The Evolution of a Regional Economy

New NotationIntroduction

Steady State Solutions in REGExperiments with REG

EC6012 Lecture 8The Open Economy

Stephen Kinsella

Dept. Economics,University of Limerick

March 11, 2008

Stephen Kinsella EC6012 Lecture 8



Objectives today

1 New Notation

2 Introduction

3 Steady State Solutions in REG

4 Experiments with REGIncreasing µS

Increasing GST

Increasing (1! µS)Changing Liquidity Preferences




New Notation

All the notation you’re no doubt familiar with (C ,G ,Y ), etc is stillin use, but for space and sanity, I’m only including the newervariables and parameters to be used in this model.

Symbol MeaningN,S North and South Holdings, respectively. µ Propensity to Import.X ExportsIM ImportsGN

T Total Government expenditures injected in a period.




Introduction

PC and PCEX are extended here to show the interactions andfeedbacks from a two region economy with trade. We partition PCinto a North (N) and a South (S) and allow imports and exportsto and from these regions.




Balance Sheet Matrix for REG

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Introducing the Open Economy 171

Table 6.1 Balance sheet of two-region economy (Model REG)

North South Centralhouseholds households Government bank !

Cash money +HNh +HS

h !H 0

Bills +BNh +BS

h !B +Bcb 0

Wealth (balancing item) !VNh !VS

h !Vg 0 0

! 0 0 0 0 0

temic approach, methodologically identical with the closed economy modelsalready presented.2

Our open-economy models will evolve organically in stages from modelPC in Chapter 4. We start off with the very same (closed) economy describedby model PC, and then imagine how the economies of two componentregions, which together make up the total, interact with one another andwith the government. This will be Model REG. In subsequent sections we dealwith a two-country system, each with its own currency. This will be ModelOPEN.

6.2 The matrices of a two-region economy

We introduce open-economy macroeconomics by splitting a closed economyinto two parts, the ‘North’ and the ‘South’ but retaining a single government,a single fiscal and monetary system and (of course) a single currency. Theeconomy described here is the very same economy as in Model PC; we justdisaggregate it into two regions, which will be differentiated by adding theS superscript sign to symbols describing one (the ‘South’) and N to describethe other (the ‘North’).

Table 6.1 shows the balance sheet of this two-region economy. Table 6.1is no different from Table 4.1, except that households have been subdividedinto two groups, the households living in the North and those in the South.Vg represents the net wealth of the federal government and it takes on anegative value, since the government has no asset and only a liability, repre-sented by B. As a consequence Vg describes total net wealth acquired by thehouseholds of both regions.

2 See also Gray and Gray (1988–89: 241) for the advantages of adopting a flow-of-funds matrix for the world, thus identifying the ‘constraints and interdependencieswhich must characterize the international financial system’ and transforming ‘balance-of-payments analysis from a partial to a general framework’.

Figure: Balance Sheet Matrix for REG




National Income Equations

Y N = CN + GN + XN ! IMN , (1)

IMN = µN · Y N , (2)

XN = IMS . (3)

(4)




Other Key Equations

The next equations describe the evolution of regional disposableincome, taxes, wealth, consumption, money demand and bills (wecall them bonds) demand functions.

YDN = Y N ! TN + r!1 · BNh!1 (5)

TN = ! · (Y N + r!1 · BNh!1) 0 < ! < 1 (6)

V N = V N!1 + (YDN ! CN) (7)

CN = "N1 · YDN + "N

2 · V N!1 0 < "1 < "2 < 1 (8)

HNh = V N ! BN

h (9)

BNh

V N= #N

0 + #N1 · r ! #N

2 ·!

YDN

V N

"(10)




Other Key Equations


YDN = Y N ! TN + r!1 · BNh!1 (5)

TN = ! · (Y N + r!1 · BNh!1) 0 < ! < 1 (6)

V N = V N!1 + (YDN ! CN) (7)

CN = "N1 · YDN + "N

2 · V N!1 0 < "1 < "2 < 1 (8)

HNh = V N ! BN

h (9)

BNh

V N= #N

0 + #N1 · r ! #N

2 ·!

YDN

V N

"(10)




Other Key Equations


YDN = Y N ! TN + r!1 · BNh!1 (5)

TN = ! · (Y N + r!1 · BNh!1) 0 < ! < 1 (6)

V N = V N!1 + (YDN ! CN) (7)

CN = "N1 · YDN + "N

2 · V N!1 0 < "1 < "2 < 1 (8)

HNh = V N ! BN

h (9)

BNh

V N= #N

0 + #N1 · r ! #N

2 ·!

YDN

V N

"(10)




Other Key Equations


YDN = Y N ! TN + r!1 · BNh!1 (5)

TN = ! · (Y N + r!1 · BNh!1) 0 < ! < 1 (6)

V N = V N!1 + (YDN ! CN) (7)

CN = "N1 · YDN + "N

2 · V N!1 0 < "1 < "2 < 1 (8)

HNh = V N ! BN

h (9)

BNh

V N= #N

0 + #N1 · r ! #N

2 ·!

YDN

V N

"(10)




Other Key Equations


YDN = Y N ! TN + r!1 · BNh!1 (5)

TN = ! · (Y N + r!1 · BNh!1) 0 < ! < 1 (6)

V N = V N!1 + (YDN ! CN) (7)

CN = "N1 · YDN + "N

2 · V N!1 0 < "1 < "2 < 1 (8)

HNh = V N ! BN

h (9)

BNh

V N= #N

0 + #N1 · r ! #N

2 ·!

YDN

V N

"(10)




Other Key Equations


YDN = Y N ! TN + r!1 · BNh!1 (5)

TN = ! · (Y N + r!1 · BNh!1) 0 < ! < 1 (6)

V N = V N!1 + (YDN ! CN) (7)

CN = "N1 · YDN + "N

2 · V N!1 0 < "1 < "2 < 1 (8)

HNh = V N ! BN

h (9)

BNh

V N= #N

0 + #N1 · r ! #N

2 ·!

YDN

V N

"(10)




Steady State Solutions

A region reaches their steady state when the change in householdwealth from period to period is zero, so !V = 0. The conditionwhere this holds is

GNT + XN = TN + IMN (11)

In the stationary state, GDP in the North will depend on thefollowing condition:

Y N" =GN

T + XN

! + µN(12)




Harrod’s Foreign Trade Multiplier

Discussion

Equation 12 shows the Harrod foreign trade multiplier, whichshows how the North’s output is dependent on the North’sgovernment expenditure and their exports, divided by the tax andimport propensities.What does this imply for policies to get the economy to the steadystate?




Increasing µS

Increasing GST

Increasing (1! µS )Changing Liquidity Preferences

Experiments: Evolution of Balances North and South

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1950 1955 1960 1965 1970 1975

North region GDP

South region GDP

1980 1985 1990 1995 2000102.0

108.0

109.5

106.5

105.0

103.5

Figure 6.1 Evolution of GDP in the North and the South regions, following an increasein the propensity to import of the South region

The evolution of output in each region, as described in the precedingparagraph, is illustrated in Figure 6.2. It shows that the step increase in thepropensity to import of the South generates a sudden increase in output inthe North, and a corresponding decrease in the South’s output. The changes,however, quickly taper off, because the model incorporates the counter-activefeedback effects that each region is imposing upon the other. These feedbackeffects are such that a new steady state is soon reached, each region producinga constant output.

While demand in the South region falls when its import propensity rises,demand in the North region rises, and this may be inflationary if it startsoff fully employed. This may induce a central government to take deflation-ary fiscal measures even though output and employment in the South havefallen. It should be possible to draw conclusions along Kaldorian lines aboutthe beneficial effect of regionally differentiated fiscal policy (Kaldor 1970b).Note too that in reality taxes are progressive and that government outlays areautomatically differentiated because the central government is responsiblefor all unemployment benefit. This implies, de facto, some kind of regionallydifferentiated fiscal policy, provided the tax system is sufficiently progressiveand the unemployment benefits are sufficiently generous.

These are, we believe, important ‘real’ results which, with only a little imag-ination, can be applied to the current discussion of the European MonetaryUnion (EMU) and its common currency – the Euro. It sheds light on the vexedquestion of what is the difference between a balance-of-payments deficit

Figure: Evolution of Balances North and South




Increasing µS

Increasing GST


Evolution of GDP in North-South Regions following anincrease in µS

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182 Monetary Economics

1951

0.00

–0.25

–0.50

–0.75

–1.00

–1.25

1956 1961 1966 1971 1976 1981 1986 1991 1996 2001

Government balance with the South region

Trade balance of the South region

Change in household wealthof the South region

Figure 6.2 Evolution of the balances of the South region – net acquisition of financialassets by the household sector, government budget balance, trade balance – followingan increase in the propensity to import of the South region

which exists between two parts of a single country which has a unitary fiscaland monetary system – not, however, the current euro zone arrangements –and one which exists between two different economies. These differenceswill be clearer when we present a similar model of two economies, each withits own currency.

In the meantime, the dramatic consequences of the twin-deficit accountingproposition in all steady states should be noted, especially within the contextof the EMU. In the example illustrated with Figures 6.1 and 6.2, it is clear thatany region, or country within the EMU, which experiences an increase in thepropensity to import, will end up with a regional government deficit, eventhough it started out with a balanced budget. In the steady state, that is, ina stationary steady state without growth, and excluding any third party, it isimpossible for both regions of a country, or for both countries of a monetaryunion, to simultaneously enjoy government budget surpluses or balancedbudgets.

This proposition is rarely understood, in contrast to another, more obviousproposition, that says that all countries in the world cannot simultaneouslyenjoy a trade surplus or a balance-of-payments surplus. In Model REG, it isobvious that the South and the North regions cannot simultaneously, in orout of the steady state, enjoy a positive trade balance. One of them musthave a deficit, since the conditions required for balanced trade, as seen withequation (6.35), are so stringent.

Figure: Evolution of GDP in North-South Regions following an increasein µS




Increasing µS

Increasing GST


Increasing G ST

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184

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

124.0

128.0

120.0

116.0

112.0

108.0

South region GDP

North region GDP

Figure 6.3 Evolution of GDP in the South and the North regions, following an increasein the government expenditures in the South region

1951

2.0

1.0

0.0

–1.0

–2.0

–3.0

1956 1961 1966 1971 1976 1981 1986 1991 1996 2001

Government balancewith the South region



Figure 6.4 Evolution of the balances of the South region – net acquisition of financialassets by the household sector, government budget balance, trade balance – followingan increase in the government expenditures in the South region

Figure: Evolution of GDP in North-South Regions following an increasein GS

T




Increasing µS

Increasing GST


Evolution of Balances following an increase in G ST

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184

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

124.0

128.0

120.0

116.0

112.0

108.0

South region GDP

North region GDP

Figure 6.3 Evolution of GDP in the South and the North regions, following an increasein the government expenditures in the South region

1951

2.0

1.0

0.0

–1.0

–2.0

–3.0

1956 1961 1966 1971 1976 1981 1986 1991 1996 2001

Government balancewith the South region



Figure 6.4 Evolution of the balances of the South region – net acquisition of financialassets by the household sector, government budget balance, trade balance – followingan increase in the government expenditures in the South regionFigure: Evolution of Balances following an increase in GS

T




Increasing µS

Increasing GST


Evolution of GDP following an increase in SouthernPropensities to Save

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1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

106.25

107.50

105.00

103.75

102.50

101.25

South region GDP

North region GDP

Figure 6.5 Evolution of GDP in the North and South regions, following an increasein the propensity to save of South region households

to a higher steady-state level of output. What happens now in our two-regioneconomy if the households in one region decide to increase their propensityto save? This is the subject of our third experiment. Let us assume, againstarting from a steady state with balanced trade and balanced budgets, thatthe households of the South decide to reduce their propensity to consumeout of current income – the !1 parameter. What happens to output levels,trade balances, and fiscal positions?

Figure 6.5 shows that there is a slowdown in economic activity in the South.Because of the interdependence of the two regions, a similar but less abruptslowdown also occurs in the North, since their exports to the South willdecrease. However, as in Model PC, both regions eventually recover, and thelong-run steady-state effect of this increase in the propensity to save turnsout to be slightly positive.

Figure 6.6 shows that the higher degree of thriftiness on the part of theSouth region households leads to an accumulation of additional wealth,which is compensated both by the central government deficit in the Southand the trade surplus of the South, both of which appear as a result of theeconomic recession occurring in the South region. Eventually, all balancesapproach equilibrium. Figure 6.6 however shows that twin deficits, or twinsurpluses, only need to occur in (quasi) steady states. During the transition,before a stationary state is reached, a government surplus in the region maywell accompany a trade deficit, or vice-versa.

Figure: Evolution of GDP following an increase in Southern Propensitiesto Save




Increasing µS

Increasing GST


Evolution of Balances following an increase in µS

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1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

106.25

107.50

105.00

103.75

102.50

101.25

South region GDP

North region GDP

Figure 6.5 Evolution of GDP in the North and South regions, following an increasein the propensity to save of South region households

to a higher steady-state level of output. What happens now in our two-regioneconomy if the households in one region decide to increase their propensityto save? This is the subject of our third experiment. Let us assume, againstarting from a steady state with balanced trade and balanced budgets, thatthe households of the South decide to reduce their propensity to consumeout of current income – the !1 parameter. What happens to output levels,trade balances, and fiscal positions?

Figure 6.5 shows that there is a slowdown in economic activity in the South.Because of the interdependence of the two regions, a similar but less abruptslowdown also occurs in the North, since their exports to the South willdecrease. However, as in Model PC, both regions eventually recover, and thelong-run steady-state effect of this increase in the propensity to save turnsout to be slightly positive.

Figure 6.6 shows that the higher degree of thriftiness on the part of theSouth region households leads to an accumulation of additional wealth,which is compensated both by the central government deficit in the Southand the trade surplus of the South, both of which appear as a result of theeconomic recession occurring in the South region. Eventually, all balancesapproach equilibrium. Figure 6.6 however shows that twin deficits, or twinsurpluses, only need to occur in (quasi) steady states. During the transition,before a stationary state is reached, a government surplus in the region maywell accompany a trade deficit, or vice-versa.

Figure: Evolution of Balances following an increase in µS




Increasing µS

Increasing GST


Evolution of Balances following a change in Southernliquidity preferences.

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1951

0.120

0.080

0.040

0.000

–0.040

–0.080

1956 1961 1966 1971 1976 1981 1986 1991 1996 2001

Government deficit with the South region

Trade deficit of the South region

Increase in household wealthof the South region

Figure 6.7 Evolution of the balances of the South region – net acquisition of financialassets by the household sector, government budget balance, trade balance – followinga decrease in the liquidity preference of South region households

in liquidity preference by Southern households has some positive economicrepercussions on the South, as it now benefits from higher total governmentexpenditures. But all these effects are of a second-order magnitude.

6.6 The matrices of a two-country economy

The next stage is to turn Model REG into a two-country model with no over-arching or federal, government. This will be Model OPEN. However, movingin steps, it will for the time being be assumed that the private residents ofeach country are not allowed to hold any kind of foreign asset. The matri-ces for the regional model must be changed so that each country has itsown government and its own central bank. The main change, however, isthat we now assume that the currencies in the two countries are differentfrom one another; hence all transactions between them require conversionso that the transaction can be made in common units. It will also be assumedthat exchange rates are fixed, so any discrepancy between sales and pur-chases on the exchange market are made good by transactions of the centralbanks.

As always we introduce this new model by presenting the balance sheetmatrix and the transactions-flow matrix. These are shown in Tables 6.3and 6.4.

Figure: Evolution of Balances following a change in Southern liquiditypreferences.




Increasing µS

Increasing GST


Next Time

The Open Economy. Read GL, pages 187–211.


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The Evolution of a Regional Economy

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