2008
2. Objectives today EC6012 Lecture 7
Stephen Kinsella
Notation
Review
Notation Equation System
Steady State
Solutions
Portfolio Choice
with Expectations
Puzzling Results from
Review the model
Real World
Equation System Applications
Steady State Solutions
Portfolio Choice with Expectations
Puzzling Results from the model
Real World Applications
3. Notation
Symbol Meaning
G Pure government expenditures in nominal terms
Y National Income in Nominal Terms
C Consumption of goods supply by households, in nominal terms
T Taxes
θ Personal Income Tax Rate
YD Disposable Income of Households
α1 Propensity to consume out of regular (present) income
α2 Propensity to consume out of past wealth
∆Hs Change in cash money supplied by the central bank
∆Hh Cash money held by households
H, H−1 High Powered cash money today, and yesterday (−1 )
V Wealth of Households, in nominal terms
Bh,cb Bills held by households, central banks.
4. Review
Households Production Government Central Bank
Money +H −H 0
Bills +Bh −B +Bcb 0
Balance (net worth) -V +V 0
0 0 0 0
Table: Balance Sheet for PC.
5. Transactions Matrix
Central Bank
Households Production Government Current Capital
Consumption -C +C 0
Govt. Expenditures +G -G 0
Income = GDP +Y -Y 0
Interest Payments +r−1 · Bh−1 −r−1 · B−1 +r−1 · Bcb−1 0
Central Bank Proﬁts +r−1 · Bcb−1 −r−1 · Bcb−1 0
Taxes -T +T 0
Change in Money −∆H +∆H 0
Change in Bills −∆Bh +∆B −∆Bcb 0
0 0 0 0 0 0
Table: Transactions matrix for PC.
6. Equation Systems
Y = G +C (1)
YD = Y − T + r−1 · Bh−1 (2)
T = θ · (Y + r−1 · Bh−1 ) (3)
V = V−1 + (YD − C ) (4)
C = α1 · YD + α2 · V−1 , 0 < α1 < α2 < 1 (5)
Hh YD
= (1 − λ0 ) − λ1 · r + λ2 · (6)
V V
Bh YD
= λ0 + λ 1 · r − λ 2 · (7)
V V
Hh = V − Bh (8)
∆Bs = Bs − Bs−1 = (G + r−1 · Bs−1 ) − (T + r−1 · Bcb−1 )
(9)
∆Hs = Hs − Hs−1 = ∆Bcb (10)
Bcb = Bs − Bh (11)
r = r (12)
7. Steady States EC6012 Lecture 7
Stephen Kinsella
Notation
Review
α3 = α2 · (1 − α1 )/α2 (13) Equation System
Steady State
Solutions
∆V = α2 · (α3 − V−1 ) (14)
Portfolio Choice
V∗ with Expectations
= α3 (15) Puzzling Results from
YD ∗ the model
Real World
∗
Bh · r Applications
r∗ = (16)
V∗
8. PCEX EC6012 Lecture 7
Stephen Kinsella
Introducing expectations into PC is done through including
Notation
an expectation on disposable income, YD e . This changes Review
the consumption function to Equation System
Steady State
Solutions
C = α1 · YD e + α2 · V−1 . (17) Portfolio Choice
with Expectations
Puzzling Results from
the model
Real World
Applications
9. Expectation-Augmented Modeling EC6012 Lecture 7
Stephen Kinsella
Notation
Bd YD e Review
= λ 0 + λ 1 · r − λ2 · (18) Equation System
Ve Ve Steady State
Solutions
Hd YD e Portfolio Choice
with Expectations
= (1 − λ0 ) − λ1 · r + λ2 · (19)
Ve Ve Puzzling Results from
the model
Real World
Hd = V e − Bd (20) Applications
e e
V = V−1 + (YD − C ) (21)
10. Puzzling Results from the Model EC6012 Lecture 7
Stephen Kinsella
∗
↑ G ⇒↑ YD, ∂YD < 0
∂G Notation
∗
↑ r ⇒↑ YD, ∂YD > 0
∂r
Review
Equation System
↑ λ0 ⇒ Govt. taking Bills ⇒↑ Y . So dropping liquidity Steady State
Solutions
preference implies increasing Y in PCEX. Portfolio Choice
with Expectations
↑ α3 ⇒↑ Y (Paradox of Thrift?) Puzzling Results from
the model
Real World
Applications
11. Real World Applications EC6012 Lecture 7
Stephen Kinsella
Application 1 Notation
Review
PCEX implies that targeting debt to income ratios will have Equation System
Steady State
a positive eﬀect on the fortunes of the country, if the Solutions
government does the targeting in a credible way. In Portfolio Choice
with Expectations
particular, PCEX gives us a targeting rule of Puzzling Results from
the model
Real World
V∗
Applications
α3
= . (22)
Y∗ 1+ θ
· r · [(λ0 + λ1 · r ) · α3 − λ2 ]
1−θ
12. EC6012 Lecture 7
Debt/GDP
Stephen Kinsella
Notation
Review
Equation System
Steady State
Solutions
Portfolio Choice
with Expectations
Puzzling Results from
the model
Real World
Applications
Figure: Debt/GDP Ratio in Ireland, 1990-2006
13. Interest Cost EC6012 Lecture 7
Stephen Kinsella
Notation
Review
Equation System
Steady State
Solutions
Portfolio Choice
with Expectations
Puzzling Results from
the model
Real World
Applications
Figure: Interest Cost Trend
14. Other Oddities EC6012 Lecture 7
Stephen Kinsella
Application 2 Notation
PCEX also implies that knowing α3 is important in Review
Equation System
forecasting behaviour. What does today’s news about the Steady State
Solutions
percentage of SSIA money actually spent imply about the Portfolio Choice
with Expectations
level of α3 in the Irish economy at present? Puzzling Results from
the model
According to yesterday’s Sunday Times, only three billion of Real World
Applications
the estimated ten billion to be paid out in the SSIAs has
been spent, leaving seven billion sitting in banks. Why do
you think this is?
15. Next Time EC6012 Lecture 7
Stephen Kinsella
Presentations → Check Site.
Notation
Read Godley, Chapter 6 Review
Equation System
Read Expectations In Economics by Lachman (Link on Steady State
Solutions
Site, be in college) Portfolio Choice
with Expectations
The Open Economy! Puzzling Results from
the model
Real World
Applications
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