ec6012 lecture 7

EC6012 Lecture 7

Stephen Kinsella

Notation

ReviewEquation SystemSteady StateSolutions

Portfolio Choicewith ExpectationsPuzzling Results fromthe modelReal WorldApplications

EC6012 Lecture 7Government Money with Portfolio Choice II

Stephen Kinsella

January 24, 2008

EC6012 Lecture 7

Stephen Kinsella

Notation



Objectives today

Notation

ReviewEquation SystemSteady State Solutions

Portfolio Choice with ExpectationsPuzzling Results from the modelReal World Applications

Notation

Symbol MeaningG Pure government expenditures in nominal termsY National Income in Nominal TermsC Consumption of goods supply by households, in nominal termsT Taxes! Personal Income Tax Rate

YD Disposable Income of Households"1 Propensity to consume out of regular (present) income"2 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.

Review

Households Production Government Central Bank!

Money +H !H 0Bills +Bh !B +Bcb 0

Balance (net worth) -V +V 0!0 0 0 0

Table: Balance Sheet for PC.

Transactions Matrix

Central Bank

Households Production Government Current Capital!

Consumption - C + C 0Govt. Expenditures + G -G 0

Income = GDP +Y -Y 0Interest 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 0Taxes -T +T 0

Change in Money !!H +!H 0Change in Bills !!Bh +!B !!Bcb 0!

0 0 0 0 0 0

Table: Transactions matrix for PC.

Equation Systems

Y = G + C (1)

YD = Y ! T + r!1 · Bh!1 (2)

T = ! · (Y + r!1 · Bh!1) (3)

V = V!1 + (YD ! C ) (4)

C = "1 · YD + "2 · V!1, 0 < "1 < "2 < 1 (5)

Hh

V= (1! #0)! #1 · r + #2 ·

"YD

V

#(6)

Bh

V= #0 + #1 · r ! #2 ·

"YD

V

#(7)

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)

EC6012 Lecture 7

Stephen Kinsella

Notation



Steady States

"3 = "2 · (1! "1)/"2 (13)

!V = "2 · ("3 ! V!1) (14)V "

YD" = "3 (15)

r" =B"

h · r

V " (16)

EC6012 Lecture 7

Stephen Kinsella

Notation



PCEX

Introducing expectations into PC is done through includingan expectation on disposable income, YDe . This changesthe consumption function to

C = "1 · YDe + "2 · V!1. (17)

EC6012 Lecture 7

Stephen Kinsella

Notation



Expectation-Augmented Modeling

Bd

V e= #0 + #1 · r ! #2 ·

"YDe

V e

#(18)

Hd

V e= (1! #0)! #1 · r + #2 ·

"YDe

V e

#(19)

Hd = V e ! Bd (20)

V e = V!1 + (YDe ! C ) (21)

EC6012 Lecture 7

Stephen Kinsella

Notation



Puzzling Results from the Model

! " G #" YD, !YD!

!G < 0

! " r #" YD, !YD!

!r > 0

! " #0 # Govt. taking Bills #" Y . So dropping liquiditypreference implies increasing Y in PCEX.

! " "3 #" Y (Paradox of Thrift?)

EC6012 Lecture 7

Stephen Kinsella

Notation



Real World Applications

Application 1PCEX implies that targeting debt to income ratios will havea positive e"ect on the fortunes of the country, if thegovernment does the targeting in a credible way. Inparticular, PCEX gives us a targeting rule of

V "

Y " ="3

1 +$

"1!"

%· r · [(#0 + #1 · r) · "3 ! #2]

. (22)

EC6012 Lecture 7

Stephen Kinsella

Notation



Debt/GDP

Figure: Debt/GDP Ratio in Ireland, 1990-2006

EC6012 Lecture 7

Stephen Kinsella

Notation



Interest Cost

Figure: Interest Cost Trend

EC6012 Lecture 7

Stephen Kinsella

Notation



Other Oddities

Application 2PCEX also implies that knowing "3 is important inforecasting behaviour. What does today’s news about thepercentage of SSIA money actually spent imply about thelevel of "3 in the Irish economy at present?According to yesterday’s Sunday Times, only three billion ofthe estimated ten billion to be paid out in the SSIAs hasbeen spent, leaving seven billion sitting in banks. Why doyou think this is?

EC6012 Lecture 7

Stephen Kinsella

Notation



Next Time

! Presentations $ Check Site.

! Read Godley, Chapter 6

! Read Expectations In Economics by Lachman (Link onSite, be in college)

! The Open Economy!

ec6012 lecture 7

Economy & Finance