Antebellum Period

Table 1 presents information on the four crises that took place during the Antebellum period when both the United Kingdom and the United States were on gold: 1836, 1839, 1845, and 1856. These Antebellum crises share the following stylized facts: A drain of specie reserves in the United Kingdom was followed by (or coincident with) a business contraction there and a reaction by the Bank of England. The immediate effect was gold inflows from the United States to the United Kingdom, which caused a contraction in the specie stock and a financial crisis in the United States due to the lack of means of payments. The latter was followed by or coincident with a business contraction in the United States, which, in most of the cases, was more severe than the one in the United Kingdom. Hence, when both countries were on gold, it is noticeable that the scarcity of specie as means of payments was transmitted from the financial center (where they originated) to the financial periphery, with the subsequent transmission of the associated business contractions.

The policies implemented by the Bank of England during this period can be classified as follows: an increase in discount rates, quantitative restrictions, or a suspension of the Bank Charter of 1844 (known as Peel's Act). The discount rate was the tool used by the Bank of England when trying to sterilize gold flows by buying or selling domestic securities. Quantitative controls were used by the Bank of England as an attempt to restrict lending to the United States: The Bank of England would refuse to discount the bills of joint-stock banks or to handle acceptances of Anglo-American discount houses, even at the higher rates of interest, as observed in 1836. Finally, a suspension of the Bank Charter of 1844 would allow the Bank of England to issue “uncovered” notes, a policy somehow close to an elastic currency regime. This policy was in operation during the crises of 1845 and 1856.

The model that I present in Section 3 is consistent with these facts. In that environment, unforeseen shocks that reduce the availability of reserves in the financial center are transmitted to the periphery when there is reserves sharing and a common outside currency. This shock causes reductions in output in both the center and the periphery.

Greenback Period

Table 2 shows the sequence of events during the only reserve crisis that originated in the United Kingdom during the Greenback period, in 1866. The origin of the contraction was a drain of specie reserves in the Bank of England, followed by a sharp increase in the British discount rates. However, the monetary and business contraction that followed in the United Kingdom did not spread to the United States. The model presented in Section 4 of this paper is consistent with these facts. In that environment, the effects of liquidity shocks are confined to the financial center in the absence of reserves sharing, when there are country-specific outside currencies and full foreign currency controls.

Endowments, Preferences, and Production

A constant number of two-period-lived heterogeneous agents are born every period in each country. In each country, there is a central island surrounded by groups of outer islands. A central island is the only place where all contracts can be enforced and where a monetary authority resides.

In each country, there are three types of agents in each generation: capitalists, debtors, and bankers. Each of these types lives on a separate outer island. Thus, in Country i (i = 1, 2), there is a continuum of capitalists with unit mass, a continuum of debtors with unit mass, and a continuum of bankers with mass y_i. I assume that y₁ < 1. We will see that, in equilibrium, this assumption implies that the United States is liquidity constrained in autarky: Gold reserves will be insufficient to settle all debt at par. In addition, since the United Kingdom is the financial center, I assume that y₁ < y₂.

Each capitalist in each country is endowed when young with one unit of a specific good, and with an investment technology that allows her to transform one unit of the endowment good at time t (only if saved) into one unit of physical capital at t + 1. When old, she can use this capital together with hired labor to produce F(k_it, L_i,t+1) units of a final good, where k_it and L_i,t+1 denote, respectively, physical capital and labor used by a capitalist born in Country i at t. F(·, ·) is a constant-returns-to-scale and twice continuously differentiable production function with the following properties: F_K > 0, F_L > 0, F_KK < 0, F_LL < 0, and, F_KL > 0. I also assume that both physical capital and labor are essential for production. Note that the investment and the production technologies are homogeneous across countries. Finally, the initial old capitalists in both countries are endowed with k₀>0 units of physical capital each.

Each debtor and banker is endowed with one unit of nonstorable labor when young (and nothing when old). Labor is homogeneous across countries and agent types.

A capitalist born in Country i at t only wishes to consume when old the final good he produces (

. Her utility is monotonically increasing in this argument. A debtor born in Country i wishes to consume only the capitalist's endowment good when young (c_it) and nothing when old; her utility is monotonically increasing in this argument. Finally, a banker born in Country i consumes only the services produced by other people's labor when old (n_i,t+1), and her utility is monotonically increasing in this argument. For simplicity, I assume that each agent's utility is linear in its arguments.

In the initial period, there exists a fixed stock of M units of gold in the world, which is distributed equally among the initial old capitalists and bankers.

Interaction Between Countries and Trade and Travel Patterns

As I mentioned before, investment and production technologies are homogeneous across countries. However, I henceforth focus on the case in which the capitalists' endowment good, physical capital, and the capitalists' final good are island-specific. Therefore, the capitalists' endowment good, physical capital, and the capitalists' final good are not internationally mobile: Domestic young agents cannot lend/borrow from the rest of the world, there is no international trade of goods, and physical capital is country-specific. This assumption⁸

It is crucial to notice that each period has two parts. During the first part, we observe only intragenerational trade: A young agent trades with other young agents in the outer islands, and an old agent trades with other old agents at either one of the central islands. During the second part of the period, both intra- and intergenerational trade will take place: An old agent trades with other old agents at either one of the central islands, and then young workers trade with old agents.

In addition, notice that, when old, all the agents must travel to a central island. There are two elements to keep in mind as you read the description of the timing of events that will follow: First, the arrivals of the different types of old agents will not be synchronized, creating problems for both debt clearing and the payment to the factors of production. Second, note that the bilateral clearing of debt would require that the old debtors bring enough gold balances to the central island while the old capitalists are there. Bilateral clearing of debt will not always be possible, and thus debt will be cleared by third parties (banks).

I now describe the timing of events and the nature of transactions within a period.

First Part of the Period

At the beginning of each period, trade in the capitalists' endowment good takes place in both countries. Young debtors would like to buy some of this good from the young capitalists of their country. To do so, they issue debt for the nominal value of the amount of the good they want to purchase, to be repaid in gold (money).¹⁰

It may be useful to note at this point that in this environment, in equilibrium, the interest rate on the debt issued by the young debtors will be fixed by the rate of return on money (gold). Therefore, it will be the price of the young capitalists' endowment good that will adjust to clear the market for loans. This will occur because in each country the young debtors will use the loans only to purchase the goods of the island-specific capitalists' endowment good in their own country.

The young capitalists accept this debt in exchange for part of their endowment good, and invest the rest in capital. The young debtors then go back to their island with the amount of the capitalists' endowment good they purchased and consume it.

The old capitalists travel to the central island in their country. They can stay at a central island only for the first part of the period. However, at this time, none of the U.S.'s old debtors have arrived, and only a fraction λ_t+1 of the UK's old debtors have arrived at their own country's central island. This is the lack of synchronicity in arrival times mentioned earlier. Thus, the bilateral clearing of debt cannot occur at this time. The serially uncorrelated random variable λ_t+1 has a strictly stationary distribution with support on the interval (0, 1). The realization of λ_t+1 is known at the beginning of period t + 1. Notice that λ_t+1 will represent the availability of reserves in the financial center at t + 1. As mentioned earlier, we use a normalization that makes the two countries different in the following sense: Only the financial center displays random changes in the availability of reserves, so that we can focus on reserve crises that originated in the United Kingdom.

At the same time, the old bankers arrive at a central island. The old bankers can wait for the remainder of the old debtors to arrive during the next part of the period, but the old capitalists cannot. The old capitalists, instead of going back home with no gold balances, sell the debt in their hands to the old bankers in exchange for gold. Profit seeking by the bankers gives room for the opening of a resale market for debt. Moreover, the old bankers from either country are free to take reserves to any central island they want. Therefore, the old bankers use gold balances (reserves) to purchase debt from the old capitalists until the resale price of the debt is equalized across central islands. Figure 1 illustrates the transactions performed by the old agents during the first part of a period.

Travels and trade, old agents, first part of a period.

Notice that a lack of nominal means of payment may arise during the first part of a period at the world level. Specifically, there is a shortage of liquidity if the total reserves available in both central islands¹¹

The total reserves available in both central islands at this time are given by the total of gold balances held by the old bankers.

are scarce relative to the face value of the not-yet-settled debt held by the old capitalists of both countries, and this is related to the value of the realization of λ_t+1: A low realization of λ_t+1 is associated with low availability of reserves for the clearing of debt. At the end of this part, the old capitalists sell their debt to the old bankers and go back to their island with the gold received. The old bankers stay on the central island waiting for the remaining old debtors to arrive.

Second Part of the Period.

At the beginning of the second part of a period, the remaining old debtors arrive at their own country's central island and repay their debt to the old bankers. Next, all the old agents go back to their own islands and the competitive labor market opens. Notice that the debt needs to be cleared before the labor market opens because both old bankers and old capitalists must carry gold balances in order to purchase labor. Figure 2 illustrates the transactions performed by the old agents during the second part of a period, before the labor market opens.

Travels and trade, old agents, second stage of a period before the labor market opens.

Finally, the labor market opens. Free mobility of labor across countries implies that young debtors and young bankers travel to the old capitalists' and old bankers' islands either in their own country or in the foreign country to supply labor inelastically in exchange for gold. Also, the nominal wage rate is equalized across both islands and countries. The old bankers purchase labor for consumption. The old capitalists use both the labor they purchased this period and the capital in which they invested when young to produce the final good, and they consume it.

Equilibrium

Behavior of Individual Agents

Debtors

Let p_it denote the unit price (in gold) of the capitalists' endowment good faced by a young debtor born in Country i at time t, and c_it her consumption of this good. Let w_it be the nominal wage in Country i at t, d_it the nominal value of the debt issued by a young debtor born in Country i at t, and m_it her nominal balances of gold. The collapsed budget constraints that describe the debtor's behavior are

Capitalists

Let s_it be the nominal value of the debt accepted by a young capitalist born in Country i at t and let k_it be her investment in physical capital. A young capitalist born in Country i at t can either invest her endowment of the island-specific good or sell it to a young debtor. Her budget constraint is

Define L_i,t+1 to be the amount of labor that a capitalist born in Country i at t buys when old and let q_i,t+1 be the resale price of the debt on Country i's central island at time t + 1. The budget constraints that define the purchases of labor by an old capitalist born in the United States at t and an old capitalist born in the United Kingdom at t are, respectively,

An old capitalist born in Country i at t will use physical capital and labor to produce an island-specific final good. Let

denote her consumption of this good. Then,

A capitalist born in the United States maximizes (4) subject to (2) and (3a), taking q_1,t+1, p_1t and w_1,t+1 as given. The (interior) solution for this problem is described by

Similarly, a capitalist born in the United Kingdom maximizes (4) subject to (2) and (3b), taking q_2,t+1, p_2t, and w_2,t+1 as given. The (interior) solution for this problem is described by

Equations (5a) and (5b) require that the expected return on physical capital equal the expected return on gold reserves.

Bankers

Let m^{[bull ]}_it be the nominal balances of gold held by a young banker born in Country i at t. A young banker supplies labor inelastically in exchange for gold. Hence, the budget constraint faced by a young banker born in Country i is

When old, a banker born in Country i will use her balances of gold to purchase debt from the old capitalists. She can take any fraction x_i,t+1 ∈ [0, 1] of her gold balances (reserves) to the other country's central island and purchase foreign debt, using the remaining reserves to acquire domestic debt. Once the old debtors repay their debt, an old banker born in Country i will spend all the profits earned in purchasing labor. She can buy labor from any country. Let n_i,t+1 be the total consumption of labor by an old banker born in Country i at t. The budget constraint of an old banker is given by

Market-Clearing Conditions¹²

It can be shown that all the results in this section and in the remaining sections hold also for the case when no mobility of the labor supply is allowed across countries. We can assume international mobility in either labor supply or labor demand. Therefore, mobility of old bankers (labor demand) is sufficient, without mobility of workers (labor supply). A proof is available from the author upon request.

There is a single world market for labor. This market clears when the world aggregate supply of labor equals the world aggregate demand for labor:

On the other hand, in this environment the young workers (debtors and bankers) are the only holders of gold balances. Therefore, as a result of a single world market for labor, the market for gold is also integrated at the world level. This market clears when the world aggregate demand for gold equals the world fixed supply:

Equations (1), (6), and (9) imply that

In addition, free international mobility of the labor supply and competitive markets imply nominal wage equalization across countries, so that

However, the demand for the capitalists' endowment good is island-specific. This implies that the domestic markets for loans are not internationally integrated. Therefore, Country i's market for loans clears when

In equilibrium, the old bankers transfer reserves across central islands until the resale price of the debt is equalized across countries:

Also, in equilibrium, the debt offered by the old capitalists cannot exceed the balances of gold brought to the central islands by the old bankers. Therefore, at time t + 1, the resale market for debt clears when

Equation (14) holds with strict equality if there is a shortage of reserves with which to clear the debt:

If this is the case, the debt is sold at a discount (0 < q_t+1 < 1). It follows that there is a shortage of reserves with which to clear the debt at period t + 1 when

If (16) holds for all possible realizations of λ_t+1, we say that the world economy is liquidity constrained. In contrast, we say that there are plentiful reserves in the central islands when

In this case, debt is sold at par (q_t+1 = 1), and the value of debt sold clears this market. Thus, there are plentiful reserves at t + 1 if

If equation (18) holds for all the possible realizations of λ_t+1, we say that the world economy is not liquidity constrained. The analysis that follows focuses on the case in which (16) holds; that is, the world economy is liquidity constrained for all the relevant values of λ_t+1.

Finally, for a given q_t+1, the short-run gross interest rate (liquidity premium) prevailing on the central islands between the departure of the old capitalists and the arrival of the old debtors is given by (1/q_t+1).

General Equilibrium

The proof of the following proposition is straightforward and it is not included here.

PROPOSITION 1. In the liquidity-constrained world-integrated equilibrium with a common outside currency, the following holds as a result of arbitrage in the resale market for debt: (a) The financial center shares gold reserves with the financial periphery, and (b) the liquidity premium is such that (1/y₂) < (1/q_t+1) < (1/y₁).

Thus, in equilibrium, the choice of physical capital by a capitalist born in the United States at t is given by

whereas the equilibrium choice of physical capital by a capitalist born in the United Kingdom at t is

Moreover, it also follows from Proposition 1 that, in equilibrium, the consumption of labor by old bankers born at t is equalized across countries:

Optimality

In this section, I state the conditions that must be satisfied by a Golden Rule allocation in the world economy. Then, I compare the steady-state integrated competitive equilibrium with a common outside currency with the Golden Rule allocation.

The Golden Rule

Consider a benevolent social planner who maximizes a weighted average of the agents' steady-state utility, subject only to feasibility constraints.¹³

The planner is not constrained by the timing of the transfers or by any settlement rule.

This problem may be stated as follows:

where γ_j, j = 1, 2, …, 6, are arbitrary weights. For the world economy to reach the Golden Rule allocation, the following must hold:

where k_i^GR and L_i^GR denote Country i's allocation of physical capital and labor, respectively, under the Golden Rule. Hence, when the world economy is in the Golden Rule allocation, the ratio of marginal product of labor to marginal product of capital in both countries must be equal.

Integrated Competitive Equilibrium and the Golden Rule

In this section, for the sake of comparability, I consider a steady-state competitive equilibrium where the young agents born at t know the value of λ_t+1 at the moment of making their decisions.

PROPOSITION 2. The liquidity-constrained world-integrated steady-state competitive equilibrium with a common outside currency does not satisfy the Golden Rule.

Proof. In the steady-state competitive equilibrium, the following holds:

From (25), (26a), and (26b), a necessary condition for the competitive equilibrium to coincide with the Golden Rule is the following:

However, from (1), (2), (11), (12), (19a), and (19b), equation (27) is satisfied if and only if

and p_1t = p_2t. Combining (1), (2), (11), and (12), I get

Thus, for p_1t = p_2t, k_1t = k_2t is also needed. From (19a) and (19b), this is true only when (28) holds.

Therefore, for the world economy to reach the Golden Rule allocation, not only must there be international financial integration, but in addition, the nominal constraint on output (the liquidity constraint) must not be operative. The latter is not true in the integrated equilibrium when the world economy is liquidity constrained.

The Effects of Unanticipated Drains of Reserves from the United Kingdom

This section discusses the effects, in a (stochastic) steady state, of an unanticipated drain of reserves from the United Kingdom on both capital-based output and profits earned by the reserves-holding sector.¹⁴

Let Y_it denote the stationary real capital-based output in Country i at time t. Then,

PROPOSITION 3. In the liquidity-constrained world-integrated equilibrium with a common outside currency, unforeseen drains of reserves from the financial center (innovations that reduce λ_t) reduce (capital-based) output not only in the financial center but also in the periphery.

Proof. A sufficient condition for Proposition 3 to hold is that Y_1t and Y_2t are increasing in λ_t. Given the fact that k_i remains constant when unforeseen changes in λ_t occur, it is easy to show that

Notice that, in the (stochastic) steady-state equilibrium, L_1t = (y₁ + y₂)/(2 − λ_t) and L_2t = [λ_t + (1 − λ_t)(y₁ + y₂)/(2 − λ_t)]. Also, F_L(k_i, L_it)>0, ∀i = 1, 2. It is easy to show that ∂L_1t/∂λ_t>0 and ∂L_2t/∂λ_t>0. Hence, it follows that

Next, define Π_it as the gross real profits earned by the owners of gold reserves (old bankers) in Country i at time t:

PROPOSITION 4. In the liquidity-constrained world-integrated equilibrium with a common outside currency, unforeseen drains of reserves from the financial center (innovations that reduce λ_t) increase the gross real profits earned by the reserves-holding sector in both the financial center and periphery.

Proof. A sufficient condition for Proposition 4 to hold is that Π_1t and Π_2t are decreasing in λ_t. Using (33), it is easy to show that

Notice that, from (20), in the (stochastic) steady-state equilibrium n_1t = n_2t = (2 − λ_t)/(y₁ + y₂). It follows that ∂n_1t/∂λ_t = ∂n_2t/∂λ_t < 0. Then,

Thus, an unforeseen drain of reserves from the United Kingdom (financial center) is transmitted to the United States (financial periphery) when there is international financial integration (reserves sharing) and a common international currency. This shock causes a reduction in (capital-based) output not only in the United Kingdom (center) but also in the United States (periphery). In contrast, the owners of gold reserves in both countries benefit from this kind of shock. Notice that these results are consistent with the historical evidence presented in Section 2 for the Antebellum period.

Policy

In the presence of an unforeseen drain of reserves in the financial center, the severity of the decline in output is directly related to the scarcity in the stock of reserves available for purchasing debt. However, liquidity shocks have these effects only when the liquidity constraint is operative, that is, when y₁ + y₂ < 2 − λ_t holds. Moreover, the constraint on output is artificial in the sense that it is due only to a temporary lack of nominal liquidity that limits payments to factors of production (labor).

In this section, I discuss two possible policies: an elastic currency regime and a policy of restrictive lending. In the first case, I focus on a discount window that may be operated by any of the monetary authorities.¹⁵

An Elastic Currency Regime: a Discount Window

In this section, I show the potential benefits of appropriate discount window activity. Consider a discount window that is operated as follows: In the first part of period t + 1, the monetary authority lends fiat money¹⁶

The monetary authority could issue “gold certificates” instead, to be redeemed at the end of the period for money (gold). In this case, the gold certificates would be fully backed with gold by the monetary authority. For further discussion, see Freeman (1996b).

at some chosen short-run (within-period) gross interest rate r_t+1 to the old bankers who can demonstrate that they are using the loan to purchase real bills (debt). When there is a common outside currency, the country where the debt was issued is irrelevant in the sense that all the debt is denominated in the same currency. An absence of arbitrage opportunities implies that

At the beginning of the second part of the period, old debtors arrive at their own country's central island to repay their debt to the old bankers. The old bankers are then able to repay the monetary authority's loan. Once the debt is repaid, the monetary authority can avoid inflationary pressures by removing from circulation the extra amount of fiat money lent to the old bankers. Notice that, if net transfers of fiat money across countries occurred when implementing this policy, some communication may be needed between the monetary authorities of both countries. In this event, either the other country's monetary authority may directly remove the extra money from circulation or it may send the extra money to the other central island for its retirement.

It is important to note that, by choosing r_t+1, the monetary authority determines the extent to which the liquidity constraint is binding.¹⁷

For an example of the implementation of this policy (in the absence of a central bank) in Canada during the period between 1880 and 1910, see Champ et al. (1996). They construct a model where seasonal variations in the demand for liquidity and credit play a central role in generating banking panics and argue that these panics do not occur if private banks can issue bank notes backed by general assets.

The lower r_t+1 is, the weaker is the liquidity constraint at the world level. In the limit, when r_t+1 = 1, the debt is sold at par, there is no liquidity constraint, and capital-based output cannot be increased further. Additionally, by setting r_t+1 = 1 the Golden Rule allocation is attained.

An example of a close-enough policy but not as general is the suspension of the Bank Charter of 1844. As I mentioned earlier, this policy would allow the Bank of England to issue “uncovered” notes, a policy somehow close to an elastic currency regime. This policy was in operation during the crises of 1845 and 1856.

Trade and Travel Patterns

The trade and travel patterns are affected by the presence of country-specific currencies and a legal restriction on the use of foreign exchange as a means of payment. The timing of travels and transactions remains unchanged relative to the one described in Section 3. However, the nature of some of the transactions will be modified as is described below.

In the first part of a period, when young debtors issue debt for the nominal value of the amount of the good they want to purchase, the presence of a foreign currency control restricts the denomination of the debt. Thus, it matters if the debt issued in a given country is denominated in dollars or in pounds.

In addition, the legal restriction in both countries and free labor mobility imply that young workers may need to carry a currency different than the one circulating in the country in which they are working. The need for a different currency arises from the fact that young workers working abroad must perform transactions in specific domestic locations the next period. Therefore, the operation of an exchange market is required for trading outside currencies. After supplying labor and exchanging currency, young workers go back to their own islands with the outside currency they earned working.

As before, a resale market for debt will open at the beginning of each period. However, the restrictions on the denomination of the debt along with restrictions on the use of foreign exchange determine that the old capitalists in a given central island accept only domestic currency in exchange for debt. This implies that both domestic and foreign old bankers must use only domestic currency to purchase debt. Thus, the operation of a foreign exchange market plays a crucial role in the sharing of reserves among countries.

At the beginning of the second part of a period, the remaining debtors arrive at their own country's central island and repay their debt to the old bankers using their own country's outside currency. Next, all the old agents go back to their own islands and the competitive labor markets open.

Finally, notice that the operation of a foreign-exchange market is needed twice within a period. The first one relates to the operation of the international market for gold reserves at the beginning of the period. The second corresponds to the operation of the international labor market, during the second part of the period.

Equilibrium and Optimality

In equilibrium, the young capitalists born in the United States accept the debt offered to them only if it is a promise of receiving dollars next period, since they must purchase labor using only dollars. Similarly, the young capitalists born in the United Kingdom only accept debt that promises pounds next period. Thus, because of the presence of full foreign currency controls in both countries, in equilibrium, U.S. debt is dollar-denominated and UK debt is pound-denominated.

On the other hand, young workers born in the United States (United Kingdom) work only for dollars (pounds), regardless of their location: The debtors must repay their debt using dollars (pounds) while the bankers must use dollars (pounds) to purchase labor.

By Proposition 1, the old bankers born in the United Kingdom have an incentive to take reserves to the U.S. central island. However, they must previously exchange their pounds for dollars (U.S. old capitalists accept only dollars). Unfortunately, because of the combination of the lack of synchronicity (at the heart of the financial crises discussed in this paper) and the legal restrictions on the means of payments to be used in both countries, at this time there are no agents in the United States—the only dollar holders—who will sell dollars for pounds. Therefore, no trade occurs in the exchange market at this stage,²⁵

Thus, in the environment described, the presence of full foreign currency controls in a world of country-specific currencies leads to a lack of trade in the foreign exchange markets. The latter precludes financial integration, preventing the operation of an international market of reserves: The countries cannot share reserves anymore and country-specific reserves (the autarkic situation) displace international reserves. This equilibrium is the autarkic (closed-economy) situation for both countries.

Moreover, in this autarkic equilibrium, the resale price of the debt will not be equal across countries. In addition, due to the short supply of reserves in at least one of the countries, the debt will not be always sold at par in equilibrium. This causes a difference in the marginal rates of substitution across countries. Therefore, from Proposition 2, the autarkic equilibrium allocation does not maximize the steady-state utility for the world economy.

Effects of Unanticipated Drains of Reserves from the United Kingdom

This section discusses the effects, in a (stochastic) steady-state equilibrium with financial autarky, of an unforeseen drain of reserves from the United Kingdom (financial center) on both capital-based output and the real profits earned by the reserves-holding sector. Because of the absence of financial integration, the results in this section will differ from the ones discussed in Section 3.5. Once again, the analysis focuses on the consequences of innovations in λ_t, which represent unforeseen and unpredictable changes in the availability of reserves in the United Kingdom (financial center) at time t.

The proofs for Propositions 5 and 6 follow directly from the proofs of Propositions 3 and 4, and are not included here.

PROPOSITION 5. In the liquidity-constrained equilibrium with no financial integration, country-specific outside currencies and full foreign currency controls, unforeseen drains of reserves from the financial center (innovations that reduce λ_t) do not affect capital-based output or gross real profits in the financial periphery.

PROPOSITION 6. In the liquidity-constrained equilibrium with no financial integration, country-specific outside currencies and full foreign currency controls, unforeseen drains of reserves from the financial center (innovations that reduce λ_t) will reduce capital-based output but will increase gross real profits in the financial center.

Thus, an unforeseen shock that reduces the availability of reserves in the United Kingdom (financial center) is confined to the United Kingdom in the absence of reserves sharing, when there are country-specific outside currencies and full foreign-currency controls. This shock causes a reduction in capital-based output only in the United Kingdom, while the owners of gold reserves in the United Kingdom benefit from this kind of shock. Notice that the results presented in this section are consistent with the historical evidence presented in Section 2 for the Greenback period.