Eco 328Divergence, diversification and demand

The Lucas Paradox: Why Doesn’t Capital Flow from Rich to Poor Countries?

In his widely cited article “Why Doesn’t Capital Flow from Rich to Poor Countries?,” Nobel laureate Robert Lucas wrote:

If this model were anywhere close to being accurate, and if world capital markets were anywhere close to being free and complete, it is clear that, in the face of return differentials of this magnitude, investment goods would flow rapidly from the United States and other wealthy countries to India and other poor countries. Indeed, one would expect no investment to occur in the wealthy countries. . . .

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Countries Have Different Productivity Levels

To see why capital does not flow to poor countries, we now suppose that A, the productivity level, is different in the United States and Mexico, as denoted by country subscripts:

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• The data show that Mexico’s capital per worker is about one-third that of the United States.

• If productivity was the same, Mexico would have a level of output level per worker of (1/3)1/3 = 0.69 or 69% of the U.S. level. However, Mexico’s output per worker was much less, 43% of the U.S. level.

• This gap could be explained by lower productivity in Mexico. We infer A in Mexico equals 0.43/0.69 = 62% of that in the United States, meaning Mexico’s production function and MPK curves are lower than those for the United States.

• The MPK gap between Mexico and the United States is much smaller, which reduces the incentive for capital to migrate to Mexico from the United States.

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Why Doesn’t Capital Flow to Poor Countries? This doesn’t happen in reality. Poor and rich countries have different levels of productivity (different production functions) and so MPK may not be much higher in poor countries than it is in rich countries, as shown in panel (b). The poor country (Mexico) is now at C and not at B. Now investment occurs only until MPK falls to the rest of the world level at point D.

The result is divergence. Capital per worker k and output per worker q do not converge to the levels seen in the rich country.

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A Versus k• For many developing countries, the predicted gains due to

financial globalization are large with the benchmark model, but small once we correct for productivity differences.

• Allowing for productivity differences, investment will not cause poor countries to reach the same level of capital per worker or output per worker as rich countries.

• Economists describe this outcome as one of long-run divergence between rich and poor countries.

• Unless poor countries can lift their levels of productivity, access to international financial markets is of limited use.

• There are not enough opportunities for productive investment for complete convergence to occur.

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Why Capital Doesn’t Flow to Poor Countries

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Why Capital Doesn’t Flow to Poor Countries

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A Versus k• An older school of thought focused on A as reflecting a

country’s technical efficiency, construed narrowly as a function of its technology and management capabilities.

• Today, many economists believe that the level of A may primarily reflect a country’s social efficiency, construed broadly to include institutions, public policies, and cultural differences.

• And indeed there is some evidence that, among poorer countries, capital tends to flow to the countries with better institutions.

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A Versus kMore Bad News?

Other factors are against the likelihood of convergence.

• The model makes no allowance for risk premiums to compensate for the risk of investing in an emerging market (e.g., risks of regulatory changes, tax changes, expropriation, and other political risks).

• Risk premiums can be substantial, and may be large enough to cause capital to flow “uphill” from poor to rich.

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Risk Premiums in Emerging Markets The risk premium measures the difference between the interest rate on the country’s long-term government debt and the interest rate on long-term U.S. government debt.

The larger the risk premium, the more compensation investors require, given their concerns about the uncertainty of repayment.

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A Versus k

• The model assumes that investment goods can be acquired at the same relative price, but in developing countries, it often costs much more than one unit of output to purchase one unit of capital goods.

• The model assumes that the contribution of capital to production is equal across countries, but the capital’s share may be much lower in many developing countries. This lowers the MPK even more.

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Diversification can help smooth shocks by promoting risk sharing. With diversification, countries may be able to reduce the volatility of their incomes without any net lending or borrowing.

• Consider two countries, A and B, with outputs that fluctuate asymmetrically.

• There are two possible “states of the world,” with equal probability of occurring.

• State 1 is a bad state for A and a good state for B; state 2 is good for A and bad for B.

• Assume that all output is consumed, and that there is no investment or government spending.

• Output is divided 60-40 between labor income and capital income.

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Risk sharing

Home PortfoliosBoth countries are closed, and each owns 100% of its capital. Output is the same as income.

In state 1, A’s output is 90, of which 54 units are payments to labor and 36 units are payments to capital; in state 2, A’s output rises to 110, and factor payments rise to 66 for labor and 44 units for capital. The opposite is true in B: in state 1, B’s output is higher than it is in state 2.

The variation of GNI about its mean of 100 is plus or minus 10 in each country. Because households prefer smooth consumption, this variation is undesirable.

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World PortfoliosTwo countries can achieve partial income smoothing if they diversify their portfolios of capital assets.

For example, each country could own half of the domestic capital stock, and half of the other country’s capital stock.

Indeed, this is what standard portfolio theory says that investors should try to do.

Capital income for each country is smoothed at 40 units.

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The figure shows fluctuations in capital income over time for different portfolios, based on the data from the table. Countries trade claims to capital income by trading capital assets. When countries hold the world portfolio, they each earn a 50-50 split (or average) of world capital income. World capital income is constant if shocks in the two countries are asymmetrical and cancel out. All capital income risk is then fully diversifiable.

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Portfolio Diversification and Capital Income: Diversifiable Risks

Generalizing

• Each country’s payments to capital are volatile. A portfolio of 100% country A’s capital or 100% of country B’s capital has capital income that varies by plus or minus 4 (between 36 and 44). But a 50-50 mix of the two leaves the investor with a portfolio of minimum, zero volatility (it always pays 40).

• In general, there will be some common shocks, which are identical shocks experienced by both countries. In this case, there is no way to avoid this shock by portfolio diversification.

• But as long as some shocks are asymmetric, the two countries can take advantage of gains from the diversification of risk.

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The charts plot the volatility of capital income against the share of the portfolio devoted to foreign capital. The two countries are identical in size and experience shocks of similar amplitude. In panel (a), shocks are perfectly asymmetric (correlation = −1), capital income in the two countries is perfectly negatively correlated. Risk can be eliminated by holding the world portfolio, and there are large gains from diversification.

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Return Correlations and Gains from Diversification

In panel (b), shocks are perfectly symmetric (correlation = +1), capital income in the two countries is perfectly positively correlated. Risk cannot be reduced, and there are no gains from diversification. In panel (c), when both types of shock are present, the correlation is neither perfectly negative nor positive. Risk can be partially eliminated by holding the world portfolio, and there are still some gains from diversification. 19

Return Correlations and Gains from Diversification

The Home Bias Puzzle

In practice, we do not observe countries owning foreign-biased portfolios or even the world portfolio.

Countries tend to own portfolios that suffer from a strong home bias, a tendency of investors to devote a disproportionate fraction of their wealth to assets from their own home country, when a more globally diversified portfolio might protect them better from risk.

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The figure shows the return (mean of monthly return) and risk (standard deviation of monthly return) for a hypothetical portfolio made up from a mix of a pure home U.S. portfolio (the S&P 500) and a pure foreign portfolio (the Morgan Stanley EAFE) using datafrom the period 1970 to 1996.

Portfolio Diversification in the United States

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U.S. investors with a 0% weight on the overseas portfolio (point A) could have raised that weight as high as 39% (point C) and still raised the return and lowered risk. Even moving to the right of C (toward D) would make sense, though how far would depend on how the investor viewed the risk-return trade-off. The actual weight seen was extremely low at just 8% (point B) and was considered a puzzle. 22

Portfolio Diversification in the United States

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The Globalization of Cross-Border Finance

Demand in the Open Economy

Consider a two country model

The foreign economy could be thought of as “the rest of the world” (ROW).

We are in the short run, so home and foreign price levels, �𝑃𝑃 and �𝑃𝑃*, are fixed due to price stickiness.

As a result expected inflation is fixed at zero, πe = 0 and all quantities can be viewed as both real and nominal quantities because there is no inflation.

Assume that government spending �̅�𝐺 and taxes �𝑇𝑇 are fixed, but subject to policy change.

−

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Demand in the Open Economy

Let foreign output �𝑌𝑌* and the foreign interest rate i* be fixed.

For now let home income, Y be equivalent to output: GNDI=GDP

That means net factor income from abroad (NFIA) and net unilateral transfers (NUT) are zero,

So the current account (CA) equals the trade balance (TB).

−

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Demand in the Open Economy

Consumption

• The simplest model of aggregate private consumption relates household consumption C to disposable income Yd.

• This equation is known as the Keynesian consumption function.

Marginal Effects The slope of the consumption function is called the marginal propensity to consume (MPC). We can also define the marginal propensity to save (MPS) as 1 − MPC.

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The Consumption Function The consumption function relates private consumption, C, to disposable income, Y − T. The slope of the function is the marginal propensity to consume, MPC.

⎯

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Demand in the Open EconomyInvestment

• The firm’s borrowing cost is the expected real interest rate re, which equals the nominal interest rate i minus the expected rate of inflation π e:

re = i − πe.

• Since expected inflation is zero, the expected real interest rate equals the nominal interest rate, re = i.

• Investment I is a decreasing function of the real interest rate; investment falls as the real interest rate rises.

• This is true only because when expected inflation is zero, the real interest rate equals the nominal interest rate.

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The Investment Function The investment function relates the quantity of investment, I, to the level of the expected real interest rate, which equals the nominal interest rate, i, when (as assumed here) the expected rate of inflation, πe, is zero. The investment function slopes downward: as the real cost of borrowing falls, more investment projects are profitable.

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Demand in the Open EconomyThe Government

• The government collects an amount T of taxes from households and spends an amount G on government consumption.

• Ignore government transfer programs, such as social security, medical care, or unemployment benefit systems - they do not generate any change in the total expenditure on goods and services; they merely change who gets to spend the money.

• In the unlikely event that G = T exactly, we say that the government has a balanced budget.

• If T > G, the government is said to be running a budget surplus (of size T − G).

• If G > T, a budget deficit (of size G − T or, equivalently, a negative surplus of T − G).

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Demand in the Open EconomyThe Trade Balance

The Role of the Real Exchange Rate

• When aggregate spending patterns change due to changes in the real exchange rate, this is expenditure switching from foreign purchases to domestic purchases.

• If home’s exchange rate is E, and home and foreign price levels are �𝑃𝑃 and �𝑃𝑃* (both fixed in the short run), the real exchange rate q of Home is defined as q = E �𝑃𝑃*/ �𝑃𝑃.

o We expect the trade balance of the home country to be an increasing function of the home country’s real exchange rate. As the home country’s real exchange rate rises, it will export more and import less, and the trade balance rises.

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Oh! What a Lovely Currency War

In September 2010, the finance minister of Brazil accused other countriesof starting a “currency war” by pursuing policies that made Brazil’scurrency, the real, strengthen against its trading partners, thus harming thecompetitiveness of his country’s exports and pushing Brazil’s trade balancetoward deficit. By 2013 fears about such policies were being expressed bymore and more policy makers around the globe.

The Curry Trade

In 2009, a dramatic weakening of the pound against the euro sparked an unlikely boom in cross-Channel grocery deliveries. Many Britons living in France used the internet to order groceries from British supermarkets, including everything from bagels to baguettes (French products).

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Demand in the Open EconomyThe Trade Balance

The Role of Income Levels

o We expect an increase in home income to be associated with an increase in home imports and a fall in the home country’s trade balance.

o We expect an increase in rest of the world income to be associated with an increase in home exports and a rise in the home country’s trade balance.

• The trade balance is, therefore, a function of three variables: the real exchange rate, home disposable income, and rest of world disposable income.

),,/(function

Increasing

**

function ng Decreasi

function Increasing

* TYTYPPETBTB −−=

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The trade balance is an increasing function of the real exchange rate, EP*/P. When there is a real depreciation (a rise in q), foreign goods become more expensive relative to home goods, and we expect the trade balance to increase as exports rise and imports fall (a rise in TB).

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The Trade Balance and the Real Exchange Rate

The trade balance may also depend on income. If home income rises, then some of the increase in income may be spent on the consumption of imports. For example, if home income rises from Y1 to Y2, then the trade balance will decrease, whatever the level of the real exchange rate, and the trade balance function will shift down.

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The Trade Balance and the Real Exchange Rate

Demand in the Open EconomyThe Trade Balance

Marginal Effects Once More

We refer to MPCF as the marginal propensity to consume foreign imports.• Let MPCH > 0 be the marginal propensity to consume home goods.

MPC = MPCH + MPCF.

• For example, if MPCF = 0.10 and MPCH = 0.65, then MPC = 0.75; for every extra dollar of disposable income, home consumers spend 75 cents, 10 cents on imported foreign goods and 65 cents on home goods (and they save 25 cents).

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The Trade Balance and the Real Effective Exchange Rate

• A composite or weighted-average measure of the price of goods in all foreign countries relative to the price of U.S. goods is constructed using multilateral measures of real exchange rate movement.

• Applying a trade weight to each bilateral real exchange rate’s percentage change, we obtain the percentage change in home’s multilateral real exchange rate or real effective exchange rate:

%)(in changes rate exchange real bilateral

of average weighted-Trade

2

22

1

11

%)(in change rate exchange effective Real

effective

effective

TradeTrade

TradeTrade

TradeTrade

∆++

∆+

∆=

∆

N

NN

qq

qq

qq

qq

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For example,

if we trade 40% with country 1 and 60% with country 2, and we have a real appreciation of 10% against 1 but a real depreciation of 30% against 2, then the change in our real effective exchange rate is (40% × −10%) + (60% × 30%) = (0.4 × −0.1) + (0.6 × 0.3) = −0.04 + 0.18 = 0.14 = + 14%. That is, we have experienced an effective trade-weighted real depreciation of 14%.

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The Real Exchange Rate and the Trade Balance: United States, 1975-2012 The data show that the U.S. trade balance is correlated with the U.S. real effective exchange rate index. Because the trade balance also depends on changes in U.S. and rest of the world disposable income, it may respond with a lag to changes in the real exchange rate, so the correlation is not perfect (as seen in the years 2002–2007).

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Pass-Through

The price of all foreign-produced goods relative to all home-produced goods is the weighted sum of the relative prices of the two parts of the basket. Hence,

When d is 0, all home goods are priced in local currency and we have our basic model. A 1% rise in E causes a 1% rise in q. There is full pass-through from changes in the nominal exchange rate to changes in the real exchange rate. As d rises, pass-through falls.

If d is 0.5, then a 1% rise in E causes just a 0.5% rise in q. The real exchange rate becomes less responsive to changes in the nominal exchange rate, and this means that expenditure switching effects will be muted.

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Many countries produce goods which are priced in dollars, or something other than the home currency, like Qatar producing oil.

Trade DollarizationThe table shows the extent to which the dollar and the euro were used in the invoicing of payments for exports and imports of different countries in the 2002–2004 period. In the United States, for example, 100% of exports are invoiced and paid in U.S. dollars but so, too, are 93% of imports. In Asia, U.S. dollar invoicing is very common, accounting for 48% of Japanese exports and more than 75% of exports and imports in Korea, Malaysia, and Thailand.

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When prices are sticky and there is a nominal and real depreciation of the home currency, it may take time for the trade balance to move toward surplus. In fact, the initial impact may be toward deficit. If firms and households place orders in advance, then import and export quantities may react sluggishly to changes in the relative price of home and foreign goods. Hence, just after the depreciation, the value of home exports, EX, will be unchanged.

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The J Curve

However, home imports now cost more due to the depreciation. Thus, the value of imports, IM, would actually rise after a depreciation, causing the trade balance TB = EX − IM to fall. Only after some time would exports rise and imports fall, allowing the trade balance to rise relative to its pre-depreciation level. The path traced by the trade balance during this process looks vaguely like a letter J.

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The J Curve

(a) When households decide to consume more at any given level of disposable income, the consumption function shifts up. For example, an increase in household wealth following a stock market or housing market boom (as seen in expansions since 1990) could lead to a shift of this sort. This is a change in consumption demand unconnected to disposable income.

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(b) When firms decide to invest more at any given level of the interest rate, the investment function shifts right. For example, a belief that high-technology companies had great prospects for success led to a large surge in investment in this sector in many countries in the 1990s. This is a change in investment demand unconnected to the interest rate.

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(c) When the trade balance increases at any given level of the real exchange rate, the trade balance function shifts up. For example, a shift away from the large domestic automobiles made in Detroit toward smaller fuel-efficient imported cars manufactured in Japan. This is a switch in demand away from U.S. and toward Japanese products unconnected with the real exchange rate. 46

Goods Market Equilibrium: The Keynesian Cross

Supply and Demand

Given our assumption that CA = TB and Y = GNDI = GDP:

Aggregate demand, or just “demand,” consists of all the possible sources of demand for this supply of output.

Substituting we have

The goods market equilibrium condition is

Supply = GDP = Y

Demand = D = C + I + G + TB

( )*** ,,/)()( TYTYPPETBGiITYCD −−+++−=

( )

D

TYTYPPETBGiITYCY *** ,,/)()( −−+++−=

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Equilibrium is where demand, D, equals real output or income, Y. In this diagram, equilibrium is at point 1, at an income or output level of Y1. The goods market will adjust toward this equilibrium.

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At point 2, the output level is Y2 and demand, D, exceeds supply, Y; as inventories fall, firms expand production and output rises toward Y1. At point 3, the output level is Y3 and supply Y exceeds demand; as inventories rise, firms cut production and output falls toward Y1. 49

The goods market is initially in equilibrium at point 1, at which demand and supply both equal Y1. An increase in demand, D, at all levels of real output, Y, shifts the demand curve up from D1 to D2.Equilibrium shifts to point 2, where demand and supply are higher and both equal Y2. Such an increase in demand could result from changes in one or more of the components of demand: C, I, G, or TB.

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Summary

YD

D

TBI

CP

PE

i

T

output of levelgiven aat demandin Increase

*

up shifts curve Demand

function balance tradein the upshift Any function investment in the upshift Any

function n consumptio in the upshift Any prices homein Fall

pricesforeign in Rise rate exchange nominal in the Rise

rateinterest home in the FallG spending governmentin Rise

in taxes Fall

⇒

The opposite changes lead to a decrease in demand and shift the demand curve in. 51