Six Puzzles in International Finance

If international markets allow countries to trade goods, transfer resources, and share risks, why do national borders still have such a strong influence on trade, saving, consumption, portfolios, and exchange rates?

This is a central question for the course. We will begin with models that produce clear predictions, confront those predictions with international evidence, and examine which frictions, risks, or measurement problems may explain the distance between them. The objective is not to collect anomalies. It is to learn how to use a discrepancy between theory and evidence as the starting point for research.

International integration

In a world favorable to international integration:

• goods are inexpensive to transport
• capital can move toward its most productive use
• investors can acquire assets issued in many countries
• contracts provide payments in every possible state of the world
• prices adjust quickly
• relevant information is accessible
• arbitrage is not constrained by risk, regulation, or transaction costs.

Political borders should matter relatively little. Location would continue to affect costs and comparative advantage, but merely crossing a national border should not radically alter a transaction.

In practice:

1. countries trade far more within their own borders
2. domestic investment remains closely related to domestic saving
3. investors strongly overweight domestic equities
4. consumption does not display the degree of international risk sharing that financial markets should permit
5. international price differences disappear very slowly
6. exchange rates appear excessively volatile and difficult to connect with observable fundamentals.

M. Obstfeld and K. Rogoff (2000) proposed that trade costs could explain an important part of these regularities. A powerful unifying hypothesis, but not a complete answer. Imperfect information, incomplete markets, currency risk, rigidities, heterogeneity, and measurement also play central roles.

We will describe the six major puzzles in the following order:

Market	Question	Puzzle
Goods	From whom do we buy?	Home bias in trade
Intertemporal resources	Who finances investment?	Feldstein–Horioka
Assets	What do we own?	Equity home bias
Welfare	Who absorbs country-specific shocks?	Consumption correlations
Goods prices	Does arbitrage operate?	PPP puzzle
Asset prices	What information does a currency incorporate?	Exchange-rate disconnect

What is an economic puzzle?

An economic puzzle is a robust and economically significant discrepancy between a clearly stated prediction of a benchmark model and the behavior observed in the data, for which no generally accepted explanation is available.

Concept	Meaning	Example
Statistical anomaly	An unexpected estimate whose robustness remains uncertain	A low consumption correlation appears only in one sample or specification
Stylized fact	A recurring empirical regularity that survives reasonable changes in data, samples, and methods	International consumption correlations are generally lower than domestic correlations
Economic puzzle	A robust empirical regularity that conflicts with a precise prediction of a relevant benchmark model	Complete markets predict strong international consumption comovement, but the observed correlations are low

• A surprising estimate is not automatically a puzzle.
• If it survives robustness checks, it may become a stylized fact.
• It becomes a puzzle when it contradicts an identifiable theoretical prediction.

Economic puzzle if clear theoretical prediction & robust conflicting evidence

Part I. Quantities and assets

Puzzle 1. Home bias in trade

The question

Why do two regions within the same country trade much more than two comparable regions separated by an international border?

1 Original prediction

The starting point is the gravity model. In its simplest form, bilateral trade increases with economic size and decreases with trade costs:

\(X_{ij} = A \frac{Y_iY_j}{D_{ij}}\)

Here, \(X_{ij}\) denotes bilateral volume of trade; \(Y_i\) and \(Y_j\) are the sizes of the two economies (GDP); and \(D_{ij}\) measures geographic distance.

After controlling for size and distance, a relatively open border, such as that between Canada and the United States, should not reduce trade by an order of magnitude.

2 Evidence

J. McCallum (1995) estimated that a Canadian province traded approximately 22 times more with another Canadian province than with a comparable U.S. state. The result revealed an effect that physical distance alone could not capture.

Trade inside and across a national border. The value 22 is McCallum’s historical benchmark and should not be treated as a universal constant.

3 Why is this a puzzle?

Canada and the United States shared a relatively open border, infrastructure, similar levels of development, and a common language across many regions. If size and physical distance exhausted the relevant costs, a border indicator should have added little explanatory power. It added far too much.

4 Remarks

Business decision. A firm evaluating nearshoring should not confuse geographic proximity with effective integration. Customs procedures, certification, supplier networks, regulatory uncertainty, and input availability can preserve important border costs.

Foundations studied later: balance of payments, trade costs, tradable and nontradable goods, and the real exchange rate.

Possible research questions. Have trade (dis)agreements reduced/incresed border effects? Is the effect equal for intermediate and final goods?

Puzzle 2. The Feldstein–Horioka puzzle

The question

If capital can cross borders, why do countries that save more also appear to invest more within their own territory?

1 The identity organizing the problem

In an open economy,

\[ Y=C+I+G+NX, \]

and national saving is

\[ S=Y-C-G. \]

Therefore,

\[ CA=NX=S-I. \]

A country can invest more than it saves by financing the difference with foreign saving. It can also save more than it invests and acquire foreign assets.

M. Feldstein and C. Horioka (1980) estimated

\[ \frac{I_i}{Y_i}=\alpha+\beta\frac{S_i}{Y_i}+\varepsilon_i. \]

The original interpretation compared two polar cases:

• With low capital mobility, additional saving finances domestic investment and \(\beta\) approaches one;
• With highly mobile capital, investment can be financed globally and \(\beta\) should be much smaller.

2 Evidence

The original estimate for OECD economies was approximately \(\hat\beta=0.887\): a one-percentage-point increase in the saving rate was associated with nearly 0.89 additional points of domestic investment.

The estimated coefficient was much closer to the low-mobility benchmark than to the extreme benchmark of perfect capital mobility.

3 Why is this a puzzle?

The result appeared precisely among advanced economies, where financial mobility was expected to be greatest. Yet the saving–investment correlation does not identify capital mobility by itself. It may also reflect:

• the intertemporal budget constraint;
• common shocks affecting saving and investment;
• policies designed to stabilize the current account;
• country size;
• demographic growth or productivity;
• endogeneity of both variables; and
• differences between short-run financial mobility and the persistent financing of real investment.

4 Remarks

The saving–investment relationship weakened during some periods of financial globalization, but it varies across samples, crises, and groups of countries.

Financial and policy decision. If an investment expansion depends primarily on national saving, saving incentives and domestic financial development matter more. If it depends on foreign financing, refinancing risk, currency denomination, and the possibility of a sudden stop become central.

Foundations studied later: intertemporal trade, the current account, saving, investment, the international investment position, and capital mobility.

Possible research question. Does the saving–investment relationship increase after episodes of global financial stress?

Puzzle 3. Equity home bias

The question

If international diversification can reduce risk, why do investors concentrate such a large share of their wealth in domestic equities?

1 Original prediction

Under integrated markets, symmetric information, and similar preferences, investors should hold a portfolio close to the world market portfolio. The weight of country \(j\) would be approximately

\[ w_j^{*}=\frac{MC_j}{MC_W}, \]

where \(MC_j\) is the country’s stock market capitalization and \(MC_W\) is world capitalization. Investors from different countries should not hold radically different portfolios.

A common measure is

\[ HB_i=1-\frac{w^{F}_{i,\,obs}}{w^{F}_{i,\,mark}}, \]

where \(w^{F}_{i,\,obs}\) is the observed foreign share and \(w^{F}_{i,mark}\) is the foreign-equity share implied by a world portfolio. A value close to one indicates strong home bias.

Example:

Suppose Mexico equities represent 40% of global market capitalization. The benchmark foreign share for a Mexican investor is therefore:

\[ w^F_{M,mark} =1−0.40=0.60 \]

If the observed foreign share is only 15%:

\[ HB_M=1− \frac{0.15}{0.60}=0.75 \]

Note: a \(HB<0\) would mean that investors hold more foreign equity than the world market benchmark, this is called a foreign bias

2 Evidence

K. R. French and J. M. Poterba (1991) documented portfolios that were overwhelmingly concentrated in domestic equities. The concentration was difficult to reconcile with the familiar benefits of international diversification.

Historical domestic equity shares. The proper theoretical comparison is not a 50/50 split, but the optimal market weight after accounting for relevant risks and hedges.

3 Why is this a puzzle?

National equity returns do not move identically. In principle, foreign assets expand the opportunity set and reduce exposure to domestic shocks. Rationalizing the observed portfolios through expectations alone would sometimes require investors to expect persistently higher domestic returns.

4 Remarks

Portfolio decision. An unhedged global portfolio does not separate equity diversification from currency exposure. At least three alternatives should be compared: a domestic portfolio, an unhedged international portfolio, and a hedged international portfolio. VaR or Expected Shortfall should evaluate a hypothesis about the source of risk rather than appear as decorative exercises.

Foundations studied later: international risk sharing, portfolio choice, currency hedging, VaR, Expected Shortfall, and the cost of capital.

Possible research question. What explains the home bias of Mexican investors?

Puzzle 4. The consumption correlations puzzle

The question

If countries can share risk through assets and credit, why is international consumption less synchronized than output?

6.1 Original prediction

With complete markets, households can acquire state-contingent claims. A negative country-specific output shock should not translate fully into domestic consumption. In a simple formulation, the risk-sharing condition equates marginal utilities adjusted by relative prices. A familiar implication is

\[ \operatorname{corr}(C_i,C_j)> \operatorname{corr}(Y_i,Y_j). \]

2 Evidence

D. K. Backus et al. (1992) found the reverse ordering: output was more highly correlated across countries than consumption.

Historical benchmark for the quantity anomaly: average international correlations reported for advanced economies relative to the United States.

6.3 Why is this a puzzle?

It is not surprising that international consumption correlation is below one. The difficult result is that it is lower than output correlation, even though international insurance should decouple consumption from national shocks.

4 Remarks

Policy and wealth-management decision. Accumulating foreign assets does not guarantee that they pay precisely when a domestic shock occurs. Covariances, currency denomination, liquidity, and the state of the world in which insurance is needed all matter.

Foundations studied later: Consumption smoothing, complete and incomplete markets, contingent assets, international correlations, portfolios, and welfare.

Possible research question. Has financial integration increased international risk sharing in North America, how capital flows behave during crises?

Part II. Prices

Puzzle 5. The purchasing power parity puzzle

The question

How can enormous short-run real exchange rate volatility coexist with such slow convergence toward purchasing power parity?

7.1 Original prediction

Define the log real exchange rate as

\[ q_t=s_t+p_t^{*}-p_t, \]

where \(s_t\) is the domestic-currency price of foreign currency, \(p_t^{*}\) is the foreign price level, and \(p_t\) is the domestic price level. Under PPP, \(q_t\) should be stable. If a deviation appears, goods-market arbitrage should eliminate it.

An elementary empirical representation is

\[ q_t=\rho q_{t-1}+\varepsilon_t, \qquad |\rho|<1. \]

The half-life of a deviation is

\[ HL=\frac{\ln(0.5)}{\ln(\rho)}. \]

7.2 Evidence

K. Rogoff (1996) summarized estimates with half-lives of approximately three to five years. The difficulty was not persistence alone, but reconciling it with the very high short-run volatility of real exchange rates.

The figure is a numerical illustration of different half-lives, not a new empirical estimate.

3 Why is this a puzzle?

Monetary shocks and nominal rigidities can generate short-run deviations. Yet prices and wages should adjust in less than three to five years. Real shocks may be persistent, but they do not easily account for all high-frequency exchange rate volatility.

4 Remarks

Business decision. PPP should not be used as a mechanical short-run forecast. It is more useful as a long-run anchor for scenarios, valuation assessments, and stress tests involving prices, margins, and cash flows in different currencies.

Foundations studied later: the real exchange rate, the law of one price, PPP, nontradable goods, rigidities, and pass-through.

Possible research question. Do peso–dollar real exchange rate deviations close in the short-term ?

Puzzle 6. The exchange-rate disconnect puzzle

The question

If the exchange rate is a central price for international trade and finance, why is it so difficult to explain and forecast with macroeconomic variables?

why do exchange rates move so dramatically when observed macroeconomic fundamentals move much less?

1 Original prediction

Monetary and asset-pricing models connect the exchange rate to money, output, inflation, interest rates, and expectations. Schematically,

\[ s_t=\mathbb{E}_t\left[\sum_{k=0}^{\infty}\delta^k f_{t+k}\right]+rp_t, \]

where \(f_{t+k}\) contains expected fundamentals and \(rp_t\) is a currency risk premium. The equation contains a warning: the exchange rate depends on the expected future, not only on contemporaneous observed variables.

2 Classical evidence

R. A. Meese and K. Rogoff (1983) showed that several structural models did not consistently outperform a random walk in out-of-sample forecasts. The finding was especially uncomfortable because some exercises even supplied the models with realized values of fundamentals.

The disconnect contains at least two distinct problems:

1. Explanation: a weak and unstable contemporaneous relationship with observable fundamentals.
2. Prediction: an inability to outperform simple benchmarks out of sample.

Recent evidence

V. Stavrakeva and J. Tang (2024) find that macroeconomic surprises can explain a majority of quarterly exchange rate variation. The apparent disconnect becomes smaller when researchers measure the new information reaching markets and the resulting change in expectations.

The recent result recovers a connection with fundamentals, but it does not mean that exchange rates are easy to forecast.

8.5 Remarks

Weakened in its extreme form, but not eliminated

Recent evidence challenges the claim that exchange rates are disconnected from macroeconomic fundamentals. However, unstable risk premia and expectations preserve the forecasting problem.

Hedging and valuation decision. A strategy should not depend on a single point forecast. It should use distributions, scenarios, and error costs: no hedge, partial hedge, full hedge, and exchange rate stress. The exchange rate affects cash flows, discount rates, and terminal value.

Foundations studied later: currency exposure, risk premia, hedging, international valuation, country risk, the cost of capital, and WACC.

Possible research question. Do inflation and monetary policy surprises explain movements in the Mexican peso differently during episodes of global risk aversion?

Part III. A common diagnosis

9. Is there a common cause?

The six puzzles are not independent. Nor is there a one-to-one relationship between a puzzle and an explanation.

Mechanism	Trade	F–H	Equity	Consumption	PPP	FX disconnect
Trade costs	●	●	○	●	●	●
Imperfect information	●	○	●	○	○	●
Incomplete markets	○	●	●	●	○	●
Currency risk	○	●	●	●	●	●
Rigidities and pass-through	○	○	○	○	●	●
Measurement and identification	●	●	●	●	●	●
Heterogeneity	●	●	●	●	●	●

● central or frequent mechanism; ○ indirect or model-dependent mechanism.

The economic chain

Trade costs reduce the international exposure of firms and consumers. Less trade may weaken incentives to hold foreign assets and limit the ability of portfolios to insure national shocks. At the same time, nontradable goods and home-biased preferences alter the relationship between relative consumption and the real exchange rate. Rigidities and risk premia further separate exchange rate movements from contemporaneous fundamentals.

The unifying hypothesis does not mean that “everything is transportation cost.” A national border summarizes multiple costs:

• distance and logistics;
• currency and financial risk;
• regulation and contracts;
• information and trust;
• institutions and political risk;
• language, culture, and networks; and
• fiscal, monetary, and trade policies.

Final remarks

The six puzzles show that international integration is deep but incomplete. Borders reappear in goods, flows, assets, consumption, and prices. The conclusion, however, is not that economic theory should be abandoned. The productive question is different:

Which assumption produces an excessively strong prediction, and what evidence would allow us to distinguish among the competing explanations?

In later sessions, we will derive the models that have only been anticipated today. We will return to these puzzles with better tools to determine whether each discrepancy represents model failure, an omitted friction, a measurement problem, or an economically meaningful form of heterogeneity.

10. For the final project

In teams of two, select two puzzles and complete the following diagnosis.

Question	Puzzle A	Puzzle B
What exactly does the model predict?
What regularity appears in the data?
What is the precise gap between them?
Which assumption would you modify first?
Is the explanation a friction, measurement problem, or heterogeneity?
What additional evidence would distinguish two explanations?
Which financial or policy decision would change?

Rule of the activity

“The model is unrealistic” is not an acceptable diagnosis. Identify:

1. the assumption producing the prediction;
2. the mechanism that would change that prediction; and
3. the evidence that could evaluate the mechanism.

Document

Write 200–250 words for each option.

Required structure

1. Model prediction
   If the assumptions of ______ hold, we should observe ______.

2. Evidence generating the puzzle
   However, international evidence shows ______.

3. Preliminary hypothesis
   The discrepancy may be explained by ______.

4. Empirical setting
   Countries, sectors, firms, portfolios, currencies, or episodes that could be studied.

5. Possible method
   Comparative description, panel data, time series, event study, portfolio construction, valuation, or simulation.

6. Relevance
   Answering this question would help us understand or decide ______.

7. Connection with the course
   The theoretical foundations and financial tools that would be required.

References

D. K. Backus, P. J. Kehoe, and F. E. Kydland. (1992). International real business cycles. Journal of Political Economy, 100(4), 745–775. https://doi.org/10.1086/261838.

M. Feldstein and C. Horioka. (1980). Domestic saving and international capital flows. The Economic Journal, 90(358), 314–329. https://doi.org/10.2307/2231790.

K. R. French and J. M. Poterba. (1991). Investor diversification and international equity markets. American Economic Review, 81(2), 222–226.

J. McCallum. (1995). National borders matter: Canada–u.s. Regional trade patterns. American Economic Review, 85(3), 615–623.

R. A. Meese and K. Rogoff. (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics, 14(1–2), 3–24. https://doi.org/10.1016/0022-1996(83)90017-X.

M. Obstfeld and K. Rogoff. (2000). The six major puzzles in international macroeconomics: Is there a common cause? NBER Macroeconomics Annual, 15, 339–390. https://doi.org/10.1086/654423.

K. Rogoff. (1996). The purchasing power parity puzzle. Journal of Economic Literature, 34(2), 647–668.

V. Stavrakeva and J. Tang. (2024). A fundamental connection: Exchange rates and macroeconomic expectations. Review of Economics and Statistics, 1–49. https://doi.org/10.1162/rest_a_01520.