May 29

Decision theory selection criteria

Decision making under uncertainty is not only characterized by ignorance of the final outcome, as with risk, but also by the impossibility of assigning a probability of the outcome’s distribution, as this is also unknown. Both subjective and objective information is unavailable. However, there are a few different criteria that can be applied in order to choose one strategy over others, when facing a decision under uncertainty.

Considering three potential nature states (N₁, N₂, N₃) and three possible strategies (S₁, S₂, S₃) to follow. Their combination results in different outcomes. Let’s see how these criteria work using the example in the following figure:

1) Wald’s maximin model, also known as pessimist model: select the maximum of the minimum, in other words the lesser of evils. We choose S_1,since -3>-5>-7;

2) Optimist model (maximax): select the maximum of the maximum, the best amongst the best. We choose S₂since 9>6>2;

3) Laplace criterion: equal probabilities are assigned to the result of each strategy, from which the highest is chosen. We choose S₃ because ¹⁰/₃>⁵/₃>0 (S₃>S₂>S₁);

4) Hurwicz criterion or optimist-pessimist index: an optimum constant (α) is defined and assigned to the best result, and another is assigned to the worst (1-α). The average weighted value is then calculated and the highest value is chosen. The results will depend on the value of the constant (α) defined.

5) Savage criteria or “minimax Regret”: the agent determines the maximum results for the competitor and choses the strategy that will lead his competitor to the lowest result. This will make the agent better-off.

May 22

Lope Gallego

IS-LM-BP model

The IS-LM-BP model (also known as IS-LM-BoP or Mundell-Fleming model) is an extension of the IS-LM model, which was formulated by the economists Robert Mundell and Marcus Fleming, who made almost simultaneously an analysis of open economies in the 60s. Basically we could say that the Mundell-Fleming model is a version of the IS-LM model for an open economy. In addition to the balance in goods and financial markets, the model incorporates an analysis of the balance of payments.

Even though both economists researched about the same topic, at about the same time, both have different analyses. Mundell’s paper “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates”, 1963, analyses the case of perfect mobility of capital, while Fleming´s model, depicted in his article “Domestic Financial Policies under Fixed and under Floating Exchange Rates”, 1962, was more realistic as it assumed imperfect capital mobility, and thus made this one a more rigorous and comprehensive model. However, nowadays, his model has lost cogency, as the actual world situation has more resemblance with total capital mobility, which corresponds better to Mundell’s view.

In order to understand how this model works, we’ll first see how the IS curve, which represents the equilibrium in the goods market, is defined. Secondly, the LM curve, which represents the equilibrium in the money market. Thirdly, the BP curve, which represents the equilibrium of the balance of payments. Finally, we’ll analyse how the equilibrium is reached.

IS curve: the market for goods and services

In an open economy, the equilibrium condition in the market for goods is that production (Y), is equal to the demand for goods, which is the sum of consumption, investment, public spending and net exports. This relationship is called IS. If we define consumption (C) as C = C(Y-T) where T corresponds to taxes, the equilibrium would be given by:

Y = C(Y-T) + I + G + NX

We consider that investment is not constant, and we see that it depends mainly on two factors: the level of sales and interest rates. If the sales of a firm increase, it will need to invest in new production plants to raise production; it is a positive relation. With regard to interest rates, the higher they are, the more expensive investments are, so that the relationship between interest rates and investment is negative. Now, in addition to what we have in the IS-LM model, since we have net exports, we have also to take into account the exchange rates, which directly affect net exports. Let’s say e is the domestic price of foreign currency or, in other words, how many units of our own currency have to be given up to receive 1 unit of the foreign currency. The new relationship is expressed as follows (where i is the interest rate):

Y = C (Y- T) + I (Y, i) + G + NX(e)

If we keep in mind the equivalence between production and demand, which determines the equilibrium in the market for goods, and observe the effect of interest rates, we obtain the IS curve. This curve represents the value of equilibrium for any interest rate.

An increasing interest rate will cause a reduction in production through its effect on investment. Therefore, the curve has a negative slope. The adjacent graph shows this relationship.

As stated before, we also need to analyse changes in exchange rates (here, e). If e decreases, then we’ll be able to buy more foreign currency with less of our own currency. On the other hand, foreigners we’ll need to pay more of their currency to buy our own. Therefore, when e decreases, also called an appreciation under flexible exchange rates or a revaluation under fixed exchange rates, domestic residents have more purchasing power, thus being able to buy the same amount of goods using less domestic currency. The opposite works in the same way: if e increases (also called a depreciation under flexible exchange rates or a devaluation under fixed exchange rates), domestic residents will pay more for the same goods. To sum up, an increase in e causes net exports to increase (IS curve shifts to the right) and a decrease in e causes net export to decrease (IS curve shifts to the left).

LM curve: the market for money

The LM curve represents the relationship between liquidity and money. In an open economy, the interest rate is determined by the equilibrium of supply and demand for money: M/P=L(i,Y) considering M the amount of money offered, Y real income and i real interest rate, being L the demand for money, which is function of i and Y. Also, the exchange rate must be analysed since it affects money demand (investors may decide buy or sell bonds in a country depending on the exchange rate).

The equilibrium of the money market implies that, given the amount of money, the interest rate is an increasing function of the output level. When output increases, the demand for money raises, but, as we have said, the money supply is given. Therefore, the interest rate should rise until the opposite effects acting on the demand for money are cancelled, people will demand more money because of higher income and less due to rising interest rates.

The slope of the curve is positive, contrary to what happened in the IS curve. This is because the slope reflects the positive relationship between output and interest rates.

BP curve: the balance of payments

The BP curve shows at which points the balance of payments is at equilibrium. In other words, it shows combinations of production and interest rates that guarantee that the balance of payments is viably financed, which means that the volume of net exports that affect total production must be consistent with the volume of net capital outflows. It will usually slope up since the higher the production, the higher the imports, which will disturb the equilibrium of the balance of payments, unless interest rates rise (which would cause capital inflows to maintain the equilibrium). However, depending in how great the mobility of capital is, it will have a greater or smaller slope: the higher the mobility, the flatter the curve.

Once the BP curve is derived, there is an important thing to know about how to use it. Any point above the BP curve will mean a balance of payments surplus. Any points below the BP curve will mean a balance of payments deficit. This is important since depending where we are, different things may affect the interest rates.

The IS-LM-BP model

In the model we distinguish between perfect and imperfect capital mobility, but also between fixed and flexible exchange rates. For each of these cases, we’ll see what happens when both an expansionary monetary and fiscal policy are applied to the economy. We’ll first review Mundell’s model, which deals with perfect mobility. Then, we’ll analyse Fleming’s imperfect mobility model.

1 Perfect capital mobility

1.1 Fixed exchange rate

An expansionary monetary policy will shift the LM curve to LM’, which makes the equilibrium go from point E₀ to E₁. However, since we are below the BP curve, we know the economy has a balance of payments deficit. Since exchange rates are fixed, government intervention is required: the government will purchase domestic currency and sell foreign currency, which will drop the money supply and therefore shift the LM’ curve to its original position (which makes the equilibrium go to E₂). Monetary policy has therefore no effect under these circumstances.

An expansionary fiscal policy will shift the IS curve to IS’, moving the equilibrium form point E₀ to point E₁. Since the economy has now a balance of payments surplus, and because the exchange rate is fixed, government will intervene in the exact opposite way: they’ll purchase foreign currency and sell domestic currency. This will increase the money supply, shifting the LM curve to the right. The final equilibrium is reached at point E₂ where, at the same interest rate, production has increased greatly: fiscal policy works perfectly under these circumstances.

1.2 Flexible exchange rate

An expansionary monetary policy will shift the LM curve to LM’, which makes the equilibrium go from point E₀ to E₁. However, since now exchange rates are flexible, we have a different situation: the balance of payments deficit will depreciate the domestic currency. This will increase net exports (since foreigners can now buy more of our products with the same amount of money), which will shift the IS curve to the right (to IS’). The final equilibrium is reached at point E₂ where, at the same interest rate, production has increased greatly: monetary policy works perfectly under these circumstances.

An expansionary fiscal policy will shift the IS curve to IS’, moving the equilibrium from point E₀ to point E₁. The economy will therefore have a balance of payments surplus, which in this case of flexible exchange rate will appreciate the domestic currency. This will decrease net exports, since we are able to import more goods and services with less money, while foreigners will import less of our products because of our appreciated domestic currency. This drop in net exports will shift the IS’ curve back to its original position. Since now the final equilibrium E₂ corresponds to the initial equilibrium, we know fiscal policy is no good in this case.

It is easy to see why Mundell devised what is known as the impossible trinity. In a few words, no economy can have the following three: perfect capital mobility, fixed exchange rates and an independent and efficient monetary policy. Under the perfect capital mobility assumption, and in order to have an efficient monetary policy, exchange rates must be flexible. Or have fixed exchange rates but assume that monetary policy won’t be efficient.

2 Imperfect capital mobility

2.1 Fixed exchange rate

Here we have the exact same situation as before: an expansionary monetary policy will shift the LM curve to LM’, which makes the equilibrium go from point E₀ to E₁. However, since we are below the BP curve, we know the economy has a balance of payments deficit. Since exchange rates are fixed, the government will purchase domestic currency and sell foreign currency, which will drop the money supply and therefore shift the LM’ curve to its original position (which makes the equilibrium go to E₂). Monetary policy has again no effect, no matter how great or small capital mobility is.

An expansionary fiscal policy will shift the IS curve to IS’, moving the equilibrium from point E₀ to point E₁. Now, depending on capital mobility, we’ll either have a balance of payments surplus (high capital mobility, BP+ curve) or a balance of payments deficit (small capital mobility, BP- curve). Since exchange rates are fixed, government will need to intervene: its acquisitions and disposals of both domestic and foreign currency will shift the LM curve to either LM’ or to LM* (you can review what happens above: a balance of payments surplus is the same scenario as in a fiscal policy with perfect capital mobility and fixed exchange rates, while the balance of payments deficit corresponds to the monetary policy scenario). Under these circumstances, fiscal policy is completely efficient. It’s actually the more efficient the higher capital mobility is.

2.2 Flexible exchange rate

An expansionary monetary policy will shift the LM curve to LM’, which makes the equilibrium go from point E₀ to E₁. However, since now exchange rates are flexible, the balance of payments deficit will depreciate the domestic currency. This will increase net exports, shifting the IS curve to IS’. Also, since domestic assets are less expensive, the BP curve will shift to the right (to either BP’+ or BP’-). Therefore, with high capital mobility, final equilibrium will be at point E₂. Monetary policy works well under these assumptions. It’s actually the more efficient the higher capital mobility is.

An expansionary fiscal policy will shift the IS curve to IS’, moving the equilibrium from point E₀ to point E₁. Now, depending on capital mobility, we’ll either have a balance of payments surplus (high capital mobility, BP+ curve) or a balance of payments deficit (small capital mobility, BP- curve). In the case of a balance of payments surplus, and considering flexible exchange rates, there will be an appreciation of the domestic currency. This will decrease net exports, which will shift the IS’ curve to the left. Also, since domestic assets are more expensive, the BP+ curve will shift to the left. The final equilibrium will therefore be at point E₂. If there is a balance of payments deficit (the case for the BP- curve), the result will be the same one as in the monetary policy case (being E₂* the final equilibrium). In this scenario, fiscal policy will be more efficient the smaller capital mobility is.

The Mundell-Fleming model is a very useful tool when dealing with the analysis of open economies. A great deal of textbooks and papers argue for or against each of these models. However, there’s no denying the world is moving towards liberalizing international trade and capital movements (mostly through WTO’s agreements), which would make us lean towards Mundell’s view. To sum up, under perfect capital mobility, monetary policy will only work with flexible exchange rates, while fiscal policy will only work with fixed exchange rates.

May 20

Lope Gallego

Financial account

The financial account is one of the components of the balance of payments. It shows the net acquisition and disposal of both financial assets and liabilities. As stated in the sixth edition of the Balance of Payments Manual (BPM), by the International Monetary Fund, “The financial account records transactions that involve financial assets and liabilities and that take place between residents and nonresidents”. The table below, taken from the BPM, shows an overview of the financial account.

The financial accounts may correspond to either entries to goods, services, income or capital account, or to entries of opposite sign to the financial account itself. For instance, when a country sells goods to another country, there will be an entry in the current account (an increase in the goods and services account, since the country is exporting), but also an entry in the financial account, such as currency, deposits or trade credit. Sometimes, entries in the financial account will be matched by other entries in the same account: bonds may be exchanged for deposits or currency.

Therefore, the balances of both the current account and the capital account will be conceptually equal to the net balance of the financial account, as seen in the following formula:

CAB + KAB = NFA

where:

CAB = current account balance
KAB = capital account balance
NFA = net financial account

This must be understood as follows: the sum of the balances on the current and capital accounts represent the surplus(net lending) or deficit(net borrowing) that an economy has with the rest of the world. This is equal to the financial account, since it measures how the net lending or borrowing from non-resident is financed.

May 15

Lope Gallego

Capital account

The capital account is one of the components of the balance of payments. It mainly reflects net foreign holdings of capital. When a country incurs on a deficit on current account, it needs to be financed by capital from abroad, it needs to have a capital account surplus. The opposite occurs in the case of current account surplus, there will be an outflow of capital to foreign countries. As stated in the sixth edition of the Balance of Payments Manual (BPM), by the International Monetary Fund, “the capital account in the international accounts shows (a) capital transfers receivable and payable between residents and nonresidents and (b) the acquisition and disposal of nonproduced, nonfinancial assets between residents and nonresidents”.

In other words, the capital account shows acquisitions and disposals of nonproduced nonfinancial assets, such as the sales of leases and licenses, as well as capital transfers (when one party provides capital resources without anything of economic value being supplied as a counterpart). The table below, taken from the BPM, shows an overview of the capital account.

May 13

Lope Gallego

Current account

The current account is one of the components of the balance of payments. It mainly shows the value of movements in exports and imports and income derived form transactions related to net purchases of goods and services. As stated in the sixth edition of the Balance of Payments Manual (BPM), by the International Monetary Fund, “the current account shows flows of goods, services, primary income, and secondary income between residents and nonresidents”. Let’s review all these components:

“The goods and services account shows transactions in items that are outcomes of production activities”. The first thing to mention is that, even though goods are physical, and services are a production that changes the consuming units, or facilitates some kind of exchange, both are considered as products, and are measured at the moment of exchange and at market value. The table below, taken from the BPM, shows an overview of the goods and services account.

“The primary income account shows primary income flows between resident and nonresident institutional units”. In other words, these are income flows concern to some extent governments and other institutions. For instance, taxes, subsidies or other income associated with the production process and with the ownership of financial assets and renting natural resources. It’s worth mentioning that cross-border primary income flows constitute a link between gross domestic product and gross national income. The table below, taken from the BPM, shows an overview of the primary income account.

Current account-Primary income account

“The secondary income account shows current transfers between residents and nonresidents”. These transfers, which might be in cash or in kind, do not include capital transfers, which are shown in the capital account. This is because, as opposed to secondary income, capital transfers do not affect disposable income. The table below, taken from the BPM, shows an overview of the secondary income account.

Current account-Secondary income account

The balance on these three account is known as the current account balance, which shows the difference between the sum of exports and income receivable, and the sum of imports and income payable. It’s also worth mentioning that the current account balance equals the savings-investment gap for the economy, as seen in the following formula:

S – I = CAB

where

S = savings

I = investment

CAB = current account balance

May 8

Lope Gallego

Balance of payments

The balance of payments consists of a series of accounts that reflect the transactions made between an open economy and the rest of the world. As stated in the sixth edition of the Balance of Payments Manual, by the International Monetary Fund, “the balance of payments [is] a statement that summarizes economic transactions between residents and nonresidents during a specific time period”.

These international accounts, which grow greater every day thanks to globalization, are harmonized with the System of National Accounts, so comparisons can be made. They provide a broad view required for the analysis of international trade, exchange rate regimes, and the economic relation between countries, which may translate into vulnerabilities. Therefore, it is of great importance to understand them so business cycles can be anticipated and its consequences diminished.

The balance of payments “consists of the goods and services account, the primary income account, the secondary income account, the capital account, and the financial account”. The first three components form what is known as the current account balance, which mainly shows movements in goods and services and income derived form transactions related to these. The capital account is the sum of two accounts: capital transfers between residents and non-residents; and credit and debit entries for nonfinancial assets. Finally, the financial account shows net acquisitions and disposals of financial assets and liabilities.

The relationship between these accounts is shown in the following formula:

CAB + KAB = NFA

where

CAB = current account balance

KAB = capital account balance

NFA = net financial account

May 6

Lope Gallego

Transformation curve

The transformation curve is defined, in international economics, as the maximum amount of commodity X obtainable for any given amount of commodity Y, and vice versa. This concept is basically the same as the production-possibility frontier studied in microeconomics. In this case, however, the transformation curve shows the trade-off (or opportunity cost) for a country when deciding to produce one commodity or good instead of some other.

Transformation curves may be graphically represented in two alternative ways. The first one will show the marginal rate of transformation between good Y and good X. In other words, it shows the amount of X that the economy has to give up to obtain an additional unit of Y (and vice versa). As seen in the adjacent figure, it resembles the graphical representation of the production possibility frontier. The transformation curve can be either concave, convex or both at the same time. However, with constant returns to scale in the production of both commodities, and different capital-labour ratios (in which case it will be linear), it will always be concave to the origin.

All points on the curve represent an efficient production: countries with a production bundle inside the transformation (such as point A) can be better off by producing more of one of the commodities, moving to the transformation curve (for instance, more of good Y, to point E); bundles outside the transformation curve (such as B or C) are unattainable, because either the technology or inputs are insufficient. Since the transformation curve is derived from an optimizing procedure (as when analysing production optimization in a general equilibrium model), the amount of X (or of Y) given up is the minimum possible under the given technical knowledge.

It’s worth mentioning that, under competitive conditions, the economy will always be on the transformation curve, at a point where the marginal rate of transformation equals the relative price of the two commodities, p_X/p_Y. For instance, as seen in the adjacent figure, if the relative price was such as the one shown by the green straight line (the relative price will be equal to tan α), the economy would operate at point E’, where the marginal rate of transformation equals the relative price of the two commodities, thus being at equilibrium.

The other way to represent transformation curves is using an Edgeworth box. In the figure below, we can see the transformation curves of country A (TC_A, red) and country B (TC_B, green). Note that we consider only one factor of production, and that the technology is fixed, which makes the transformation curves linear. The slope of these transformation curves correspond to the marginal rate of transformation, which in turn represent the comparative cost: tan α corresponds to the comparative cost of country A, while tan β corresponds to the comparative cost of country B. The terms of trade, which in this case have been arbitrarily determined, are given by tan γ.

It’s worth mentioning that this graphical representation is the most common way to represent the Ricardian trade model.

May 2

Lope Gallego

Terms of trade

Terms of trade is used in international trade theory as a measure of the relative price of exports and imports. It is calculated as the ratio according to which two commodities are exchanged between two countries.

Ricardian trade model delimits the boundaries within which the terms of trade must lay in international trade for countries to trade goods. However, it does not determine the exact proportion in which these occur. Nevertheless, determining the exact terms of trade is an argued matter as there are numerous different theories which at the same time go through a wide range of complexity levels.

Probably the simplest model is that of the classical economics which states that in a two country trade, all of the excess production of one country will be exchanged for all the excess production of the second country. However, for this calculation to work, we ought to analyse also the demand of traded goods. John Stuart Mill’s equation of international demand, which basically states that the terms of trade are determined so as to equate the value of exports and imports, show this relationship. In Mill’s words “the produce of a country exchanges for the produce of other countries, at such values as are required in order that the whole of her exports may exactly pay for the whole of her imports”.

It can be easily seen the origin of the main critique regarding this calculation: it is too theoretical. If such terms of trade were applied in actual international transactions, economies would never run a trade deficit or surplus. However, since we know most of them do run a trade deficit or surplus, we must agree that both the Ricardian trade model and Mill’s equation of international demand have a few flaws. Nevertheless, as Jagdish N. Bhagwati pointed out in his article “The Pure Theory of International Trade: A Survey”, 1964, this model ought to be analysed form a normative point of view, since it does help prove the welfare proposition that trade is beneficial.

Apr 29

Lope Gallego

Ricardian trade theory

David Ricardo developed this international trade theory based in comparative advantage and specialization, two concepts that broke with mercantilism that until then was the ruling economic doctrine. He introduced this theory for the first time in his book “On the Principles of Political Economy and Taxation”, 1817, using a simple numerical example concerning the trade between Portugal and the England in the following way:

Let’s say the labour costs per unit of cloth (C) and wine (W) produced by England (E) and Portugal (P) are as those seen in the adjacent figure. Even though Portugal has an absolute advantage on wine and cloth production, England has a comparative advantage on cloth production.

Because of this advantage, both countries would benefit from international trade. This can be seen using an Edgeworth box, as seen in the figure below.

Without international trade, each country would only be able to produce (and therefore to consume) any amount of both wine and cloth inside or at the country’s production-possibility frontier (green for England and red for Portugal). For instance, point E cannot be reached by any of these countries, since it is outside their production-possibility frontier.

However, point E can be reached by trading goods.

Portugal would specialize on producing wine, which is relatively less costly to produce. This is, Portugal is better off producing more wine that it will consume in order to trade it for cloth, since production of cloth would be more costly than the production of the exported wine. For the same reason, England would specialize on cloth. Portugal would produce only wine, consuming C_w and exporting X_w to England, while England would produce only cloth, consuming C_c and exporting X_c to Portugal.

As a result of international trade, point E would become reachable, defining the terms of trade line, which shows how great the gains from trade are. The further from each production-possibility frontier, the better the terms of trade are, and therefore the gains from trade are also greater.

The implications of this theory were great as it meant a breakthrough in the economic science, especially, due to the contribution of the comparative advantage principle.

However, this theory is not spared of flaws as some critics pointed out. John Stuart Mill was concerned with reciprocal demand as he argued that it was not necessarily true that demand and supply across countries would be met. Furthermore, although Ricardian theory of comparative costs may show the limits within which the equilibrium must be, it does not show how to determine the terms of trade, and hence the price of the goods. As this is an unresolved matter, it considerably limits a model that aims to explain international trade. Nevertheless, as Jagdish N. Bhagwati pointed out in his article “The Pure Theory of International Trade: A Survey”, 1964, this model ought to be analysed form a normative point of view, since it does help prove the welfare proposition that trade is beneficial.

Apr 25

Lope Gallego

Comparative advantage

The principle of comparative advantage explains why countries obtain gains from international trade. This term was first mentioned by Adam Smith when talking about specialization, and later by David Ricardo, who developed the concept as we know it nowadays in his trade theory explained in his book “On the Principles of Political Economy and Taxation”, 1817.

When comparing two countries, even if one of them has absolute advantage in producing two goods compared to the other, it may be possible for both to obtain benefits from the trade of these two goods. The key is that each country should produce the good with the lowest opportunity cost. When a country specializes in the good for which it has a comparative advantage, total production rises.

Following the example by Ricardo, Portugal can produce cloth and wine with fewer inputs than England. However, for Portugal the opportunity cost of producing wine is lower than that of producing cloth, whereas, in the case of England the opportunity cost of producing cloth is lower than of wine. If Portugal specializes in producing wine and import cloth, and England specializes in producing cloth and import wine, both countries could make the most of its comparative advantage.

Let’s see a numerical example, following Ricardo’s hypothesis. If England requires 10 men for one year for the production of cloth (let’s say, one unit), and 12 men for the production of wine (also one unit), while Portugal requires 7 men for the production of one unit of cloth and 8 men for the production of one unit of wine, Portugal has an absolute advantage on the production of both cloth and wine, as seen in the adjacent figure.

However, we must consider the opportunity cost of producing each commodity. Comparative costs are 10/12=0.83 in England and 7/8=0.875 in Portugal; these are called the terms of trade.

We can easily see that Portugal produces at lower costs than England: for cloth, (10-7)/10=30% cheaper; and for wine, (12-8)/12=33.3%. Since it can produce both products at a lower cost, we know that Portugal has an absolute advantage in the production of both commodities. However, we can also see that Portugal has a comparative advantage in the production of wine, since it’s comparatively cheaper than cloth (33.3% for wine instead of 30% for cloth).

We obtain the same results with the opposite reasoning. England produces at higher costs: for cloth, (10-7)/7=42.8% more expensive; for wine, (12-8)/8=50% more expensive. Therefore, England has a comparative advantage in the production of cloth, since it’s comparatively less expensive than wine (42.8% for cloth instead of 50% for wine).

In this case, trade will benefit both countries as long as the terms of trade stay between 0.83 and 0.875 units of cloth per unit of wine. As a conclusion, trade can benefit every country because it allows each to specialize in the production of goods and services in which they have a comparative advantage.