EC6012 The OPEN Economy Slides

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IntroductionWages and Profits in the OPEN economy

Equations of the ModelSteady State

EC6012 Lecture 9The Really OPEN Economy

Stephen Kinsella

Dept. Economics,University of Limerick

April 30, 2007

Stephen Kinsella EC6012 Lecture 9

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numeraires and gold standards

OPEN

Simulations with OPEN

Course Summary


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

T Total Government expenditures injected in a period.or Quantity of Gold Reservespg Market price of Gold reservesxr Exchange Rate


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The Notion of numeraire and generalised equivalences.Gold Standards

NumeraireExample

Example 1

In a supermarket, Mary can buy 1 can of soup for ¤1.20. In thiscase, the numeraire is the currency - euros. The same trade couldbe analysed di!erently: Mary could also sell ¤1 with 5/6 of a canof soup, 6/5 times. In the latter case, the numeraire is the can ofsoup. This also works for barter economies quite well. Imagine astandard commodity and try to construct trade sequences fromthis single monetary unit. What you have is a monetary systembuilt from the inside out, using the money-good as numeraire.


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NumeraireExample

Example 2

We could change numeraires to a third good: for instance a packetof peanuts. Suppose now that 1 packet of pasta costs ¤2.80. IfMary had 3/7 (= 1.20/2.80) of a packet of pasta, she couldpurchase one packet of soup. In the latter case, the numeraire isthe packet of pasta. Again, because of the di"culty of breaking apacket of pasta into fractions, it is significantly easier to use cash.


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Gold Standards

OPEN assumes a Gold Standard, which operated from 1830–1938,where the currencies of each country are backed by stocks of gold.Gold stocks are valued in each country’s currency, so the price ofgold is mitigated by the exchange rate, xr .


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Wages and Profits in the OPEN economy

Schumpeterian Output

Causal Story implies S = I

w ! P ! i ! I ! CandY

because

sY = C + I + G + (X "M) (1)

X = Y (2)

C = f (Y ) (3)


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OPEN balance Sheet

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188 Monetary Economics

Table 6.3 Balance sheet matrix of two-country economy (Model OPEN)

North North South Southhouse- North central house- South centralholds Govt. bank holds Govt. bank !

Cash money +HNh !HN

h +HSh !HS

h 0

Bills +BNh !BN +BN

cb +BSh !BS +BS

cb 0

Gold orN · pNg · xr

reserves + orN · pNg · xr + orS · pS

g + orS · pSg

Wealth(balancing ! (orN · pN

g · xritem) !VN

h !VNg 0 !VS

h !VSg 0 + orS · pS

g)

! 0 0 0 0 0 0 0

Each country now has its own government which issues bills, and eachcountry has a central bank which issues its own currency. But in addition,each central bank owns a stock of gold reserves which, not being financialassets, have no liability as their counterpart. This is why the value of thegold reserves appearing in the ! column is not zero. Despite that, centralbanks have zero net worth, as they did in the previous model without goldreserves.

As with Model REG, all the variables relevant to the North have an N super-script, while all the variables relevant to the South have an S superscript. Thevalue of gold reserves is given by a physical quantity (‘or’) times the priceof gold (pg) expressed in the appropriate currency.7 The exchange rate xris defined as the number which converts North values and prices into theirequivalents in the currency ruling in the South. For example, if North valuesare in dollars, while South values are in yens, with one dollar being exchangedfor 100 yen, then the exchange rate xr is equal to 100.

When adding items in a given column, we need not worry about theexchange rate, because all items are in the same currency. This is not thecase when dealing with rows. However, because, as a simplification device,we have assumed that the inhabitants of each country can only purchasedomestic assets, each half of each row sums to zero (the half dealing withdomestic assets), so that we need not worry about the exchange rate when

7 In French, or means gold.

Figure: Balance Sheet Matrix for OPEN.


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Points to Note

North and South are denominated with superscript N and S asbefore;

the value of gold is a physical quantity times the price of goldexpressed in the relevant currency;

Not all rows sum to zero now, because we have to takeaccount of transactions between countries in gold;

This model assumes away inter-national fiscal transfers, so astock of gold or other value-bearing commodity is required tomake settlements for international debts.


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OPEN and the Specie Flow Mechanism

Equations of the Model

OPEN is an adaptation of last week’s REG model, so the equationsaren’t very di!erent, apart from equations designed to takeaccount of imports and exports, and home and abroad taxes.

XN =IMS

xr(4)

X S = IMN · xr (5)

TN = !N · (Y N + rN!1 · BN

h!1), 0 < !N < 1 (6)

T S = !S · (Y S + rS!1 · BS

h!1), 0 < !S < 1 (7)

(8)


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We also now need to take account of the 13 extra variable we’vecreated. So our liquidity and balance constraints now look like this:

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Next, one must delete from Model REG all references to a general governmentand a unique central bank. We now have two separate governments and twodifferent central banks. Each government can set its own tax rate, as shownin equations (6.O.9) and (6.O.10).

TN = !N · (YN + rN!1 · BN

h!1) 0 < !N < 1 (6.O.9)

TS = !S · (YS + rS!1 · BS

h!1) 0 < !S < 1 (6.O.10)

Third, the four equations of Model REG that were defining the aggregates ofthe two-region economy – equations (6.19) to (6.23) – are now meaninglessin the two-country economy of Model OPEN, and must be deleted. Becausethere are now two governments and two central banks, the financial variablesrelated to these institutions double in size: there are now eight such variables,namely the supply of bills by each of the two governments, the demand forbills and the supply of cash money by each central bank, and finally the rate ofinterest set by each central bank. There are also four additional variables, thatdid not exist in Model REG: the change in gold holdings by each central bank,and the price of gold in each country. The exchange rate may be consideredas the last additional variable, but we have assumed fixed exchange rates, sothat the exchange rate is a constant. We thus have 13 additional variables,and so we must define 13 extra equations to determine Model OPEN. This isthe task that we now tackle.

"BNs = BN

s ! BNs!1 = (GN + rN

!1 · BNs!1) ! (TN + rN

!1 · BNcb!1) (6.O.19)

"BSs = BS

s ! BSs!1 = (GS + rS

!1 · BSs!1) ! (TS + rS

!1 · BScb!1) (6.O.20)

BNcb = BN

s ! BNh (6.O.21)

BScb = BS

s ! BSh (6.O.22)

"orN. · pNg = "HN

s ! "BNcb (6.O.23)

"orS. · pSg = "HS

s ! "BScb (6.O.24)

HNs = HN

h (6.O.25)

HSs = HS

h (6.O.26)

Equations (6.O.19) and (6.O.20) describe the budget constraint of each gov-ernment; there is nothing new here. Equations (6.O.21) and (6.O.22) arenot new either: they say that each central bank is ready to purchase anybill outstanding which is not bought by households of its constituency.Equations (6.O.23) and (6.O.24) reflect the balance-sheet constraint of thecentral bank. While the balance sheet constraint of the central bank was


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Introducing the Open Economy 193

already used in Model PC and Model REG, these two equations are newequations insofar as they incorporate changes in gold holdings by eachcentral bank. But now, because gold holdings appear on the left-hand side ofthe equations, while the supply of cash money by the central bank appearson the right-hand side of these two equations, we need two new equationsdefining the supply of cash money in each country. These two equationsare equations (6.O.25) and (6.O.26). They indicate that each central bankis supplying the amount of cash money which is being demanded by thehouseholds and explicitly reflect the proposition that money is endogenous,in the sense that it is demand-led, determined by the portfolio choice ofhouseholds.

Five more equations need to be found. Two of these are straightfor-ward. The price of gold in each country must be determined. Withequation (6.O.27) we assume that the price of gold in the North is agiven, expressed in the currency ruling in the North and set by its centralbank. By the law of one price, the price of gold in the South is deter-mined by the exchange rate, given the price of gold in the North, asshown in equation (6.O.28). Since we have room for three more equations,this means that, in addition to a fixed exchange rate, as shown byequation (6.O.29), it is possible for both central banks to set the rate ofinterest of their choice, as reflected by equations (6.O.30) and (6.O.31). Inother words, despite each country being an open economy with a fixedexchange rate, the rates of interest in each country can be set exoge-nously. The rates of interest do not need to play any price-equilibratingmechanism.

pNg = pN

g (6.O.27)

pSg = pN

g · xr (6.O.28)

xr = xr (6.O.29)

rN = rN (6.O.30)

rS = rS (6.O.31)

The redundant equation is now the one which describes the equivalencebetween reserve gains by one country and reserve losses by the other, as canbe assessed from the row ‘Change in reserves’ in the transactions-flow matrixof Table 6.4. That is to say, the structure of the model implies that:

!orS = !!orN (6.O.32)

and in the simulations this is invariably found to be true, although it doesnot appear as an equation in the model.


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OPEN and Specie Flow

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1951

1.00

0.50

0.00

–0.50

–1.00

–1.501956 1961 1966 1971 1976 1981 1986 1991 1996 2001

Value ot the change in gold reservesheld by the South central bank

Change in the South country stock of money

Change in stock of bills heldby the South central bank

Figure 6.10 Evolution of the three components of the balance sheet of the Southcentral bank – gold reserves, domestic Treasury bills and money – following an increasein the South propensity to import

the loss of reserves is supposed to be exercising on the monetary system.Although there is no deliberate ‘sterilization’ of falling reserves by the centralbank, the fall in foreign reserves is nonetheless continuously compensatedby the increase in the amount of bills held by the central bank, as is shownin Figure 6.10. This increase is entirely endogenous to the behaviour of thecentral bank and of that of the entire economic system. One could say that itarises as a consequence of the decision of the central bank to keep constantthe rate of interest on bills. But beyond that, the relative constancy of themoney supply in the new steady state is not the result of a discretionary deci-sion made in an attempt to keep the money supply constant, as ‘sterilization’is portrayed by mainstream authors.

A very similar process is arising in the North, which, with its trade surplus,sees its foreign reserves rise continuously. The rise in these reserves is coun-terbalanced by the fall in the amount of bills that the North central bankis required to hold. This is known as the compensation thesis (Lavoie 2001b:206). The compensation principle asserts that changes in foreign reserveswill generally be compensated by endogenous mechanisms that are tied tothe normal behaviour of the central bank and to that of the other economicagents in the economy. The compensation principle would also operate inan open economy with private bank money.

6.8.3 Two kinds of money supply endogeneity

Mainstream economists usually hold that, whereas otherwise it may be con-sidered to be an exogenous variable, the money supply is endogenous in

Figure: Hume: Not so hot.Stephen Kinsella EC6012 Lecture 9

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Steady State

In the steady state (i.e. when we allow foreign reserves to go tozero and the government requires fiscal measures to cope withforex losses, as in Thailand in 1998), we see the followingrelationship:

Y N =GN

NT

!N=

XN

µN(9)

The only way for the economy to reach the steady state is throughreducing government expenditures or increasing it’s tax rate, asappropriate.


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Course Summary


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EC6012 The OPEN Economy Slides

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