This document introduces new notation and concepts for modeling an open economy using the Regional Economy (REG) model. It defines symbols for variables such as exports (X), imports (IM), government expenditures (GTN), and regional holdings (N, S). It also presents the national income equations and other key equations that describe regional disposable income, taxes, wealth, consumption, money demand, and bond demand for the open REG model. The objectives are to analyze steady state solutions and conduct experiments by changing parameters like trade propensity (μS) and government spending.

1. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
EC6012 Lecture 8
The Open Economy
Stephen Kinsella
Dept. Economics,
University of Limerick
March 11, 2008
Stephen Kinsella EC6012 Lecture 8

2. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Objectives today
1 New Notation
2 Introduction
3 Steady State Solutions in REG
4 Experiments with REG
Increasing µS
Increasing GTS
Increasing (1 − µS )
Changing Liquidity Preferences
Stephen Kinsella EC6012 Lecture 8

3. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
New Notation
All the notation you’re no doubt familiar with (C , G , Y ), etc is still
in use, but for space and sanity, I’m only including the newer
variables and parameters to be used in this model.
Symbol Meaning
N, S North and South Holdings, respectively. µ Propen
X Exports
IM Imports
GTN Total Government expenditures injected in a period.
Stephen Kinsella EC6012 Lecture 8

4. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Introduction
PC and PCEX are extended here to show the interactions and
feedbacks from a two region economy with trade. We partition PC
into a North (N) and a South (S) and allow imports and exports
to and from these regions.
Stephen Kinsella EC6012 Lecture 8

5. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Balance Sheet Matrix for REG
Introducing the Open Economy 171
Table 6.1 Balance sheet of two-region economy (Model REG)
North South Central
households households Government bank
Cash money N
+Hh S
+Hh −H 0
Bills +BN
h
+BS
h
−B +Bcb 0
Wealth (balancing item) N
−Vh S
−Vh −Vg 0 0
0 0 0 0 0
temic approach, methodologically identical with the closed economy models
Figure: Balance Sheet Matrix for REG
already presented.2
Our open-economy models will evolve organically in stages from model
PC in Chapter 4. We start off with the very same (closed) economy described
by model PC, and then imagine how the economies of two component
regions, which together make up the total, interact with one another and
with the government. This will be Model REG. In subsequent sections we deal
with a two-country system, each with its own currency. This will be Model
OPEN.
6.2 The matrices of a two-region economy
Stephen Kinsella EC6012 Lecture 8

6. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
National Income Equations
YN = C N + G N + X N − IM N , (1)
N N N
IM = µ ·Y , (2)
N S
X = IM . (3)
(4)
Stephen Kinsella EC6012 Lecture 8

7. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Other Key Equations
The next equations describe the evolution of regional disposable
income, taxes, wealth, consumption, money demand and bills (we
call them bonds) demand functions.
YD N = Y N − T N + r−1 · Bh−1
N
(5)
TN = θ · (Y N + r−1 · Bh−1 )
N
0<θ<1 (6)
N
V = V−1 + (YD N − C N )
N
(7)
N
C = N N
α1 · YD N + α2 · V−1
N
0 < α1 < α2 < 1 (8)
N
Hh = V N − BhN
(9)
N
Bh YD N
= λN + λ N · r − λN ·
0 1 2 (10)
VN VN
Stephen Kinsella EC6012 Lecture 8

8. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Other Key Equations
The next equations describe the evolution of regional disposable
income, taxes, wealth, consumption, money demand and bills (we
call them bonds) demand functions.
YD N = Y N − T N + r−1 · Bh−1
N
(5)
TN = θ · (Y N + r−1 · Bh−1 )
N
0<θ<1 (6)
N
V = V−1 + (YD N − C N )
N
(7)
N
C = N N
α1 · YD N + α2 · V−1
N
0 < α1 < α2 < 1 (8)
N
Hh = V N − BhN
(9)
N
Bh YD N
= λN + λ N · r − λN ·
0 1 2 (10)
VN VN
Stephen Kinsella EC6012 Lecture 8

9. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Other Key Equations
The next equations describe the evolution of regional disposable
income, taxes, wealth, consumption, money demand and bills (we
call them bonds) demand functions.
YD N = Y N − T N + r−1 · Bh−1
N
(5)
TN = θ · (Y N + r−1 · Bh−1 )
N
0<θ<1 (6)
N
V = V−1 + (YD N − C N )
N
(7)
N
C = N N
α1 · YD N + α2 · V−1
N
0 < α1 < α2 < 1 (8)
N
Hh = V N − BhN
(9)
N
Bh YD N
= λN + λ N · r − λN ·
0 1 2 (10)
VN VN
Stephen Kinsella EC6012 Lecture 8

10. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Other Key Equations
The next equations describe the evolution of regional disposable
income, taxes, wealth, consumption, money demand and bills (we
call them bonds) demand functions.
YD N = Y N − T N + r−1 · Bh−1
N
(5)
TN = θ · (Y N + r−1 · Bh−1 )
N
0<θ<1 (6)
N
V = V−1 + (YD N − C N )
N
(7)
N
C = N N
α1 · YD N + α2 · V−1
N
0 < α1 < α2 < 1 (8)
N
Hh = V N − BhN
(9)
N
Bh YD N
= λN + λ N · r − λN ·
0 1 2 (10)
VN VN
Stephen Kinsella EC6012 Lecture 8

11. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Other Key Equations
The next equations describe the evolution of regional disposable
income, taxes, wealth, consumption, money demand and bills (we
call them bonds) demand functions.
YD N = Y N − T N + r−1 · Bh−1
N
(5)
TN = θ · (Y N + r−1 · Bh−1 )
N
0<θ<1 (6)
N
V = V−1 + (YD N − C N )
N
(7)
N
C = N N
α1 · YD N + α2 · V−1
N
0 < α1 < α2 < 1 (8)
N
Hh = V N − BhN
(9)
N
Bh YD N
= λN + λ N · r − λN ·
0 1 2 (10)
VN VN
Stephen Kinsella EC6012 Lecture 8

12. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Other Key Equations
The next equations describe the evolution of regional disposable
income, taxes, wealth, consumption, money demand and bills (we
call them bonds) demand functions.
YD N = Y N − T N + r−1 · Bh−1
N
(5)
TN = θ · (Y N + r−1 · Bh−1 )
N
0<θ<1 (6)
N
V = V−1 + (YD N − C N )
N
(7)
N
C = N N
α1 · YD N + α2 · V−1
N
0 < α1 < α2 < 1 (8)
N
Hh = V N − BhN
(9)
N
Bh YD N
= λN + λ N · r − λN ·
0 1 2 (10)
VN VN
Stephen Kinsella EC6012 Lecture 8

13. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Steady State Solutions
A region reaches their steady state when the change in household
wealth from period to period is zero, so ∆V = 0. The condition
where this holds is
GT + X N = T N + IM N
N
(11)
In the stationary state, GDP in the North will depend on the
following condition:
GT + X N
N
Y N∗ = (12)
θ + µN
Stephen Kinsella EC6012 Lecture 8

14. New Notation
Introduction
Steady State Solutions in REG
Experiments with REG
Harrod’s Foreign Trade Multiplier
Discussion
Equation 12 shows the Harrod foreign trade multiplier, which
shows how the North’s output is dependent on the North’s
government expenditure and their exports, divided by the tax and
import propensities.
What does this imply for policies to get the economy to the steady
state?
Stephen Kinsella EC6012 Lecture 8

15. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
Experiments: Evolution of Balances North and South
Introducing the Open Economy 181
North region GDP
109.5
108.0
106.5
105.0
103.5
South region GDP
102.0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Figure 6.1 Evolution of GDP in the North and the South regions, following an increase
in the propensity to import of the South region
Figure: Evolution of Balances North and South
The evolution of output in each region, as described in the preceding
Stephen Kinsella EC6012 Lecture 8

16. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
Evolution of GDP in North-South Regions following an
increase in µS
182 Monetary Economics
0.00
Change in household wealth
of the South region
–0.25
–0.50
Government balance with the South region
–0.75
–1.00
Trade balance of the South region
–1.25
1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001
Figure 6.2 Evolution of the balances of the South region – net acquisition of financial
Figure:assets by the household sector, in North-South Regions following an increase
Evolution of GDP government budget balance, trade balance – following
in µS an increase in the propensity to import of the South region
which exists between two parts of a single country which has a unitary fiscal
Stephen Kinsella EC6012 Lecture 8

17. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
S
Increasing GT
184
128.0
124.0
South region GDP
120.0
116.0 North region GDP
112.0
108.0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Figure 6.3 Evolution of GDP in the South and the North regions, following an increase
Figure: Evolution of GDP in North-South Regions following an increase
in the government expenditures in the South region
S
in GT
2.0
Stephen Kinsella EC6012 Lecture 8

18. 108.0
New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Experiments with REG Changing Liquidity Preferences
S
Figure 6.3 Evolution of GDP in the South and the North regions, following an increase
Evolution of Balances following an increase in GT
in the government expenditures in the South region
2.0
1.0 Change in household wealth
of the South region
0.0
–1.0
Trade balance of the South region
–2.0
Government balance
with the South region
–3.0
1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001
Figure 6.4 Evolution of the balances of the South region – net acquisition of financial
assets by the household sector, government budget balance, trade balance – following
S
Figure: Evolution of Balances following an increase in GT
an increase in the government expenditures in the South region
Stephen Kinsella EC6012 Lecture 8

19. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
Evolution of GDP following an increase in Southern
Propensities to Save
Introducing the Open Economy 185
107.50
106.25 North region GDP
105.00
103.75
South region GDP
102.50
101.25
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Figure 6.5 Evolution of GDP in the North and South regions, following an increase
Figure: Evolution of GDP following an increase in Southern Propensities
in the propensity to save of South region households
to Save
to a higher steady-state level of output. What happensLecture 8our two-region
Stephen Kinsella EC6012 now in

20. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
Evolution of Balances following an increase in µS
Introducing the Open Economy 185
107.50
106.25 North region GDP
105.00
103.75
South region GDP
102.50
101.25
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Figure 6.5 Evolution of GDP in the North and South regions, following an increase
Figure: Evolution of Balances following an increase in µS
in the propensity to save of South region households
to a higher steady-state level of output. What happens now in our two-region
economy if the households in one region decide to increase their propensity
Stephen Kinsella EC6012 Lecture 8

21. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
Evolution of Balances following a change in Southern
liquidity preferences.
Introducing the Open Economy 187
0.120
0.080
Increase in household wealth
of the South region
0.040
0.000
Trade deficit of the South region
–0.040
Government deficit with the South region
–0.080
1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001
Figure 6.7 Evolution of the balances of the South region – net acquisition of financial
assets by the household sector, government budget balance, trade balance – following
Figure: Evolution of Balances following a change in Southern liquidity
a decrease in the liquidity preference of South region households
preferences.
in liquidity preference by Southern households has some positive economic
repercussions on the South, as it now benefits from higher total government
expenditures. But all these effects are of a second-order magnitude.
Stephen Kinsella EC6012 Lecture 8

22. New Notation Increasing µS
S
Introduction Increasing GT
Steady State Solutions in REG Increasing (1 − µS )
Experiments with REG Changing Liquidity Preferences
Next Time
The Open Economy. Read GL, pages 187–211.
Stephen Kinsella EC6012 Lecture 8